**Characteristics of a Debris Flow Disaster and Its Mitigation Countermeasures in Zechawa Gully, Jiuzhaigou Valley, China**

**Xing-Long Gong 1,2,3,**† **, Kun-Ting Chen 1,**† **, Xiao-Qing Chen 1,2,3, \*, Yong You 1 , Jian-Gang Chen 1,2 , Wan-Yu Zhao <sup>1</sup> and Jie Lang 4**


Received: 5 March 2020; Accepted: 26 April 2020; Published: 28 April 2020

**Abstract:** On 8 August 2017, an Ms 7.0 earthquake struck Jiuzhaigou Valley, triggering abundant landslides and providing a huge source of material for potential debris flows. After the earthquake debris flows were triggered by heavy rainfall, causing traffic disruption and serious property losses. This study aims to describe the debris flow events in Zechawa Gully, calculate the peak discharges of the debris flows, characterize the debris flow disasters, propose mitigation countermeasures to control these disasters and analyse the effectiveness of countermeasures that were implemented in May 2019. The results showed the following: (1) The frequency of the debris flows in Zechawa Gully with small- and medium-scale will increase due to the influence of the Ms 7.0 Jiuzhaigou earthquake. (2) An accurate debris flow peak discharge can be obtained by comparing the calculated results of four different methods. (3) The failure of a check dam in the channel had an amplification effect on the peak discharge, resulting in a destructive debris flow event on 4 August 2016. Due to the disaster risk posed by dam failure, both blocking and deposit stopping measures should be adopted for debris flow mitigation. (4) Optimized engineering countermeasures with blocking and deposit stopping measures were proposed and implemented in May 2019 based on the debris flow disaster characteristics of Zechawa Gully, and the reconstructed engineering projects were effective in controlling a post-earthquake debris flow disaster on 21 June 2019.

**Keywords:** debris flow; Zechawa Gully; mitigation countermeasures; Jiuzhaigou Valley

#### **1. Introduction**

A debris flow—a very to extremely rapid surging flow of saturated debris in a steep channel—is a widespread hazardous phenomenon in mountainous areas [1–3]. Because of their characteristics of high flow velocities, high impact forces and long run-out distances, debris flows pose a great threat to the safety of people, can cause catastrophic damage to infrastructure elements (such as roads and houses), and can even block rivers, leading to fatalities and property damage downstream [4–10]. In recent years, post-earthquake debris flow hazards have been widely investigated due to their long activity duration, high occurrence frequency and catastrophic damage [11–14]. Numerous studies have focused on rainfall thresholds and sediment supply to characterize the occurrence of post-earthquake

debris flows. In the areas affected by the 1999 Chi-Chi earthquake and the 2008 Wenchuan earthquake, the thresholds for rainfall triggering post-earthquake debris flows were analysed, and it was recognized that the rainfall threshold in periods shortly after the earthquakes was markedly lower than that before the earthquake and gradually recovered over time [14–20]. In fact, a devastating earthquake generates a large sediment supply in the form of co-seismic collapses and landslides and changes the grain size of the material and the watershed permeability characteristics, thereby indirectly reducing the debris flow-triggering rainfall thresholds [18,21]. Because earthquakes tend to produce abundant loose material, if sufficient rainfall occurs soon after an earthquake, a catastrophic debris flow can be triggered. For example, influenced by the Wenchuan earthquake on 12 May 2008, a catastrophic debris flow event was triggered on 14 August 2010 in Hongchun Gully, claiming the lives of 32 people [8]. Similarly, five debris flow events were triggered in Wenjia Gully in the three rainy seasons after the Wenchuan earthquake, including a giant debris flow event on 13 August 2010 [9,13].

As an effective way to mitigate debris flow hazards, engineering countermeasures have attracted widespread attention [22–33], and the mitigation of debris flows is usually carried out by stabilizing, blocking, drainage and deposit stopping measures [11,23]. Check dams, which act to stabilize the bed, consolidate hillslopes, decrease the slope, and retain and control the transport of sediment, are commonly used engineering structures for controlling debris flows and can generally be divided into solid-body dams and open dams [25,28,29]. Because solid-body dams are associated with many drawbacks, such as the erosion of the dam foundation and changes in the hillslope-to-channel connectivity [26,27], open dams are more efficient at controlling debris flows [28,29]. After the Wenchuan earthquake, to protect people's lives and property and ensure smooth traffic, a large number of debris flow engineering structures, especially check dams, were built. However, due to the insufficient realization on the characteristics and formation mechanisms of post-earthquake debris flows, many newly-built engineering structures have failed to mitigate debris flows and have instead caused catastrophic damage. For example, due to the failure of check dams in Sanyanyu Valley on 8 August 2010, more than 200 buildings were damaged, and approximately 1700 people died [34]. Similarly, during the "8.13" Wenjiagou debris flow event, engineering structures failed, causing seven deaths and the burial of more than 497 houses [9,35]. Therefore, further research should be carried out to propose appropriate mitigation countermeasures for post-earthquake debris flows.

Recently, an Ms 7.0 earthquake struck Jiuzhaigou Valley on 8 August 2017, triggering abundant landslides and providing a vast source of material for debris flows. Due to the influence of heavy rainfall, post-earthquake debris flows were triggered in Jiuzhaigou Valley and heavily damaged infrastructure elements, such as pedestrian walkways and scenic roads, causing traffic disruption and serious property losses [36–38]. It is necessary to evaluate the characteristics of post-earthquake debris flows in Jiuzhaigou Valley, and to propose appropriate mitigation countermeasures to avoid catastrophic events, but only a few studies related to post-earthquake debris flow mitigation in this area have been published to date. In this paper, Zechawa Gully is taken as a case study to characterize a debris flow disaster and then discuss mitigation countermeasures. To improve the accuracy of parameter calculation, four different methods were used to calculate the debris flow peak discharge and quantify the debris flow magnitude. According to the survey and analysis, the destructive debris flow event in 2016 was caused by a dam breach. After the Ms 7.0 Jiuzhaigou earthquake on 8 August 2017, abundant loose solid material was available for debris flow activity, and at least one post-earthquake debris flow occurred in September 2017. The risk of dam breaches led to the implementation of engineering countermeasures with blocking and deposit stopping measures. Such works were finished on May 2019. On 21 June 2019, a post-earthquake debris flow was triggered by heavy rainfall, and the engineering countermeasures played a useful role in controlling the debris flow disaster even though the debris flow magnitude was greater than the design standard of the reconstruction engineering projects.

#### **2. Background**

#### *2.1. Formation Conditions of the Zechawa Gully Debris Flow*

Zechawa Gully, with gully mouth coordinates of 103◦55′22.8" E, 33◦08′34.8" N, is located in Jiuzhaigou Valley, Sichuan Province, China, and lies approximately 13.9 km from a scenic entrance (Figure 1a,b). The outlet of the Zechawa Gully debris flow coincides with the location of the only scenic road from Nuorilang Waterfall to Long Lake (Figure 1c). The study area is the transition zone from the Qinghai-Tibet Plateau to the Sichuan Basin and belongs to the peripheral mountainous area of the Sichuan Basin. The watershed covers an area of 1.96 km<sup>2</sup> and features five tributaries; the main channel is 2.57 km long and has a 61.1% longitudinal slope. The elevation difference of Zechawa Gully is approximately 1601 m, with a maximum elevation of 4040 m in the southwest of the watershed and a minimum elevation of 2439 m at the gully mouth near the scenic road. The topography of Zechawa Gully is steep, with 86.9% of the total area of the watershed having a slope exceeding 25◦ . The flow path of debris flow along Zechawa Gully can be divided into a formation zone, transport zone and deposition zone (Table 1). The formation zone is located in the upper reaches of Zechawa Gully (elevation above 3620 m), with an area of 0.26 km<sup>2</sup> and a channel length of 470 m. The transport zone is situated in the middle reaches, with the elevations ranging from 3620 m to 2600 m. The area of the transport zone is approximately 1.47 km<sup>2</sup> , and the channel length is approximately 1530 m. The deposition zone, with an area of 0.23 km<sup>2</sup> and a channel length of approximately 570 m, is located in the area below an elevation of 2600 m.

**Figure 1.** Location of Zechawa Gully and its full view. (**a**) Location of Jiuzhaigou Valley in Sichuan Province; (**b**) Location of Zechawa Gully in Jiuzhaigou Valley; (**c**) The full view of Zechawa Gully. The flow direction of the debris flow is perpendicular to the pedestrian walkways and the scenic road (from Nuorilang Waterfall to Long Lake).


**Table 1.** Zone division of Zechawa Gully.

Compared with the characteristics of the formation zone and transport zone, the topography of the deposition zone is gentle, with no collapses and landslides, and debris flow material tends to be deposited in this area, forming a large debris flow fan. Zechawa Gully is generally a "v"-shaped channel with the characteristics of a narrow gully bed, steep lateral slopes and a high longitudinal slope, providing favourable topographic conditions for the formation of debris flows.

The study area is located in the Songpan-Ganzi Block, and the outcropping strata are mainly Quaternary and Mesozoic (Figure 2a). The lithology consists mainly of limestone and slate with a small amount of sandstone, which were intensely deformed by folding and thrusting during the Late Triassic and Early Jurassic [39,40]. In addition, since the Quaternary, the geological tectonic movement in this area has been intense due to the influence of the Tazang fault (the eastern part of the East Kunlun Fault Zone), Minjiang fault and Huya fault [41–45] (Figure 2b). Historically, seismicity has occurred on the Minjiang fault and Huya fault, including the 1960 Zhangla Ms 6.7 earthquake, the 1973 Huanglong Ms 6.5 earthquake, and the 1976 Songpan-Pingwu earthquake swarm (Ms = 7.2, 6.7, and 7.2). A recent earthquake was the Jiuzhaigou 7.0 earthquake, which occurred on 8 August 2017 on the north-western extension of the Huya fault; the rupture was dominated by left-lateral strike-slip motion [41,46–48]. On the whole, seismicity is frequent in the study area due to the geological conditions of the region, resulting in the fracture of the rock mass in the study area and triggering abundant collapses and landslides, which provide a rich source of loose material for incorporation into debris flows.

**Figure 2.** Study area maps. (**a**) Geologic map of the study area; (**b**) Topographic map of the Tazang fault (TZF), the Minjiang fault (MJF), the Huya fault (HYF) and the blind extension of the HYF (modified from Zhao et al. [41]).

The study area features a plateau cold temperate-subarctic monsoon climate. Due to the blocking effect of the Longmen Mountains to the southeast of the study area, most of the warm and humid air currents from the Pacific Ocean stay to the east of the Longmen Mountains. Therefore, the rainfall in Jiuzhaigou Valley west of the Longmen Mountains is relatively low, and the annual average precipitation is only 761.8 mm. The impact of cold air and high-pressure cold air currents from Mongolia in the winter is greatly weakened by the blocking of the Qinling Mountains to the north of the study area, causing this region to exhibit a mild climate, moderate precipitation and an annual average temperature of 7.3 ◦C [49]. There are more than 150 rainfall days annually in the study area, and the rainfall is concentrated mainly in May to September in the form of rainstorms. According to the rainfall data from the Jiuzhaigou Administration Bureau, the maximum rainfall over 24 h in Jiuzhaigou Valley is greater than 50 mm, and the precipitation increases with increasing elevation. The lowest average annual precipitation, at 696.6 mm, is found at the outlet of Jiuzhaigou Valley at an elevation of 1996 m. The highest annual average precipitation, at 957.5 mm, is found at Long Lake at an elevation of 3100 m. The snowpack period is from October to April, and the largest recorded snowpack depth exceeded 150 mm. The rainfall conditions of the study area are characterized by concentrated heavy rainfall, which is favourable for the formation of debris flows.

#### *2.2. Description of the Debris Flow Events in Zechawa Gully*

Due to the steep topography, adequate supply of loose material and intense precipitation in the study area, debris flows are active in Zechawa Gully. The earliest recorded debris flow event occurred in August 2006 and buried pedestrian walkways. In July 2008, another debris flow occurred again and blocked the scenic road. To prevent debris flows from causing further damage to the downstream pedestrian walkways and the only scenic road and to ensure the safety of residents and tourists in scenic areas, engineering countermeasures were taken in 2009. These countermeasures were designed to resist a debris flow with a 20-year return period. One stone masonry check dam 34.7 m long and 8 m high was constructed at the end of the transport zone of Zechawa Gully in 2009 (Figure 1c), and one auxiliary dam was constructed close to the stone masonry check dam. The stone masonry check dam was designed to be able to trap a volume of 2.24 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> of debris flow material [50].

On 4 August 2016, another destructive debris flow was triggered in Zechawa Gully. The rainfall data from the Zechawa precipitation station (103◦55′04.8" E, 33◦09′18.0" N, Figure 1b) showed that the preceeding rainfall that accumulated from 26 July 2016 to 3 August 2016 was only 8.8 mm, and the intraday rainfall was 6.7 mm on 4 August 2016. During this debris flow event, large amounts of sediment were trapped in front of the stone masonry check dam, resulting in a deposited thickness of 7 m and width of 30 m, and the length of the debris flow deposit behind the check dam was 44 m according to field measurements (Figure 3a). As sediments deposited, a breach formed in the check dam. Ultimately, the average width of the breach was 20.5 m, and the residual height of the check dam was 6 m (Figure 3b). The large kinetic energy of strong flow waves formed by the breach of check dam caused a high erosion of the downstream gully bed. During the movement of the debris flow material, the trees on both sides of the channel were impacted, leaving noticeable mud marks (Figure 3c). According to the field investigation, the total volume of the debris flow material transported downstream the failed check dam was approximately 1.39 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> . Some of the material was deposited on the debris flow fan with a deposit area of 0.77 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>2</sup> , a thickness of 0.8–1.5 m and a volume of 0.89 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> . Additional material with a volume of 0.5 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> was transported to the scenic road. During this debris flow event, the pedestrian walkways were buried again, and the only scenic road from Nuorilang Waterfall to Long Lake was blocked, causing traffic disruption and serious property loss [37,51].

**Figure 3.** Images of Zechawa Gully debris flow in different periods: (**a**)–(**c**) 6 August 2016, (**d**)–(**f**) 16 August 2017, (**g**)–(**i**) 23 October 2017; (**j**) large boulder transported by the debris flow that occurred in September 2017.

On 8 August 2017, the Ms 7.0 Jiuzhaigou earthquake struck the study area, and abundant landslides were triggered (Figure 3d), providing a vast source of material for debris flows. However, this earthquake had little influence on the breach shape of the check dam (Figure 3e) or the downstream topography of the check dam (Figure 3f). Subsequently, heavy rainfall occurred in the study area in September 2017. The rainfall data from Zechawa precipitation station showed that the total rainfall in September 2017 was 243.2 mm, accounting for approximately 32% of the total annual rainfall (Figure 4). Affected by the heavy rainfall in September 2017, a debris flow occurred, and the topography changed significantly. At the upstream check dam, the erosion caused by the debris flow was intense. An erosional trench approximately 1.0 m in depth was formed upstream of the dam (Figure 3g), and the breach in the dam was detectably deepened due to the erosion induced by the debris flow (Figure 3h). Due to the very high transport capacity of the debris flow, a large boulder with a long-axis length of 1.3 m, an intermediate-axis length of 1.1 m and a short-axis length of 0.7 m was transported to a point 20 m downstream of the check dam, and this boulder was composed of masonry (Figure 3j). Downstream of the check dam, the debris flow material was deposited in the channel. Additionally, trees on both sides of the channel were broken due to the very large destructive power of the debris flow, and new mud marks were left on the trees (Figure 3i). Fortunately, pedestrian walkways and scenic roads were not destroyed again. To reduce the disaster risk of the post-earthquake debris flow in Zechawa Gully, one concrete check dam, one concrete auxiliary dam and one concrete retaining wall were constructed in May 2019.

**Figure 4.** Rainfall distribution in September 2017 recorded by the Zechawa precipitation station.

A rainfall event started at 20:00 on 20 June 2019 and ended at approximately 08:00 on 21 June 2019 in Jiuzhaigou Valley. According to reports from patrol personnel, a post-earthquake debris flow was triggered by this storm at approximately 03:00 on 21 June 2019, and the rainfall data from the Zechawa precipitation station showed that the accumulated rainfall from 21:00 on 20 June 2019 to 02:00 on 21 June 2019 was 18.1 mm. According to the field investigation, the total volume of debris flow material was approximately 2.3 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> . The debris flow material volume trapped by the concrete check dam was approximately 0.48 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> (Figure 5). Some of the other debris flow material was trapped behind the retaining wall with a deposit area of 0.3 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>2</sup> , a maximum deposit thickness of

4 m at the middle of the retaining wall and a deposit volume of 0.66 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> (Figure 6). The middle of the retaining wall was partially damaged, resulting in a breach with a width of 8.5 m, due to the high impact force of the debris flow. This breach allowed a portion of the debris flow material with a volume of 1.16 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> to be transported to the debris flow fan and scenic road (Figure 7). The material volume deposited on the fan was approximately 0.93 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> with a deposit area of 0.62 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>2</sup> and an average deposit thickness of 1.5 m. The volume of the material blocking the scenic road was approximately 0.23 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , with a deposit length of 180 m and an average deposit thickness of 1.8 m.

**Figure 5.** Overview of the reconstructed check dams in Zechawa Gully (taken on 25 June 2019).

**Figure 6.** Overview of the reconstructed retaining wall in Zechawa Gully (taken on 23 June 2019).

**Figure 7.** The debris flow that occurred on 21 June 2019 buried pedestrian walkways and blocked the scenic road (taken on 22 June 2019).

#### **3. Calculation of the Debris Flow Peak Discharge**

In the mountainous areas of China, due to the lack of observation data, the rain-flood method and cross-section survey method have been widely used to calculate the debris flow peak discharge [52]. Under the assumption that the occurrence frequencies of rainstorms, floods and debris flows are the same, the rain-flood method is widely employed to calculate the debris flow peak discharge under different occurrence frequencies [53,54]. The cross-section survey method calculates the peak discharge of a debris flow that has occurred based on the mud mark and cross-sectional morphology of the channel [7,55].

For the debris flow event that occurred on 4 August 2016, two obvious typical cross-sections downstream of the stone masonry check dam are available for the calculation of the debris flow discharge through the cross-section survey method. Moreover, the pedestrian walkways were buried, and the scenic roads were blocked, and the stone masonry check dam in the channel was broken during this debris flow event. According to previous research, the amplification effect caused by dam breakage can contribute to debris flow damage in downstream towns [9,56]. Therefore, to characterize the relationship between dam failure and the occurrence of the debris flow on 4 August 2016, the dam-breaking peak discharges were estimated through the dam-breaking calculation method.

During the debris flow event that occurred in September 2017, the cross-section survey method was unavailable due to the lack of an available cross-section. A coarse boulder with dimensions of 1.3 m, 1.1 m and 0.7 m was transported 20 m downstream of the check dam by the debris flow in September 2017. According to previous studies, the largest transported particle reflects the maximum kinetic energy of flooding in mountain streams, and the maximum particle size parameters are widely used to reconstruct the velocity, depth and peak discharge of floods [57]. Thus, in this study, based on the assumption that the rainstorm, flood and debris flow frequencies were the same, the maximum particle size parameters were used to calculate the flood peak discharge, and the peak discharge of the debris flow in September 2017 was then estimated by using the methodology proposed by Lanzoni [58] according to the calculated flood peak discharge.

#### *3.1. Rain-Flood Method*

The debris flow peak discharges under different occurrence frequencies are computed by Ref. [54]:

$$\mathbf{Q}\_{df} = \mathbf{D}\_{df} \{ \mathbf{1} + \boldsymbol{\psi}\_{df} \} \mathbf{Q}\_{f} \tag{1}$$

$$
\psi\_{df} = (\gamma\_{df} - \gamma\_w) / (\gamma\_s - \gamma\_{df}) \tag{2}
$$

where *Ddf* is the blockage coefficient, whose value varies with the degree of blockage, namely, very serious blockage (*Ddf* = 3.0–2.6), serious blockage (*Ddf* = 2.5–2.0), normal blockage (*Ddf* = 1.9–1.5) and minor blockage (*Ddf* = 1.4–1.1); ψ*df* is the amplification coefficient of the debris flow peak discharge; γ*df* is the density of the debris flow (t/m<sup>3</sup> ); γ*<sup>w</sup>* is the density of water (t/m<sup>3</sup> ), usually taken as 1.00 t/m<sup>3</sup> ; γ*s* is the density of the solid material (t/m<sup>3</sup> ), usually taken as 2.65 t/m<sup>3</sup> ; and *Q<sup>f</sup>* is the flood peak discharge under different return periods (m<sup>3</sup> /s), which is calculated by:

$$Q\_f = 0.278 \varrho \frac{\mathcal{S}}{t^n} \mathcal{F} \tag{3}$$

where ϕ is the runoff coefficient of the flood peak, which is related to the convergence of runoff; *S* is the rainfall intensity (mm); *t* is the runoff confluence time of the rainstorm (h); *n* is the attenuation index of the rainstorm; and *F* is the watershed area (m<sup>2</sup> ). Here, ϕ, *S*, *t* and *n* are calculated by the following empirical equations:

$$
\varphi = 1 - 1.1 \frac{\eta}{\text{S}} t\_0^{\text{in}} \tag{4}
$$

$$S = H\_1 K\_1 \tag{5}$$

$$t = t\_0 \rho^{-\frac{1}{4-n}} \tag{6}$$

$$n = 1 + 1.285(lg \frac{H\_1 K\_1}{H\_6 K\_6}) \tag{7}$$

where *H<sup>1</sup>* and *H<sup>6</sup>* are the 1-hour average rainfall and 6-hour average rainfall, respectively (mm), which are obtained from "The Rainstorm and Flood Calculation Manual of Medium and Small Basins in Sichuan Province" (published in 2010, with rainfall data from 1978 to 2004); *K<sup>1</sup>* and *K<sup>6</sup>* are the modulus coefficients corresponding to *H<sup>1</sup>* and *H<sup>6</sup>* under different return periods, respectively, which can be obtained from a Pearson type III distribution table; η is the runoff yield parameter, which reflects the average infiltration intensity (mm/h); *t<sup>0</sup>* is the runoff confluence time of the rainstorm when ϕ equals 1, which can be calculated by:

$$
\eta = \text{3.6}K\_{\text{P}}F^{-0.19} \tag{8}
$$

$$t\_0 = \left[\frac{0.383}{mS^{1/4}/\theta}\right]^{\frac{4}{4-n}}\tag{9}$$

where *K<sup>p</sup>* is the modulus coefficient when the variation coefficient is equal to 0.23, which is obtained from the Pearson type III distribution table; *m* is the runoff confluence parameter; and θ is the watershed characteristic parameter, which is obtained from:

$$m = 0.221\theta^{0.204} \tag{10}$$

$$\theta = \frac{L}{I^{1/3} \mathcal{F}^{1/4}}\tag{11}$$

where *L* is the main channel length and *J* is the longitudinal slope of the channel.

#### *3.2. Cross-Section Survey Method*

Because natural channels have irregular channel bottoms, information on the channel roughness is not easy to obtain and measure. Therefore, an empirical formulation (Manning formula) was developed for turbulent flows in rough channels. It can be applied to calculate the discharge for fully rough turbulent flows and water flows. Although it is an empirical relationship, it has been found to be reasonably reliable [59,60]. Thus, the Manning formula was employed to obtain debris flow peak discharge when computing by the cross-section survey method. Based on the mud marks and cross-section morphology of the channel, the debris flow peak discharge *Qdf* (m<sup>3</sup> /s) can be obtained by Ref. [54]:

$$Q\_{df} = A\_{df} V\_{df} \tag{12}$$

where *Adf* is the area of the cross-section (m<sup>2</sup> ), and *Vdf* is the average velocity of the debris flow (m/s), which can be calculated by:

$$\mathbf{V}\_{df} = \frac{1}{\mathfrak{n}\_{df}} \mathbf{R}\_{df} \mathbf{r}^{2/3} \mathbf{I}\_{df} \mathbf{r}^{1/2} \tag{13}$$

where *ndf* is the roughness coefficient of the debris flow gully, *Rdf* is the hydraulic radius of the debris flow (m), and *Idf* is the longitudinal slope gradient of the channel bed (m/m).

#### *3.3. Dam-Breaking Calculation Method*

Considering the scarcity of observational data in this study, three commonly used semi-empirical methods are employed to obtain the dam-breaking peak discharge during the debris flow event on 4 August 2016. The semi-empirical method of the Ministry of Water Resources of the People's Republic of China (MWR) [61] estimates the debris flow peak discharge *Qdf* through:

$$Q\_{df} = \frac{8}{27} \sqrt{\text{g}} [B\_0 h\_0 / B\_m]^{0.28} B\_m (h\_0 - h\_d)^{1.22} \tag{14}$$

$$Q\_{df} = \frac{8}{27} \sqrt{g} (\frac{B\_0}{B\_m})^{0.4} \left(\frac{h\_0 + 10h\_d}{h\_0}\right)^{0.3} B\_m (h\_0 - h\_d)^{1.5} \tag{15}$$

where *g* is acceleration due to gravity (9.8 m<sup>2</sup> /s); *B<sup>0</sup>* is the debris flow width before breakage (m); *h<sup>0</sup>* is the debris flow depth before breakage (m); *B<sup>m</sup>* is the breach width (m), and *h<sup>d</sup>* is the residual height of the dam.

The semi-empirical method of Dai and Wang [62] calculates the debris flow peak discharge *Qdf* by:

$$Q\_{df} = 0.27 \sqrt{\text{g}} (L\_b/B\_0)^{1/10} (B\_0/B\_m)^{1/3} B\_m (\text{l}\_0 - \text{rk}\_d)^{3/2} \tag{16}$$

where *L<sup>b</sup>* is the deposit length of the debris flow material behind the check dam (m); κ is the influence factor that accounts for residual height, which is obtained by:

$$\kappa = \begin{cases} 1.4 \left( B\_m h\_d / B\_0 h\_0 \right)^{1/3}, B\_m h\_d / B\_0 h\_0 < 0.3 \\\\ 0.92, B\_m h\_d / B\_0 h\_0 > 0.3 \end{cases} \tag{17}$$

#### *3.4. Maximum Boulder Size Method*

Based on the particle size parameters of the maximum-sized boulder, the debris flow peak discharge can be obtained through Ref. [58]:

$$\mathcal{Q}\_{df} = \frac{1}{1 - \mathcal{C}} \mathcal{Q}\_f \tag{18}$$

$$\mathcal{C} = \frac{\rho\_f \tan \beta}{(\rho\_s - \rho\_f)(\tan \phi\_{df} - \tan \beta)} \tag{19}$$

where *C* is the transported sediment concentration; ρ*<sup>f</sup>* is the fluid density (kg/m<sup>3</sup> ); ρ*<sup>s</sup>* is the sediment density; β is the bed slope angle (degrees), and the value of β is usually between 15◦ to 25◦ when using Equation (19) [63]; ϕ*df* is the quasi-static friction angle (degrees); and *Q<sup>f</sup>* is the flood peak discharge (m<sup>3</sup> /s), which was estimated by the methods of Schoklitsch, Helley, Williams and Clarke.

#### 3.4.1. Method of Schoklitsch

This method estimates the flood peak discharge *Q<sup>f</sup>* (m<sup>3</sup> /s) by computing the unit width flux by Ref. [64,65]:

$$q\_f = \frac{0.0194d\_I}{\left(\tan \beta\right)^{4/3}}\tag{20}$$

$$\mathcal{Q}\_f = q\_f \ast \mathcal{B}\_f \tag{21}$$

where *q<sup>f</sup>* is the unit width flux; *d<sup>I</sup>* is the diameter of the boulder intermediate axis (m), and *B<sup>f</sup>* is the channel width (m).

#### 3.4.2. Method of Helley

This method computes the "bed velocity" for incipient motion (overturning) by equating the turning moments for fluid, drag, and lift with the resisting moment of the submerged particle weight. The critical velocity *V<sup>f</sup>* (bed velocity) can be calculated by Ref. [66]:

$$\left[V\_f = 3.276 \frac{\left(\rho\_b/1000 - 1\right)d\_L(ds + d\_I)^2 MR\_L}{\left(C\_D d\_S d\_L MR\_D + 0.178 d\_I d\_L MR\_L\right)}\right]^{0.5} \tag{22}$$

$$\text{MR}\_{\text{L}} = d\_{\text{I}} \cos \alpha / 4 + \sqrt{\frac{3}{16} d\_{\text{S}}^2} \sin \alpha \tag{23}$$

$$MR\_D = 0.1d\_\mathcal{S} \cos \alpha + \sqrt{\frac{3}{16}S\_2^d \cos \alpha - d\_I \sin \alpha/4} \tag{24}$$

where ρ*<sup>b</sup>* is the maximum boulder density (kg/m<sup>3</sup> ); *d<sup>L</sup>* is the diameter of the boulder long axis (m); *d<sup>S</sup>* is the diameter of the boulder short axis (m); *C'<sup>D</sup>* is the drag coefficient; *MR<sup>D</sup>* and *MR<sup>L</sup>* are the drag turning arm and lift turning arm, respectively; and α is the original imbrication angle of the deposited boulder. During the calculation process, Equation (22) uses English units of feet, and the units of critical velocity calculated by Equation (22) need to be converted into metres per second.

The critical velocity *V<sup>f</sup>* calculated by Equation (22) needs to be converted to the average velocity *Vavg* [57]:

$$V\_{\text{avg}} = 1.2V\_f \tag{25}$$

The flood peak discharge *Q<sup>f</sup>* can then be calculated as the product of the average velocity, mean depth and channel width by:

$$Q\_f = V\_{w \circ g} h\_f B\_f \tag{26}$$

where *h<sup>f</sup>* is the mean flood depth (m). Given that the channel width was much larger than the mean depth of flooding, the hydraulic radius obtained by the Manning formula can estimate the average depth; thus, *h<sup>f</sup>* was obtained by the Manning formula:

$$h\_f = \left(\frac{V\_{avg}n\_f}{\sqrt{\tan \beta}}\right)^{1.5} \tag{27}$$

where *n<sup>f</sup>* is the roughness coefficient of a mountain stream.

#### 3.4.3. Method of Williams

This approach calculates either the bed shear stress or the stream power needed to entrain the boulder. First, the intermediate axis diameter of the largest boulder *d<sup>I</sup>* is obtained through field investigation, and then the empirical relationship between the unit stream power *w*, bed shear stress τ, average velocity *Vavg* and *d<sup>I</sup>* is established by Ref. [67]:

$$w = 0.079d\_{l}^{1.3} \tag{28}$$

$$
\pi = 0.17d\_{\text{I}} \tag{29}
$$

$$V\_{avg} = 0.065d\_I^{0.5} \tag{30}$$

*Vavg*, *h<sup>f</sup>* and *Q<sup>f</sup>* based on the shear stress can be determined by Equations (30)–(32), respectively:

$$h\_f = \frac{\pi}{\rho\_b g \tan \beta} \tag{31}$$

$$Q\_f = \frac{w \ast B\_f}{\rho\_b g \tan \beta} \tag{32}$$

*Vavg* and *h<sup>f</sup>* based on the stream power can be obtained by:

$$V\_{\text{avg}} = \frac{Q\_f \rho\_b \text{g} \tan \beta}{B\_f \pi} \tag{33}$$

$$h\_f = \frac{w}{\rho\_b g \tan \beta \* 0.065 \sqrt{d\_I}} \tag{34}$$

The value of *Q<sup>f</sup>* in Equation (33) is obtained by Equation (32); then, *Q<sup>f</sup>* based on the stream power can be obtained by inserting the calculated values of *Vavg* and *h<sup>f</sup>* from Equations (33) and (34), respectively, into Equation (26).

#### 3.4.4. Method of Clarke

This method assumes that the critical force (i.e., the minimum force needed to move the boulder) is equal to the resisting force and that the critical force is equal to the sum of the lift force and drag force. The critical velocity *V<sup>f</sup>* (bed velocity) required to carry the maximum-sized boulder is solved by the following formula [68]:

$$V\_f = \left\{ 2\left[ (\mathbf{F\_D}/\mathbf{C\_D})/\rho\_f \right]/A\_\mathcal{B} \right\}^{0.5} \tag{35}$$

where *C<sup>D</sup>* is the lift coefficient of the boulder, which is dependent on the shape of the largest boulder, with *C<sup>D</sup>* = 1.18 for a cubic boulder and 0.20 for a spherical boulder; *A<sup>B</sup>* is the cross-sectional area of the largest boulder; and *F<sup>D</sup>* is the drag force, which is obtained by:

$$F\_D = \mathbb{C}\_D \text{F}\_{\mathbb{C}} / (\mathbb{C}\_L + \mathbb{C}\_D) \tag{36}$$

where *C<sup>L</sup>* is the lift drag coefficient, which is dependent on the shape of the largest boulder, with *C<sup>L</sup>* = 0.178 for a cubic boulder and 0.20 for a spherical boulder; and *F<sup>C</sup>* is the critical force, which is calculated by:

$$F\_{\mathbb{C}} = F\_{\mathbb{R}} \tag{37}$$

$$F\_R = M\_B[(\rho\_b - \rho\_f) / \rho\_b] \text{g} \left(\mu \cos \beta - \sin \beta\right) \tag{38}$$

where µ is the shape coefficient, which is dependent on the shape of the largest boulder, with µ = 0.675 for a cubic boulder and 0.225 for a spherical boulder; and *M<sup>B</sup>* is the boulder mass (kg). *M<sup>B</sup>* can be obtained for a cubic boulder and a spherical boulder by Equations (39) and (40), respectively:

$$M\_B = \rho\_b D^3 \tag{39}$$

$$M\_B = \rho\_b[(\pi/6)D^3] \tag{40}$$

where *D* is the nominal diameter of the boulder (m), which is solved by:

$$D = \left(d\_{\rm L}d\_{\rm I}d\_{\rm S}\right)^{0.33} \tag{41}$$

The flood peak discharge *Q<sup>f</sup>* can be obtained by inserting the calculated value of *V<sup>f</sup>* into Equations (25)–(27).

#### **4. Results**

#### *4.1. The Calculated Debris Flow Peak Discharge in 2016*

With the data collected during the field investigation, the peak discharge of the debris flow that occurred on 4 August 2016 was estimated by the cross-section survey method and dam-breaking calculation method. Table 2 shows the calculation results for the debris flow peak discharge. The permissible debris flow peak discharges at the two typical mud mark cross-sections estimated by the cross-section survey method were 33.29 m<sup>3</sup> /s and 36.69 m<sup>3</sup> /s. The values of *Adf*, *Rdf* and *Idf* were obtained through field investigation. The roughness coefficient of the debris flow gully (*ndf*) is related to the properties of the debris flow fluid and channel characteristics, and the value in this case is 0.1 according to a field survey [54].

**Table 2.** Calculation results of the debris flow peak discharge by using the cross-section survey method and dam-breaking calculation method.


According to the calculation results in Table 2, the permissible maximum debris flow peak discharges resulting from the breach in the check dam varied from 36.5 m<sup>3</sup> /s to 43.6 m<sup>3</sup> /s. The calculation result by Equation (14) was the lowest (36.5 m<sup>3</sup> /s), and the calculation result by Equation (15) was the highest (43.6 m<sup>3</sup> /s). The values of *B0*, *h0*, *Bm*, *hd*, and *L<sup>b</sup>* were obtained by field investigation. Since the data inputs used in Equations (14)–(16) were the same, the differences among the results arose from the different combinations of data used for a given technique. The calculated values are reasonable and are similar to the debris flow peak discharge estimated by the cross-section survey method.

#### *4.2. The Calculated Debris Flow Peak Discharge in 2017*

With data collected during the field investigation, the peak discharge of the debris flow that occurred in September 2017 was calculated by the maximum boulder size method. Table 3 shows the calculation results. The calculated values of *Q<sup>f</sup>* vary from 0.58 m<sup>3</sup> /s to 6.05 m<sup>3</sup> /s, and the calculated values of *Qdf* range from 1.76 m<sup>3</sup> /s and 18.33 m<sup>3</sup> /s. The minimum permissible debris flow peak discharge of 1.76 m<sup>3</sup> /s is estimated through the method of Schoklitsch, and the maximum discharge of 18.33 m<sup>3</sup> /s is estimated through the method of Helley. ρ*<sup>f</sup>* is usually taken as 1150 kg/m<sup>3</sup> considering the turbidity of the flood waters [68]. ρ*<sup>s</sup>* is usually taken as 2650 kg/m<sup>3</sup> . Owing to the absence of information, a value of 36.5◦ was given for ϕ*df* based on previous studies [58]. The values of *dL*, *d<sup>I</sup>* , *dS*, ρ*b* , *B<sup>f</sup>* , β, and α were obtained through field investigation. The transported sediment concentration (C) is 0.67 by inserting the values of ρ*<sup>f</sup>* , ρ*<sup>s</sup>* , β and ϕ*df* into Equation (19). The roughness coefficient of a mountain stream (*n<sup>f</sup>* ) is related to the channel characteristics, and a value of 0.05 was used here according to a field survey [69].


**Table 3.** Summary of the calculation results based on the maximum boulder size methods.

*4.3. The Calculated Debris Flow Peak Discharge under Di*ff*erent Occurrence Frequencies*

According to the magnitude of the debris flow, hazard degree and importance of the protection object, mitigation countermeasures in Zechawa Gully were required to resist a debris flow with a return period of 20–50 years [70]. Thus, the debris flow peak discharges under 10-, 20- and 50-year return periods were computed, and the calculated results of related parameters are listed in Table 4. The possible debris flow peak discharges under 10-year, 20-year and 50-year return periods are 22.27 m<sup>3</sup> /s, 32.73 m<sup>3</sup> /s and 48.27 m<sup>3</sup> /s respectively. In the calculation sections, the values of *F*, *L* and *J* are different, resulting in different debris flow peak discharges estimated by the rain-flood method.


**Table 4.** Calculation results of the debris flow peak discharge by using the rain-flood method.

To better compare with the debris flow peak discharges calculated by the cross-section survey method, dam-breaking calculation method and maximum boulder size method, the calculation section located at the check dam site was selected to compute the debris flow peak discharges through the rain-flood method. The values of *F*, *L* and *J* were obtained from a topographic map with a scale of 1:5000. According to the results of the querying specification table and spot investigation, the average density of the debris flow was 1.8 t/m<sup>3</sup> . Under given conditions, the debris flow density is positively related to the debris flow peak discharge [54,71], thus the densities of the debris flows γ*df* under the three return periods (10-year, 20-year and 50-year) were 1.8 t/m<sup>3</sup> , 1.85 t/m<sup>3</sup> and 1.9 t/m<sup>3</sup> , respectively. According to the site investigation, the blockage degree of the channel was normal, and the values of *Ddf* were considered to be 1.8–1.9.

#### **5. Discussion**

#### *5.1. The Applicability and Limitations of the Calculated Debris Flow Peak Discharge*

The debris flow peak discharge is an important parameter for debris flow disaster prevention and risk assessment. As debris flows occur in remote mountain areas, it is difficult to measure the peak discharge and other parameters of debris flow under the conditions of severe weather and traffic delays. At present, the debris flow peak discharge is usually calculated by the rain-flood method and cross-section survey method based on certain assumptions, resulting in calculation results with low credibility. In this study, under certain assumptions, the peak discharge of debris flow was estimated by the rain-flood method, the cross-section survey method, the dam-breaking calculation method and the maximum boulder size method, and comparative analysis of the calculation results was conducted to obtain an accurate peak discharge. The limitations of the calculation results are explained as follows:


a higher calculated peak discharge. The methods of Schoklitsch and Williams estimate the peak discharge by establishing an empirical correlation based on boulder size parameters without considering the influence of the boulder shape on the calculation results. In addition, the values of *w*, τ and *Vavg* in the method of Williams represent the lowest values, and the actual values are higher than the calculated value.

(4) In summary, certain assumptions and simplifications were made in the calculation process, causing the peak discharge of the debris flow calculated by a single method to exhibit low accuracy. Thus, multiple methods should be used to comprehensively obtain the peak discharge, further quantifying the scale of debris flow disasters. It is worth noting that the method for calculating the debris flow peak discharge proposed in this study is mainly based on the specifications in China, especially the selection of some parameters. When calculating the debris flow peak discharge in other countries, local specifications should be considered.

#### *5.2. The Scales of the Debris Flow Disasters in 2016 and 2017*

To identify the disaster characteristics and the occurrences of debris flow events, the peak discharges of the debris flows occurring on 4 August 2016 and in September 2017 were estimated based on field investigations, and the calculation results were compared with the debris flow peak discharges under different occurrence frequencies to quantify the scale of the debris flow disasters. The related explanations are as follows:

(1) The debris flow peak flow obtained by the cross-section survey method and dam-breaking calculation method are essentially the same and are generally equivalent to the peak discharge of the debris flow with a 20-year return period (Tables 2 and 4). In addition, the total volume of the debris flow material *Wdf* is estimated by Ref. [54]:

$$\mathcal{W}\_{df} = 0.264 Q\_{df} T\_{df} \tag{42}$$

where *Tdf* is the duration time of the debris flow (s), and its value is approximately 1500 s based on the reports of patrol personnel. The value of *Qdf* is the average calculation result through the cross-section survey method and dam-breaking calculation method, and its value is 37.38 m<sup>3</sup> /s. The total volume of debris flow material from Equation (42) is 1.48 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> , which is consistent with the value of 1.39 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> based on the field investigation. Thus, it is reasonable that the scale of the debris flow on 4 August 2016 is equivalent to that of a debris flow with a 20-year return period. Moreover, based on the study above, the debris flow peak discharges calculated by Equations (14)–(16) were similar to the values obtained by the cross-section survey method. Thus, we conclude that the debris flow peak discharge on 4 August 2016 was amplified by the failure of the check dam, causing widespread damage, and this aspect also explains why the magnitude of the debris flow on 4 August 2016 was large even though the accumulated rainfall and rainfall intensity were extremely low. Similarly, check dam failures have led to catastrophic disasters in other regions, such as the "8.13" Wenjiagou debris flow event [72] and the "8.8" Zhouqu debris flow event [73,74].


influence of terrain, resulting in inconsistencies between the triggering rainfall and the scale of debris flow disasters. Thus, the relationships between the occurrence of debris flow disasters and the triggering rainfall are not researched in this paper.

#### *5.3. Mitigation Countermeasures in Zechawa Gully*

More than 23 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> of loose solid material was generated by the Ms 7.0 Jiuzhaigou earthquake and remains available as material for debris flows in Zechawa Gully in the near future [37,75]. Therefore, appropriate engineering countermeasures must be taken in a timely manner to mitigate post-earthquake debris flow disasters. According to the field investigation and calculation results above, the stone masonry check dam built in 2009 were broken, and the failure of the check dam amplified the debris flow peak discharge, resulting in a very large amount of damage during the debris flow event on 4 August 2016. Thus, the potential failure of a check dam should be fully taken into account during engineering design processes, and an integrated strategy including blocking measures and deposit stopping measures should be adopted for debris flow mitigation. On the one hand, the construction of deposit stopping structures (e.g., retaining walls) can increase the retention capacity of engineering structures; on the other hand, the debris flow material can be trapped by the deposit stopping structures even if the blocking structures (e.g., check dams) in the channel are damaged, thereby reducing the disaster risk downstream.

The engineering countermeasure taken in 2009 were designed to resist a debris flow with a 20-year return period but were damaged during the debris flow event in 2016. Considering the high-frequency and large-scale characteristics of post-earthquake debris flows, engineering countermeasures were designed to resist a debris flow with a 50-year return period after the Ms 7.0 Jiuzhaigou earthquake based on the scale, damage degree and threatened objects threatened by the subsequent debris flows. The total volume of debris flow material with a 50-year return period can be obtained by inserting the calculated value of *<sup>Q</sup>df* into Equation (42), and the resulting value is 1.91 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> (Table 4). Thus, the designed engineering structures are required to trap at least 1.91 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> of debris flow material. In addition, the control principles of prevention projects should not only control the debris flow itself but also operate in harmony with the landscape and reduce the harm to landscape resources, as required in Jiuzhaigou Valley [76]. Under the guidance of these principles, in conjunction with the specific characteristics of the Zechawa debris flows, a concrete check dam and a concrete auxiliary dam were constructed in the channel, and a concrete retaining wall was constructed on the debris flow fan. The concrete check dam, 42.6 m long and 6 m high, was built close to but downstream of the broken stone masonry check dam in order to reduce the peak discharge, stabilize the gully bed, minimize scouring along the bottom and sides of the gully, and stabilize the debris flow material trapped behind the broken check dam. The downstream concrete auxiliary dam, 38.1 m long and 3 m high, was constructed close to the concrete check dam to protect the latter's foundation (Figure 5). Moreover, the reconstructed check dams were located somewhat upstream in the gully and were satisfactorily concealed. The retaining wall with a total length of 95.6 m was built 93 m away from the scenic road and is out of sight of tourists, and it can trap a volume of 2.27 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> of debris flow materials (Figure 6). In May 2019, new control works (the reconstructed check dam and the retaining wall) were finished.

#### *5.4. E*ff*ectiveness of Mitigation Countermeasures and Evaluation of Debris Flow Impact Force*

On 21 June 2019, one post-earthquake debris flow was triggered by heavy rainfall, and a volume of 2.3 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> of debris flow material was transported; this value was greater than the calculated total volume of debris flow material with a 50-year return period in Table 4. A volume of 0.48 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> of debris flow sediment was trapped by the concrete check dam (Figure 5), which contributed to stabilizing the gully bed and preventing entrainment of additional material. Moreover, a volume of approximately 0.66 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> debris flow sediment was trapped by the retaining wall (Figure 6), and a portion of material with a volume of 1.16 <sup>×</sup> <sup>10</sup><sup>4</sup> <sup>m</sup><sup>3</sup> emerged from the breach in the middle of

the retaining wall and was transported downstream. During the debris flow event on 21 June 2019, the prevention projects played a satisfactory role in controlling the debris flow disaster even though the flow magnitude exceeded the design standard.

In addition, studying the damage mechanism of mitigation structures is significant for effective debris flow mitigation. According to previous studies, the huge impact force of a debris flow can contribute significantly to the destruction of mitigation structures [34,77], and numerous impact models have been established [77–80]. Through comprehensive analysis of the existing debris flow impact models, a modified hydro-static model with a good prediction capability was proposed by Vagnon [77]. Therefore, the impact force of debris flow on the retaining wall was evaluated to study the damage mechanism by Ref. [77]:

$$P\_{\text{peak}} = 2.07 F\_r^{1.64} \gamma\_{df} \text{g} \hbar\_{df} \tag{43}$$

$$F\_r = V\_{df} / \sqrt{\text{g} \text{h}\_{df}} \tag{44}$$

where *Ppeak* is the peak impact pressure (kN/m<sup>2</sup> ); *F<sup>r</sup>* is the Froude number; and *hdf* is the mean debris flow depth (m). Considering the large scale of the debris flow disaster on 21 June 2019, γ*df* is taken as 1.9 t/m<sup>3</sup> according to Table 4. Based on field investigation, the average velocity of the debris flow (*Vdf*) near the retaining wall was calculated through Equation (13), and related parameters are shown in Table 5.

Based on the related report, the designed resistance of the retaining wall is 51.34 KN/m<sup>2</sup> [75], which is far below the calculated value of the peak impact pressure (80.39 kN/m<sup>2</sup> ) in Table 5. The debris flow impact force was greater than the resistance of the retaining wall, causing partial failure of the retaining wall on 21 June 2019. Thus, the resistance of the retaining wall should be increased during the design processes. In general, considerable attention should be given to the post-earthquake debris flow disaster in Zechawa Gully in the future, and it is necessary to repair the broken retaining wall with a greater design resistance and remove the debris flow material deposited behind the retaining wall to prepare for the next post-earthquake debris flow in the near future.

**Table 5.** Calculation results of the debris flow impact force on the retaining wall on 21 June 2019.


#### **6. Conclusions**

This study is intended to describe the debris flow events in Zechawa Gully, characterize the debris flow disaster, propose appropriate mitigation countermeasures and analyse the effectiveness of mitigation countermeasures that were already implemented in May 2019. Field investigations were conducted in a timely manner to determine the debris flow peak discharge, and the disaster characteristics and occurrence of debris flows in 2016 were analysed. The following conclusions can be drawn:


equivalent to that of a debris flow with a 20-year return period. After the Ms 7.0 Jiuzhaigou earthquake, at least one debris flow with a scale less than that of a debris flow with a 10-year return period was triggered in September 2017, and a destructive debris flow with a scale greater than that of a debris flow with a 50-year return period was triggered in June 2019.


#### **Notation**


**Author Contributions:** X.-L.G. and K.-T.C. contributed to the conceptualization, methodology, analysis and manuscript writing of the study. X.-Q.C. proposed the main structure of this study and approved the final version. Y.Y. and J.-G.C. helped perform the analysis with constructive discussions. W.-Y.Z. and J.L. provided resources and participated in the field investigations. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the "8.8" Jiuzhaigou earthquake stricken area ecological disaster prevention and control of key scientific and technological support project of Land and Resources Department of Sichuan Province (Research on Prevention and Control Technology of Ecological Debris Flow Disasters, Grant No. KJ-2018-24), the National Natural Science Foundation of China (Grant No. 51709259), the Foundation for Young Scientists of the Institute of Mountain Hazards and Environment, CAS (Grant No. SDS-QN-1912), CAS "Light of West China" Program, the Youth Innovation Promotion Association CAS (2017426) and the Open Foundation of Key Laboratory of Mountain Hazards and Earth Surface Processes, CAS.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **A Study on Interaction between Overfall Types and Scour at Bridge Piers with a Moving-Bed Experiment**

**Wei-Lin Lee <sup>1</sup> , Chih-Wei Lu 2, \* and Chin-Kun Huang 1**


**Abstract:** River slopes can be changed due to an extreme event, e.g., a large-scale earthquake. This can uplift a riverbed greatly and thereby change the behavior of the river flow into a free or submerged overfall. Corresponding damage, including extreme erosion, on bridge piers located in the river can take place due to the aforementioned flow conditions. A reconstructed bridge pier in the same location would also experience a similar impact if the flow condition is not changed. It is important to identify these phenomena and research the mechanism in the interaction between overfall types and scour at bridge piers. Therefore, this paper is aimed at studying a mechanism of free and submerged overfall flow impacts on bridge piers with different distances by a series of moving-bed experiments. The experiment results showed clearly that bridge pier protection requires attention particularly when the pier is located in the maximum scour hole induced by the submerged overfall due to the z directional flow eddies. In many other cases, such as when the location of the bridge pier was at the upstream slope of a scour hole induced by a flow drop, a deposition mound could be observed at the back of the pier. This indicates that, while a pier is at this location, an additional protection takes place on the bridge pier.

**Keywords:** bridge pier; overfall; scour; landform change impact on pier

#### **1. Introduction**

Unexpected free or submerged overfall conditions in a river flow can occur due to a force within the earth that causes the riverbed to uplift. The changed condition of river flow could have an impact on the safety of downstream river structures. A major earthquake that occurred in 21 September 1999 dramatically changed many landforms in central Taiwan, such as a local rise in the Da-Ja River inducing a flow drop in the riverbed. This flow drop is very close to the Pai-Furn bridge pier and could induce additional erosion. Figure 1a demonstrates a bridge that was damaged in the 921 Earthquake in 1999 in Taiwan and the surrounding river bed was significantly affected. The newly constructed bridge was completed in less than 2 years due to the importance for transportation (shown in Figure 1b). However, it can be seen in Figure 1c that the bridge pier was again exposed to river flow in six years due to significant nearby scour. Figure 1b,c display that the riverbed level had been apparently lowered down 4.5 m deep near the pier with a diameter of 3.6 m.

**Citation:** Lee, W.-L.; Lu, C.-W.; Huang, C.-K. A Study on Interaction between Overfall Types and Scour at Bridge Piers with a Moving-Bed Experiment. *Water* **2021**, *13*, 152. https://doi.org/10.3390/w13020152

Received: 15 December 2020 Accepted: 8 January 2021 Published: 11 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

(**c**)

**Figure 1.** (**a**) Changed river bed and damaged bridge due to the 921 Earthquake in 1999; (**b**) Newly constructed bridge in the same location; (**c**) Water drop and local scour at the bridge piers.

> Many researchers devoted themselves to studying local scour below drop structures and at bridge piers (Dey 2014) [1]. Some researchers focused on the local scour below drop structures; for example, Schoklitsch (1932) has been the pioneering researcher and proposed an empirical relationship to estimate the equilibrium scour depth for flow-over structures [2]. Moore (1943), Rand (1955), Akram (1979), and Little and Murphey (1982) studied the energy change due to the drop [3–6]. Smith and Strang (1967) found that the profile change of a riverbed was strongly affected by the size of the river bed materials [7]. Mason and Arumugam (1985) reviewed the empirical formulas of equilibrium scour depth under a falling jet that started in 1932, and they proposed a modified formula that includes the effect of tailwater depth [8]. Hoffmans (1998) derived relations to predict the maximum scour depth in the equilibrium phase based on the Newton's second law of motion [9].

> Hoffmans (2009) introduced an index to represent the strength of loose material and extended previous relations to predict the sum of the maximum scour depth and the tailwater depth [10]. D'Agostino and Ferro (2004) proposed an empirical formula to estimate the equilibrium scour depth of weir type drop structures based on the high crest of the weir and the flow depth over a weir [11]. Yager et al. (2012) extrapolated an approach to predict the scour depth and geometry of A-, U-, and W-shaped rock weirs from the case of two-dimensional flow [12]. Melville (2014) used a small-scale experiment to investigate the scour at a bridge foundation in the vicinity of a sluice gate and low wire [13].

With the aforementioned research, the effect of different types of drop structures, different conditions of approach flow, and different materials of sediment have been investigated, and varied empirical formulas for the characteristic of local scour due to the drop structure have been proposed. On the other hand, some researchers focused on the local scour at bridge piers; for example, Breusers et al. (1977) reviewed a series of literature regarding theory, model, and field data about the local scour around cylindrical piers and suggested a set of designs for protection against scour [14]. Ahmed and Rajaratnam (1998) reported that smooth, rough, and mobile beds impacted the flow features and pier scour [15]. Graf and Istiarto (2002) experimented with the equilibrium scour depth around a cylinder pier and investigated the vortex system around a cylinder pier based on measurement of the acoustic Doppler velocity profiler (ADVP) [16].

Dey and Raikar (2007) experimented with the developing scour depth around a cylinder pier and investigated the features of the vortex system in the intermediate and equilibrium stages [17]. Ataie-Ashtiani and Aslani-Kordkandi (2013) experimented with the developing scour depth around a single pier and two piers in tandem on a roughly flat bed and investigated the difference of flow features in the implemented experiments [18]. Euler et al. (2014) investigated the local scour in the vicinity of pillar-like objects through experimental studies and compared the results with field data [19].

These studies contribute to the flow feature impact on pier scour. Other studies focused on scoring features. For example, Baker (1980) derived a formula to estimate the equilibrium scour depth in front of a cylindrical bridge pier and compared the results with the results of Baker (1979), Breusers et al. (1977), and Chabert and Engeldinger (1956) [14,20–22]. Chiew and Melville (1987) proposed an empirical relationship that was related to the equilibrium depth scour, particle size of sediment, and flow condition, and compared their results with the findings of Chee (1982) and Melville (1984) [23–25]. Elliott and Baker (1985) investigated the feature of scour depth under the effect of lateral spacing between bridge piers [26]. Melville and Chiew (1999) indicated that the development of the equilibrium scour depth can be related with the size of the pier, size of the sediment, and approach flow velocity [27].

Sheppard et al. (2004) indicated that the wash load concentration impacts the scale of the equilibrium scour depth under clear-water conditions [28]. Ataie-Ashtiani and Beheshti (2006) derived an empirical relationship to estimate the maximum local scour depth for the pile group and compared their results with the reports of Melville and Coleman (2000) and Richardson and Davis (2001) [29–31]. Khosronejad et al. (2012) investigated the features of clear-water scour around the geometry of cylindrical, square, and diamond bridge piers through experiments and numerical simulation [32]. According to the aforementioned research, the mechanism of local scour at bridge piers has been investigated comprehensively by the theory, experiment, field data, and numerical model, and empirical formulas for the equilibrium depth scour at bridge piers have been proposed. However, there are few papers, to the authors' knowledge, focusing on the interaction between overfall types and scour at bridge piers.

This paper was focused on probing the mechanism of the scouring effect on piers considering the different bridge locations and a flow-drop-induced scour hole. Two types of overfall, which included the submerged type and free overfall type, were researched herein. In the submerged type, the velocity component in the vertical direction was relatively smaller and, therefore, gave a smaller effect on the riverbed scour. The free type of overfall, on the other hand, produced a strong velocity component in the vertical direction and induced a more dramatic riverbed change. It is necessary to discuss in detail the response of piers suffering these two types of overfall and to take these responses into consideration in engineering practice.

#### **2. Procedure of the Experimental Work**

The configuration for the experiment flume equipped with a circulation flow system is shown in Figure 2a. The total length of the flume was 15 m, the width was 1 m, and slope of the flume bed was 1/1000. The wall of the flume was 0.8 m in height composed of transparent tempered glass. A deeper part of the flume bed had 2 m length, 1 m width, and 0.4 m depth located at 7 m upstream from the scour development. A flat flume bed was provided with 4.4 m in length, which was 81 times the hydraulic radius of 5.4 cm for a fully developed flow. *H* represents the difference in height from the water level upstream of the lifted platform to the tailwater level. *d*<sup>s</sup> indicates the depth of scouring.

**Figure 2.** (**a**) Configuration of experiment flume. (**b**) Schematic of free overfall condition. (**c**) Schematic of submerged overfall condition.

For the sediment using in the experiment, we assumed that the river bed was composed of medium sand. The median diameter (*D*50) of sediments in this experiment was 0.46 mm, and the standard deviation of the sediments (*σg*) was 1.69. Randkivi and Ettema (1977) suggested that the *σ<sup>g</sup>* should be smaller than 1.3 to avoid the armor layer in the development of local scour [33]. The flume was paved using homogenous sediments at a 2.5 cm depth in the zone out of the scour area to provide a similar roughness in the alluvial bed.

40 This was a clear-water scour test. The experiment was designed so that the local scour occurred only due to the influence of the drop structure and pier. In other words, the clearwater flow could trigger scour in the moving-bed when there was no drop structure and pier in the experiment flume. Accordingly, the ratio of the designed velocity of approach flow (*V*) and the critical mean approach flow velocity of the using sediment (*Vc*) was given as 0.5. Melville and Sutherland (1988) suggested that the critical mean approach flow velocity (*Vc*) can be estimated using following equation:

$$\frac{V\_c}{V\_{\ast c}} = 5.75 \times \log \left[ 5.53 \times \frac{h\_d}{D\_{50}} \right] \tag{1}$$

25 30 where *h<sup>d</sup>* is the depth of the downstream flow, and *V\*c* is the shear velocity of the using sediment [34]. Melville and Sutherland (1988) proposed a Shields chart for the threshold condition of uniform sediment in water, and the shear velocity was suggested as

0 120 240 360 480 600 720 840 960 1080 1200 1320 1440 Time (min)

0

5

10

15

20

Scour depth (cm)

35

0.018 m/sec for using sediment [34]. To satisfy the aforementioned conditions, in the experiment, the boundary conditions of flow were: critical flow depth *h<sup>c</sup>* = 2.4 cm, upstream flow depth *hu*= 5.4 cm, upstream velocity 27.6 cm/sec, upstream Froude number Fr = 0.38, downstream flow depth *h<sup>d</sup>* = 9.5 cm, downstream velocity (*V*) 15.9 cm/sec, and downstream Froude Number Fr = 0.16.

The authors changed the difference in height between the river bed and the crest of flow-control structure (*Z*) to produce two different conditions: free overfall and submerged overfall, with the same boundary conditions upstream and downstream, to study the interacting behaviors between the pier and overfall. The schematics of the free overfall and submerged overfall are shown in Figure 2b,c. The values of *Z* were selected as 8 and 12 cm in which the submerged overfall took place at *Z* = 8 cm (*H* = 3.9 cm) with no air vent occurrence and the free overfall took place at *Z* = 12 cm (*H* = 7.9 cm) with air vent occurrence.

Melville and Chiew (1999) and Dey (2014) indicated that the approach flow can no longer move the sediment from the scour hole when the scour is at equilibrium in the clear-water condition [1,27]. Accordingly, the equilibrium time was selected based on the development process of the scour hole in the free overfall test, in which 83.5% of the 24 h erosion was reached in 5 h as shown in Figure 3. We also observed that the deposition of the dune downstream was segregated after 4 h of erosion due to the lack of sediment supplementation from upstream. This showed that the overfall energy was dispersed in the scour hole so that the erosion was reduced. Therefore, the scouring behavior in the fifth erosion hour was chosen for discussion in this paper.

**Figure 3.** Development of the scouring process (the broken line was selected as the equilibrium hour).

A significant bed would be changed in the free overfall test; therefore, piers were installed at five locations:


5. At the deposition zone of the downstream, which was 130.8 cm (*Le*) to the flow-control structure, namely Case E.

On the other hand, piers were installed at three different locations for the submerged overfall test:


The above-mentioned cases are summarized in Table 1, and the schematic of the pier locations for free overfall and submerged overfall is shown in Figure 4. In addition, the free type and submerged type of overfall where no pier was installed in the experiment flume were also carried out and named "free overfall w/o pier" and "submerged overfall w/o pier", respectively. Lastly, a pier in the experiment flume was implemented without any type of overfall condition (*Z* = 0 cm) and named "Pure Bridge".

**Table 1.** List of the locations of piers.


<sup>1</sup> A–E: free overfall flow F–H: Submerged overfall flow. <sup>2</sup> A and F: Pier located at the upstream slope of the flow-drop-induced scour hole. <sup>3</sup> B and G: Pier located at the maximum scour point of the flow-drop-induced scour hole. <sup>4</sup> C and H: Pier located at the downstream slope of the flow-drop-induced scour hole. <sup>5</sup> D: Pier located at the edge of the flow-drop-induced scour hole. <sup>6</sup> E: Pier located far from the scour hole.

**Figure 4.** Schematic graphs of the pier locations: (**a**) Free overfall condition. (**b**) Submerged overfall condition.

#### **3. Observations from the Experiment and Discussion**

*3.1. Profile of the Scouring Development of Free Overfall without the Effect of the Pier*

In Figure 5, the time history of profile of scouring development in the case of free overfall w/o a pier is shown.

**Figure 5.** Development of the scouring process in the case of free overfall w/o a pier.

The horizontal axis represents the direction of flow, 0 is at the location of the flowcontrol structure, the vertical axis is the scouring depth, and the broken red line in the figure links the maximum scour depth at each observed time. We investigated that the maximum scour depth moved deeper and more downstream. During the scouring process, we also found that the slope of the scouring hole sometimes fell backward toward the scouring hole. Two counter-rotation eddies that were produced by the overfall affected the slope of the scouring hole where the slope at upstream was less steep than the slope at downstream because the counter-rotating eddies downstream were stronger than the ones that rotated upstream. The eddy provided the drag force along the slope surface, which increased the resistance of the sediment fall due to gravity.

The mechanism of development of the scouring hole was that the two counter-rotating eddies brought up the sediment to the slope at the downstream side, and gradually a small dune was formed. Euler et al. (2014) investigated the mechanism using a tracer, which allowed a visualization of the turbulent eddying and was similar to the observations in our experiments [19]. While a deeper and wider scouring hole was dug by the overfall, the dune was moved further downstream. On the other hand, the sediment of the slope of the scouring hole upstream occasionally slid into the hole while the hole was being dug wider and deeper. The sliding sediment was brought away downstream randomly. The slope at the downstream of the scouring hole was steeper than the original at-rest angle of the sediment deposits because the eddies provided a floating force along the slope surface that supported the sediments to stay at the same location until slope instability due to the occurrence of toe erosion induced by scour.

The maximum equilibrium scour depth was about 26.7 cm at 1440 min in the condition of free overfall w/o pier as shown in Figure 5. Many researchers proposed different empirical formulas for the maximum equilibrium scour depth under varied conditions of structure, sediment material, and approach flow [2,8–11,21,24,29]. For the condition of free overfall, Mason and Arumugam (1985) mentioned that the empirical formula for the maximum equilibrium scour depth has general form.

$$d\_s = a\_1 \frac{V^{a\_2} H^{a\_3}}{D\_{50}^{a\_3}} \tag{2}$$

–

2 3 3

50

1

*α α α α*

in which *α*1, *α*2, *α*3, and *α*<sup>4</sup> are all coefficients [8]. These coefficients were represented by different values in individual studies, and our study lists some suggested values from Mason and Arumugam (1985) in Table 2 [8]. In the procedure of the experiment work, the approach velocity (*V*) was 15.9 cm/sec, the value of *H* was 7.9 cm in the condition of free overfall, and the median diameter (*D*50) of sediments was 0.46 mm. The comparison of the equilibrium scour depth in the experiment and with the empirical formulas of other authors can be obtained in Table 2. These results illustrated that the scour depth had close to an equilibrium state in the experiment.

**Table 2.** Coefficients for use in Equation (2) (Mason and Arumugam) [8].


*3.2. Interaction between Piers and Overfall-Induced Erosion in Plain View*

#### 3.2.1. Free Overfall Impact on Pier at Different Location

Regarding free overfall, there were five locations in the experiment as shown in Figure 6. Figure 6a shows the case where no pier was installed in the experiment, and we observed that the geographic changes in the flume were mostly two-dimensional except at the boundaries. The distance of the maximum scour depth was about 32 cm, and the distance to the original bed level was about 80 cm.

**Figure 6.** *Cont*.

**-40**

**-20**

**0**

**20**

**40**

(a)

**Figure 6.** Contour lines of the river bed in the free overfall condition: (**a**) Free overfall w/o pier; (**b**) Case A; (**c**) Case B; (**d**) Case C; (**e**) Case D; (**f**) Case E.

**0 20 40 60 80 100 120 0 20 40** Figure 6b shows the results of Case A where the location of the pier was upstream of the scouring hole. In this case, the nappe directly impacted onto the pier instead of the river bed. The neighborhood of the pier was influenced by the pier and, therefore, deformed largely. Two sides of the pier were further eroded than in the previous case because the circulating flow took place after the nappe hit on the pier and the flow increased the erosion. However, the energy of the nappe reduced after hitting the pier, and thus less erosion occurred to the downstream.

**-20** Figure 6c shows Case B where the pier was located at the location of the maximum scour depth. A similar geography to the case without piers was observed, and therefore we concluded that the erosion induced by the pier in this case was not influential.

**0 20 40 60 80 100 120 -40** Figure 6d or 6e demonstrate a slight change of the river bed near the pier (Case C and D). Figure 6f shows that the erosion took place only at the neighborhood of the pier while the pier was located at the deposition area (Case E).

> *)* Overall speaking, in the free overfall condition, when the pier location was upstream of the scouring hole (*La*), significant erosion was found in the front of the pier along with a significant deposition in the back. When the pier location was far from the local scour (*Le*), some erosion and deposition took place in the front of the pier and in the back of the pier, respectively. The localized scour in the vicinity of the pier was induced by the approaching flow similar to classical local scour at the bridge (Dey 2014) [13]. When the pier location was at the edge of the local scour (*L<sup>d</sup>* ), the erosion depth in the front was lower than the original river bed, and the erosion took place in the back of the pier as well. However, the eroded river bed level was still higher than the original bed.

> As to the above discussions, while the pier location was at the downstream slope of the scour hole (*Lc*), the erosion in the front of pier was similar to the case of free overfall w/o pier. This indicates that the pier did not affect the characteristics of erosion. However, significant deposition occurred in the back of the pier in this case, and this caused the total erosion to be reduced. When the pier location was at the maximum scour point (*L<sup>b</sup>* ), greater erosion took place compared with at the maximum scouring depth, and slight deposition occurred in the back of the pier.

#### 3.2.2. Submerged Overfall Impact on Piers at Different Locations

Figure 7a shows that, in the case of submerged overfall without pier installation, the erosion was much less than in the case of free overfall, and the major scouring area was moved downstream. In Case F with the pier located upstream of the scour hole (*L<sup>f</sup>* ), Figure 7b shows that no significant geography changes of the river bed in the front of pier were found when comparing with the previous cases. However, significant deposition was observed at the back of the pier. When the pier location was at the maximum scouring

depth (Case G, *Lg*), the erosion in the front of pier became much more significant compared with the previous case, and it decreased in the back of pier in Figure 7c. In this case, the maximum scour depth shows a significant increase. In Figure 7d, the overfall condition shows a limited impact on the pier in Case H (*L<sup>h</sup>* ).

**Figure 7.** Contour lines of the river bed in the submerged overfall condition: (**a**) Submerged overfall w/o pier; (**b**) Case F; (**c**) Case G; (**d**) Case H.

Overall, in the submerged overfall condition, the scouring depth was clearly much smaller than in the free overfall cases. The most significant result was in Case G.

#### *3.3. Interaction between Piers and Overfall-Induced Erosion in Side View*

The profile change of the center line of the river bed can be seen in Figure 8. This demonstrates that there was no significant change of the landforms at the location in the front of pier when the water drop induced scour located upstream (Case A). The situation is similar to the case of the free overfall w/o pier. However, a relatively large deposition was observed in the back of pier for the pure water drop scour condition (Case A). This condition presented increased scour depth due to the pier when the pier was located at the maximum erosion depth of the flow drop hole (Case B). A relatively larger scour to pure water drop condition but no significant deposition was observed when the pier was located at the downstream slope of the scour hole (Case C). When the pier was located far from the scour hole, a localized scour was found in the front of the pier, and some deposition was also observed in the back of the pier (Case E). Case D presented the pier located at the edge

of the scour hole scour hole, and the erosion occurrence in the front of pier became more significant and lower than the initial bed level. On the other hand, erosion in the back of pier took place as well. However, the river bed level was still higher than the initial river bed level.

**Figure 8.** Comparisons of the center line of the vertical profile of the channel in the free type overfall drop.

We concluded that, while the pier located at the upstream slope of the maximum scour depth was induced by overfall, the scour that occurred in the front of pier was similar to the pure water drop inducing scour, which indicates that the scouring characteristic was not influenced by the pier. However, a significant deposition was observed in the back of pier. This revealed that the total scouring was reduced. This implies that better protection for the river bed can be found compared with the case of free overfall o/w pier when the pier is located at the upstream slope of the scour hole.

When the pier was located at the downstream slope of the scour hole, an increased scour depth was found in the front of pier when compared with the original scour hole, and some deposition was observed at the back of pier. The experiments demonstrated that the change in depth of the river bed was at the minimum when the pier was located at the edge of the scour hole. When the pier was located far from the scour hole, a localized scour in the vicinity of pier was induced by the approaching flow without the impact of free overfall. These results imply that that the bridge pier was more secure when it was located at the edge of the scour hole.

The scour depth in the submerged overfall condition was found to be smaller than in the free overfall condition as shown in Figure 9. When the pier was located upstream of the maximum scour point (Case F), a deeper scour was found in the front of pier compared with the initial river bed, and there was a deposition at the back of pier. When the pier was located at the point of maximum scour (Case G), a significant scour was observed in the front and the back of the pier, and this was also deeper than for the initial river bed. When the pier was located in the initial river bed (Case H), scour was found at the front and back of the pier and was smaller than in Case G.

**Figure 9.** Comparisons of the center line of the vertical profile of the channel in the submerged type overfall drop.

We concluded that the scouring characteristics would be varied with the pier locations at the scour hole and that the most significant scour was found at the point of the maximum scour location induced by water drop. This implies that the bridge pier was a smaller influence of the local scour when it was closer to the location of the submerged overfall.

The maximum scour depth and its location change due to the interaction between overfall type and pier's location can be investigated based on our experiments. The pier's location (*L<sup>i</sup>* ), the maximum scour depth (*ds*), and its location (*Lscour*) in each experiment were listed in Table 3. By comparing the conditions with and without pier, *ds*/*do*−*<sup>s</sup>* and *Lscour*/*Lo*−*scour*, the effect of pier's location on the maximum scour depth and its location can be investigated. In the condition of free overfall, when *<sup>L</sup><sup>i</sup>* <sup>&</sup>gt; *<sup>L</sup>o*−*scour*, the maximum scour depth and its location due to drop structure were not affected by the pier. When *<sup>L</sup><sup>i</sup>* <sup>&</sup>lt; *<sup>L</sup>o*−*scour*, the location of maximum scour depth was changed according to *<sup>L</sup><sup>i</sup>* , and the maximum scour depth became smaller than in the case of w/o pier. In the condition of submerged overfall, when *<sup>L</sup><sup>i</sup>* <sup>&</sup>gt; *<sup>L</sup>o*−*scour*, the location of maximum scour depth was changed based on *L<sup>i</sup>* , and the maximum scour depth was larger than in the case of w/o pier obviously. This result implied that the empirical formulas for the characteristic of local scour due to the drop structure, i.e., Mason and Arumugam (1985) [21], could be used when the overfall condition is free type and *<sup>L</sup><sup>i</sup>* <sup>&</sup>gt; *<sup>L</sup>o*−*scour*.


− **Table 3.** Maximum scour depth and its location change due to the overfall type and pier's location.

#### *3.4. Scour Conditions at Pier Surroundings Due to Overfall* − −

In the condition that the flow drop depth (*Z*) was set at 12 cm, the model of the pier was positioned at five different locations in the experiment facility. The centerline of the vertical profile of the flow drop inducing scour was represented by Case A–E in this paper. We used a camera in the hollow pier model to record the process of the experiment tests over 5 h, and Figure 10 shows the scour depth of the surroundings of the pier in the condition of free overfall. In the same way, a model of pier was positioned at three different locations in the condition of submerged overfall and represented by Case F–H in the centerline of the vertical profile of the flow drop inducing scour. Figure 11 depicts the sour depth of the surroundings of the pier in the condition of submerged overfall. In Figures 10 and 11, the position of the pier at 0 degrees is the location where the approaching flow hits the pier. −

**Figure 10.** Scour depth distributions of the pier's surroundings in the free type of overfall drop.

**Figure 11.** Scour depth distributions of the pier's surroundings in the submerged type of overfall drop.

#### 3.4.1. Scour Conditions at the Pier Surroundings Due to Free Overfall

Figure 10 shows that, in Case A, although the location of the pier was at the upstream slope of the scour hole, the bottom of the pier was scoured due to a reversed flow induced by the flow drop. The maximum scour point of the surroundings of the pier was at the position of 0 degrees. This reveals that a water jet along the river bed from upstream dominated the scour characteristics. There was an unstable condition at 90 degrees and 270 degrees due to interactions from the reversed flows and water jet from upstream, which led to an asymmetric scour at the surroundings of the pier. In Case B, when the pier was located at the point of the maximum scour, the water jet lost most of its energy after hitting the river bed; therefore, the scour depth located from 0 degrees to 45 degrees on the upstream side was almost the same.

The deposition, found in the downstream, was out of 45 degrees, and it deposited greater at around 60 degrees and scoured the least at 180 degrees. In Case C, we found that the scour distribution curve of the pier's surroundings appeared to be greatly affected by the pier inducing scour. However, this was not true, in fact, as the occurrence of the scour mostly occurred upstream of the scour hole. Cases D and E presented cases with the location of the pier at the edge of the scour hole and far from the scour hole. We found that Case D was affected by the sediment loaded flow from the bottom of the scour hole, and therefore, the local scour in front of the pier was not apparent. The scour hole in front of the pier in Case E, on the other hand, was mostly dominated by the pier itself, as the location of the pier in this case was away from the flow drop induced scour hole.

#### 3.4.2. Scour Conditions at the Pier Surroundings Due to the Submerged Overfall

Figure 11 shows that, in Case F, the pier was located in the deposited mound and was hit by a submerged flow jet directly. The results show a full scour hole developed right after the deposited mound was affected by the overfall surrounding the pier, and was not found to be strongly affected by the water jet. In Case G, no significant landform was found in the pier's surrounding, we found in Figure 7c that scour holes developed with a shape of mullet roe surrounding the pier. Both depths in the holes were found to be greater than the ones in front of the pier. This indicates that the water jet caused by the submerged overfall in the x direction was stronger than in the z direction. In Case H, the pier was located downstream of the scour hole, and therefore a greater range of landforms could be observed.

#### **4. Conclusions**

This paper focused on probing the mechanism of the scouring effect on piers considering different bridge locations and the flow drop induced scour hole through a series of experiments. Two types of overfall, submerged and free overfall, were applied in the experiment. This mechanism is expected to draw attention from both engineering and academic specialists regarding protecting bridges in newly changed landforms.

Our concluding remarks can be drawn as follows:

Location of the pier vs. the free overfall:


Location of pier vs. submerged overfall:


**Author Contributions:** Conceptualization, C.-K.H. and C.-W.L.; methodology, C.-K.H. and C.-W.L.; formal analysis, C.-K.H., C.-W.L., and W.-L.L.; C.-W.L. and W.-L.L. wrote the manuscript, and all authors contributed to improving the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Acknowledgments:** We thank the reviewers for their useful comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


*Article*

### **Landslide Susceptibility Based on Extreme Rainfall-Induced Landslide Inventories and the Following Landslide Evolution**

### **Chunhung Wu**

Department of Water Resources Engineering and Conservation, Feng Chia University, Taichung 40724, Taiwan; chhuwu@fcu.edu.tw; Tel.: +886-4-2451-7250 (ext. 3223)

Received: 15 September 2019; Accepted: 6 December 2019; Published: 11 December 2019

**Abstract:** Landslide susceptibility assessment is crucial for mitigating and preventing landslide disasters. Most landslide susceptibility studies have focused on creating landslide susceptibility models for specific rainfall or earthquake events, but landslide susceptibility in the years after specific events are also valuable for further discussion, especially after extreme rainfall events. This research provides a new method to draw an annual landslide susceptibility map in the 5 years after Typhoon Morakot (2009) in the Chishan River watershed in Taiwan. This research establishes four landslide susceptibility models by using four methods and 12 landslide-related factors and selects the model with the optimum performance. This research analyzes landslide evolution in the 5 years after Typhoon Morakot and estimates the average landslide area different ratio (LAD) in upstream, midstream, and downstream of the Chishan River watershed. We combine landslide susceptibility with the model with the highest performance and average annual LAD to draw an annual landslide susceptibility map, and its mean correct ratio ranges from 62.5% to 73.8%.

**Keywords:** extreme rainfall-induced landslide susceptibility model; landslide ratio-based logistic regression; landslide evolution; Typhoon Morakot; Taiwan

#### **1. Introduction**

Deaths and economic losses due to natural disasters have drastically increased in Taiwan over the past two decades, especially after the 1999 Chichi earthquake [1]. In Taiwan, landslides and debris flows are the major causes of serious rainfall-induced disasters. The death toll due to Typhoon Morokot in 2009 was around 703, and the death toil due to the associated landslides and debris flow disasters was over 500, including 465 deaths caused by the Xiaolin deep landslide [2]. The number and intensity of the heavy rainfall events are expected to increase in the future in Taiwan [3], and the occurrences of landslides and debris flows over the next decade are expected to increase. Therefore, the assessment of landslide susceptibility is an important consideration for disaster prevention or mitigation in Taiwan.

Landslide susceptibility assessment models can be created based on heuristic, deterministic, and statistical approaches. Among these approaches, statistical methods are the most popular because of the development of geographic information systems and remote sensing techniques. The processes involved in evaluating landslide susceptibility by establishing a susceptibility model using statistical approaches include selecting landslide-related factors, creating a database, acquiring the most suitable fitting equations from the statistical model for landslide occurrence, and calibrating or validating models. The prediction accuracy of most statistical landslide susceptibility models can exceed 70% [4–7]. Technological statistical methods for predicting landslide susceptibility have improved to involve artificial neural networks [8], machine learning [9,10], empirical methods based on big data [11,12], and artificial intelligence [13]; the prediction accuracy of landslide susceptibility models using these technologies range from 80% to 90%.

Several rainfall events with a return period of more than 100 years have occurred in Taiwan, particularly in the Central and Southwestern regions, over the past two decades. Extreme rainfall events in Taiwan typically occur when daily rainfall >800.0 mm (such as that in Southern Taiwan during Typhoon Morakot in 2009 and Northern Taiwan during Typhoon Soudelor in 2015) or hourly rainfall intensity >80.0 mm/h (such as that in Northeastern Taiwan during Typhoon Megi in 2010). Extreme rainfall events also result in serious disasters. The accumulated rainfall and rainfall intensity during Typhoon Morakot in Southern Taiwan is representative of extreme rainfall events. The 48 and 72-h accumulated rainfall at most rainfall stations during Typhoon Morakot in Southwestern Taiwan exceeded the accumulated rainfall record of the 200-year return period [2], and the average rainfall intensity from 12:00 a.m. to 8:00 p.m. on 8 August 2009 in the midstream of the Chishan River watershed was more than 80.0 mm/h. Some studies have started to emphasize the seriousness of extreme rainfall-induced landslide or debris flow [8,9] or have created landslide susceptibility models for regions with high annual and daily rainfall [10] because of the increasing occurrence frequency of extreme rainfall events. Rainfall is widely used as a factor for building landslide susceptibility models, but the pattern and extent of rainfall should be emphasized [14,15]. Therefore, the assessment of landslide susceptibility is a crucial consideration for disaster prevention and mitigation in Taiwan [16].

The novelty of this research includes the applicability of landslide susceptibility models using statistical modeling in areas with dense landslide distribution and the process of drawing annual landslide susceptibility maps in the years after extreme rainfall events. The landslides induced by Typhoon Morakot in the Chishan River watershed were densely distributed, and the landslide types mainly included debris falls, translational landslides, riverbank landslides, and large-scale landslides. Areas with dense landslide distributions induced by an extreme rainfall event are uncommon globally, and discussing the performance of landslide susceptibility maps using statistical models in dense landslide distribution areas is valuable. Another novelty in this research is that a large amount of sediment was deposited downhill or transported into the river after numerous landslides occurred in the area. The large amount of sediment deposited randomly in the river resulted in sinuous rivers and subsequent riverbank landslides. Landslide susceptibility in some specific areas in the years after extreme rainfall events did not decrease; they instead increased, because riverbank landslides increased substantially. Numerous articles have focused on predicting landslide susceptibility for specific rainfall or earthquake events, and this research suggests that annual landslide susceptibility maps after specific rainfall or earthquake events should be emphasized as well.

This research compares and analyzes the applicability of landslide susceptibility assessment models based on four methods by using the extreme rainfall-induced landslide inventory and suggests a process of drawing landslide susceptibility maps in the years after extreme rainfall events. The four methods used in the study include landslide ratio-based logistic regression (LRBLR) [17], frequency ratio (FR), weights of evidence (WOE), and instability index (II) [18]. The landslide susceptibility model is combined with 12 factors. The validation of the landslide susceptibility model in this research adopts the area under receiver operating curves and confusion matrix methods. The research selected the landslide susceptibility model with the best performance of the four as the basis for drawing landslide susceptibility maps after Typhoon Morakot. Furthermore, this study analyzes the long-term landslide evolution from 2008 to 2014 in the Chishan River watershed. The landslide evolution analysis from 2008 to 2009 identifies geomorphic characteristics of extreme rainfall-induced landslide-prone locations, whereas the analysis from 2009 to 2014 analyzes the difference in landslide count and area induced by Typhoon Morakot from 2010 to 2014 to understand the long-term evolution of landslides in the Chishan River watershed. Finally, the study draws annual landslide susceptibility maps from 2010 to 2014 by combining the extreme rainfall-induced landslide susceptibility model and the statistical data from landslide evolution from 2010 to 2014 in the Chishan River watershed. Figure 1 presents the flowchart of this research.

**Figure 1.** The flow chart of this research.

#### **2. Materials and Methods**

#### *2.1. Research Area and Extreme Rainfall Event*

#### 2.1.1. Research Area: Chishan River Watershed in Southwestern Taiwan

The Chishan river watershed (Figure 2) is a tributary watershed of Kaoping river watershed in Southwestern Taiwan. Kaoping river watershed ranks 11th in terms of suspended load in the world [19,20]. The mean sediment yield (5.9 kg/m<sup>2</sup> /year) and physical denudation rate (655.8 g/m<sup>2</sup> /year) of the Kaoping watershed are 1.96 and 4.37 times larger than that of mountainous rivers throughout the world [21,22]. The high suspended sediment quantity show that Kaoping river watershed is a soil erosion-, landslide-, and debris flow-prone watershed due to the fragile geology, steep terrain, and heavy rainfall.

The area of the Chishan river watershed is around 819 km<sup>2</sup> with the mean elevation and slope of 838 m (Figure 2) and 22.4◦ (Table 1). The average annual precipitation is 4468 mm. The mean precipitation in the rainy season, i.e., from May to October, occupies 83% to 89% of the mean annual precipitation, and that in the dry seasons, from November to April, only occupies 11% to 17%. The land use in the research area consists of forest (65.0%), agriculture (23.2%), development (4.2%), river (2.7%), and bare land (5.0%) based on the land use investigation maps produced in 2008 by National Land Surveying and Mapping Center in Taiwan. The main strata (Figure 3 and Table 2) in the research area includes the Miocene Changchihkeng formation (26.2% of the watershed), the Holocene alluvium (17.8% of the watershed), middle Miocene Nankang formation and equivalents (10.8% of the watershed), and the Miocene Tangenshan sandstone (10.5% of the watershed) based on the 1/5000 basin geological map in Taiwan [23].

**Figure 2.** The distribution of elevation, river, and landslide inventory induced by 2009 Typhoon Morakot in the Chishan river watershed.

**Table 1.** The statistical data of twelve landslide-related factors in this research in the Chishan river watershed.


**\*** Note: The S.D. indicates the standard deviation.


**Table 2.**The geological settings in the Chishan river watershed.

Note: Ab. means abbreviation and Oc. refers to the occupied percentage of the strata in the Chishan river watershed.

**Figure 3.** The geological settings of the Chishan river watershed.

#### 2.1.2. Extreme Rainfall Event: 2009 Typhoon Morakot

Typhoon Morakot struck Southern Taiwan between 6 and 10 August 2009. The rainfall distribution in the Chishan river watershed based on the rainfall records from 22 rainfall stations is shown in Figure 4. The rainfall ranges from 1083 to 1990 mm with an average of 1528.0 mm. The 24-h, 48-h, and 72-h accumulated rainfall exceeded the 200-year return-period accumulated rainfall [2]. The accumulated rainfall during the most intense rainfall period, i.e., 1 pm to 12 pm on 8 August 2009, was 577.0 mm to 786.5 mm, equal to a mean rainfall intensity of 48.1 mm/h to 65.5 mm/h in this period. The 2389 landslide cases (Figure 2) induced by 2009 Typhoon Morakot in the Chishan river watershed were extracted from high resolution SPOT 5 images [24,25]. The area of each identified landslide polygons ranges from 264 m<sup>2</sup> to 3.5 km<sup>2</sup> . The total landslide area in the Chishan river watershed is around 33.5 km<sup>2</sup> with the landslide ratio (*LR*) of 4.1%.

**Figure 4.** The distribution of accumulated rainfall during the 2009 Typhoon Morakot and rainfall stations in the Chishan river watershed.

#### *2.2. Research Methodology for Landslide Susceptibility Mapping and Long-Term Landslide Evolution*

#### 2.2.1. Landslide-Related Factors

Based on the literature [18] and data availability, this research selects a total of 12 factors as the basis for establishing the landslide susceptibility model and can be classified into geomorphological, geological, and hydrological. Geomorphological factors include elevation, slope, aspect, land use, plan curvature, and profile curvature. The elevation (Figure 2), slope, aspect, plan curvature, and profile curvature factors are derived from a 5-m digital elevation model (DEM), whereas the land use factor adopts the land use investigation map in Taiwan, which was produced in 2008 by the National Land Surveying and Mapping Center. Because the Chishan River watershed is an erosionand landslide-prone watershed, we adopt plan and profile curvature factors to describe divergence and convergence of water flow and runoff and infiltration mechanisms.

Geological factors include geology and fault density, and this study adopts a 1/50,000 geological map of the Chishan River watershed [23] to draw the geological setting map and estimate fault density. Geological formations in the Chishan River watershed are fragile and landslide-prone, and six fault lineaments pass through the Chishan River watershed, particularly in midstream. Hydrological factors include the accumulated rainfall during Typhoon Morakot, proximity to the rivers, topographic wetness index (TWI), and stream power index (SPI). This research uses the accumulated rainfall during Typhoon Morakot (from 20:30 on 5 August to 05:30 on 10 August 2009) to describe the influence of heavy rainfall on landslides. Rainfall records from 22 rainfall stations within or near the Chishan River watershed were collected to draw the distribution of accumulated rainfall in the watershed (Figure 3). Furthermore, headward erosion- and bank erosion-induced landslide cases occupy a considerable portion of the landslide inventory. The area within 300 m of the rivers occupies approximately 43.9% of the Chishan River watershed area, but the landslide area within 300 m of the rivers after Typhoon Morakot occupies approximately 52.8% of the total landslide area. This research adopts the hydrology module in ArcGIS to draw the river distribution and estimate the TWI and SPI. The TWI is defined as the natural logarithm ratio of the local upslope area drainage per contour length to the local slope angle and describes the water saturation in the surface soil layer. The SPI is defined as the product of the natural logarithm of both slope and flow accumulation. The SPI describes the erosion strength of river flow and is suitable for determining riverbank landslide locations.

#### 2.2.2. Landslide Susceptibility Methodology: Landslide Ratio-Based Logistic Regression Method (LRBLR)

The purpose of logistic regression analysis is to find the best fitting equation (Equation (1)) to describe the dependent variable (landslide or not landslide, *Y* in Equation (1)) and the independent parameters (landslide-related factors, *X<sup>n</sup>* in Equation (1)):

$$\text{logit}(Y) = \beta\_0 + \beta\_1 X\_1 + \beta\_2 X\_2 + \dots \tag{1}$$

$$\ln \frac{p}{1-p} = \text{logit}\left(Y\right) = \beta\_0 + \beta\_1 X\_1 + \beta\_2 X\_2 + \dots + \beta\_n X\_n \tag{2}$$

where β<sup>0</sup> is a constant and β*<sup>n</sup>* is the *n*th regression coefficient. The landslide susceptibility *P* can be written as Equation (2). Wu [17] suggested that the performance of landslide susceptibility model using the logistic regression method with the *LR* index is better than that using the original logistic regression method. Landslide ratio (*LR*) refers to the ratio of the landslide area in a specific area to that in the total watershed area. This research follows the suggestions from Wu [17] and reclassifies the categories of all variables according to *LR*. The number of landslide ratio classifications (*LRC* number) in a specific category is marked as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 as the *LR* in a specific category is <1.0%, 1.0–2.0%, 2.0–3.0%, 3.0–4.0%, 4.0–5.0%, 5.0–6.0%, 6.0–7.0%, 7.0–8.0%, 8.0–9.0%, 9.0–10.0%, and >10.0%, respectively. All variables in the *LRBLR* analysis are categorical variables.

The total grid count in the Chishan river watershed is approximately 3.17 <sup>×</sup> <sup>10</sup><sup>7</sup> grids, including 3.14 <sup>×</sup> <sup>10</sup><sup>7</sup> non-landslide grids and 1,356,104 landslide grids. The non-landslide grid count is approximately 23.2 times greater than the landslide grid count. In this study, all grid counts were attempted to be placed into the statistical software for logistic regression analysis, which was difficult to be analyzed in the statistical software, and the result was dominated by the non-landslide grid. This research was based on the study conducted by Yesilnacar and Topcal [26], who performed a random sampling analysis. Twenty random sampling datasets were picked, and each dataset included 1,356,104 and 1,356,104 landslide and non-landslide grids, respectively. The 20 random sampling datasets were analyzed using the SPSS software to obtain the Cox-Snell R<sup>2</sup> value and Nagelkerke R<sup>2</sup> value. Only when the Cox-Snell R<sup>2</sup> and Nagelkerke R<sup>2</sup> values from the logistic regression analysis were greater than 0.15, the dataset was considered as useful and valid [26] in the research. In this research, datasets with the highest Cox-Snell R<sup>2</sup> and Nagelkerke R<sup>2</sup> values were picked from 20 random sampling datasets, and coefficients from logistic regression were used to develop the landslide susceptibility model.

#### 2.2.3. Landslide Susceptibility Methodology: Frequency Ratio Method (FR)

Lee and Talib [27] suggested that landslide susceptibility should be directly proportional to *LR* in a specific area, i.e., the landslide susceptibility in an area with a dense landslide distribution should be high. Frequency ratio value (*FR*) can be a useful index when establishing a landslide susceptibility map. The *FR* value can be calculated as the ratio of the occupied percentage of landslide area in specific category in specific landslide-related factor to the occupied percentage of area in specific category in specific landslide-related factor. The *FR* value in each category of each factor is estimated in Table 3. The *FR* value in each category of every landslide-related factor can be calculated, and the sum of *FRs* can be used as the landslide susceptibility index (*LSI*, Equation (3)). *FR<sup>n</sup>* represents the frequency ratio value of the *n*th landslide-related factor. If the *FR* value in a specific category of the specific landslide-related factor >1, this means the landslide in the specific category of the specific landslide-related factor has a high correlation to the landslide distribution, while a value of <1 indicates a lower correlation.

$$LSI = \sum\_{1}^{n} FR\_{n} \tag{3}$$


**Table 3.** Coefficient values of landslide-related factors based on four methods.



**Table 3.** *Cont.*


The *WOE* method was proposed by Bonham-Carter (1994) [28], and the assessment equations in *WOE* method can be written as Equations (4)–(6) [5]:

$$\mathcal{W}^+ = \ln \left[ \frac{A\_1 / (A\_1 + A\_2)}{A\_3 / (A\_3 + A\_4)} \right] \tag{4}$$

$$\mathcal{W}^- = \ln \left[ \frac{A\_2 / (A\_1 + A\_2)}{A\_4 / (A\_3 + A\_4)} \right] \tag{5}$$

$$\mathbf{C} = \mathbf{W}^+ - \mathbf{W}^- \tag{6}$$

where *A*<sup>1</sup> (*A*3) is the landslide area (not-landslide) in a specific category of specific landslide-related factor and *A*<sup>2</sup> (*A*4) is the total landslide (not-landslide) area not in the specific category of specific landslide-related factor. The *W*<sup>+</sup> (*W*−) value represents the landslide-induced positive (negative) weight of the specific category in the landslide-related factor. The weights contrast value (*C*) is the difference between *W*<sup>+</sup> and *W*<sup>−</sup> and represents the spatial association between the specific category in the landslide-related factor and landslide occurrence [5]. The landslide susceptibility in a specific grid can be calculated as the summation of *C* values in each landslide-related factor.

#### 2.2.5. Landslide Susceptibility Methodology: Instability Index Method (II)

The instability index (*II*) method was proposed by Jian [29] to assess the slope stability. The calculation process for assessing the landslide susceptibility using the *II* method can be divided into two parts: the normalized grades (*D*) of each category in each landslide-related factor and the weighting value (*We*) of each landslide-related factor. The *D* and *We* values can be written as Equations (7) and (8) [30]:

$$D\_i = \frac{9(X\_i - X\_{\min})}{X\_{\max} - X\_{\min}} + 1\tag{7}$$

$$We\_{l} = \frac{V\_{l}}{V\_{1} + V\_{2} + \dots + V\_{n}} \tag{8}$$

$$\text{landslide susceptibility} = D\_1^{\text{We}\_1} \times D\_2^{\text{We}\_2} \times \dots \, D\_n^{\text{We}\_n} \tag{9}$$

where *X<sup>i</sup>* can be calculated as the ratio of *LR* in the *i*th category to the total *LR* in all categories in a specific landslide-related factor, while *Xmin* (*Xmax*) represents the minimum (maximum) ratio value in all categories of the landslide-related factor. *V<sup>n</sup>* in Equation (9) is the coefficient of variation of the *X<sup>i</sup>* values in all categories for the nth landslide-related factor. The *D* value is a normalization value to show the landslide-induced influence of a specific category in all categories.

#### 2.2.6. Validation and Similarity of Landslide Susceptibility Models

The area under the receiver operating characteristic curve (*AUC*) and the confusion matrix are the two methods to assess the model performance of landslide susceptibility models in this research. The receiver operating characteristic curve is obtained by plotting the sensitivity value on the vertical axis and the 1-specificity value on the horizontal axis, and the *AUC* value is adopted as an index to assess the model performance. The model performance can be considered as failed, poor, fair, good, and excellent with *AUC* values (the area under the receiver operating characteristic curve) ranges of 0.5–0.6, 0.6–0.7, 0.7–0.8, 0.8–0.9, and 0.9–1.0, respectively.

This research uses the confusion matrix [18] concept to set four indexes. The *PLCR* (*PLWR*) is the ratio of the predicted-landslide area within (not within) the range of landslide inventory to the total landslide area, and the *PNLCR* (*PNLWR*) is the ratio of the predicted-non-landslide area outside (not outside) the range of landslide inventory to the total non-landslide area. The mean correct ratio (*MCR*) is the mean of *PLCR* and *PNLCR*, while the mean wrong ratio (*MWR*) is the mean of *PLWR* and *PNLWR*.

This research adopts the correlation analysis to assess the similarities of four landslide susceptibility models. The similarities between the two models is very weak, weak, moderate, strong, and very strong when the correlation coefficient from the correlation analysis is 0.0–0.2, 0.2–0.4, 0.4–0.7, 0.7–0.9, and 0.9–1.0, respectively.

#### 2.2.7. Long-Term Landslide Evolution Analyses

The analysis of long-term landslide evolution includes the analysis of long-term rainfall records and the difference analysis of the annual landslide distribution from 2008 to 2014 in the Chishan river watershed. We collect the rainfall record in the Chishan river watershed from 2008 to 2014 to analyze the long-term rainfall distribution. The Chishan river watershed can be classified into three sun-watersheds, including upstream, midstream, and downstream watersheds (Figure 3). This research selects a representative rainfall station in each watershed, including the Xingaokou station in the upstream watershed, the Jiaxian station in the midstream watershed, and the Chishan station in the downstream watershed (Figure 3), based on the rainfall station location and rainfall record data availability. The research estimates the annual rainfall, the accumulated rainfall in the rainy seasons, i.e., from May to October, and also estimates the counts of the accumulated rainfall of three days in a row over 500 mm to understand the inducing strength from heavy rainfall in a specific year.

The long-term landslide evolution analyses in this research means that we adopt the annual landslide inventories from 2008 to 2014, and analyze the difference of annual landslide distribution and expanding or contracting of the total landslide area in every year. The annual landslide inventory used in this research was produced by the Forestry Bureau in Taiwan and the landslide inventory was identified from the Formosat-2 images with the spatial resolution of 2 m shot during January to July every year.

The landslide distribution of the Chishan river watershed after 2009 Typhoon Morakot was strongly related to the landslide location and proximity to the river [27]. In this study, the landslide distribution of the upstream, midstream, and downstream of the Chishan river watershed in 2008 to 2014 was analyzed. The areas of the upstream, midstream, and downstream river watershed were 210.0, 250.3, and 357.9 km<sup>2</sup> , respectively. Furthermore, areas within 300 m of the rivers were defined as riverbank areas and areas 300 m outside the rivers were identified as non-riverbank areas. A landslide located on the riverbank area was recognized as a riverbank landslide and a landslide that was not located on the riverbank area was recognized as a non-riverbank landslide.

In this study, the count and area of the landslide and the new and old landslide ratio of each year of the Chishan river watershed were estimated. A new landslide grid refers to when a landslide was identified this year, but was not identified as a landslide in the previous year, whereas the old landslide grid refers to when a landslide was identified both in this year and the previous year. The new and old landslide ratio is the ratio of the sum of the new and old landslide area to the total landslide area in a specific year. The purpose of the new or old landslide comparison from two annual landslide inventories from 2008 to 2009 is different to that from 2009 to 2014. In this study, the definition of new or old landslide from 2008 to 2009 is according to the aforementioned definition but that from 2009 to 2014 is the comparison of the landslide inventory in 2009 and the following year. For example, the old landslide ratio of 62.9% in 2014 suggests that 62.9% of the landslide grid in 2014 was also identified as a landslide grid in 2009.

#### **3. Results**

#### *3.1. Extreme Rainfall-Induced Landslide Characteristics*

The extreme rainfall-induced landslide characteristics in the Chishan river watershed can be explained based on the statistical data in Table 3. If we consider the *LR* of >5.0% as an obvious landslide-prone area, the top three obvious landslide-prone areas in all categories of 12 landslide-related factors are the bare land category in land use factor (*LR* = 22.8%), the area with fault density <sup>&</sup>gt;<sup>20</sup> <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>m</sup>/km<sup>2</sup> category in fault density factor (*LR* = 16.0%), and the Yushanchushan formation (*Yn*) category in geology factor (*LR* = 13.1%). The three factors with the largest variance of *LR* are the land use factor (154.71), accumulated rainfall factor (112.18), and the geology factor (108.52), while those with the smallest variance of *LR* are the profile curvature factor (17.80), the proximity to the river factor (19.06), and the plan curvature (32.05). The geological setting and rainfall distribution are key factors for landslide distribution in the Chishan river watershed. The area of the strata with the *LR* > 5.0 occupies 42.6% of the total area in the Chishan river watershed, but the landslide area in the same area occupies 75.0% of the total landside area. Lithology in the categories with the *LR* > 5.0 in the geology factor is all about sandstone, shale, siltstone, and slate. The total area with accumulated rainfall >1400 mm during the 2009 Typhoon Morakot occupies 68.2% of the watershed area, while the landslide area with accumulated rainfall >1400 mm occupies 99.4% of the total landslide area in the watershed.

#### *3.2. Landslide Susceptibility Models Usinf Four Methods*

The landslide susceptibility mapping is followed by using four methods, and the research selects the landslide susceptibility model with the best performance from four models for the following research. In the process of establishing the landslide susceptibility model using the *LRBLR* method, every category in each landslide-related factor is marked a *LRC* number based on *LR* (Table 3). The highest mean *LRC* number is 9.4 in the fault density factor, while the highest variation of *LRC* number is 94.5% in the land use factor. The research picks 20 random sampling datasets for the logistic regression analyses and selects the result for the random sampling dataset with the largest Cox & Snell R<sup>2</sup> value and Nagelkerke R<sup>2</sup> value. Only if the two indexes, including Cox & Snell R<sup>2</sup> value and Nagelkerke R<sup>2</sup> value, from the logistic regression analysis result using the random sampling datasets are greater than 0.15, the dataset is useful and valid [7] in the research. This research picks the dataset with the highest Cox & Snell R<sup>2</sup> value (0.346) and Nagelkerke R<sup>2</sup> value (0.461) from 20 random sampling datasets, and uses the coefficients resulted from the logistic regression for developing the landslide susceptibility model. The coefficient of each landslide-related factor from logistic regression analysis is listed in Table 4.


**Table 4.** Coefficients of landslide-related factors in the landslide ratio-based logistic regression analyses.

Note: Coe\* means the coefficient of category in the twelve landslide-related factors from landslide ratio-based logistic regression analysis.

The *FR* and *C* values in the process of establishing the landslide susceptibility map using *FR* and *WOE* methods are listed in Table 3, while the *D* and *W* values using *II* method are also listed in Tables 3 and 5. The landslide susceptibility maps using four methods are shown in Figure 5. The mean landslide susceptibility, standard deviation and variance of landslide susceptibility values using the *LRBLR* method are 0.533%, 0.280%, and 52.5%, while those using the *FR* method are 0.387%, 0.185%, and 47.8%. The mean landslide susceptibility, standard deviation and variance of landslide susceptibility values by the *WOE* method are 0.549%, 0.222%, and 40.4%, while those using the *II* method are 0.325%, 0.199%, and 61.2%. The accumulated percentages from 0 to 0.5 of landslide susceptibility using *FR* and *II*

methods are 71.1% and 79.2%, while those from 0.5 to 1.0 of landslide susceptibility using *LRBLR* and *WOE* methods are 65.6% and 65.8%.

**Figure 5.** The landslide susceptibility maps using four methods based on the landslide inventory after 2009 Typhoon Morakot in the Chishan river watershed.


**Table 5.** Weights of landslide-related factors based on the *II* method.

Note: S.D. means the standard deviation, W.V. means the weighting value, TWI refers to the Topographic wetness index, and SPI refers to stream power index.

The performance of landslide susceptibility models based on four methods is considered from good to fair [28], because the *AUC* value of each method is *LRBLR* (0.803) > *WOE* (0.789) > *FR* (0.762) > *II* (0.721). The confusion matrix of four landslide susceptibility models is shown in Table 6. This research only explains the *PLCR*, *PNLCR*, and *MCR* data of landslide susceptibility models using four methods, because the summation of *MCR* and *MWR* is 1.0. The *PLCR* value of the landslide susceptibility model is 96.2% for *LRBLR*, 75.3% for *FR*, 92.3% for *WOE*, and 62.7% for *II*, while the *PNLCR* is 45.6% for *LRBLR*, 60.3% for *FR*, 46.3% for *WOE*, and 62.2% for *II*. The *MCR* of landslide susceptibility model is 70.9% for *LRBLR*, 67.8% for *FR*, 69.3% for *WOE*, and 64.0% for *II*. Based on the performance of landslide susceptibility models, including the *AUC* and *MCR* values, this research considers that the landslide susceptibility model using the *LRBLR* method is the most suitable model in four landslide susceptibility models in the Chishan river watershed.

**Table 6.** Confusion matrix of landslide susceptibility models using the four methods and in 2010 to 2014.


Note: *PLCR* and *PNLCR* refer to the predicted landslide correct ratio and the predicted non-landslide correct ratio, respectively, *PLWR* and *PNLWR* refer to the predicted landslide wrong ratio and predicted non-landslide wrong ratio, respectively, and *MCR* and *MWR* refer to the mean correct ratio and mean wrong ratio, respectively.

#### *3.3. Rainfall Records from 2008 to 2014 in the Chishan River Watershed*

The rainfall records in the Chishan river watershed from 2008 to 2014 are shown in Figure 6 and Table 7. The mean accumulated rainfall during the rainy seasons and annual rainfall from 2008 to 2014 are 2784 mm and 3488 mm in the upstream watershed, 2478 mm and 3168 mm in the midstream watershed, and 2408 mm and 2595 mm in the downstream watershed. The accumulated rainfall during the rainy seasons in the upstream watershed occupied 72.5% to 85.6% of the annual rainfall from 2008 to 2014, while those in the midstream and downstream watershed occupied over 87.0%.

**Figure 6.** The annual rainfall (solid lines) and accumulated rainfall during the rainy season (dash lines) from three representative rainfall stations, including Xingaokou station (red line), Jiaxian station (blue line), and Chishan station (black line), in the Chishan river watershed from 2008 to 2014.


**Table 7.** The 3-day accumulated rainfall >500 mm records from 2008 to 2014 in the Chishan river watershed.

The research collects the heavy rainfall or typhoon events with the 3-day accumulated rainfall over 500 mm from 2008 to 2014 in the Chishan river watershed and lists in Table 7. The most accumulated rainfall in 3 days were 1018 mm in 2008 and 2142 mm in 5 days in 2009 in the midstream watershed, and 604 mm in 2008 and 2076 mm in 2009 in the upstream watershed. Furthermore, the most accumulated rainfall was 572 mm in 3 days in 2008 and 900 mm in 5 days in 2009 in the downstream watershed.

The comparison of the rainfall concentration in 2008 and 2009 can explain why the landside ratio in 2009 is larger than that in 2008. The accumulated rainfall during the rainy season in 2008 ranges from 3012 mm to 4615 mm, and that in 2009 ranges from 1747 mm to 3173 mm. The concentrated rainfall during 2009 Typhoon Morakot is the key factor for the dense landslide distribution in the Chishan river watershed. The 3-day accumulated rainfall in 2008 in the Chishan river watershed ranges from 566 mm to 1018 mm, while that in 2009 ranges from 900 mm to 2142 mm. The rainfall concentration during specific heavy rainfall or typhoon events is a key factor for inducing landslides in the Chishan river watershed.

#### *3.4. Landslide Distribution from 2008 to 2014 in the Chishan River Watershed*

The annual landslide distributions and statistical data from 2008 to 2014 are shown in Figure 7 and Table 8. The landslide distributions from 2008 to 2014 in the Chishan river watershed are concentrated in the midstream and upstream watersheds. The landslide counts and area in 2009 are 3.4 times and 7.4 times larger than those in 2008 due to 2009 Typhoon Morakot. The landslide area lowers gradually from 2009 to 2012, and raises slight from 2012 to 2013, and lower again from 2013 to 2014. The landslide counts and area in 2014 are only 69.8% and 53.4% of those in 2009. The landslide area from 2010 to 2014 shows that the landslide area in the following years after 2009 Typhoon Morakot gradually decreases if without any heavy rainfall event with more accumulated rainfall than that during 2009 Typhoon Morakot.

**Figure 7.** The landslide distribution from 2008 to 2014.



Notes: N and A refer to the landslide count and landslide area (km<sup>2</sup> ), respectively, and OP and NP refer to the old and new landslide percentage (%), respectively.

The new landslide ratio in 2009 rises to 91.3% due to the concentrated rainfall during 2009 Typhoon Morakot. The new landslide occupied percentage from 2009 to 2014 is <38.3%. This means that the landslide induced by 2009 Typhoon Morakot still plays an important role in the annual landslide inventory from 2010 to 2014.

Table 9 lists the statistical data of landslide ratio, new and old landslide percentage in the upstream, midstream, and downstream watershed of the Chishan river watershed from 2008 to 2014. Most of landslide distribution from 2010 to 2014 still overlaps the landslide distribution induced by 2009 Typhoon Morakot. The mean old landslide percentage from 2010 to 2014 in the upstream, midstream, and downstream watersheds are 60.1%, 76.1%, and 49.7%, respectively. The old landslide percentage in the upstream, midstream, and downstream watersheds in 2014 are 56.7% and 76.0%, and 45.8%, respectively, and this means that near or over 50% of landslide induced by Typhoon Morakot in 2009 is still hard to recover in 2014.


**Table 9.** The landslide ratio, new and old landslide percentages in the upstream, midstream, and downstream of the Chishan river watershed from 2008 to 2014.

The statistical data of riverbank-landslide and non-riverbank-landslide from 2008 to 2014 in the Chishan river watershed is shown in Figure 8. The area of the riverbank-landslide and non-riverbank-landslide in the downstream of the Chishan river watershed from 2008 to 2014 are still smaller than 1.0 km<sup>2</sup> , and the downstream watershed can be considered as a non-landslide-prone area. The area of riverbank-landslide and non-riverbank-landslide in the upstream watershed in 2009 are 3.3 and 3.5 times larger than those in 2008, while those in the midstream watershed are 13.5 and 17.9 times larger than those in 2008. The area of riverbank-landslide and non-riverbank-landslide in the midstream watershed in 2014 are only 25.3% and 30.5%, respectively, of those in 2009, while those in the upstream watershed are 122% and 112%, respectively, of those in 2009. This shows that most of landslide induced by 2009 Typhoon Morakot in the midstream watershed has been gradually recovery in 2014, but that in the upstream watershed was still hard to recover in 2014.

**Figure 8.** Area of the riverbank-landslide (solid lines) and non-riverbank-landslide (dash lines) in the upstream (black line), midstream (blue line), and downstream (red line) from 2008 to 2014.

#### *3.5. Landslide Susceptibility in the Following 5 Years after the 2009 Typhoon Morakot in the Chishan River Watershed*

The long-term landslide evolution analysis in this research has proved that the landslide distribution in 2010 to 2014 has a high correlation to the landslide distribution induced by the 2009 Typhoon Morakot. We suggest that the annual landslide susceptibility maps of the Chishan river watershed from 2010 to 2014 can be the combination of the landslide susceptibility map after the 2009 Typhoon Morakot and the average landslide area different ratio (*LAD*) to the power of the year interval number between 2009 to the specific year in 2010–2014. The *LAD* ratio in this study can be defined as the ratio of the total landslide area in a specific year from 2010 to 2014 to the total landslide area in 2009 of the watershed. For example, the annual landslide susceptibility map in 2012 is the production of the landslide susceptibility model after the 2009 Typhoon Morakot and the *LAD* value to the power of 3.

The annual landslide susceptibility map in 2010 to 2014 of the Chishan river watershed was drawn based on two assumptions. The first assumption was that no previous heavy rainfall event occurred with more accumulated rainfall than that of the 2009 Typhoon Morakot. This assumption is valid for the Chishan river watershed based on data shown in Figure 5 and Table 7. Second, the *LAD* ratio in a specific area was considered to be constant in the 5 years following the 2009 Typhoon Morakot.

Given the difference in the landslide evolution in the upstream, midstream, and downstream areas of the Chishan river watershed and for the riverbank and non-riverbank areas, the Chishan river watershed was classified into six subareas, including the riverbank and non-riverbank areas in the upstream, midstream, and downstream watersheds. The research uses the landslide area in 2009 and 2014 in the same subareas to calculate the *LAD* value. The average *LAD* values in the riverbank and non-riverbank areas in the midstream watershed from 2010 to 2014 were 0.760 and 0.788, respectively, whereas those in the downstream watershed were 0.732 and 0.789, respectively. The average *LAD* values of the riverbank and non-riverbank areas in the upstream watershed from 2010 to 2014 were 1.04 and 1.02, respectively.

The annual landslide susceptibility of each subarea of the river watershed in a specific year from 2010 to 2014 is the production of landslide susceptibility in 2009 and the *LAD* ratio to the power of the year interval. The annual landslide susceptibility distributions of the Chishan river watershed from 2010 to 2014 are shown in Figure 9, and the statistical data of the annual landslide susceptibility from 2010 to 2014 are shown in Table 6. The *MCR* value of the landslide susceptibility model using the landslide ratio-based logistic regression (*LRBLR*) method in 2009 was 70.9%, and the *MCR* values of the annual landslide susceptibility models from 2010 to 2014 ranged from 62.5% to 73.8%. The *MCR* values of the annual landslide susceptibility maps from 2010 to 2014 are still acceptable.

**Figure 9.** The annual landslide susceptibility from 2010 to 2014 in the Chishan river watershed.

#### **4. Discussion**

#### *4.1. Applicability of Landslide Susceptibility Models to the Areas with Dense Landslide Distribution*

The similarity and difference of landslide susceptibility models using four methods can help to understand the applicability of each landslide susceptibility model to the areas with dense landslide distribution induced by extreme rainfall events. The correlation analysis result of the four landslide susceptibility models is listed in Table 10.

**Table 10.** The correlation coefficients of landslide susceptibility models based on four methods.


The similarity between the landside susceptibility models based on *LRBLR*, *FR*, *WOE*, and *II* methods is strong to very strong. The four landslide susceptibility models can be classified into two groups based on the similarity, including the first group with the landslide susceptibility maps based on *LRBLR* and *WOE* methods and the second group with the landslide susceptibility maps based on *FR* and *II* methods. The distribution of landslide susceptibility based on the methods in the first group is somewhat different to that in the second group.

The difference of landslide susceptibility models based on four methods is the process how the assessing grade of each category and weighting value of each landslide-related factor are decided in the specific method. The concept of landslide ratio is used in the four methods, such as *LRC* classification in *LRBLR*, *FR* value in *FR*, *W*<sup>+</sup> value in *WOE*, and the *D* value in *II*. The landslide susceptibility value by using *FR* or *WOE* methods is with equal weighting value, while using *LBRLR* or *II* methods gives a different weighting value. The accumulated rainfall, geology distribution, and land use factors should be the top three key factors for building the landslide susceptibility models based on the variance of landslide ratio in each factor in the Chishan river watershed based on the above-mentioned analysis. The factors used in building the extreme rainfall-induced landslide susceptibility model should be with different weighting values, so the *FR* and *WOE* methods are not suitable methodologies to build the landslide susceptibility model in the Chishan river watershed after the 2009 Typhoon Morakot.

The process of building the landslide susceptibility models by using *LRBLR* and *II* methods are with *LR* ratio and weighting values, but the difference between the two methodologies is the method by which landslide susceptibility values can be estimated. The landslide susceptibility value by using the *II* method is the product of the landslide susceptibility value of each factor, and the landslide susceptibility value in each factor was <1.0. The mean landslide susceptibility value by using the *II* method was 0.325, which is only 60.9% of the mean landslide susceptibility value obtained using the *LBRLR* method. Using the product to combine each landslide susceptibility value of each factor by using the *II* method underestimates the landslide susceptibility. In this study, the *II* method is considered suitable to develop the landslide susceptibility in the area with mild landslide distribution. The landslide susceptibility value using the *LRBLR* method is the summation of the assessment value of each category of each factor, and the assessment value of each category of each factor is determined by the SPSS software. The *LRBLR* method was considered suitable to develop the landslide susceptibility model for the extreme rainfall-induced landslide susceptibility model.

#### *4.2. Evolution of Landslide Distribution in the Following 5 Years after the 2009 Typhoon Morakot*

The landslide evolution in 2010 to 2014 is different in the upstream, midstream, and downstream of the Chishan river watershed and must be discussed in detail. The landslide ratio in the upstream watershed was 1.37% in 2008, 4.62% in 2009, and 5.40% in 2014. The landslide ratio in the upstream watershed from 2010 to 2014 was larger than that in 2009, except 2012. On average, the landslide inventory from 2010 to 2014 in the upstream watershed was composed of 60.1% old landslide that had originated from the 2009 typhoon Morakot and 39.9% new landslide. This means that the landslide in the upstream watershed following the 2009 typhoon Morakot is difficult to recover and easily induced by the mild heavy rainfall events. The landslide distribution in the upstream watershed in 2009, 2010, 2012, and 2014 is shown in Figure 10 for detailed discussion. The river intersection area (red rectangles in Figure 10) and the river source area (red circles in Figure 10) are the two main areas where the landslide is problematic to recover and easily induced from 2010 to 2014.

The midstream watershed has the most landslide area after 2009 Typhoon Morakot in the Chishan river watershed. The landslide ratio in the midstream reaches peak (9.19%) in 2009 and decreases gradually to 2.56% in 2014. On average, the landslide inventory from 2010 to 2014 in the midstream watershed is composed of 76.1% old landslide originating from 2009 Typhoon Morakot and 23.9% new landslide. This means that the landside in the midstream watershed is easily induced only by extreme rainfall events and recovers quickly in 5 years after extreme rainfall events. The composition of strata should be among important factors for the different landslide recovery in the upstream and midstream watersheds. The main strata in the upstream watershed include the Nankang formation, Changchihkeng Formation, and Nanchuang formation. The accumulated occupied percentage of the three strata in the upstream is around 87.9%. The composition of the three strata is slate, sandstone and shale, i.e., three landslide-prone lithologies. The landslide occurred in the three strata in the

upstream watershed in 2009 occupied 85.3% of the total landslide in the upstream, while that in 2014 still occupied 87.8% of the total landslide in the upstream.

**Figure 10.** The landslide distributions in 2009, 2010, 2012, and 2014 in the upstream of the Chishan river watershed.

The recovery of riverbank landslide from 2010 to 2014 was different in the upstream and midstream of the Chishan river watershed. Wu [31] mentioned that the riverbank landslide after the 2009 Typhoon Morakot in Taiwan was difficult to recover because of the excessive sediment yield from numerous landslides and debris flow that deposited randomly in the river and resulted in serious riverbank landslide. The area of the riverbank landslide induced by the 2009 Typhoon Morakot in the midstream watershed was recovered in 2014, whereas that in the upstream watershed increased in 2014. This is a notable and valuable observation for further discussion.

The riverbank landslide areas from 2012 to 2013 in the upstream and midstream watersheds are obvious comparisons for the difference in landslide recovery. The midstream watershed had suffered two heavy rainfall events with a 3-day accumulated rainfall of over 500.0 mm in August 2013 (Table 7), but the riverbank landslide area still decreased from 2012 to 2013. Additionally, the upstream watershed had suffered two heavy rainfall events on the same date, but the 3-day accumulated rainfall of Xingaokou station on 21–23 August and 29–31 August were only 449.5 mm and 353.5 mm, respectively. The riverbank landslide area in the upstream watershed in 2013 increased by 1.63 times of that in 2012, and the non-riverbank landslide area also increased by 1.66 times. In this study, the statistical data of landslide and rainfall in 2008 in the upstream watershed were adopted for obvious comparison. The annual rainfall in 2008 and in 2013 in the upstream watershed were 4049 and 3846 mm, respectively, and there were three heavy rainfall events with accumulated rainfall over 500.0 mm in 2008 and zero event in 2013 in the upstream watershed. The riverbank landslide ratio in the upstream in 2008 was 1.5%, and that in 2013 was 6.5%. These data demonstrate that the landslide proneness in the upstream watershed increased significantly after the 2009 Typhoon Morakot, whereas that in the midstream and downstream watershed decreased gradually. The upstream watershed should be

considered the most important area in the Chishan river watershed to implement further engineering and disaster prevention based on the long-term landslide evolution analysis.

Another key consideration for future studies can be that the landslide distribution in a river watershed in the following years after extreme rainfall events is mostly overlapped with that induced by extreme rainfall events. The old landslide percentages in the upstream and midstream of the Chishan river watershed were still over 60.0% from 2010 to 2014. The landslide susceptibility maps after extreme rainfall events can be the basis for the annual landslide susceptibility in the years following extreme rainfalls. We suggest that the landslide susceptibility model should be developed after extreme rainfall or earthquake events, and the annual landslide maps in the years following extreme rainfall or earthquake events can be the combination of the landslide susceptibility model and LAD values to the power of the year interval. The LAD values should be estimated carefully in each of the subareas. The annual landslide susceptibility maps from 2010 to 2014 in the Chishan river watershed in this research also proves the aforementioned concept and can be used with acceptable accuracy.

#### **5. Conclusions**

This research draws annual landslide susceptibility maps in the years after specific extreme rainfall events. Numerous landslides were induced by Typhoon Morakot in the Chishan River watershed. Based on our analysis result, 61.7% of the landslide area from 2010 to 2014 upstream and midstream of the Chishan River watershed overlapped with that induced by Typhoon Morakot in 2009. This indicates that the landslide distribution following specific extreme rainfall events are strongly related to that induced by the events. We suggest that annual landslide susceptibility maps in the years after specific extreme rainfall events can be drawn on the basis of the landslide susceptibility maps induced by specific extreme rainfall events. Most landslides in the years after specific extreme rainfall events were riverbank landslides induced by sinuous rivers that resulted from the large amount of sediment deposited in the river from the dense landslide after Typhoon Morakot. We emphasize the importance of riverbank landslides and explain how to assess susceptibility to them in the 5 years after Typhoon Morakot.

The research selects 12 landslide-related factors as the basis for establishing landslide susceptibility models using four methods, and the highest-performing landslide susceptibility model of the four methods is the *LRBLR* method. Accumulated rainfall, geology distribution, and land use are the top three key factors for establishing the landslide susceptibility model based on the variance of landslide ratios in each factor. Furthermore, we adopt the annual landslide inventories from 2008 to 2014 in the Chishan River watershed to analyze the long-term landslide evolution. The mean old landslide percentages from 2010 to 2014 upstream, midstream, and downstream of the Chishan River watershed are 60.1%, 76.1%, and 49.7%, respectively. The study calculates the mean LAD in the riverbank and non-riverbank areas upstream, midstream, and downstream of the Chishan River watershed. We suggest that the annual landslide susceptibility maps of the Chishan River watershed from 2010 to 2014 can be the combination of the landslide susceptibility map after Typhoon Morakot and the average LAD to the power of the year interval number between 2009 to the specific year from 2010 to 2014. We can roughly draw the annual landslide susceptibility map in the Chishan River watershed from 2010 to 2014. We compare the annual landslide inventories and susceptibility map from 2010 to 2014 in the Chishan River watershed, and the mean correct ratios from 2010 to 2014 range from 62.5% to 73.8%.

**Funding:** This research was funded by National Science Council in Taiwan (MOST 107-2313-B-035-001). And The APC was funded by National Science Council in Taiwan.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**


© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

**Kinuko Noguchi 1,2 , Ching-Ying Tsou 1, \* , Yukio Ishikawa 3 , Daisuke Higaki <sup>4</sup> and Chun-Yi Wu 5**


**Abstract:** The N-Ohkawa landslide, and the southern section of the Ohkawa landslide, occurred during the snow-melt seasons of 1999 and 2006, respectively, in the Shirakami Mountains, Japan. This paper examines the response of trees in the Shirakami Mountains to landslides, and also investigates the spatio-temporal occurrence patterns of landslide events in the area. Dendrogeomorphological analysis was used to identify growth suppression and growth increase (GD) markers in tilted deciduous broadleaved trees and also to reveal the timing of the establishment of shade-intolerant tree species. Analysis of the GD markers detected in tree-ring width series revealed confirmatory evidence of landslide events that occurred in 1999 and 2006 and were observed by eyewitnesses, as well as signals from eight additional (previously unrecorded) landslide events during 1986–2005. Furthermore, shade-intolerant species were found to have become established on the N-Ohkawa and southern Ohkawa landslides, but with a lag of up to seven years following the landslide events causing the canopy opening.

**Keywords:** tree ring; dendrogeomorphology; landslide; landslide activity; deciduous broadleaved tree; Shirakami Mountains

#### **1. Introduction**

Landslides are common in mountainous regions, and can be driven by tectonic, climatic, and/or human activities [1,2]. Landslides can create permanently unstable sites, and as a result, can drastically alter landscape morphology, damage forest environments, and even endanger life. Identifying the spatial and temporal patterns of landslide occurrence is vital for environmental management and minimizing the losses associated with landslides. However, information regarding past landslide events is scarce and almost always incomplete.

Dendrogeomorphology can be used as a proxy indicator of past landslide activity at the scale of years [3–5]. This dating technique is based on the analysis of annual growth rings in trees, with the mixed signals being filtered to isolate the signal indicative of landslide events from non-landslide disturbances, such as climate variations, insect epidemics, and human activity, encoded within the tree-ring chronologies [6,7]. Landslides cause disturbances in tree growth that are preserved as variations within the tree-ring width series. These growth disturbances (hereafter GD) can take several forms, namely, abrupt growth release (wider annual rings), suppression (narrower annual rings), and the formation of compression wood that results from the elimination of neighboring trees, damage to the root, crown or stems, and stem tilting [5,8]. Dating of landslide reactivation

**Citation:** Noguchi, K.; Tsou, C.-Y.; Ishikawa, Y.; Higaki, D.; Wu, C.-Y. Tree-Ring Based Chronology of Landslides in the Shirakami Mountains, Japan. *Water* **2021**, *13*, 1185. https://doi.org/10.3390/ w13091185

Academic Editor: Matthew Therrell

Received: 22 March 2021 Accepted: 23 April 2021 Published: 25 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

by interpretation of these GD markers preserved within annual-ring-width series has been performed using a moving-window approach to smooth out non-landslide fluctuations [9] or evaluating the change rate of the annual ring width if it exceeds a certain threshold value [10]. Additionally, other studies have dated landslides using different thresholds (e.g., the event-response (*It*) index and number of GD markers) [10,11]. Although the amount of research has increased in recent years, no systematic standard approach has yet been proposed and the choice of an appropriate definition and threshold appears to be site-specific.

Dendrogeomorphological studies of landslides have been performed using conifers in the European Alps and Americas [5,8,12]. In North America, Carrara [13] identified synchronous abrupt reductions in annual ring width in tree samples. He suggested that these tree responses were the result of damage during a landslide and was thus able to date the landslide event to 1693 or 1694 and infer that the trigger was an earthquake. With a focus on abrupt reductions in annual ring width and the formation of compression wood on the tilted side stem in the French Alps, Lopez-Saez et al. [10] assessed eight different stages of landslide reactivation over the past 130 years and found that landslide reactivation was associated with seasonal rainstorms. Recently, Lopez-Saez et al. [14] added abrupt increases in annual ring width as another type of growth disturbance, and this enabled reconstruction of 26 reactivation phases of landslides between 1859 and 2010 in the Swiss Alps. In the Orlické hory Mountains (Czech Republic), Šilhán [11] found that landslide activity is particularly associated with slide and creep effects, and the consequent growth disturbance can be identified in trees growing on the scarp and the landslide block. In contrast, there have been few such studies in Asia [3,12,15]. Recent studies have demonstrated that broadleaved trees are also useful for dating landslides and shown the need for additional case studies that consider, for example, an adequate variety of species and age classes [5,12].

Coherent landslides, which often move slowly (*Jisuberi* in Japanese), dominate in the Shirakami Mountains [16], but historical records relevant to landslide activity are scarce. In this study, we investigate the spatio-temporal patterns of landslide occurrence through analysis of the dendrogeomorphological record of 90 deciduous broadleaved trees from 12 species growing on landslide scarps and landslide moving bodies, which we refer to as the displaced blocks, on the right flank of the Ohakawa River, a tributary of the Iwaki River, within the Shirakami Mountains. Our main aims are: (i) to identify and interpret the GD markers (i.e., abrupt growth increase and growth suppression) preserved in the tree-ring series of trees growing on the landslide slopes; (ii) to investigate how these trees responded to landslides known to have occurred in the area; and (iii) to reconstruct the spatial and temporal patterns of landslide occurrence over the past 70 years using our GD data, as well as the timing of the establishment of shade-intolerant trees, and compare this with the limited eyewitness reports of landslides.

#### **2. Study Area**

The coherent landslides studied here were located on the right bank, and on an outside bend, of the meandering Ohkawa River, which originates from the eastern side of the Shirakami Mountains, northern Honshu Island, Japan (Figure 1). These landslides are covered by deciduous broadleaved trees dominated by Siebold's beech (*Fagus crenata*). The forest is a naturally regenerated, unmanaged secondary forest that developed after the original forest was selectively felled until 1967 [17]. The study area has a cool-temperate climate, with an average temperature of 8.1 ◦C and average annual rainfall of 2589 mm [18]. Each year, from November to the following April, the area is covered by snow to a maximum depth of about 2.2 m [18].

**Figure 1.** Coherent landslides, topographic map, and aerial photographs from the study area. (**a**) Landslide topogr –I', II–II', and III–III') are shown in F **Figure 1.** Coherent landslides, topographic map, and aerial photographs from the study area. (**a**) Landslide topography. Aerial photographs are from (**b**) 1975 and (**c**) 2015. The topographic map was constructed from a 1-m digital elevation model (DEM) based on LiDAR data provided by the Geospatial Information Authority of Japan (https://www.gsi.go.jp/, accessed on 12 April 2020). The landslide topography was interpreted using the slope image and the results were checked in the field. Topographic cross-sections (I–I', II–II', and III–III') are shown in Figure 2.

Our study area contains two neighboring landslide slopes: the N-Ohkawa and Ohkawa landslides, that are located along a 40-m-high terraced scarp, with the river terrace top at elevations of 285 to 295 m (Figures 1a and 2). Terrace gravels were exposed at the edge of the terrace after the landslides. The bedrock is formed from the mid-Miocene Hayaguchigawa Formation, which consists primarily of acidic pyroclastic deposits, but also contains andesitic pyroclastic deposits, sandstones, and conglomerates [19] (Figure 2). The N-Ohkawa landslide comprises a single displaced block. In contrast, distinctive stair-like features are evident on the displaced block of the Ohkawa landslide, which also comprises two secondary scarps that separate the individual blocks within the larger block at its northern and southern ends (Figure 2). Minor gully features are present in the landslide slope. Based on its slope geometry, we divided the Ohkawa landslide into three sections; i.e., the eastern, northern, and southern sections, for the following discussion. The timing of these movements is not well constrained. However, limited information obtained from several eyewitness accounts recorded during site visits suggests that the major movements of the N-Ohkawa landslide and the southern section of the Ohkawa landslide occurred in April 1999 and May 2006, respectively [20]; other slope movements of the Ohkawa landslide occurred recently, as described in Section 4.3. In addition, the lower slope of the N-Ohkawa landslide seems to have failed beforehand, as indicated by the bare area seen on the aerial photograph from 1975 (Figure 1b). The N-Ohkawa landslide and the northern and southern sections of the Ohkawa landslide are visible on the aerial photograph from 2015 (Figure 1c).

– II' –II'), and the southern section of the Ohkawa –I' **Figure 2.** Topography and geological cross-sections of the studied landslide slopes. (**a**) A photograph of the study area. (**b**) Geological cross-sections of the N-Ohkawa landslide (III–III'), the eastern and northern sections of the Ohkawa landslide (II–II'), and the southern section of the Ohkawa landslide (I–I'). The photograph was taken in 2017. The cross-sections are based on the LiDAR DEM.

#### **3. Methods**

#### *3.1. Sampling and Cross-Matching of Ring-Width Series*

– Increment cores were extracted from the upper side of the tilted stems of 90 living broadleaved trees using a Pressler increment borer (maximum length of 40 cm and diameter of 5.15 mm) between June and November 2019, on the main and secondary landslide scarps and on landslide-displaced blocks (Figure 3). The trees were sampled at trunk heights of 20–120 cm. According to the standard methods of dendrochronological research, increment core should be taken parallel to contour to avoid the development of reaction wood in tilted trees [21]. Tension wood develops on the upper side of leaning hardwood trees and typically has wider annual rings than on the lower side [3]. However, in the present study, we obtained cores oriented in the slope direction, because the formation of tension wood is, in itself, a good indicator of landslide movement [3]. Indeed, tension wood may not form in all tilted trees; therefore, wider annual rings may also be the result of growth release owing to, for example, the formation of canopy opening after landslide [5,8]. As such, responses resulting from both tilting and gap formation after landslides are included in our results.

**3.** Locations of sampled trees and frequency distribution of tree species. (**a**) Locations of sampled trees at **Figure 3.** Locations of sampled trees and frequency distribution of tree species. (**a**) Locations of sampled trees at the N-Ohkawa landslide. (**b**) Locations of sampled trees in the eastern and northern sections of the Ohkawa landslide. (**c**) Locations of sampled trees in the southern section of the Ohkawa landslide. (**d**) Frequency distribution of tree species. The numbers on the maps are sample ID numbers.

We selected 21 samples from four shade-intolerant species (*Alnus hirsuta* (*Ah*), *Betula maximowicziana* (*Bm*), *Salix bakko* (*Sb*), and *Salix sachalinensis* (*Ss*)), 57 samples from three shade-tolerant species (*Acer pictum subsp. mono* (*Am*), *Fagus crenata* (*Fc*), and *Quercus crispula* (*Qc*)), and 12 samples from five intermediate shade-tolerant species (*Aesculus turbinata* (*At*), *Magnolia obovata* (*Mo*), *Prunus grayana* (*Pg*), *Prunus sargentii* (*Psa*), and *Sorbus commixta* (*Sc*); Figure 3). We collected 11 samples from the N-Ohkawa landslide and 79 samples (including 39 from the southern (2006) section) from the Ohkawa landslide. The cores were prepared and analyzed using standard procedures following Stokes and Smiley [22] and Speer [21]. The sample cores were prepared using a razor blade to maximize the visual resolution of the ring widths and were measured to the nearest 0.01 mm under a binocular zoom microscope (Olympus SZ61) using a precision measurement stage (Chuo Seiki LTD. LS-252D) attached to a digital output unit (Mitsutoyo Digimatic). After measurement, all cores were visually cross-dated by matching well-defined wide or narrow rings. In addition, longer chronologies (>60 years) of shade-tolerant species and several intermediate species were cross-dated by using a simple list method [23].

#### *3.2. Identification of Growth Disturbance by Landslides in Tree-Ring Width Series and Age Determination of Shade-Intolerant Species*

In this study, we considered two types of GD markers in the tree-ring width series: abrupt growth increase and abrupt growth suppression. GD markers were identified using the method described by Ishikawa et al. [7], in which a five year moving average of ring width is used to identify periods of abrupt growth increase or suppression as follows. A

growth increase is defined as a doubling of the five year moving average of the ring width when compared with that of the previous five year period and a defined growth rate that fluctuates continuously above 1 for at least 10 consecutive years. Conversely, a growth suppression is defined as a halving of the five year average ring-width and a growth rate fluctuating continuously below 1 for at least 10 consecutive years. In addition, because of spatial irregularities in tree growth, the duration of the GD also depends on the sampling position [4,13]. Therefore, we took into account moderate levels of GD in which the defined growth rate persisted for less than 10, but more than five, consecutive years. In some cases, there is a slight time lag from the casual disturbance event in the GD markers extracted using the moving average method because of growth variation prior to and/or after the event. To avoid this inaccuracy, we carefully checked the ring-width pattern around the timing of the GD markers, and used the information to decide on the GD marker years in the tree-ring width series. Figure 4a–d shows representative examples of how the GD marker years were identified in the tree-ring series using the above method. No significant changes in annual ring width were found in 30 of the cores from the sampled trees (33%) and these cores were not considered for further analysis.

**Figure 4.** Representative cases from the N-Ohkawa landslide. (**a**) A micro-section of *Nu*. 10 (*Quercus crispula, Qc*) on the landslide scarp showing an abrupt increase in annual ring width in 1999. (**b**) A tree-ring width series and the 5 year moving average of the tree-ring width series of *Nu*. 10. Light blue and black arrows indicate identified response years of GD, growth suppression, and growth increase, respectively. (**c**) GD (i.e., growth suppression and growth increase) defined using growth rate of the tree *Nu*. 10. Note that the defined growth rate of growth suppression was continuously below 1 for 6 consecutive years, and that of growth increase was continuously above 1 for 7 consecutive years. (**d**) The tree-ring width series and identified GD from *Nu*. 17 (*Fagus crenata, Fc*) on the displaced landslide block. The annual ring width increased abruptly in 1999, followed by successive decreases in 2000 and 2001, and then by an increasing trend. (**e**) The tree-ring width series from *Nu*. 15 (*Alnus hirsuta, Ah*, the dominant shade-intolerant species in the study area). Open circle indicates the number of years for the tree to grow to the sample height.

– –

The chronology of each of the previous landslides was expressed using the eventresponse (*It*) index, following Shroder [24], as follows:

$$I\_t(\%) = \frac{\sum \text{GD}\_t}{\sum N\_t} \times 100 \tag{1}$$

–

–

where GD*<sup>t</sup>* is the number of trees showing GD in their tree-ring record in year *t*, and *N<sup>t</sup>* is the number of sampled trees for each landslide alive in year *t*. Due to the limited number of samples and detected GD markers available to identify landslide reactivation years, thresholds of GD*<sup>t</sup>* ≥ 2 and *I<sup>t</sup>* ≥ 15% were used. Additionally, the reported year of landslide events and year of establishment of shade-intolerant tree species were also used to assist our interpretation of the dendrochronological effects of landslide activity.

The establishment of shade-intolerant species is indicative of the development of large gaps in the canopy at some point in the past, and these gaps were most probably caused by landslides [25,26]. Consequently, the ages of individual younger trees from shade-intolerant species were determined (Figure 4e) based on the number of rings counted in the cores and the number of years required for seedlings to reach coring height estimated using an age–height regression relationship. The age–height regression (age (years) = 0.025 × height (cm), *R* <sup>2</sup> = 0.27) was established from 15 specimens of *Ah* (<2.5 m in height) sampled at the Shirakami Natural Science Park of Hirosaki University, 4 km from the study area, where the growth conditions are similar to those in our study area because of their similar elevations. However, the ages for trees of shade-tolerant species and intermediate shade-tolerant species to reach coring height were not estimated, and these trees were used only to identify GD markers on tree-ring width series, as described above. The tree-ring record of these samples were inspected between 1950 and 2019.

#### **4. Results and Discussion**

#### *4.1. Spatial Distribution of Tree Ages and GD in Tree-Ring Width Series*

The age of the trees sampled around the N-Ohkawa and Ohkawa landslides was 48.2 ± 22.4 years (average ± 1 SD), with a median of 56 years. The youngest tree was 6 years old and the oldest was 101 years old. Figure 5a shows the spatial distribution of the tree ages of 60 trees used for landslide dating. Older ages tend to be concentrated near the scarps, where the majority of trees were 51–70 years old. Trees of 51–90 years in age were also sparsely distributed on the displaced block and many of these were back-tilted, which suggests that the trees were moved down hillsides during landslide transport by rotation along a circular feature of the sliding surface [11,27]. The younger trees (<20 years old) on the scarps and displaced blocks were the shade-intolerant species *Ah*, *Sb*, and *Ss*. GD markers were not detected in these younger trees (Figure 5).

**Figure 5.** Spatial distribution of tree ages and detected GD markers and trees with no GD markers. (**a**) Spatial distribution of the ages of 60 trees sampled for dendrogeomorphological analysis. (**b**) Spatial distribution of detected GD markers for individual trees.

–

In total, 64 GD events (including 39 moderate GDs) were identified from 47 trees (Figure 5b). Growth suppression (34 GDs, 53%) occurred in slightly more trees than growth increase (30 GDs, 47%). This higher frequency of growth suppression has also been reported in other similar works [14,28]. The highest frequency (45%) of first-detected GD within the tree-ring width series occurred for trees aged between 16 and 30 years. Individual trees with two GDs (e.g., growth suppression and increase or multiple growth-suppression events) were detected mainly on the landslide scarps. Nevertheless, in a few cases, two GD markers were also detected in trees on the landslide blocks.

#### *4.2. Summary of GD in Tree-Ring Width Series*

The GD markers associated with the N-Ohkawa landslide occurred mainly between 1998 and 2001 (Figure 6a). Samples *Nu*. 9 and 20 on the landslide scarp and the displaced landslide block, respectively, showed wider annual rings in 1998, one year before the landslide event that eyewitnesses reported as occurring in 1999. Two samples (*Nu*. 17 and 18) on the displaced landslide block showed wider annual rings in 1999 in response to the landslide occurrence. Following the event in 1999, trees on the landslide scarp presented wider annual rings in 2000 and 2001. Furthermore, narrow annual rings in 1970, 1982, and 1983 were detected in trees on the landslide scarp. In addition, shade-intolerant trees on the displaced block appeared in the early 2000s, which is a lag of 3–5 years after the growing season following the landslide in 1999 (Figure 6a).

Figure 6b–d summarizes the GD for the Ohkawa landslide. In the eastern area of the landslide, a sample (*Nu*. 82) from the landslide scarp showed wider annual rings in 1956 as the earliest GD marker in the study area (Figure 6b). The majority of GD events appear to be clustered after the 1980s, with six GDs on the landslide scarp and eight GDs on the displaced block. In the northern section of the landslide, samples Nu. 95 and 96 on the landslide scarp showed wider annual rings in 1973 and 1995, respectively. In addition, three trees on the landslide scarp recorded GD markers in 2000 and narrow annual rings were also identified for the same year in a sample (*Nu*. 78) from the displaced block (Figure 6c). Furthermore, wider annual rings were detected in 2005 and 2006 in samples from the displaced blocks. In the southern section of the landslide, 29 GDs were identified between the 1960s and the 2010s (Figure 6d). GDs appear to be concentrated in the 1980s and the late 2000s. In particular, GDs detected between 2006 and 2009 are considered to be the consequence of the landslide event that occurred (based on eye-witness reports) in 2006. Notably, shade-intolerant species appeared for the first time on the scarp and displaced block between the late 2000s and the 2010s, a lag of 2–7 years behind the growing season following the landslide event in 2006 (Figure 6d). The two major eye-witnessed landslide events, the N-Ohkawa landslide in 1999 and the southern section of the Ohkawa landslide in 2006, can be identified in the tree-ring records, which suggests that other GDs detected in the study area may also be indicative of historical landslides that were large enough to remove and damage the trees.

**Figure 6.** Summary of GD markers identified in the trees and year of establishment of shade-intolerant species for the: (**a**) N-Ohkawa landslide, (**b**) eastern section of the Ohkawa landslide, (**c**) northern section of the Ohkawa landslide, and (**d**) southern section of the Ohkawa landslide. Black and red text indicates samples from the landslide scarp and the displaced landslide block, respectively. Sample locations are shown in Figure 3.

#### *4.3. Dendrochronological Investigations of Spatial and Temporal Patterns of Landslide Reactivation*

The analysis of GD markers enabled the identification of landslide events on the studied slopes (Figure 7). These previous slides are summarized in Figure 8 with reference to the locations of trees with GD markers and field observations. For the N-Ohkawa landslide, apart from the landslide reported in 1999, additional landslide activity was detected in 1998 (Figure 7a). In addition, an event took place in 2000 that was detected using

samples from the landslide scarp, implying an enlargement of the scarp (Figures 7a and 8). In the eastern section of the Ohkawa landslide, for which there are no reported landslides, we detected two landslide events that took place in 1993 and 2007 (Figure 7b). The landslide events in 1993 and 2007 may suggest an episode of regressive enlargement of the landslide scarp along the terrace scarp (Figure 8). This is supported by field observations showing terrain below the landslide scarp with collapsed debris deposited on a pre-existing landslide mass. The observations suggest that the present landslide unit may have grown from gradual accumulation of landslide debris from repeated landslides, in combination with retrogressive enlargement. For the northern section of the Ohkawa landslide, two landslide events were identified in 2000 and 2005 (Figure 7c). These landslide events have not been previously reported; however, the landslide aftermath can be observed on the aerial photograph from 2015 (Figure 1c). Our analysis suggests that a large landslide might have been initiated in 2000 (as three of the four GDs were identified on the scarp; Figure 6c) and experienced further downward movement in 2005 (as GDs were detected on the landslide block; Figures 6c and 8). Furthermore, ongoing movement is evident on the downslope section, which is bounded by a secondary scarp up to 7 m in height in the lower section. This section is cut by a minor gully, in which surface water is concentrated, and which affected the area before and after a local failure in 2017 (Figure 9a). For the southern section of the Ohkawa landslide, apart from the landslide in 2006, two additional previously unknown events were dated to 1986 and 1987 (Figure 7d). Tension cracks were observed on the crown of the Ohkawa landslide along a ridgeline (Figure 9b,c), from which a crack developed into a lateral scarp of the southern section of the Ohkawa landslide in 2006 (Figure 9c).These observations suggest progressive movement prior to the catastrophic failure in 2006 (Figure 8). In addition, in the middle portion of the southern section of the Ohkawa landslide, a disrupted slide (5 m wide, 25 m long, and 20 m travel distance) was also observed in 2009 [29] (Figure 9d). At the northeastern end of the disrupted slide, within the landslide block of the southern section of the Ohkawa landslide, downward slope movement of about 8 m occurred between 2009 and 2014 [29]. The foot of the downslope section is undergoing river toe erosion, this may steepen the slope and facilitate further movement [29,30]. The landslide activity in 1998, as indicated by the GD markers, might also have progressed to become the major event in 1999 on the N-Ohkawa landslide block.

Our dendrochronological study using 60 deciduous broadleaved trees from 12 species for landslide analysis is unique on global scale [12]. In this contribution, we illustrate that the obtained chronology of landslide activity is in agreement with eyewitness reports of the major landslide events in 1999 and 2006, which suggests the GD markers and index values (where GD*<sup>t</sup>* ≥ 2 and *I<sup>t</sup>* ≥ 15% are adjusted based on the number of disturbed trees available for analysis) employed in this study may provide a critical assessment of past landslide occurrence in the study area and in those areas with similar environmental conditions. Shade-intolerant tree species are typically established between 2–7 years after landslides. However, this lag may reflect the severe erosion that can continue for several years after a landslide, thus limiting tree establishment [26].

slide.

≥ 2 and ≥ 15% are adjusted based on the number of

–

**Figure 7.** Dendrochronological investigations of past landslide events (dark red columns) expressed using the *I<sup>t</sup>* index and number of disturbed trees. (**a**) Chronology of the N-Ohkawa landslide. (**b**) Chronology of the eastern section of the Ohkawa landslide. (**c**) Chronology of the northern section of the Ohkawa landslide. (**d**) Chronology of the southern section of the Ohkawa landslide.

**Figure 8.** Summary of past landslide events in the study area and distribution of detected GDs and **Figure 8.** Summary of past landslide events in the study area and distribution of detected GDs and trees established after the landslide events.

**Figure 9.** Representative examples of slope movements in the study area. **Figure 9.** Representative examples of slope movements in the study area. (**a**) Ongoing movement on the downslope part of the northern section of the Ohkawa landslide. (**b**) Enlargement of about 2 m tension crack identified in the landslide scarp of the eastern section of the Ohkawa landslide. (**c**) Close-up view of the tension crack. The crack became the lateral scarp of the southern section of the Ohkawa landslide and had enlarged to about 20 m by July 2006. (**d**) A disrupted slide in the downslope part of the southern section of the Ohkawa landslide. The month and year in which photographs were taken are indicated at bottom-right in each panel. Locations of the photographs are indicated in Figure 8.

#### **5. Conclusions**

The spatial and temporal development of the coherent N-Ohkawa and Ohkawa (consisting of the eastern, northern, and southern sections) landslides were investigated using tree-ring chronologies from tilted deciduous broadleaved trees in the Shirakami Mountains, northern Honshu Island, Japan. In total, we identified 64 GD markers (i.e., periods of growth suppression or growth increase) from 47 trees, as well as the year of establishment of 13 trees from shade-intolerant species over about 70 years.

Our dendrogeomorphological analysis allowed us to identify the GD markers related to two major eye-witnessed landslide events; i.e., the N-Ohkawa landslide in 1999 and the southern section of the Ohkawa landslide in 2006. Shade-intolerant tree species became established after a lag of 2–7 years after the events in response to canopy opening by the landslides. Other GDs were used to reconstruct previously unknown events within the local landslide chronology. The reconstruction of the N-Ohkawa landslide added precursory landslide activity in 1998 and a local enlargement of the landslide scarp in 2000. In addition, the reconstruction of the Ohkawa landslide indicated episodes of regressive enlargement of the landslide scarp from 1993 to 2007 in the eastern section. In the northern section of this landslide, the landslide slope might have been undergoing sliding to form the current landslide scarp observed in 2000. The slope may have moved progressively downwards in 2005 and its secondary scarp on the downslope locally expanded in 2017. In addition, the reconstruction of the southern section of the Ohkawa landslide suggested that progressive movements may have developed in 1986 and 1987; i.e., before the landslide event in 2006.

**Author Contributions:** K.N. conducted field investigations, collected tree samples, and analyzed the tree cores, and also collaborated with the corresponding author in the preparation of the manuscript. C.-Y.T. conducted field investigations, landslide interpretation, and the collection and interpretation of tree samples, and also drafted this manuscript. Y.I. conducted field investigations, collected tree samples, and analyzed and interpreted the tree cores. D.H. conducted field investigations and landslide interpretation. C.-Y.W. conducted landslide interpretation and performed calculations. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by JSPS KAKENHI Grant Numbers 16K20893 and 19K15257.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The authors are grateful to Hajime Makita and Mitsuharu Kudo of Shirakami-Matagisha for providing useful and informative discussions regarding our study. We also thank Hisako Furukawa and Ryunosei Sato of Hirosaki University for their assistance in the field. We acknowledge the Tsugaru Forest Management Office, Tohoku Forest Management Bureau, and Ministry of Agriculture Forestry and Fisheries, Japan for permission to access mountain areas within their territories, and for generous logistical support. The Geospatial Information Authority of Japan provided the LiDAR DEM. We are grateful to three anonymous reviewers whose comments improved the paper.

**Conflicts of Interest:** The authors declare that they have no competing interests.

#### **References**


### *Article* **Experimental Study on Landslides in Terraced Fields in the Chinese Loessial Region under Extreme Rainfall**

**Yongfu Wen <sup>1</sup> , Peng Gao 2,3, \*, Xingmin Mu 2,3 , Mengzhen Li 1 , Yongjun Su <sup>1</sup> and Haixing Wang 1**


**Abstract:** Due to the development of the scale of tractor-ploughed terraces, terraces have been increasing in number, while global climate change is causing frequent extreme rainfall events in the Loess Plateau, resulting in many terrace landslides. To study the mechanism and process of shallow landslides and deep slip surface of terraces induced by extreme rainfall in loess hill and gully area, we conducted a laboratory model test of a terrace under artificial rainfall and used the Swedish arc strip method. The research results are as follows. The mechanism of shallow landslides in terraces is rill erosion accelerating rainfall infiltration, suspending the slope, and increasing its bulk density. The destruction process of shallow landslides can be roughly divided into six processes, and the earth volume of the landslide is 0.24 m<sup>3</sup> . The mechanism of the deep sliding surface in terraces occurs under the combined action of water erosion and gravity erosion. The soil moisture content increases, which decreases the anti-sliding moment and increases the sliding moment, and the safety factor becomes less than the allowable limit for terraces. The deep sliding deformation area of the terrace was 0~1.0 m below the slope surface, slip surface radius was 1.43 m, the slip surface angle was 92 ◦ , and the deep sliding surface began to form earlier than terraced shallow landslides. The displacement of the characteristic points increased from the slope top, to the slope center, and to the slope foot, with maximum displacements of 40.3, 15.5, and 6.0 mm, respectively.

**Keywords:** laboratory model test; extreme rainfall; rill erosion; shallow landslides; deep lip surface; safety factor

#### **1. Introduction**

With the implementation and promotion of slope-to-terrace projects, large areas of sloping fields have been built into terraced fields [1]. The construction of terraced field projects has changed the minor features of sloping fields, reducing surface runoff and increasing soil infiltration, thus effectively improving soil moisture content, which plays a crucial role in reducing soil erosion and increasing grain yield in the surrounding areas [2,3]. However, after the implementation of slope-to-terrace projects, back-slope terraces in particular experience significantly increased rainfall infiltration, which also leads to the reduction in soil shear strength, thus increasing the risk of landslides [4,5]. For example, an extreme rainstorm event occurred in Yan'an China, which caused a large area of terraces to collapse and landslide in July 2013, as shown in Figure 1.

In recent years, due to the large-scale development of tractor-ploughed terraces, terraces have been constantly increasing in number, while global climate change has led to frequent occurrences of extreme rainfall events in the Loess Plateau, resulting in many terrace landslides [6]. Long-term production practice has proved that the outer edges

**Citation:** Wen, Y.; Gao, P.; Mu, X.; Li, M.; Su, Y.; Wang, H. Experimental Study on Landslides in Terraced Fields in the Chinese Loessial Region under Extreme Rainfall. *Water* **2021**, *13*, 270. https://doi.org/10.3390/ w13030270

Received: 17 December 2020 Accepted: 19 January 2021 Published: 22 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of exposed terraces experience shallow landslides over time, which leads to the loss of its water storage and soil conservation functions [7]. When extreme rainfall produces runoff on a field's surface, the terraces seriously erode. This kind of hillslope is featured by collapsibility, strong water permeability, vulnerability, and so on, so rainfall conditions can easily induce shallow landslides, which seriously affect agricultural production [8]. As a consequence, an in-depth study of the process and mechanisms of shallow landslides and deep slip surface of terraces under extreme rainfall is theoretically significant for disaster prevention and mitigation and has practical value for agricultural production in Northern Shaanxi [9–13]. **2021**, , x FOR PEER REVIEW 2 of 22

**Figure 1.** Shallow landslides of terraces in Yan'an China, in July 2013.

Research on the mechanisms of the rainfall-induced general slope instability of soil, rock, and soil–rock mixture has mainly focused on field measurements, numerical simulations and model tests [14–17]. The model test has favorable intuition and can comprehensively consider various factors, simulate complex boundary conditions, and reflect the deep interaction of landslides under the condition of basically meeting the similarity principle [18]. Using the model test of soil slope instability induced by rainfall, Lin et al. [19] discussed the influence of the characteristics of precipitation on slope instability, and thereby selecting appropriate rainfall warning parameters. Zuo et al. [20] studied the laws of seepage, deformation, damage, and particle migration of accumulating soil slope under rainfall conditions through a rain-triggered landslide model test of accumulation bodies with different gradations; they also discussed the influence of particle size on the stability of accumulation soil slope. Li et al. [21] constructed an artificial rainfall simulation test of slopes with different angles and studied the changing laws of the front-end thrust, moisture content and deformation of the slope. Jeong et al. [22] comprehensively analyzed landslides caused by rainfall through laboratory tests, field tests and numerical analysis. Their results showed that landslide activity is closely related primarily to rainfall, soil properties, slope geometry, and vegetation. Numerical analysis was also performed to confirm the effect of these factors on landslide occurrence. Aleotti [23] identified the empirical triggering thresholds for Piedmont and proposed an NI-NCR (where NI is normalized intensity with respect to the annual precipitation, where NCR is the normalized cumulative critical rainfall) diagram. Xu et al. [24], Wang et al. [25], Tohari et al. [26], and Huang et al. [27] conducted rainfall landslide model tests and study the influence of compactness, silt particle content, water level, and other factors on pore water pressure, water content, landslide start-up and development, and failure mode.

The above studies considered the deformation of slope under the condition of rainfall infiltration–seepage interaction, which is mainly concentrated on engineered and natural slopes in China [28,29]. Current research on terraces has mostly focused on the benefits of water and sediment reduction and the rill erosion of terraces [30–33]. However, research on rainfall-induced shallow landslides of terraces is still lacking in China. A number of studies have performed some advantageous explorations. For instance, Jiang [34] discussed the design of terrace sections in the Loess Plateau by considering the requirements for small construction quantity, less land loss, good stability, convenience for cultivation, and conduciveness for crop growth of the terrace ridge. Given the problem of the steep or slow ridges in terrace construction in the sandy, mountainous area of Linqu County, Ge [35] analyzed the stability of the ridge shear test, and the results showed that the slope angle of fine gravel sand ought to be 37◦ , and that of fine sand should be 34◦ . Zhang et al. [36] used the Green–Ampt model to study the slope stability of terraced fields based on crop irrigation infiltration and discussed the position of the potential sliding surface. Yang et al. [37] selected the terraced ridge in Southern Shaanxi province as the research object and explored the failure forms and causes of the ridge through an indoor conventional triaxial shear test. Liu [38] studied the changes in the failure time and safety factor of a horizontal terrace, a separated slope terrace and an original slope (for contrast) under a rainfall infiltration intensity of 28~38 mm/h and a side slope gradient of 15–30◦ using ABAQUS software. Derbyshire [39] discusses how terraces in the Loess Plateau can maintain good stability under a natural state, but tend to be eroded and collapse under rainfall infiltration.

In this study, we selected terraces as the research object, and indoor model tests and the Swedish arc strip method were used to study the mechanism and mode of shallow landslides and deep sliding surfaces in terraces under extreme rainfall conditions. The following assumptions were made for the test. We ignore the influence of: (1) the model's side wall on the test results; (2) the internal sensors on the test results; and (3) the soil disturbance on the test results. The research is important for the agricultural development of the loess hilly and gully region as it provides: (1) a reliable theoretical basis and abundant experimental data for slope collapse and instability prevention, and disaster mitigation, monitoring, and forecasting of terraces; (2) parameters for the optimized design of terraces; and (3) a method for studying multi-level terraces and terraced landslides in the basin.

#### **2. Materials and Methods**

#### *2.1. Test Soil Properties*

The soil used in this model test was obtained from Zhifanggou, Ansai County, Shaanxi province, China; the depth of sediment deposition is 6~8 m, so it belongs to the category of loessal deposits [40]. The basic parameters of the test soil are shown in Table 1. According to the light compaction test, the maximum dry bulk was 1.703 g/cm<sup>3</sup> and the optimal moisture content was 19.3%. The particle size of the soil was measured by a Marven laser hondrometer, with a measured range of 0~2 mm, and the characteristic values of average grading in the Table 1 are as follows: clay particle (≤0.002 mm) content was 12.1%, silt particle (0.05–0.002 mm) content was 52.6%, and sand (2–0.05 mm) content was 35.4%, which showed that the soil sample contained fewer particle size series and that the difference between coarse and fine particle sizes was small. The curvature coefficient (CC) of the particle grading curve was 1.79, which is well-graded.

**Table 1.** Basic property indexes of soil.


#### *2.2. Test Device*

The test equipment was divided into four major systems: test object, rain, data monitoring, and image capture systems (Figure 2).

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**Figure 2.** Schematic diagram of model test device.

The test object system involved a terrace groove with a length of 2.8 m, a width of 1 m and a height of 2.1 m. The height of the slope filled in the test was 1.2 m, with a gradient of 65◦ . The front and back edges and one side of the model were surrounded by steel plates, and the wall surface of which was smoothed by applying a layer of Vaseline to reduce the influence of the model boundary effect on the test. On the remaining side, transparent plexiglass with a thickness of 1 cm was used as a visual window to help observe the movement of soil at any time in the process of the test. To facilitate the observation of soil movement, a rectangular grid measuring 10 × 20 cm was drawn onto the transparent poly, and steps were placed close to the steel plate to facilitate the measurement of the channel shape parameters and flow velocity during the test. A catch basin was set up at the front edge to collect runoff sediment.

The rain system device was developed by the Institute of Soil and Water Conservation, Ministry of Water Resources, Chinese Academy of Sciences. The rainfall device's height is 16 m, which can measure the terminal speed of all raindrops. The range of rainfall intensity was 40–260 mm/h, the rainfall uniformity was more than 80% and the maximum duration of rainfall was 12 h. The rainfall area was composed of two independent rainfall experimental areas. The effective rainfall area of a single experimental area was 4 × 9 m, which can accurately simulate natural rainfall [41].

The data monitoring system was composed of a RR-7120 water content sensor, KPE-200 kPa pore water pressure sensor, Campbell 257 soil suction sensor, and an LDS-S-200 displacement monitoring sensor. Each sensor was connected to the corresponding collection system through a data line, and then the data in the system is exported and sorted through a computer. The data collection frequency of the water content sensor was 1 min, (unit: %); the data collection frequency of the pore water pressure sensor was 1 min (unit: Ka); the acquisition frequency of the suction sensor data acquisition system was 1 min (unit: Ka); the displacement monitoring sensor data acquisition system had an acquisition frequency of 1 min (unit: mm).

For the image capture system, a Canon EOS M50 camera was set up on the side facing the transparent plexiglass at a height of 0.85 m, to clearly capture the downward movement of the wet front on the side of the soil.

#### *2.3. Soil-Filling and Sensor Embedding*

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A square sift iron was applied for screening to ensure the maximum particle size of the model's soil filling would be less than 1 cm. Then, the soil was evenly spread, sprayed with an appropriate amount of water and evenly mixed to make the density and moisture content of the soil close to that of the undisturbed soil. However, in the process of model filling, the structure of the soil, the particle gradation, the stratum structure, the soil cracks, and so on, will change to some extent, which is inevitable. For this test, we adopted the method of layered compaction and filling: the soil prepared before the test was evenly divided into 17 layers, each layer 10 cm thick, and the side wall of the terrace was compacted with a discus. After the compaction of each layer was completed, samples were taken from several different parts with a cutting ring. The wet density of each layer of soil was 1.32~1.40 g/cm<sup>3</sup> , and the moisture content was around 7.5%. After the placement into layers was complete, the geometric dimensions of a 65◦ slope in the model was obtained by manual slope cutting after the stratified filling.

To ensure the accuracy of the monitoring data and minimize the impact of sensors on the test results, we arranged the fewest sensors possible. Figure 3a provides a crosssectional view of terraced soil filling and sensor embedding, showing that two moisture content sensors were arranged on the side close to the slope every 20 cm. Due to the large soil width, one more was arranged on the bottom side, for a total of 13 sensors. To study the mechanical properties of the slope, three pore water pressure sensors and suction sensors were arranged on the top, middle and toe of the slope with a vertical distance of 20 cm from the slope surface. To accurately determine the shape of the slip surface, 5 to 7 displacement sensors were arranged every 20 cm, for a total of 36 displacement sensors. To reduce the influence of the sensor on the test results, the sensor was arranged in the middle of the whole soil, as shown in Figure 3b.

○ □ △ ▲ **Figure 3.** Layout drawing of test sensors. (**a**) Left view of device, (**b**) top view of device. Note: Different letters indicate soil layers; Numbers indicate soil columns; # indicates soil water content sensor; indicates pore water pressure sensor; △ indicates monitor point of displacement; N indicates soil water suction sensor.

#### *2.4. Test Method*

Ⅱ The experiment started at 10:00 a.m. on 11 November 2017 and ended at 8:00 a.m. on the 12 November. It was carried out in Area II of the artificial rainfall hall of the Institute of Soil and Water Conservation, Ministry of Water Resources, Chinese Academy of Sciences. According to the hydrological data for Yan'an in July 2013, and the actual situation of slope movement, the data were divided into five periods of rainfall, each lasting for 1 hour, with rainfall intervals of 1 h, a rainfall intensity of 2.5 mm/min and a total rainfall of 750 mm. The test was repeated once on 20 November 2017, and the average of the data from the two tests was used as the test result for analysis, and the standard deviation of each dataset was found to be within 0.2, so the data were considered reasonable and reliable.

To ensure the uniformity and stability of the rain intensity, the slope of the terraces was covered with plastic sheeting before the test. The rain intensity was calibrated around the model trough and the top. When the rain intensity stabilized, we quickly uncovered the plastic sheet and started timing. When the water flow on the slope of the terraces was in a laminar flow state and flowed from top to bottom to the water outlet, it was regarded as the start of runoff. We recorded the runoff time, and then restarted the clock. After the trial runoff, runoff and sediment samples were collected every 1 min. After rills appeared on the slope, the time of rill appearance was recorded, and we measured the size with a measuring tape with an accuracy of 1 mm every 2 min. When the rill length exceeded 10 cm, we measured the width every 10 cm along the length of the rill. The average value was used as the width of the rill. The measurement density was increased in locations where the morphological mutation of the rill was obvious. Simultaneously the slope and wet front morphology were recorded every 20 min with a digital camera, and the camera shooting frequency was increased during the period of severe morphological changes. After the test was over, the sediment samples were allowed to stand for 6 h and the supernatant liquid was poured out, then the sediment samples were dried in an oven (105◦ ) and weighed by electronic scale. The sensor data were imported into an Excel table for data preprocessing.

When calculating the moisture content data, the sensor data at the same time point of each layer were averaged, and this average value was regarded as the soil moisture content of this layer. Because the data collection frequency was very fast, a large amount of data were generated. Therefore, we selected the representative data to draw figures under the premise of not affecting the changing of the parameter curve.

#### **3. Results and Discussion**

#### *3.1. Mechanism and Process of Shallow Landslides of Terraces*

3.1.1. Mechanism of Shallow Landslides of Terraces

The results suggest that the shallow landslides of terraces were caused by rill erosion. Most of the rills in the loessial soil were developed by a single drop sill, which was mainly manifested by the headway erosion of the gully head and the collapse of the side wall [42,43] (Figure 4a). By measuring the traceable erosion pattern of terraces, we found that the maximum width of the gully head was 34.25 cm, the maximum depth was 21.32 cm, and the maximum length was 75.86 cm. The total erosion amount was about 270.96 kg. The sediment yield rate of five rainfalls was 181, 475.67, 1707.17, 1624.33, and 527.83 g/min. The sediment yield rate showed a trend of increasing first and then decreasing. Before the runoff, when the exposed slope surface was hit by large raindrops, the surface soil structure was destroyed, and the soil particles splashed up and fell back to the slope surface, forming raindrop splash erosion (Figure 4b). After the runoff, the erosion developed from raindrop splash erosion to layered surface erosion. The time from splash erosion to surface erosion was one hour (Figure 4c). The reason for this finding is that the runoff was low at the initial stage of runoff generation and the runoff eroding force was less than the anti-erosion ability of soil resistance. With the increasing runoff, runoff eroding force also increased. Isolated and sporadic falling ridges were generated in the terrace ridge and the vulnerable parts of the side slope's soil. When the terrace ridge was filled with water, the terrace ridge breached under the action of hydraulic erosion (Figure 4d) and the water cut down along the breach to form obvious gullies, with an average width of 17.8 cm (Figure 4e). Due to the erosion, transportation, and accumulation of overtopping flow, the erosion gully continuously eroded and undercut longitudinally, eroding the gully bank and widening the gravity collapse horizontally. The sediment carried by the slope flow was fan-shaped deposition around the gully mouth at the toe of the slope, forming an alluvial fan, covering an area of 176.64 cm<sup>2</sup> (Figure 4f). The erosion gully further developed and constantly degraded and widened. Due to the difference in the density of terraces and the non-uniformity of the filling materials, the velocities of anti-erosion of the terraces differed. The weak position started easily, and erosion occurred first, forming a scouring pit.

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**Figure 4.** Morphological characteristics of terraces at different rainfall times; (**a**) Headward erosion, (**b**) Splash erosion, (**c**) Surface erosion, (**d**) Breach, (**e**) Gully, (**f**) Alluvial fan.

The above characteristics all indicate that many side wall collapses occur in the process of rill formation, which is consistent with the phenomenon observed in the test process. It is generally thought that the composition of soil particles is an important factor affecting soil erosion resistance. The finer the particle composition, the stronger the cohesion. To a certain extent, when the soil forms a mass structure, and its anti-erosion ability will be higher. In particular, the clay content in the soil significantly enhances the anti-dispersion ability of the wet soil layer. It can be seen from Table 1 shows that silt (0.002~0.2 mm) and clay (<0.002 mm) only accounted for around 35% of the total particles in the model. The overall stability of the soil was poor. In addition, the content of sand particles was high, and the soil was loose and porous. Therefore, the rill side wall of the loessal soil easily lost stability and collapsed under the action of runoff erosion and soil moisture. As such, the main forms of the rill development process of loessal soil are wall collapse and traceable erosion, and the randomness is significant [44]. Han et al. [45] and Acharya et al. [46] also showed that traceable erosion is the most active sediment yield factor in rill development, and the collapse of the ditch wall mainly occurred on steep slopes above 65◦ . Both the rill and cut trench in this experiment were similar in shape to the above research results, but

the size was larger, because the rainfall intensity and total rainfall were higher than in the above experimental conditions.

#### 3.1.2. Process and Mode of Shallow Landslides of the Terraces

According to a series of deformation characteristics of the side slope during the test, the mode of this kind of shallow landslide of terraces under rainfall conditions is summarized in this section. The deformation mode is shown in Figures 5 and 6 and can be described as follows: (i) The stage of water accumulation on terraced fields: As the rainfall continued, the soil of the terraces gradually became saturated, which reduced the infiltration capacity of the soil, while the rainfall gradually increased, resulting in water accumulated on the terraces. The height of stagnant water was 3.5 cm. (ii) The formation and development stage of the breach: After rainfall had been occurring for a period of time, the loess on the terrace surface and its slope surface reached saturation. The ponding on the field surface crossed the ridge, forming surface runoff and flowing down the slope. When the water flows through the ridge, the erosion of the ridge formed a breach with area of 706 cm<sup>2</sup> . With the continuous erosion of water and rainfall, the erosion degree of the ridge increased and the breach expanded. (iii) The erosion of the waterfall nappe flow: The ponding flowed along the breach and formed plumes. Under the combined action of hydraulic forces and gravity, the discharge flow formed a multi-stage drop sill on the slope surface. The maximum discharge and maximum velocity of the breach occurred at this stage, and the ponding on the terrace surface dropped rapidly. (iv) The formation and development stage of the erosion gully: With continuous rainfall, the multi-level drop sill was connected by the water flow, forming an erosion ditch, and the width and depth of the erosion ditch gradually increased along the slope shoulder to the slope toe, finally forming the alluvial fan at the slope toe. The average erosion gully width was 17.8 cm. (v) The stage of superficial-layer shallow landslides of the terraces: With increases in the width and depth of the erosion gully, the soil on both sides of the slope was suspended. In addition, the soil is constantly saturated with water, the gravity increased and the cohesion decreased, resulting in superficial-layer shallow landslides of the terraces, and the soil volume of the landslide was about 0.24 m<sup>3</sup> (vi) The terraces tend to be stable: After the superficial-layer shallow landslides of the terraces, the side slope grade of the residual slope was very small; even if the soil was in a saturated state, it would not easily collapse.

The pattern of shallow landslides in terraces is similar to that in the earth dams. Zhong et al. [47] used experimental methods to simulate the mechanism and mode of earth dam failure, they proposed that the most important reasons for earth dam failure are the overflow of water, the crest of the dam breaking, and the huge instantaneous downflow washing the earth dam. The dam break test (dam height 6 m) funded by the EU IMPACT project [48] and the dam break test (dam height 1.5 to 2.3 m) carried out by Hanson et al. [49] of the United States Department of Agriculture both simulated the earth dam break mode, which is similar to the landslide pattern of the terraces, but the mechanism is different. The dam break mechanism of action of an earth dam is through the upstream water flow forming an infiltration line inside the dam body due to the seepage effect, or the upstream water flowing over the top to destroy the earth dam. The terrace landslides mechanism is through the soil losing cohesion due to rainfall infiltration and the erosion ditch making the terraces lose their integrity, leading to local shallow landslides. The results of this study are different from those of Sun et al. [50] because there is a border dike on the loess slope in the natural state. When the rainfall intensity is greater than the infiltration rate, the slope will produce runoff. For terraced fields, the border dike plays a role in water storage and soil conservation. Therefore, under the same rainfall conditions, terraces are more capable of resisting catastrophic rainfall than sloping fields.

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**Figure 5.** Shallow landslide process in terraces. (**a**) First stage, (**b**) Second stage, (**c**) Third stage, (**d**) Fourth stage, (**e**) Fifth stage, (**f**) Sixth stage.

**Figure 6.** Three-dimensional diagram of shallow landslide process in terraces. (**a**) First stage, (**b**) Second stage, (**c**) Third stage, (**d**) Fourth stage, (**e**) Fifth stage, (**f**) Sixth stage. <sup>279</sup>

#### *3.2. The Factors of Deep Slip Surface of Terraces* 3.2.1. Rainfall Infiltration

The curve in Figure 7 shows the relationship between average rainfall (infiltration), infiltration percentage, and rainfall frequency. The infiltration rate was 79%, and the infiltration rate gradually decreased with the increase in surface runoff. In the third rainfall event, the infiltration rate decreased to 49.3% and then remained steady at approximately 26.14%. More than half of the rainfall turned into surface runoff, causing soil erosion and rain erosion on the slope's surface and formed rills. The infiltration of rainwater from the slope surface to the slope was an unsaturated-to-saturated seepage process, and the change in infiltration rate with time was related not only to the original humidity and matrix suction of unsaturated soil, but also to the physical characteristics and structure of the soil from the side slope. Generally, at the early stage of infiltration, infiltration capacity is greater than rainfall intensity and the infiltration rate is higher, so infiltration is pressureless. After a period of time, the soil begins to saturate, the gradient of soil moisture content decreases, the matrix suction reduces, and the infiltration capacity lowers. When rainfall intensity is greater than the soil's infiltration capacity, slope runoff occurs, which is pressure infiltration. Finally, with rainfall, the infiltration rate gradually decreases until it tends to be constant, reaching the stable infiltration stage. Figure 8a shows the relationship curve between infiltration rate and rainfall time for five rainfall events, and Figure 8b provides partial enlarged view; the figure shows, the infiltration rate generally presents the same decreasing trend. The steady infiltration rate ranged from 0.74 mm/min to 0.77 mm/min, and the results are similar to those in the literature [51]. This is because with progressing rainfall, the infiltrating rainwater continuously increased the soil moisture content, which saturated the surface soil causing the infiltration rate to gradually decrease. However, the infiltration rate of the topsoil was relatively low and stable after saturation, and the infiltration rate of rainwater was further reduced due to the small amount of rainwater infiltration inside. For the third and fourth rainfall events, the infiltration rate first increased and then decreased. The reason for the increase in the third rainfall's infiltration rate was that cracks appeared on the terrace surface and the infiltrated rainwater could speedily travel deep through the cracks; on the other hand, due to the water-retaining effect of the ridge, ponding formed on the horizontal surface, which accelerated the infiltration rate. The reason for the increase in the infiltration rate in the fourth rainfall was that the superficial layer of the terrace collapsed and the rainwater rapidly entered into the soil along the gully. **2021**, , x FOR PEER REVIEW 11 of 22

**Figure 7.** Rainfall amounts and percentage of infiltration.

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**Figure 8.** Relationship between infiltration rate and rainfall time in five rainfalls; (**a**) The relationship curve between infiltration rate and rainfall time for five rainfall events, (**b**) partial enlarged view of the Figure 8a.

In this study, the rainfall infiltration law of terraces is similar to that of Liu et al. [52], but the infiltration rate is lower than the latter, because Liu et al. considered the development characteristics of the root system in vegetation and soil, which has strong water storage and soil conservation capabilities and can intercept more rainfall and runoff. Compared with Huang et al. [53], the infiltration rate of this result is relatively high because of the different nature of the soil. The initial moisture content of the soil in Huang et al.'s research was high, and the initial moisture content will shorten the saturation time of the soil. The results of this test provide reference value for the study of terrace infiltration in loess hilly and gully areas, especially for mechanically-repaired horizontal terraces.

With the continuous infiltration of rainwater, the color of the soil from the model's side slope gradually darkened with the increase of in moisture content, and the infiltration peak appeared at the boundary between the dark- and light-colored soils. In this test, the change in infiltration peak was recorded by a camera set up on the side of the transparent poly to judge and calculate the infiltration depth and infiltration rate of rainwater.

Figure 9 depicts the wetting front from different rainfall time points: when the rainfall duration was 10 min, the downward depth of the wet front was 9.7 cm; when the rainfall duration was 60 min, the downward depth of the wet front was 28.8 cm; and when the rainfall duration was 180 min, the downward depth of the wet front was 35.5 cm. The wet front was basically linear with the rainfall time. The wetting front moved downward with increasing duration of rainfall and the migration rate of the horizontal wetting front was faster than that of the side slope surface. The reason for this finding is that the horizontal plane could effectively intercepted the rainwater, and the ponding accelerated the infiltration rate of the horizontal surface [54]. However, for the inclined slope, most of the rainwater formed runoff along the side slope surface, and only a small part of the rainwater infiltrated. Figure 10 shows that with continuous rainfall, a proportion of the rainwater on the terrace surface infiltrated, another part formed slope runoff, and some of it infiltrated along the back wall of the model box, where collapse deformation occurred. Due to the different materials of the back wall and the soil, the infiltration speed was faster than that of the soil; thus, the wetting front moved rapidly in the back wall.

(**a**) (**b**)

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 (**c**) (**d**)

**Figure 9.** Infiltration peaks at different rainfall time; (**a**) T = 10 min, (**b**) T = 60 min, (**c**) T = 180 min, (**d**) T = 300 min. **2021**, , x FOR PEER REVIEW 13 of 22

**Figure 10.** Collapsible deformation on the posterior wall.

The downward movement of the wet front was similar to the results reported by Tian et al. [55], but the downward movement rate of the wet front was larger than that recorded by them, because the terraced ridges have the capacity to store water, and the accumulated water increases the water infiltration gradient and accelerates the rate of water downward movement. This also proves that the measures of slope conversion can effectively intercept rainfall, and the benefits of water and sediment reduction are obvious in the Loess Plateau. This is also supported by the research results of Bai et al. [56].

#### 3.2.2. Water Content

In accordance with the monitored data from the slope moisture sensor, the change in slope moisture content in the whole process can be understood. Figure 11a shows that the moisture content of each soil layer at different depths of slope varied with rainfall duration

and post-rain duration. Within 0.5 h of the beginning of rainfall, the moisture content of layers A, B, and C of the slope increased to 0.83%/h, and the change was obvious, while the moisture content of soil in layers D, E, and F changed very little, due to the infiltration of rainwater going from shallow to deep. With the increase in rainfall time, rainwater infiltrated and the moisture content of the whole slope increased continuously. The increased rate of moisture content of the upper soil was about 2~2.83%/h, which is higher than the previous value of 0.83%/h, due to the continuous increase in soil moisture content, the decrease in matrix suction, and the increase in the permeability coefficient. For D, E, and F, there is an obvious break point in the curve, and the moisture content suddenly increased at about 4:00 p.m., which indicated that there were violent activities in the soil; deep cracks appeared in the soil, the soil began to lose stability and the sliding surface formed. Thus, the change in moisture content strongly influenced soil failure. First, the increase in moisture content led to an increase in pore water pressure and a decrease in effective stress, thus resulting in a decrease in soil shear strength; second, the increase in moisture content increased the permeability of the water, which led to a decrease in side slope stability. The dual effect of rainfall infiltration leading to water content variation may be an important reason for the side slope's rainfall-induced instability. Figure 11b shows that the moisture content at the top of the slope rose the fastest and had the largest change range. At around 1:00 p.m. on 11 November, due to the shallow landslides of the slope body, the moisture content of the slope rapidly dropped to 0%, followed by the toe of the slope, with the smallest change and the smallest range in the middle of the slope. **2021**, , x FOR PEER REVIEW 14 of 22

**Figure 11.** Variation of volumetric water content of soil layers and feature points with time; (**a**) The moisture content of each soil layer at different depths of slope varied with rainfall duration, (**b**) The moisture content at the top, center, and foot of the slope.

3.2.3. Pore Water Pressure and Suction

Figure 12 shows the variation in pore water pressure and suction with rainfall. Figure 12a shows that the pore water pressure first increased and then tended to be stable with the rainfall duration. The variation in pore water pressure at the top of the slope ranged most before the shallow landslides of the slope, and the maximum value was 2.4 kPa. Since the sensor was exposed outside the slope after shallow landslides, it rapidly dropped to 0 kPa. The change in pore water pressure at the measuring point at the toe of slope was slightly later than that at the top of slope, with a maximum value of 3.6 kPa. At the end of the rainfall event, the pore water pressure gradually decreased and finally tended to be stable around 2.5 kPa. The change in pore water pressure at the measuring point in the middle of the slope changed later than at the measuring points at the top and toe of the slope, with the water infiltration reaching the measuring point at around 4:00 p.m., then increasing gradually, and finally tending to be about 2.8 kPa. As Figure 12b

shows, the suction (negative pore water pressure) varied from 7.4 to 14.6 kPa, showing a sharp decrease at first and then a stable trend. The reason for this finding is that with rainfall infiltration, the moisture content of each measuring point increased, and the suction decreased sharply. After the rainfall, the moisture content of each measuring point decreased slowly due to evaporation, so the suction increased slowly and finally tended to be stable. Notably, the Campbell 257 soil suction sensor uses an indirect-method suction sensor (with a measuring range of 200 kPa), but the air intake value of soil material is small, so when the suction of the soil sample is lower than 10 kPa, the measurement accuracy of the sensor is poor. **2021**, , x FOR PEER REVIEW 15 of 22

**Figure 12.** Variation of pore water pressure and soil water suction of feature points with time; (**a**) Variation of pore water pressure at top, center, and foot of slope, (**b**) soil water suction at top, center, and foot of slope.

#### *3.3. Shape Characteristics and Mechanism of Deep Slip Surface*

#### 3.3.1. Shape Characteristics

The displacement of measuring points near the top of slope (A1, A2, A3, A4, and A5) was 0.5–40 mm and the direction was 40–50◦ to the horizontal; the displacement of measuring points near the slope surface (B5, C6, and D6) was 2.5–15.6 mm and the direction was 60–70◦ to the horizontal; the displacement of measuring points (E7 and F7) near the slope toe was 1.2–6.0 mm and the direction was 80–85◦ to the horizontal. The displacement of the deepest measuring points (C1, D1, D2, E1, E2, E3, F1, F2, F3, F4, and F5) was almost 0 mm. Through analysis of the above measurements, we found that the movement of the soil near the slope was the most intense; the displacement was the largest here, as was the displacement change rate, as it was the main active area of soil. With increasing depth of the measuring points, the displacement of the soil became increasingly small. When the depth reached the deepest points, there was no displacement. With the increase in depth, the angle between the displacement of each measuring point and the horizontal direction was increasingly large, and some points were close to 90◦ . This shows that both horizontal and vertical movements occurred in the soil landslides, but with the increase in depth, the horizontal movement transformed into vertical movement, and finally, at a certain depth, the soil movement was close to vertical movement. The approximate depth of the deep slip surface can be determined from the tracer point with no displacement. If the displacement of B1, D2, and F5 points is 0 mm, the depth of the deep slip surface is approximately 0.35, 0.75, and 1.15 m, respectively. Combining the depth of the deep slip surface obtained by each tracing point moving to 0 mm and the staggered fracture at the trailing edge of the landslide, the position of the deep slip surface can be determined; the slip surface radius was 1.43 m. The shape of the deep slip surface is shown in Figure 13.

**Figure 13.** The deep shape of sliding surface. Different letters indicate soil layers; Numbers indicate soil columns; # indicates soil water content sensor; indicates pore water pressure sensor; △ indicates monitor point of displacement; N indicates soil water suction sensor.

Rainfall is an important factor that causes landslides in terraces, it increases the sliding moment and reduces the anti-skid moment, finally forming a slip surface similar to a circular arc. This is similar to the results of studies by Zhang et al. [36] and Liu et al. [38]. However, the abovementioned studies used numerical simulation methods to study terraced landslides, which are less convincing. Our test explains the mechanism and process of terraced landslides and fully verifies the accuracy of the above-mentioned studies. However, this test only studied a single terrace, and we did not consider landslides on multi-level terraces, which will be the focus and direction of future research. Wu et al. [57] studied the causes of landslides in terraced fields in the loess area caused by over-irrigation, and the landslides at the Heifangtai can be classified into two different types based on their composition: loess landslides and loess-bedrock landslides, characterized by highspeed, long-distance sliding and low-speed, short-distance sliding respectively. Agnoletti et al. [58], taking terraced fields as the research object, explained that the terraced field can better reduce the possibility of shallow landslide disasters relative to slope field, and have less impact on deep landslides under extreme rainfall conditions. This is also consistent with the results of our experimental study, highlighting the guiding significance of this study for terraced landslides in the whole loess hilly and gully area.

#### 3.3.2. Mechanical Mechanism

To study the mechanism and process of deep sliding surfaces in terraces under extreme rainfall, the safety factor of sliding surfaces in terraces was calculated using the Swedish slice method. This method divides the soil above the slip surface into several strips to analyze the force and moment equilibrium on each strip, and to obtain the safety factor of soil stability under the limit equilibrium state [59]. In this experiment, the soil strips above the sliding surface are divided into seven vertical strips according to the location of the sensors. Before solving the safety factor, the following assumptions are made: (i) the force between the strips has little effect on the overall stability, which can be ignored; (ii) the moisture content of each soil strip is the average value of all moisture content sensors on the soil strip; (iii) the cohesive force and internal friction angle of each soil block are used form [60], namely, *c<sup>i</sup>* = *αw* −*β i* . As shown in Figure 14, according to the equilibrium condition of radial force

$$N\_i = \mathcal{W}\_i \cos \alpha\_i$$

ܶ =

ܿ

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ߙݏܹܿ = ܰ

݈ + ܰ

௦ܨ

ܽ݊߮ݐ

ିఉ

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= <sup>௦</sup>ܨ

ܹ ߙ

ܴܶ=ܿ

ݓߙ ∑

݈ + ܰ

ߙݏܹܿ + ݈ఉି

ߙ݅݊ݏܹ ∑

݈ ߮

ݓ ܴ

ܰ ܶ

௦ܨ

ܽ݊߮ݐ

ൈ ܴ

ܽ݊߮ݐ

ܿ <sup>௦</sup>ܨ

**Figure 14.** Analysis of the forces of the Swedish slice method.

According to the limit equilibrium condition on the arc surface,

$$T\_i = \frac{c\_i l\_i + N\_i \tan \varphi\_i}{F\_s}$$

The anti-sliding moment generated on the sliding surface is,

$$\sum T\_i R = \sum \frac{c\_i l\_i + N\_i \tan \phi\_i}{F\_s} \times R$$

From the moment balance, we can finally obtain

**−**

$$F\_s = \frac{\sum \alpha w\_i^{-\beta} l\_i + \mathcal{W}\_i \cos \alpha\_i \tan \varphi\_i}{\sum \mathcal{W}\_i \sin \alpha\_i}$$

here *α<sup>i</sup>* is the bottom slope angle of the strip *i*; *W<sup>i</sup>* is the sum of the self-weight of strip *i* and the upper load; *N<sup>i</sup>* is the total normal force at the bottom of strip *i*; *T<sup>i</sup>* is the total tangential resistance of strip *i* at the bottom; *F<sup>s</sup>* is the safety factor of the sliding arc; *c<sup>i</sup>* is the cohesion of block *i*; *l<sup>i</sup>* is the bottom length of the block *i*; *ϕ<sup>i</sup>* is the internal friction angle of block *i*; *R* is the arc radius of the sliding surface; *w<sup>i</sup>* is the soil water content, (×100) *α and β* can be obtained by linear interpolation in Tables 2 and 3.

**Table 2.** Selection of cohesion parameters of unsaturated loess [61].



**Table 3.** Selection of internal friction angle of unsaturated loess [61].

Figure 15 shows the variation law of terraces' safety factor with test time. The safety factor first decreased, then increased, and finally slowly increased and tended to be stable. From 10:00 a.m. to 3:00 p.m., with the continuous infiltration of rainfall, the self-weight of the upper soil on the sliding surface increased, which increased the sliding torque. The decrease in cohesion led to the decrease in anti-sliding torque, which was the reason for the decrease in the safety factor. From 3:00 p.m. to 4:00 p.m., due to the sliding torque being greater than the anti-sliding torque, the sliding surface gradually formed, and the time of deep sliding surface began to form earlier than the terraced shallow landslides; 4:00 p.m. to 5:00 p.m., due to the terraces forming a new stable state; the slope was slowed down and the safety factor was larger than the initial stage. From 5:00 p.m. to 9:00 p.m., the change law was similar to that of the initial rainfall, which also showed that rainfall infiltration was the dominant factor leading to safety factor; after 9:00 p.m., the safety factor increased slowly and tended to be stable, because after the rainfall, the soil inside the terraces slowly dried and evaporated naturally, so that the soil moisture content decreased slowly and tended to be stable. The mechanical mechanism of deep slip surfaces in terraces was that through the sliding moment of the sliding body being greater than the anti-sliding moment. The formation of a deep sliding surface in a terraced slope was mainly the result of the interaction of hydraulic erosion and gravity erosion, due to rainfall infiltration, soil moisture content increase, pore water pressure increase, and suction decrease. It increased the bulk density of the sliding body, thereby increasing the sliding torque; however, rainfall infiltration reducing the cohesion and internal friction angle of the sliding body, thereby reduced the anti-sliding torque. With the continuous rainfall, the anti-sliding torque was equal to the sliding torque at a certain time, and the terraced slope was in the limit equilibrium state. The sliding surface began to develop and form from this moment, and the development of the erosion gully accelerated the formation process of the sliding surface. In this study, the rainfall threshold for deep landslides in terraces was 500 mm, which is similar to the results of Zhuang et al. [3], and provides data support for landslides in loess hilly and gully areas.

#### 3.3.3. Variation in Characteristic Points Displacement with Accumulated Rainfall

Figure 16 shows the relation curve between the displacement of three characteristic monitoring points (A5, C6, and F7) and the accumulated rainfall. With the increase in accumulated rainfall, the soil displacement gradually increased, with the largest displacement occurring at the top of the slope, the second largest at the slope center, and the smallest at the foot of the slope. At around 2:00 p.m. on 11 November, the displacement increased sharply. After the collapse, the displacement increased slowly and remained unchanged at 8:00 a.m. on 12 November. The displacements of the top, center and foot of the slope were 40.3 mm, 15.6 mm, and 6.0 mm, respectively.

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**Figure 15.** The changes of safety factor of terraces with test time.

**Figure 16.** Displacement of characteristic points and its comparison with accumulative rainfall.

The variation law of the slope top, the middle of the slope, and the characteristic points of the slope foot was similar to that reported by Chen et al. [62], but the displacement was generally larger than the above research because of the high rainfall intensity and the long rainfall duration. In future studies, we must examine the impact of different rainfall intensities and total rainfall on terraced landslides.

#### **4. Summary and Conclusions**

In this paper, where we selected newly built bare-land terraces as the research object, the laboratory model test method was used to study the mechanism and process of shallow landslides and deep slip surface in terraces under extreme rainfall conditions. The main conclusions were as follows.

Shallow landslides in terraces are formed under the interaction of water erosion and gravity erosion, and the main driving force is from headward erosion and rill erosion. The superficial-layer shallow landslides of the terraces under the action of extreme rainfall can be divided into six stages. The width of the erosion ditch on the terraced slope was 17.8 cm and the volume of shallow landslides in terraces was 0.24 m<sup>3</sup> .

The mechanism of the slip surface in the terraces is rainfall infiltration, which increases the water content of the soil, increases the pore water pressure, and decreases the suction force, which leads to the anti-slip torque being less than the sliding torque, causing a slip surface to appear inside the terrace. Under extreme rainfall conditions, terraces formed a circular sliding surface with a radius of 1.43 m and an angle of 92◦ . The appearance of this slip surface was earlier than the appearance of shallow landslides in terraces, and rill erosion accelerated the formation of deep slip surfaces. The threshold of rainfall that caused deep landslides in terraces was 500 mm.

**Author Contributions:** P.G. and X.M. conceived and designed the research theme. Y.W. and P.G. collected the data and designed methods. Y.W. analyzed the data and interpreted the results. Y.W. and P.G. wrote and edited the paper. M.L.; Y.S.; H.W. processed the images and forms. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Scientific Research Project (Grant No. 2016YFC0501707).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data was contained within the article.

**Acknowledgments:** We thank the editors of the journal and the reviewers for their useful comments and suggestions to improve the paper quality greatly. Special thanks to Guangju Zhao and Wenyi Sun from Northwest A&F University, State Key Lab Soil Eros & Dryland Farming Loess P, China and Chinese Acad Sci & Minist Water Resources, Inst Soil & Water Conservat provided valuable feedback on an earlier version of this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Spatiotemporal Hotspots and Decadal Evolution of Extreme Rainfall-Induced Landslides: Case Studies in Southern Taiwan**

**Chunhung Wu \* and Chengyi Lin**

Department of Water Resources Engineering and Conservation, Feng Chia University, Taichung 40724, Taiwan; jknokiajk88@yahoo.com.tw

**\*** Correspondence: chhuwu@fcu.edu.tw; Tel.: +886-424517250-3223

**Abstract:** The 2009 Typhoon Morakot triggered numerous landslides in southern Taiwan, and the landslide ratios in the Ailiao and Tamali river watershed were 7.6% and 10.7%, respectively. The sediment yields from the numerous landslides that were deposited in the gullies and narrow reaches upstream of Ailiao and Tamali river watersheds dominated the landslide recovery and evolution from 2010 to 2015. Rainfall records and annual landslide inventories from 2005 to 2015 were used to analyze the landslide evolution and identify the landslide hotspots. The landslide recovery time in the Ailiao and Tamali river watershed after 2009 Typhoon Morakot was estimated as 5 years after 2009 Typhoon Morakot. The landslide was easily induced, enlarged, or difficult to recover during the oscillating period, particularly in the sub-watersheds, with a landslide ratio > 4.4%. The return period threshold of rainfall-induced landslides during the landslide recovery period was <2 years, and the landslide types of the new or enlarged landslide were the bank-erosion landslide, headwater landslide, and the reoccurrence of old landslide. The landslide hotspot areas in the Ailiao and Tamali river watershed were 2.67–2.88 times larger after the 2009 Typhoon Morakot using the emerging hot spot analysis, and most of the new or enlarged landslide cases were identified into the oscillating or sporadic or consecutive landslide hotspots. The results can contribute to developing strategies of watershed management in watersheds with a dense landslide.

**Keywords:** landslide evolution; spatiotemporal cluster analysis; landslide hotspots

#### **1. Introduction**

Landslides induced by large earthquakes or extreme rainfall events have been the main reason for disasters in the past two decades in Taiwan. Typhoon Morakot in 2009 dumped around 2000 mm of rainfall in 3 days in southern Taiwan [1], resulting in severe landslide-related disasters, including the catastrophic deep-seated Xiaolin landslide [2] and the following dam failure [3]. Over a decade since the 2009 Typhoon Morakot, sedimentrelated disaster events still occurred in the Kaoping River watershed in southern Taiwan. Although most landslides in southern Taiwan had been gradually recovered, the hillslope was still under high landslide susceptibility.

The rate and location of landslide recovery after the large earthquake or extreme rainfall events play essential roles in developing the watershed management strategies for watersheds with a dense landslide. The landslide recovery in the watersheds with dense landslides after large earthquake events is related to the earthquake magnitude, geological settings, and fault distribution and characteristics [4–6], while recovery after extreme rainfall events were mostly related to the distribution of drainage network [7]. The sediment yield from landslides or debris flow in the watersheds with dense landslides is usually the dominant factor behind the geomorphologic evolution, particularly in the upstream watershed. The randomly deposited sediment in narrow upstream reaches usually results in rivers gradually becoming sinuous and inducing bank-erosion landslides. Sediment from bank-erosion landslides usually increases the sinuosity of narrow reaches and changes the geomorphology of the river in the upstream watershed.

**Citation:** Wu, C.; Lin, C. Spatiotemporal Hotspots and Decadal Evolution of Extreme Rainfall-Induced Landslides: Case Studies in Southern Taiwan. *Water* **2021**, *13*, 2090. https://doi.org/ 10.3390/w13152090

Academic Editor: Su-Chin Chen

Received: 29 June 2021 Accepted: 27 July 2021 Published: 30 July 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Long-term geomorphologic landslide evolution in watersheds is strongly related to spatiotemporal landslide distribution [8], which can be observed using the spatiotemporal cluster analysis with the high-resolution digital elevation model (DEM) and multi-annual landslide inventories [4,6]. Several researchers have discussed the changes in the distribution and activeness of landslides after extreme rainfall-induced [7] or earthquakeinduced [5,8–11] events and found that the spatiotemporal distribution and activeness of landslides were key factors behind the geomorphologic evolution of watersheds. Identifying landslide hotspots and cold spots using multi-annual landslide inventories can help researchers analyze landslide activeness and recovery after large earthquake-induced landslide disasters [12].

The space-time cluster analysis (abbreviated as spatiotemporal cluster analysis) in ArcGIS Pro software [13] is a useful analysis tool that can describe data's spatial and temporal distribution patterns. This tool had been used to analyze the spread of the COVID-19 virus [14], road traffic accident occurrences [15], and the spread of air pollution [4,16] in recent years. Landslide disaster studies using the spatiotemporal cluster analysis have focused on discussing the long-term spatiotemporal distribution of disasters [5,8] and analyzing the relationship between disaster occurrence and related factors [6,9,17,18]. Spatiotemporal cluster analysis with multi-annual landslide inventories after extreme rainfall events can contribute to determining landslide hotspots and cold spots, identify locations where the landslide recovery was difficult, and analyze the reasons behind these factors. The use of spatiotemporal cluster analysis to observe landslide evolution trends and identify landslide clustering locations is more effective than only the spatial or temporal analysis of landslides.

The 2009 Typhoon Morakot (from 6–10 August 2009) caused the most severe rainfallinduced disaster event in the past two decades in Taiwan, and the return period accumulated 24 and 48 h of rainfall during the 2009 Typhoon Morakot in southern Taiwan exceeded 200 y [1]. The extreme rainfall event also caused numerous landslides and severe debris flow in southern Taiwan, and the landslide ratio (i.e., the ratio of the landslide area to watershed area) in the four sub-watersheds of the Kaoping River watershed after the typhoon exceeded 6.5% [1]. The geomorphologic evolution and developing trends of watersheds with dense landslides after 2009 Typhoon Morakot (abbreviated as after 2009) in southern Taiwan are worthy of discussion. The Ailiao river watershed (abbreviated as *ARW*) and Tamali river watershed (abbreviated as *TRW*) were the watersheds with the highest landslide ratio in southeastern and southwestern Taiwan after 2009. The *ARW* and *TRW* were selected to observe the landslide evolution from 2005 to 2015 and identify the landslide hotspots and cold spots using the spatiotemporal cluster analysis. The evolution characteristic of extreme rainfall-induced landslide events in Taiwan was also compared with that of large earthquake-induced landslide events in the world, and the cluster location and reason of new or enlarged landslides in the following years after 2009 were analyzed in the study.

#### **2. Research Areas**

#### *2.1. Ailiao River Watershed (ARW)*

The Ailiao river watershed (abbreviated as *ARW*) is located in southwestern Taiwan (Figures 1 and 2), and the area is 623.3 km<sup>2</sup> . The average elevation and average slope in the *ARW* are 1006 m and 30.5◦ . The average annual precipitation is 3716 mm based on the records of six rainfall stations from 2005 to 2015 in the neighborhood of *ARW* (Figure 2a). The average precipitation in the rainy seasons, i.e., from May to October, occupies > 90% of the average annual precipitation. The land use distribution in the *ARW* is dominated by forest, which occupies 80.8% of the total watershed area. The main geological settings in the *ARW* consist of the Chaochou Formation, the Pilushan Formation, the Alluvium, and the Kaoling Schist (Figure 2b). The total precipitation during the 2009 Typhoon Morakot in the *ARW* was 2977 mm, i.e., around 80% of the average annual precipitation. The 2995 landslide cases (Figure 2a) were induced by the 2009

Typhoon Morakot in the *ARW*, and the landslide ratio, i.e., the ratio of the landslide area to the watershed area, was estimated as 7.6%. The landslides after 2009 centralized in the northeast *ARW*, especially in the A01 (8.2 km<sup>2</sup> ), A02 (6.7 km<sup>2</sup> ), A03 (2.5 km<sup>2</sup> ), A07 (3.2 km<sup>2</sup> ), and A11 (9.5 km<sup>2</sup> ) sub-watersheds (Figure 2b). The occupied percentage of the landslide cases with area > 100,000 m<sup>2</sup> , 1000–100,000 m<sup>2</sup> , and <1000 m<sup>2</sup> to all landslide cases in 2009 in the *ARW* were 3.5%, 73.0%, and 23.0%, respectively. The relation between the landslide length to width ratio and the mean slope in the *ARW* is shown in Figure 3; 93.1% and 57.6% of the landslide cases in 2009 in the *ARW* were of the landslide length to width ratio > 1.0 and ranged from 1.0 to 5.0. The rainfall-triggered slides, including the rotational and translational slides and flows on the hillslope with the slope > 30 degree, were the main landslide types in the *ARW*.

**Figure 1.** Location of Taiwan, Ailiao river watershed (abbreviated as ARW), and Taimali river watershed (abbreviated as TRW).

**Figure 2.** The distribution of elevation, landslide after 2009 Typhoon Morakot, and sub-watersheds (**a**), geological settings (**b**), in the *ARW*.

**Figure 3.** Relationship between the ratio of landslide length to width and mean slope of the landslide cases induced by 2009 Typhoon Morakot in the *ARW* and *TRW*.

#### *2.2. Taimali River Watershed (TRW)*

The Taimali River Watershed (abbreviated as *TRW*) is located in southeastern Taiwan (Figures 1 and 4) and the area is 264.9 km<sup>2</sup> . The average elevation and slope in the *TRW* are 789.4 m and 30.4◦ , respectively. The average annual precipitation is 2185 mm based on the records of five rainfall stations from 2005 to 2015 in the neighborhood of *TRW* (Figure 4a). The average precipitation in the rainy seasons, i.e., from May to October, occupies 76% of the average annual precipitation. The land use distribution in the *TRW* consists of forest (81.59%), agricultural land (9.12%), water conservancy (4.32%), and others. The main geological settings in the *TRW* consist of three main strata, including the Chaochou Formation, the Pilushan Formation, and the Alluvium (Figure 4b). The total precipitation during the 2009 Typhoon Morakot in the *TRW* was 932.5 mm, i.e., around 42.7% of the average annual precipitation. The 1283 landslide cases (Figure 4a) were induced by 2009.

Typhoon Morakot in the *TRW*, and the landslide ratio was estimated as 10.7%. The landslide after 2009 centralized in the upstream *TRW*, especially in the T01 sub-watershed (121.6 km<sup>2</sup> ). The occupied percentage of the landslide cases with area > 100,000 m<sup>2</sup> , 1000–100,000 m<sup>2</sup> , and <1000 m<sup>2</sup> to all landslide cases in 2009 in the TRW were 4.2%, 71.2%, and 24.6%, respectively. The relation between the landslide length to width ratio and the mean slope in the TRW is shown in Figure 3; 98.1% and 64.3% of the landslide cases in 2009 in the TRW were of the landslide length to width ratio > 1.0 and ranged from 1.0 to 5.0. These data show that the majority landslide type of the landslide cases induced by the 2009 Typhoon Morakot in the TRW were rainfall-triggered slides on the steep slope.

**Figure 4.** The distribution of elevation, landslide after 2009 Typhoon Morakot, and sub-watersheds (**a**), geological settings (**b**) in the TRW.

#### **3. Data and Methods**

#### *3.1. Annual Landslide Inventories*

The annual landslide inventories from 2005 to 2015 produced by the Forestry Bureau in Taiwan were used in this study, and the minimum landslide area in the annual landslide inventories was 100 m<sup>2</sup> . Based on Varnes' classification [19], the majority of the landslide cases induced by 2009 Typhoon Morakot in southern Taiwan were rotational slides, translational slides, and flows [20–22].

#### *3.2. Effective Accumulated Rainfall Index (EAR)*

The *EAR* index (unit: mm) was used to assess the landslide-induced strength of rainfall events. The *EAR* index, defined in Equation (1), is the summation of daily rainfall on the assessment day (*Rt*) and the 7-day antecedent rainfall before the assessment day. The *K* coefficient, representing the decay constant, was set to 0.7 based on Taiwanese landslide research [23]. Equation (1) is calculated as follows:

$$EAR\_t = \sum\_{i=0}^{7} R\_t \times K^i \tag{1}$$

The rainfall records used to estimate the *EAR* index value were collected from the representative rainfall stations at watersheds. For inclusion, the representative rainfall stations had to be located within the watershed, and the rainfall records from 2005 to 2015 had to be available without any missing data. The representative rainfall stations in the two watersheds are Ali station in the *ARW* and Jinfong station in the *TRW*. The annual landslide inventories were used in this study. It is challenging to find data on the time and date of landslide occurrences and estimate the rainfall threshold to induce the landslide. Rather than determining the precise time and date of landslide occurrences, the *EAR* values used in this study serve as reference coefficients to understand the intensity of landslides induced by typhoons and other heavy rainfall events each year from 2005 to 2015.

#### *3.3. Landslide Topographic Position Analysis*

The topographic position analysis method can be used to explain the main inducing factors of landslides [24]. Three parameters of the landslide on the hillslope, including the distance between the ridge and the crown of the landslide (*DP*), the distance between the stream and the toe of the landslide (*DB*), and the distance between the ridge of the hillslope and river (*DH*), are used to explain the relative location of the landslide in the hillslope. The bubble plot is frequently used to draw the result of the topographic position analysis using the normalized distance from a landslide to the ridge (*DP*/*DH*) as the X-axis, the normalized distance from a landslide to the stream (*DB*/*DH*) as Y-axis, and the size of the bubble as the landslide area. If the bubbles are located in the upper-left portion of the bubble plot (*DP*/*D<sup>H</sup>* < 0.5 and *DB*/*D<sup>H</sup>* > 0.5), the landslide cases are located near the ridge and possibly induced by earthquake events [24]. If the bubbles are located in the lower-left portion of the bubble plot (*DP*/*D<sup>H</sup>* > 0.5 and *DB*/*D<sup>H</sup>* < 0.5), the landslide cases are located near the stream and possibly induced by rainfall or flooding events [1,21].

#### *3.4. Spatiotemporal Cluster Analysis Method*

We used the emerging hot spot analysis in the space-time cluster analysis tool in the ArcGIS Pro software to analyze the landslide evolution and identify the landslide hotspots and cold spots from 2005 to 2015. The emerging hot spot analysis tool can detect eight hotspot or cold spot trends, and the definition of the eight hot spot or cold spot trends had been described in Table 1 (revised from [14]). The emerging hot spot analysis was widely used in observing the evolution of the natural or artificial phenomenon but has still rarely been used to analyze the landslide evolution. The analysis unit in the study is a 5 m × 5 m grid, and the time step is a year. The clustering intensity of landslide in each analysis unit was estimated using the Getis-Ord Gi statistic [25], which considered the clustering intensity value for each analysis unit within the context of the values for the neighboring analysis unit. In the study, the neighborhood distance of the analysis unit was set as 25 m.


**Table 1.** The classifications and definition of emerging landslide hot spot and cold spot in the study.

**Table 1.** *Cont*.


Note: The CHS and CCS are the abbreviations of consecutive hot spot and consecutive cold spot. The regulation of abbreviation is applied to each hot spot and cold spot in the study.

#### **4. Decadal Analyses Results**

#### *4.1. Rainfall Distribution and Landslide Ratio*

The *EAR* distributions from 2005 to 2015 in the two watersheds are shown in Figure 5 and Table 2. The average *EAR* value from 2005 to 2015 was 39.7 in the *ARW* and 29.7 in the *TRW*. The highest *EAR* values (*EAR<sup>h</sup>* ) in the *ARW* and *TRW* were 1926.9 and 1123.5 on 8 August 2009. The *EAR<sup>h</sup>* and *EAR<sup>a</sup>* (the average of the three highest *EAR* values in each year) from 2005 to 2008 in the two watersheds were larger than those from 2010 to 2015. The return periods of the top ten daily rainfall events from 2005 to 2008 in the two watersheds were estimated to be 10–50 years, and those from 2010 to 2015 were estimated to only be <2 year. The data demonstrated that the *EAR* value and the return periods of rainfall events from 2005 to 2008 in the two watersheds were larger than those from 2010 to 2015.

**Figure 5.** The distribution of effective accumulated rainfall index (abbreviated as EAR) value (black bar) and landslide ratio (dash line) from 2005 to 2015 in the ARW (up figure) and TRW (down figure).

The landslide ratios in 2009 in the *ARW* and *TRW* (Figure 5) were their historical peaks. The average landslide ratios in the *ARW* and *TRW* from 2005 to 2008 were 1.6% and 2.2%, respectively, and those from 2010 to 2015 were 4.3% and 5.9%, respectively. The trends of the landslide ratios in the two watersheds after 2009 were oscillating instead of stably decaying. The *EAR<sup>h</sup>* and *EAR<sup>a</sup>* in 2011 and 2013 in the *ARW* were smaller than those from 2005 to 2007, but the landslide ratio increased in 2011 and 2013. Other similar examples are shown in comparing the *EAR<sup>h</sup>* , *EARa*, and landslide ratios in 2011 and 2013 in the

*TRW*. This data implied that landslides were more easily induced after the 2009 Typhoon Morakot. The rainfall factor was possibly not the only landslide-inducing factor in the two watersheds after 2009.


**Table 2.** The statistical data of the *EAR* values from 2005 to 2015 in the two watersheds.

Note: The *EAR<sup>h</sup>* means the highest *EAR* value, and the *EAR<sup>a</sup>* means the average of the three highest *EAR* values in each year.

#### *4.2. Landslide Statistical Data*

The research period was divided into three periods (i.e., 2005–2008, 2009, and 2010–2015) to analyze the changes in landslide distribution before and after 2009. The landslides' statistical data from 2005 to 2015 in the two watersheds are shown in Figure 6 and Table 3. The area and number of landslides from 2010 to 2015 in the two watersheds were larger than those from 2005 to 2008. From 2005 to 2015, the year with the most landslides was 2009, but the year with the most landslide numbers was 2013. In the *ARW*, for example, the landslide area in 2013 was 42% smaller than that in 2009, but the landslide number in 2013 was 31% higher than that in 2009. The same trend was observed in 2013 in the *TRW*. This data implies that most of the landslides induced by 2009 Typhoon Morakot gradually recovered, but some new landslides occurred in the two watersheds in 2013.

**Figure 6.** The area (solid line) and number (dash line) of landslide in the ARW (black) and TRW (red) from 2005 to 2015.

This study analyzed the landslide distribution at the sub-watershed scale to find the sub-watersheds in which landslides were induced in the years following the 2009 Typhoon Morakot. The landslide evolution trend index (abbreviated as *LET*) in this study was

defined as the average change ratio of the landslide area from 2010 to 2015, and the *LET* was estimated in each sub-watershed of the two watersheds (Figure 7). A negative *LET* value indicates that the total landslide area in this sub-watershed gradually decreases, while a positive *LET* value indicates that the total landslide area gradually increases. The average *LET* value in the sub-watersheds was <sup>−</sup>0.022 and <sup>−</sup>0.072 km2/year in the *ARW* and *TRW*.

**Table 3.** The average area and number of landslides in the two watersheds.


**Figure 7.** The average landslide density and landslide evolution trend index value from 2005 to 2015 in the *ARW* (**A**) and *TRW* (**B**).

The sub-watersheds with positive *LET* values were located upstream of *ARW* and *TRW*. There were 13 and 2 sub-watersheds with the positive *LET* values in the *ARW* and *TRW*, respectively, and the landslide ratio of the 15 sub-watersheds after 2009 was larger than 4.4%. There were six sub-watersheds with the LET values > 0.05, including A01, A02, A03, A07, and A11 in the *ARW* and T01 in the *TRW*, and the landslide ratio of the six sub-watersheds after 2009 was greater than 12.1%. The watershed areas in the A01, A02, A03, A07, A11, and T01 sub-watersheds were 8.2, 6.7, 24.7, 31.7, 9.5, and 121.6 km<sup>2</sup> , respectively, and the landslide ratios after the 2009 Typhoon Morakot were 27.8%, 21.2%, 26.2%, 21.5%, 12.1%, and 20.7%, respectively. These results imply that the landslides in the sub-watersheds with a landslide ratio of >4.4% after 2009 in the *ARW* and *TRW* were difficult to recover and were easily induced or re-induced from 2010 to 2015.

#### *4.3. Landslide Topographic Position Analysis*

The study used the landslide topographic position analysis to examine the landslide evolution before and after 2009 in the *ARW* and *TRW*. The A03 (*LET* = 0.32 km2/y), A31 (*LET* <sup>=</sup> <sup>−</sup>0.31 km2/y), and T01 (*LET* = 0.43 km2/y) sub-watersheds were selected for comparison of landslide evolution before and after 2009 (Table 4 and Figures 8 and 9). The area in the A31 sub-watershed was 33.9 km<sup>2</sup> , and the landslide area and landslide ratio in 2009 in the A31 sub-watershed were 2.8 km<sup>2</sup> and 8.3%. The ratio of landslide area from 2009 to 2015 in the upslope, mid-slope, and downslope were 19.4%, 25.5%, and 38.2%, respectively, in the *ARW* and 27.6%, 29.8%, and 31.1% in the *TRW*, respectively. The landslide located in the downslope was the most difficult to recover from 2009 to 2015 in the slope.

**Figure 8.** The topographic position analysis of landslide in 2008 (**a**–**d**), 2009 (**b**–**e**), and 2015 (**c**–**f**) in the A03 (up figures) and A31 (down figures) subwatersheds in the *ARW*.


**Table 4.** The topographic position analysis results in the *ARW* and *TRW*.

Note: "B" and "A" mean that the average landslide area before 2009, i.e., from 2005 to 2008 and after 2009, i.e., from 2010 to 2015. UA, MA, and DA mean the upslope, mid-slope, and downslope landslide area (km<sup>2</sup> ).

**Figure 9.** The topographic position analysis of landslide in 2008 (**a**), 2009 (**b**), and 2015 (**c**) in the T01 sub-watershed in the *TRW*.

A similar trend was also found in the A03, A31, and T01 sub-watersheds. The ratio of landslide area from 2009 to 2015 in the downslope was 79.7%, 23.0%, and 68.5% in the A03, A31, and T01 sub-watersheds, respectively. Figures 8 and 9 show that a reduction was observed in the number of upslope, mid-slope, and downslope landslides in the subwatersheds, but the landslides in 2015 were concentrated in the downslope area. From 2009 to 2015, a large cluster of small-area landslides occurred downslope in the sub-watersheds, with poor recovery. Most of the landslides in the A03 and T01 sub-watersheds in 2015 were centered in areas with a normalized distance to a ridge of >0.7, meaning that the inducing factors should be related to the bank-erosion landslide, which was possibly induced by the sinuous rivers with huge amounts of deposited sediment.

#### *4.4. Spatiotemporal Landslide Hotspot Analysis*

The landslide ratios in the *ARW* and *TRW* after 2009 were 7.6% and 10.7%, and those were the top two highest landslide ratios in the watershed scale in Taiwan. It is interesting to understand the evolution of numerous landslides and compare the characteristic of landslide distribution before and after 2009 in the two watersheds. The evolutions of the landslide from 2005 to 2015 in the *ARW* and *TRW* were observed from the spatiotemporal landslide hotspot analyses (Table 5 and Figure 10) in the study.

The total areas from 2010 to 2015 in the two watersheds are 1.15–2.23 times larger than those from 2005 to 2008, and the increases in the landslide hot spot areas from before to after 2009 in the two watersheds were evident. The landslide hot spot areas from 2010 to 2015 in the two watersheds are 2.67–2.88 times larger than those from 2005 to 2008, and the landslide cold spot area is 1.73–1.93 times larger. This result means that the total time of areas identified as landslides from 2010 to 2015 is longer than that from 2005 to 2008. The landslide recovery was more difficult, and the landslide was easier to be clustered after than before 2009 Typhoon Morakot.

**Table 5.** The statistical data of spatiotemporal landslide hot spots and cold spots in the *ARW* and *TRW*.


Note: The 05–15, 05–08, and 10–15 mean from 2005 to 2015, from 2005 to 2008, and from 2010 to 2015. The HS and CS mean the total area of all hot spots and cold spots, and the NO means the no pattern detected area.

**Figure 10.** The occupied percentage of landslide hot spots and cold spots from 2005 to 2015 (black line), from 2005 to 2008 (blue line), from 2010 to 2015 (red line), and in the *ARW* (**a**) and *TRW* (**b**).

The no pattern detected area means that the time of area identified as a landslide is shorter than 90% of the research period (Table 1). The occupied percentages of the no pattern detected areas from 2005 to 2015 in the two watersheds are 53.0–56.5%, but those from 2005 to 2008 and from 2010 to 2015 are only 15.9% to 20.2%. This data means that 36.3–37.1% of landslide areas in the two watersheds recovered to the non-landslide areas in 4 to 9 years.

The landslide hot spots are centralized in OHS, SHS, and CHS in each research period, while the landslide cold spots are centralized in OCS, CCS, and SCS. The landslide hot spots and cold spots were reclassified into the main hot spots, the main cold spots, no pattern detected, and others. The main hot spots included OHS, SHS, and CHS, the main cold spots included OCS, CCS, and SCS, and the others included all the other hot spots and cold spots except the main hot spots and cold spots. After 2009, the main hot spots constituted 34.0–41.9% of all hot spots, whereas the main cold spots accounted for 31.6–37.8% of all cold spots.

Figures 11 and 12 present the main hot spots and cold spots from 2005 to 2015 in the two watersheds. The upstream sub-watersheds with dense landslide distributions were the main hot spot cluster areas in the two watersheds.

The main hot spots from 2005 to 2008 were discretely distributed in the upstream sub-watersheds of *ARW* and *TRW*, and those from 2010 to 2015 were densely clustered in the upstream of *ARW* and *TRW*, particularly in the A01 and T01 sub-watersheds.

Obvious increases in the average landslide ratios from after to before the 2009 Typhoon Morakot in the two watersheds were noted. The CHS were the hot spots that exhibited the largest area expansion from after to before the 2009 Typhoon Morakot, and the OCS were the cold spots that exhibited the largest area reduction. The CHS percentage increased by 7.5% to 16.3% from after to before the 2009 Typhoon Morakot, and the OCS percentage decreased from 11.4% to 21.8%. This means that the recovery of landslides induced by 2009 Typhoon Morakot was slower than that before 2009.

**Figure 11.** The main landslide hot spot and cold spot from 2005 to 2015 (**a**), from 2005 to 2008 (**b**), and from 2010 to 2015 (**c**) in the *ARW*.

**Figure 12.** The main landslide hot spot and cold spot from 2005 to 2015 (**a**), from 2005 to 2008 (**b**), and from 2010 to 2015 (**c**) in the *TRW*.

The A01 sub-watershed was selected as the representative sub-watershed to explain the distribution of the main hot spots and cold spots in the study. The strata in A01 comprise the Pilushan and Chaochou formations (62.6% and 37.4%, respectively) from the Eocene epoch and Middle Miocene sub-epoch, respectively. The lithology of the Pilushan formation comprises slate with metasandstone and igneous rock, whereas that of the Chaochou formation is argillite and slate with an alternation of metasandstone or argillite. The main hot spots and main cold spots in the A01 sub-watershed increased substantially after Typhoon Morakot. From 2005 to 2008, 2010 to 2015, and 2005 to 2015, the main hot spots in the A01 sub-watershed constituted 3.0%, 17.0%, and 12.5%, respectively, and the main cold spots constituted 3.8%, 5.9%, and 4.2%, respectively. The main hotspots from 2010 to 2015 in the A01 sub-watershed were concentrated in the headwater landslides, bank-erosion landslides in sinuous reaches, and reoccurrence of older (from 2005 to 2008) landslides.

Mechanisms and triggering factors of landslide events, landslide areas with poor recovery, and geomorphological evolution trends can be explained, located, and predicted using the distributions of landslide hot spots and cold spots that were constructed through spatiotemporal analysis. The results of the spatiotemporal analysis over the various periods have different implications. Specifically, the hot spot and cold spot distributions from 2005 to 2015, from 2005 to 2008, and from 2010 to 2015 in the ARW and TRW represent the long-term landslide evolution.

#### **5. Discussion**

The prediction of landslide recovery in watersheds with dense landslides could be the key factor for watershed management. The characteristic of landslide recovery in the following years after the large earthquake or extreme rainfall events are worth comparing and discussing. We explained the recovery characteristic of extreme rainfall-induced landslides by comparing the landslide recovery conditions after the 2005 Kashmir earthquake [5], the 2008 Wenchuan earthquake [4,9], and the 2009 Typhoon Morakot in this study. The time, location, and rate of landslide recovery after the large earthquake or extreme rainfall events are the key discussion topics in this study.

The oscillating period was observed after the large earthquake or extreme rainfall events based on the annual landslide area data. The oscillating period can be defined as that the annual landslide area and landslide number in this period is an oscillating trend instead of a stable decline trend. The oscillating period for the serious earthquake-induced landslide events ranged from 3 to 5 years. The extreme rainfall-induced landslide events in the study were estimated as 5 years (Figure 4 and Table 6, from 2010 to 2014). The landslide in the watersheds in the oscillating period was active and easily induced, re-induced, or enlarged. The average annual landslide area decline rates (abbreviated as *LAD*) after 2014 were larger than that during the oscillating period (from 2010 to 2014), and the average *LAD* during or after the oscillating period in this study was also larger than those from the large earthquake-induced landslide events. This means that the recovery rate of the extreme rainfall-induced landslide was faster than that of large earthquake-induced landslide.

**Table 6.** Comparison of the average annual landslide area decline rate from the large earthquake events and the extreme rainfall events.


Note: LAD means the average annual landslide area decline rate (km2/year), and LAD<sup>O</sup> and LAD<sup>A</sup> mean the LAD during the oscillating period and after the oscillating period.

The location and reason of new or enlarged landslides after the large earthquake or extreme rainfall events are worth discussing and comparing. The new or enlarged land-

slides in the following years after the 2005 Kashimir earthquake (including the active, very active, and extremely active landslides in [5]) were mostly located along the Muzaffarabad fault or in the high fractured and jointed rocks areas, or along with the drainage network, or in the source of the river and large landslide. Moreover, the new or enlarged landslides in the following years after the 2008 Wenchuan earthquake (the active landslides in [4]) were located in deep gullies, the source of debris flow and large landslides. Three factors, including the geological setting, the drainage network, and the landslide area, dominate the rate of landslide recovery after 2009 in the *ARW* and *TRW* in the study.

The statistical data and distribution of landslide evolution in the *ARW* and *TRW* are shown in Table 7 and Figure 13. The new or enlarged landslide in the following years after 2009 centralized in the northeast *ARW* and upstream *TRW*. The strata in the northeast *ARW* comprise 62.6% Pilushan formation (metasandstone and igneous rock) and 37.4% Chaochou formations (argillite and slate with an alternation of metasandstone or argillite), and three faults and anticlines also pass through the northeast ARW. The strata in the upstream *TRW* comprise the Chaochou formations (sandstone), kaolinite schist, and Pilushan formations (metasandstone and igneous rock), and three faults and anticlines also pass through the northeast *TRW*. Fractured slate, sandstone, or argillite are the main geological composition in the northeast *ARW* and upstream *TRW*, and also explain the reasons for the centralization of new or enlarged landslides in this area.

**Table 7.** Statistical data of landslide evolution from 2009 to 2010, 2013, and 2015 in the *ARW*.


Note: The unit of area in this table is km<sup>2</sup> . R, NR, and NE mean the recovered, not recovered, and new and enlarged landslide, and the gully-related, river-related, and large-related mean the NE landslide located in the neighborhood of gully, river, and large landslide.

> The landslide evolution results from the comparison of landslide inventories in two different years can be classified into three types, including recovered landslides, not recovered landslides, and new or enlarged landslides (Figure 13). The recovered landslide area from the comparison between 2009 and 2010 (Table 7) was the area identified as landslide in 2009 but not in 2010, and the not recovered landslide area were the areas identified as landslide in 2009 and 2010. The new or enlarged landslide area was the area identified as landslide in 2010 but not in 2009. The new or enlarged landslide in the *ARW* and *TRW* also centralized along with the drainage network, particularly in the upstream watersheds. Hugh sediment yield from the landslide in the upstream watershed with dense landslide should be the main reason. The landslide volume was estimated the empirical equations from Taiwan [26] for the landslide area < 10<sup>6</sup> m<sup>2</sup> and Italy [27] for the landslide area ≧ 10<sup>6</sup> m<sup>2</sup> ]. The landslide volume induced by 2009 Typhoon Morakot was estimated as 65.0 <sup>×</sup> <sup>10</sup><sup>6</sup> <sup>m</sup><sup>3</sup> and 224.5 <sup>×</sup> <sup>10</sup><sup>6</sup> <sup>m</sup><sup>3</sup> in the *ARW* and *TRW*. There were 848 landslide cases after 2009 in the northeast upstream *ARW*, including A01, A02, A03, A07, and A11 sub-watersheds, and 1138 landslide cases in the upstream *TRW*, i.e., the T01 sub-watershed. The landslide volume was estimated as 5.2 <sup>×</sup> <sup>10</sup><sup>6</sup> <sup>m</sup><sup>3</sup> in the northeast upstream of the *ARW* and 223.9 <sup>×</sup> <sup>10</sup><sup>6</sup> <sup>m</sup><sup>3</sup> in the T01 sub-watershed. Huge sediment was yielded, deposited in the narrow reaches, and dominated the evolution of landslide and river geomorphology in the northeast *ARW* and upstream *TRW*.

> Huge sediment in the upstream watershed was continuously transported into the gullies and rivers and also resulted in the frequent occurrence of new or enlarged landslides in the neighborhood of gullies and rivers from 2010 to 2015 in the *ARW*. Moreover, 51.3%, 54.0%, and 58.2% of the landslide areas after 2009 in the *ARW* had been recovered in 2010, 2013, and 2015, respectively. The new or enlarged landslide area from 2010 to 2015 in the *ARW* showed a continuously increasing trend. The occupied percentage of a

new or enlarged landslides located in the neighborhood of gullies from 2010 to 2015 was 53.9–56.1%, and the area of a new or enlarged landslide located in the neighborhood of the river from 2010 to 2015 also showed an increasing trend.

**Figure 13.** The landslide evolution from 2009 to 2010 (**a**), to 2013 (**b**), and to 2015 (**c**) in the ARW. The left down plot in each figure is the landslide evolution in the northeast *ARW*, including the A01, A02, A03, A07, and A11 sub-watersheds.

The centralization of new or enlarged landslides in the neighborhood of large landslides was mentioned [4,5], and it was also observed in the study. The occupied percentage of a new or enlarged landslide located in the neighborhood of large landslide cases from 2010 to 2015 in the *ARW* was 31.2–35.3%, particularly in the northeast *ARW*.

The dentification of landslide hot spots using the emerging hot spot analysis in this study can show the clustering strength of old, new, and enlarged landslides in space and time and provide a potential landslide location. The advantage of the identification of landslide hot spots using the emerging hot spot analysis is that we can estimate the maintenance time of landslides from the classification of landslide hot spots, and this information also contributes to making the priority of watershed management measures in the watersheds with dense landslides. The management strategy for the watersheds with huge sediment yield should be implemented considering the landslide evolution trend. The landslide evolution cases in the *ARW* and *TRW* in Taiwan demonstrated that controlling the sediment in the drainage network and the landslide boundary should be the priority after the extreme rainfall-induced landslide events.

#### **6. Conclusions**

This study used the rainfall analysis, spatiotemporal landslide hotspot analyses, and comparison analysis of large earthquake- and extreme rainfall-induced landslide evolution to understand the characteristic of rainfall-induced landslide evolution, which was useful in assessing the landslide activeness after an extreme rainfall event. We used the *EAR* to assess the landslide-induced strength of rainfall events from 2005–2015, and the *EAR* values in the *ARW* and *TRW* were larger than before after the 2009 Typhoon Morakot. The landslide evolution trend index (*LET*) was used to assess the recovery ratio of landslide area after 2009, and the *LET* value in most of the sub-watersheds in the *ARW* and *TRW* were ranged 0.022–0.072 km2/year. However, some sub-watersheds in the *ARW* and *TRW*, particularly in the upstream watershed with the landslide ratio > 4.4%, were still of *LET* value > 0.05 km2/year after 2009. The landslides downslope of subwatersheds with positive *LET* values in the *ARW* and *TRW* after 2009 were easily induced, re-induced, or enlarged and difficult to recover based on the landslide topographic position analysis. Most of the new or enlarged landslides in the *ARW* and *TRW* after 2009 were classified into oscillating or sporadic or consecutive landslide hotspots and centralized along with the drainage network or large landslide boundary. The watersheds with dense landslides needed to spend 3–5 years, i.e., the oscillating period in the study, to achieve the stable landslide recovery based on the comparison of landslide recovery after the large earthquake or extreme rainfall events. The landslide area decline rates in the *ARW* and *TRW* after 2009 were 1.6–2.5 times larger after than during the oscillating period. The new or enlarged landslides after 2009 in the *ARW* and *TRW* was centralized in the huge sediment-deposited, narrow, and sinuous reaches or the boundary of a large landslide in the upstream watersheds with a geological composition of fractured slate, sandstone, or argillite. The findings from the study point out that the watershed management strategies in the watershed with dense landslides after the extreme rainfall-induced landslide events should be emphasized to control the huge sediment yield from the numerous landslides, particularly in the upstream watersheds.

**Author Contributions:** Conceptualization and methodology, C.W. and C.L.; software, C.L.; writing, C.W. and C.L.; supervision and funding acquisition, C.W. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by Ministry of Science and Technology, Taiwan; Grant number: MOST 108-2625-M-035-003-(Taiwan).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** Financial supports from the Ministry of Science and Technology of Taiwan (R.O.C.) under contract MOST 108-2625-M-035-003- are appreciated.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**


*Article*

## **The Analysis on Similarity of Spectrum Analysis of Landslide and Bareland through Hyper-Spectrum Image Bands**

#### **Shiuan Wan 1 , Tsu Chiang Lei 2, \*, Hong Lin Ma <sup>1</sup> and Ru Wen Cheng 1**


Received: 24 September 2019; Accepted: 12 November 2019; Published: 17 November 2019

**Abstract:** Landslides of Taiwan occur frequently in high mountain areas. Soil disturbance causes by the earthquake and heavy rainfall of the typhoon seasons often produced the earth and rock to landslide in the upper reaches of the catchment area. Therefore, the landslide near the hillside has an influence on the catchment area. The hyperspectral images are effectively used to monitor the landslide area with the spectral analysis. However, it is rarely studied how to interpret it in the image of the landslide. If there are no elevation data on the slope disaster, it is quite difficult to identify the landslide zone and the bareland area. More specifically, this study used a series of spectrum analysis to identify the difference between them. Therefore, this study conducted a spectrum analysis for the classification of the landslide, bareland, and vegetation area in the mountain area of NanXi District, Tainan City. On the other hand, this study used the following parallel study on Support Vector Machine (SVM) for error matrix and thematic map for comparison. The study simultaneously compared the differences between them. The spectral similarity analysis reaches 85% for testing data, and the SVM approach has 98.3%.

**Keywords:** landslide; image classification; spectrum similarity analysis

#### **1. Introduction**

Landslides cause a great loss of human lives and properties. Landslides are frequent phenomena in Taiwan in which a more effective solution to estimate landslide area is desired through considering the remote sensing data [1–3]. Conventionally, monitoring of landslides for their locations and distributions are generally used in situ or field geotechnical techniques through aerial photos by human-power or unmanned aerial devices [4–6]. In the past, the investigation of landslide areas requires much manpower, material resources, and funding, and is very time-consuming. Various modeling approaches have been taken in the form of multivariate statistical analyses or Data Mining techniques of landslide characteristics corresponding to past landslide records. Many researchers studied the landslide through various evaluation/estimation through a Geographic Information System [7,8] with different techniques. The usage of aerial images in large-scale land cover surveys is of great help to the problem [9–11]. Nowadays, spatial information technology is the most proper solution for spatial analysis, which is to effectively and accurately judge the landslide through remotely-sensed images [12]. Hyperspectral image data have been developed for more than 20 years. Hyperspectral image data combine the spectrum shape and image data. In general, the wavelengths of spectrum are divided into visible, near-infrared, and part-short-wave infrared—three different parts. Those instruments recorded the spectral reflection information of the material to obtain complete geospatial information quickly and

extensively [13]. Due to the high spectral resolution of hyperspectral images, it can provide rich material details in landslide analysis [14,15].

Landslides cause lots of human life and economic losses every year. With the progressing techniques of spatial data survey in geosciences, large amounts of data for observing the change in the landslide area can easily be collected. Accordingly, the advancement and development of science and technology have enabled remotely to obtain large-scale and high-resolution quantitative information in a short period of time. To find the most valuable knowledge from the target, statistical classification and data mining techniques are usually used to predict the results of the analysis [2,4,8]. The aim of this research is to produce landslide susceptibility mapping by remote sensing data processing and GIS spatial analysis. To identify the unknown species, the spectral reflection diagram of the ground object could be used [16,17]. This action is like to discover the identification code of the ground object which can help us identify different features of land cover. Hyperspectral Imaging has a large number of bands and is almost continuous, which displays a relatively narrow on the spectral range of each band is relatively narrow. The amount of data obtained is huge and it can completely show slight differences in the spectrum of different features.

Due to the lack of accurate DEM (Digital Elevation Modeling) map/data in this study, only the hyperspectral with multi-band data is used to identify landslide and bareland based on a series of spectral intensities of the band reflection (see Figure 1). Therefore, the study aims to answer the question on whether the hyperspectral data can substitute for DEM data or not. On the other hand, landslide and bareland differentiation have drawn more attention to scientists and researchers. Landslide and bareland both have the same ingredient of soil but are usually at different locations on the hill. If the spectrum similarity analysis can be done to determine these two different categories, it could reduce a great amount of time in generating the DEM data/Map.

**Figure 1.** Theory for different reflection of target category (bareland vs. landslide).

In parallel studies, this study intends to use data mining methods: Support Vector Machine (SVM). A total of 72 spectral data of hyper-spectrum remote sensing images are distinguished from the traditional high-resolution data of traditional R, G, B and IR images which can clearly resolve the topography of the surface. If each category is carefully determined, it will be beneficial to compare them by similarity analysis. Between the classification of landslide and bareland, various machine learning classifiers may have different characteristics and solutions. The classification of the image can be conducted either in stage or in combination with each other. Therefore, the study intends to adopt the following two approaches: (a) Spectrum analysis and (b) Support Vector Machine (SVM). These two approaches are used to compare the outcomes in advantages and disadvantages, respectively.

#### **2. Data Collection for Study Plan and Area**

The study area is located in Zhuzizao Mountain, Nanxi District, Tainan City, Taiwan. It is located at the northeastern end of Tainan City, north of Dongshan District and Taipu Township of Chiayi, adjacent to Nanhua District in the east, Liujia District and Dazhong District in the west and the south of Yujing District. Nanxi District is located at the tail edge of the Alishan Mountain. The central part is the Dawu Ridge Basin. The hyperspectral image telemetry can reach a large area of the empirical area. To achieve the control and prediction of the collapse disaster, this study used the image data from the Chung-Hsing measurement Company in 2016. They purchased the UAV (Unmanned Aerial Vehicle), which is used to capture the hyperspectral image of Zhuzishan Mountain in Nanxi District, Tainan City for the study material.

#### *2.1. Geomorphology*

According to the plan of the Tainan City Landslide and Geostrophic Geological Sensitive Area (2014), the Nanxi District belongs to the river valley zone. Owing to the river originating from the Eastern Mountain, it shows a remarkable stream of excavation. At the same time, the cliff end with erosion is produced. A series of river bank terraces are formed under the action of undercut and side erosion; therefore, a small-scale vertical valley development is formed. The study area is located in the east of Meiling Scenic Area with an elevation of 1110 m. To the west, overlooking the Jianan Plain, the northwest side overlooks the Zengwen Reservoir, and the southeast is the Nanhua Reservoir. The terrain of this area has a large height difference in elevation, which is mainly composed of hilly terrain and plain terrain. The average elevation is between 800 and 1300 m. The geology is mainly composed of accumulated soil, and there are faults on both sides—the east and west. The earthquake-induced landslide caused this area soil condition to be very fragile.

#### *2.2. Hydrographic System*

The rivers in Tainan City include Bazhangxi, Jiushuixi, Zengwenxi, Yanxi, and Errenxi. The Ziwen River Basin originates from the Alishan Mountains. The drainage area is 1176.6 square kilometers and the longest is 138.5 km. The average slope of the riverbed is 1/200. The main tributaries are Houtunxi, Caixixi, and Guantianxi. It flows through Dongshan, Liujia, Annan, Yujing, Nanhua, Zuozhen, Shanshang, Dain, Guantian, Shanhua Madou, Anding, Xigang, and Qiqi on the Nanxi District of the study area, respectively. The study area is located near Tainan County in which there is Zengwen Reservoir (the largest reservoir in southern Taiwan). The mainstream originates from the Alishan Mountains, flows south to Zengwenxi, and flows southwest through the mountainous area to the Zengwen Reservoir. The strip has a total length of 138.5 km, an average slope of 1/57, and an average annual rainfall of about 2726 mm.

#### *2.3. Geological Structure*

The Tainan City Regional Disaster Prevention Plan (2016) is based on the data released by the Central Geological Survey of the Ministry of Economic Affairs in December 2016. It attributes to the historical landslide and ground slide area of about 69.11 square kilometers with landslide or ground slip conditions (with a sloping slope). The area is about 50.4 square kilometers with the buffer zone of 5 m is about 21.99 square kilometers, and the demarcation range is about 0.62 square kilometers. The total area is about 135.45 square kilometers (about 6.18% the total of area city).

In Figure 2, the location map of the landslide and geostrophic geological sensitive area in Tainan City is a plan for the Tainan landslide and geostrophic geological sensitive area (2016). The figure

shows that, to increase the terrain steepness and aspect, the base map is overlaid with topographic

**Figure 2.** Study area.

### *2.4. Research Material*

The spectral application image used in this study is the hyperspectral image of the Compact Airborne Spectrographic Imager (CASI) of the Bamboo-Waste Mountain in Nanxi District, Tainan City, which was provided by Taiwan Chung-Hsing Measurement in January and April 2016 as shown in Figure 3. The image scanning system CASI-1500 is manufactured by ITRES of Calgary, AB, Canada. The CASI-1500 instrument has a series of spectral wavelengths between 365 nm and 1050 nm, which is equivalent to the visible of near-infrared range. It can acquire 72 bands for this study with a spectral resolution of 3 nm and a spatial resolution of 1 m. Each band has its range and attribute of color, which is presented in Figure 3. Thus, the corresponding number of bands in the latter parts of this study is the same number presented here.


**Figure 3.** The hyperspectral corresponding image band of range.

#### **3. Research Method**

#### *3.1. Spectrum Similarity Analysis*

We carefully selected 240 sampling data for vegetation areas (trees, grass, etc), bareland area, and landslide area, respectively. Spectrum similarity analysis becomes a well-accepted approach to reduce the data dimensionality of hyperspectral imagery. It retrieves several bands of important patterns in some sense by taking advantage of the all high spectral correlation. Verified by classification accuracy, it was expected that, just using a part of original bands, the accuracy is obtained rationally, whereas computational work is significantly reduced [18,19].

Figure 4a shows the entire research step. It includes two parallel approaches. One of the approaches is considering finding the similarity of the image bands width to attain the classification outcomes [20]. Figure 4b shows the similarity of image bands. The vegetation index threshold is found based on clustering analysis. The non-vegetation of the image is attained, which includes the bareland and landslide. All this is part of data normalization. Then, the progress of the similarity spectrum analysis is carried out. Two of the image layers are obtained (D<sup>1</sup> and D2). The latter part of this paper will introduce the details on how the similarity classification of each pixel is identified.

**Figure 4.** (**a**) research steps; (**b**) the steps for similarity classification.

} ∈ {+1, −1}

,

‖ || 1 0

‖ ||

, = 1, . . .

{ ,

Figure 5a presents the original investigation on the site for observing the location of landslide. All the image data for similarity were carefully checked by in situ investigation and compared to remote sensing data [21]. It was decided to extract serval samples as mentioned above for landslide and bareland. Thus, Figure 5b shows the longitude and latitude of the position of study and the accurate place of landslides. This area landslide belongs to block-slide. Bock slide is a kind of translational slide. The moving mass of soil and rocks has serval related units that move downslope as a relatively coherent mass. The largest size of the landslide is about 8 <sup>×</sup> 12 m<sup>2</sup> , which is roughly measured by image data. ∞ > > 1 <sup>2</sup> ,,,, 1 2 *μ ξ ξ* ≥ *μ ≥*

2

1

*ξ* ≥

1

2

, ,

0

1 1

**Figure 5.** (**a**) original inventory map: landslide location of in situ investigation; (**b**) location of training sample, landslide: a, b, c, d, and e; bareland: aa, bb, cc, dd, ee, and ff.

The parallel study was used the SVM (Support Vector Machine) to access the classification on bareland and landslide. The thematic map is compared and the error matrix is also calculated.

#### *3.2. Brief on Support Vector Machine*

Support vector machines (SVMs) are well-accepted supervised learning methods used for classification [22]. The study considers the concept of improving statistical learning theory, generally applied as an effective classifier to solve many practical problems [23]. A special feature of this classifiers is to minimize the empirical classification error and maximize the geometric margin, simultaneously. Therefore, it is also known as a maximum margin classifier [24,25].

Linearly separable classes are the simplest cases for the analysis of three various classes (vegetation, landslide, and bareland). Assume the training data with k number of samples are presented as *xi* , *y<sup>i</sup>* , where *x* ∈ *R <sup>N</sup>* with an *<sup>n</sup>*-dimensional space, and *<sup>y</sup>* <sup>∈</sup> {+1,−1} is the class label. These training patterns are linearly separable if there exists a vector *w* (determining the orientation of a discriminating plane) and a scalar *b* (determine the offset of the discriminating plane from the origin) such that

$$y\_i(w \cdot x\_i + b) - 1 \ge 0. \tag{1}$$

The hypothesis space is defined by the set of functions given by:

$$f\_{w,b} = \operatorname{sign}(w \cdot x + b). \tag{2}$$

If the set of examples is linearly separable, the goal of the SVMs is to minimize the value ||*w<sup>i</sup>* ||. It is equivalent to finding the separating hyperplanes for which the distance between the classes of training data. It also measured along a line perpendicular to the hyperplane.

This distance is called the margin. The data points that are closest to the hyperplane are used to measure the margin. Thus, these data points are also called support vectors. Consequently, the number of support vectors should be small.

The problem of minimizing ||*w<sup>i</sup>* || is solved by applying standard quadratic programming (QP) optimization techniques. It also trasforms the problem to a dual space by using Lagrangian multipliers. The Lagrangian is presented by introducing positive Lagrange multipliers λ*<sup>i</sup>* , *i* = 1, . . . *k*. The solution of the optimization problem is attained by considering the saddle point of the Lagrange function

$$L(w, b, \lambda) = \frac{1}{2} \|w\|^2 - \sum\_{i=1}^{k} \lambda\_i y\_i (w \cdot x\_i + b) + \sum\_{i=1}^{k} \lambda\_i. \tag{3}$$

The solution in Equation (5) needs *L*(*w*,*b*,λ) to be minimized with respect to *w* and *b* and maximized with respect to λ*<sup>i</sup>* ≥ 0. Therefore, for a two-class problem, the decision rule separates the two classes that can be written as:

$$f(\mathbf{x}) = \operatorname{sign}\left(\sum\_{i=1}^{k} \lambda\_i y\_i(\mathbf{x} \cdot \mathbf{x}\_i) + b\right). \tag{4}$$

A soft margin problem for the case of SVMs is to handle the linearly non-separable data by Vapnik [22]. They concluded that the restriction of each training vector of a given class on the same side of the optimal hyperplane that applies the value. In ξ*<sup>i</sup>* ≥ 0, the SVM algorithm for the hyperplane maximizes the margin. At the same time, it minimizes a quantity proportional to the number of misclassification errors. This trade-off function between margin and misclassification error is also governed by a positive constant C such that ∞ > *C* > 0. Thus, for non-separable data, Label (6) can be written as

$$L(w, b, \lambda, \xi, \mu) = \frac{1}{2} \|w\|^2 + \mathcal{C} \sum\_{i} \xi\_i - \sum\_{i} \lambda\_i \langle y\_i(w \cdot x\_i + b) - 1 + \xi\_i \rangle - \sum\_{i} \mu\_i \xi\_i \tag{5}$$

where the µ*<sup>i</sup>* are the Lagrange multipliers introduced to force the ξ*<sup>i</sup>* to be positive. The solution of (7) is determined by the saddle points of the Lagrangian, by minimizing with respect to *w*, *x*, and *b*, and maximizing with respect to ξ*<sup>i</sup>* ≥ 0 and µ*<sup>i</sup>* ≥ 0.

#### **4. Results**

As aforementioned, we select 120 of sampling data for training the model of vegetation, bareland, and landslide, respectively. The 40 pieces of data of each (vegetation, bareland, and landslide) categories to build the model. The study also randomly selects 40 pieces of data to verify the model as testing data. The study has been broken into two parts: spectral similarity analysis and support vector machine. As previously mentioned in Figure 1, the landslide mostly occurred on the slope that has the different responses of reflection on hyper-spectrum image data. Compared to the bareland, the ingredient of soil is the same as the landslide; however, most of them are located in the flat area. Thus, the reflection on hyper-spectrum image data must be different to a landslide. This is the objective to classify them by applying the similarity of a spectrum [26].

To introduce the overall accuracy, it can be formulated as

$$\mathbf{Ac} = \frac{\mathbf{TP} + \mathbf{TN}}{\text{All the samples}'} \tag{6}$$

where *TP* is the true positive and *TN* is the true negative. Ac = ்ା்ே ௧ ௦௦

*4.1. Spectral Similarity Analysis*

The spectrum analysis entire study is divided into the following two steps:


To achieve this task, the developed program scans all the bands to find the largest discrepancy of vegetation and non-vegetation for discriminating between these two categories. The program calculates and finds that the 34th band has the largest difference. The green lines in Figure 6a are rationally extracted. Figure 6b is generated to extract out vegetation parts (green line). The *r*-value on the *y*-axis is the response value of the reflection for various categories (vegetation, bareland, and landslide).

**Figure 6.** *Cont*.

**Figure 6.** (**a**) three different categories for classification; (**b**) threshold of upper range for vegetation and non-vegetation; (**c**) the lower range on the threshold for landslide; (**d**) the upper range on the threshold for bareland; (**e**) intersection parts for training data of larger than threshold: landslide; (**f**) intersection parts for training data of lower than threshold: bareland (green: vegetation; blue: landside; red: bareland).

To obtain the best classification outcomes, the 1–72 bands are scanned to find the best part to distinguish the landslide and bareland. The developed program scans the data in Figure 6c to find the maximum discrepancy for landslide and bareland. A single cannot clarify the mixup data for landslide and bareland. Thus, a combination set of bands are requested to approach the goal. It is found that 38 to 42 bands are the best part in the spectrum analysis to attain the classification outcomes. First, the program adds the 38–42 bands of each data as a single band data (transfer the five-dimensional data to the one-dimensional data).

Then, the program generates a parametric *r*-value as an interval to attain three parts of the data: (a) lower the threshold(landslide), (b) upper the threshold(bareland), and (c) intersection part (mix-up part). Please refer to Figure 6b; Figure 6c; Figure 6d; and Figure 6e. The program gradually increases the *r* value to approach the optimal classification outcomes for landslide and bareland. For example, the program starts *r* = 80 and ∆*r* = 5 and finds the error rate between classification on landslide and bareland. That is, the program gains *r* = 95, which is the best allowable value to cut the data into these three parts. The strategy is to approach the largest number of lower the threshold and upper the threshold. The minimal lowest number of intersection part is also requested. The program calculates each data after the summation and sets them as less than 95 as one group and greater than 95 as another. The strategy is the number of data of the largest group to the total number of data must be greater than 40%. The number of data of the smallest group to the total number of data must be smaller than 40%. Because in Data Mining, the portion of the number of data for each decision should be as close as possible. Applying these sets of data can be fairly and uniformly to develop the model.

Then, the program three parts for summing up band 38 to 42 is

$$\begin{cases} \text{Lower than intersection} \le 4105 \dots \text{ landside} \\ \text{Greater than intersection} \ge 4828 \dots \text{ barrel and} \\ \text{intersection} > 4105 \text{ and } < 4828 \dots \text{ mixup parts} \end{cases} \tag{7}$$

After screening the band data, it is found that the data density variety is not uniform. Hence, different stepwise of a grouping data strategy is needed. In the mix-up parts, the program restarts to find the discrepancy between landslide and bareland. The solution takes a set of band values and uses the clustering technique to search the optimal set of possible outcomes. For instance, we found that the band numbers from 45 to 52 has the largest discrepancy. Then, the program sieves out the 45, 46, 48, 50, and 51 bands are the most useful information. That is, 47, 49, and 52 bands are eliminated from the data set. The program found that the band values in 45, 46, 48, 50, and 51 have the largest discrepancy between landslide and bareland. Then, the intersection ranges of bands of each piece of data are summed into a single value (five multi-band data into one-dimensional data). The summed maximum and maximum values are calculated, and the binary classification is executed. It is found that a finer value of 30 can be gradually increased as a stepwise to each line attribute for each categories (landslide and bareland). Then, the accuracy of each segmentation value is step-by-step calculated as the classification accuracy until the highest accuracy is approached. Each band of the data in the intersection range is clustered based on the rule of a finer interval being less than 30; the other group is greater than 30.

Determination value of 45, 46, 48, 50 and 51

$$\begin{cases} \displaystyle \text{sum } r: \ge 6995 \dots \text{landslide} \\ \displaystyle \text{sum } r: < 6995 \dots \text{landeland} \end{cases} \text{} \tag{8}$$

The training data for generating this similarity model have 100% accuracy.

The thematic map (see Figure 7) is generated by inputting are the band data into the program. Green presents the vegetation, red for landslide and white for bareland. The major landslide areas (comparing in Figure 5) are almost found, and bareland is clearly found. The computational time is

fast and a rough result is qualified. We also randomly picked 40 testing data to verify our spectrum analysis model. The error matrix is presented in Table 1. The overall accuracy is about 85%.

**Figure 7.** The thematic of spectrum analysis (green: vegetation, red: landslide and white: bareland).


**Table 1.** Error matrix for spectrum analysis.

#### *4.2. SVM*

As part of the study, the Support Vector Machine is used as a parallel approach to examine the spectrum analysis. The objective of the support vector machine algorithm is to generate a hyperplane in *n*-dimensional space (*n* is the number of features) that accurately classifies the data points. The following steps are:

൫ሺ௫ିሻି.ହ൯∗ଶ

tt −

#### 4.2.1. Step1: Normalization

The original data of the collected data sets (such as hyperspectral, multi-spectral, etc.) are normalized, and the values of the attribute data are standardized within the same range. This study converts all attribute values between −1 and 1, using the formula:

$$\mathbf{d} = \frac{d - min\_d}{((max\_d - min\_d) - 0.5) \ast 2}.\tag{9}$$

#### 4.2.2. Step2: Cross-Validation

This study uses K-Fold Cross-Validation to first split the initial sample into K sub-samples (each sub-sample is independent from each other). A single sub-sample is the data for the validation model with the remaining K−1 samples. One of those sets of sub-samples is used for training. After repeating the above procedure K times, the K group classification correct rate will be obtained. In final, the data of the K group for the correct rate average value are estimated.

#### 4.2.3. Step3: Model Selection for a Core Function

The functions of the support vector machine can be divided into four types: linear functions, polynomial functions, radial basis functions, and S functions. The user should select the core function based on different conditions. The parameters are adjusted for different kernel functions that are also different. The user has to adjust the kernel function and parameters according to the situation, which will have a significant impact on the prediction accuracy rate. In this study, the Radial Basis Function kernel (RBF) is taken for consideration. To obtain better model parameters, the Grid Search method repeats the test parameters C = 4.2 (penalty parameter) and g = 0.32 (gamma function) for possible combination and calculate the correct rate of its parameters (C, g). If it meets its condition, end the repeated test and output its best C and g parameters; otherwise, re-substitute with the new parameters until the combination is found.

This step is to optimize the optimal classification model obtained in the previous step. The testing data of the unknown result are substituted into the classification model construct by the previous step, and the obtained result will be aggregated in which the overall classification accuracy rate is calculated for performing the evaluation. It explores the effectiveness of machine learning under its selection points and different attribute data. The accuracy assessment of this study is divided into two parts: (1) the thematic map and (2) the error matrix. Figure 8 presents the thematic map for the overall condition in three categories. Green presents the vegetation, red for landslide, and white for bareland. Comparing Figure 8 to Figure 7, based on the image data in Figure 5, it presents a clearer and better accurate rate for the thematic map. The error matrix is also calculated in Table 2. The overall accuracy is 98.3%.

Comparing Figures 7 and 8 for the thematic map, the difference is clear. For instance, the blue rectangle part in Figure 7 renders a better interpretation of detecting the bareland. In the inventory map (Figure 5), this part presents as a bareland. The similarity analysis spectrum seems to provide a better prediction. However, SVM has a better interpretation of the integrity on landslide and bareland. The spatial information is a fundamental multi-temporal approach. The method can successfully be applied to serval periods of this area or another area. Thus, if the based rule of similarity spectrum can be developed successfully, the approximated location of landslide mapping can be rapidly generated. −

**Figure 8.** The thematic of support vector machine (green: vegetation, red: landslide and white: bareland).



#### **5. Conclusions**

The landslide and bareland are the most interesting topics that draw great attention to scientists and researchers. They both have the same soil ingredient but different locations on the hill. Landslides mostly displayed on the hill, which may produce destructive disasters for human beings. Owing to the lack of accurate DEM (Digital Elevation Modeling) map/data in this study, the hyperspectral data have been proved to identify landslide and bareland according to spectral intensities of reflection. A parallel study is designed to compare the spectral analysis approaches.

The study has three major contributions:


**Author Contributions:** S.W.: He was responsible for plan and design of this study. He also helped the student write the computer program. T.C.L.: He analyzed the data and discussion. H.L.M.: He wrote the computer program. R.W.C.: She used the program to plot the thematic map.

**Funding:** This research was funded by grant number 106-2119-M-275-002.

**Acknowledgments:** The authors expressed their gratitude for the National Science Council (106-2119-M-275-002)-sponsoring this work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **A Landslide Probability Model Based on a Long-Term Landslide Inventory and Rainfall Factors**

### **Chun-Yi Wu \* and Yen-Chu Yeh**

Department of Soil and Water Conservation, National Chung Hsing University, Taichung 402, Taiwan; cxz7.997.9@gmail.com

**\*** Correspondence: cywu@nchu.edu.tw; Tel.: +886-4-2284-0381 (ext. 605)

Received: 11 February 2020; Accepted: 24 March 2020; Published: 26 March 2020

**Abstract:** The prediction and advanced warning of landslide hazards in large-scale areas must deal with a large amount of uncertainty, therefore a growing number of studies are using stochastic models to analyze the probability of landslide occurrences. In this study, we used a modified Thiessen's polygon method to divide the research area into several rain gauge control areas, and divided the control areas into slope units reflecting the topographic characteristics to enhance the spatial resolution of a landslide probability model. We used a 2000–2015 long-term landslide inventory, daily rainfall, and effective accumulated rainfall to estimate the rainfall threshold that can trigger landslides. We then employed a Poisson probability model and historical rainfall data from 1987 to 2016 to calculate the exceedance probability that rainfall events will exceed the threshold value. We calculated the number of landslides occurring from the events when rainfall exceeds the threshold value in the slope units to estimate the probability that a landslide will occur in this situation. Lastly, we employed the concept of conditional probability by multiplying this probability with the exceedance probability of rainfall events exceeding the threshold value, which yielded the probability that a landslide will occur in each slope unit for one year. The results indicated the slope units with high probability that at least one rainfall event will exceed the threshold value at the same time that one landslide will occur within any one year are largely located in the southwestern part of the Taipei Water Source Domain, and the highest probability is 0.26. These slope units are located in parts of the study area with relatively weak lithology, high elevations, and steep slopes. Compared with probability models based solely on landslide inventories, our proposed landslide probability model, combined with a long-term landslide inventory and rainfall factors, can avoid problems resulting from an incomplete landslide inventory, and can also be used to estimate landslide occurrence probability based on future potential changes in rainfall.

**Keywords:** landslide; rainfall threshold; landslide probability model; Taiwan

#### **1. Introduction**

Taiwan is a relatively new island formed by plate movements. Due to its high mountains, steep slopes, and relatively unstable geological conditions, as well as frequent typhoons and torrential rains, slopeland disasters are common in mountainous areas. Thus, slopeland hazard prevention and mitigation projects are necessary. In slopeland hazard prevention work, landslides have a high level of unpredictability. In particular, estimating the likelihood of landslides in large watersheds using deterministic models is difficult when no detailed geomorphological and hydrological data have been collected for the whole area. Therefore, the use of a stochastic model to assess landslide probability is more feasible. According to the definition, landslide hazard involves both spatial and temporal probability [1]. The analysis of landslide spatial probability is generally seen as a landslide

susceptibility analysis in the research [2–12]. The landslide temporal probability, normally expressed in terms of frequency, return period, or exceedance probability [13], was analyzed in the research [14–21].

Methods of performing landslide temporal probability analysis can be classified as hydrological models and approaches based on exceedance probability [22]. The hydrological models employ infiltration models to determine the critical rainfall triggering landslides, which requires the estimation and validation of soil parameters over large areas, and therefore makes these models impractical for regional-scale applications. The approaches based on exceedance probability can be further subdivided into two types, where the first type employs a landslide inventory induced by a single rainfall event and rainfall data for that event to analyze the return period of the landslide event [8,23,24], and the second type employs a long-term landslide inventory to calculate the exceedance probability for the occurrence of landslides. Concerning the latter type, the Poisson probability model [17,25–29], binomial probability model, and empirical model [20] are commonly used to analyze the recurrence probability of landslide events. As a consequence, when a research area has a long-term landslide inventory, the Poisson probability model can be employed to estimate the temporal probability of landslides under the assumption that the frequency of future landslides occurring is the same as in the past. However, due to the constraints of this assumption, the Poisson probability model cannot separate the effect of geomorphological and hydrological factors on landslides, and therefore cannot be used to infer how landslide probability will change when climate change causes changes in the frequency of torrential rain and in the rainfall patterns. If the effects of geomorphological and hydrological factors can be considered separately and the occurrence probability of torrential rain events can be estimated independently, then the landslide temporal probability can be estimated correctly based on the change trends of the estimated torrential rain occurrence probability [30]. One approach to separate the effects of geomorphological and hydrological factors in landslide probability models is to employ the concept of conditional probability to separately estimate rainfall probability and landslide probability under these rainfall conditions. In this approach, a Poisson probability model is first used to calculate the exceedance probability of rainfall events that may trigger landslides, the landslide probability under these rainfall conditions is then calculated, and the two are multiplied to obtain the temporal probability of landslides [26,28,29].

Before calculating the probability of rainfall events that may trigger landslides, the scale of rainfall events that trigger landslides or the threshold rainfall events that must be exceeded to trigger landslides must first be understood. The minimum amount of rainfall needed to trigger landslides was first considered by Endo [31], and the rainfall thresholds triggering landslide events were quantified by Onodera et al. [32]. Campbell [33] suggested that the combined effect of both antecedent rainfall and rainfall intensity on the landslides needed to be considered, and a warning system could be based on the relationship between antecedent rainfall and critical rainfall [34]. Caine [35] used rainfall intensity and rainfall duration to establish global shallow landslide rainfall thresholds. Methods of establishing rainfall thresholds were classified as physical models and empirical models [36], where physical models employ detailed spatial information on hydrological, lithological, morphological, and soil characteristics as a basis for modeling the relationship between rainfall, infiltration, and landslide events. However, the information is hard to collect accurately over large areas. Empirical models can be grouped as thresholds combining rainfall duration, total event rainfall, or rainfall intensity parameters, thresholds considering antecedent rainfall, and thresholds combining other parameters, where the first two groups can be further subdivided into the following three categories based on the parameters used for determining rainfall thresholds [21]: the first category consists of intensity and duration parameters [18,20,29,34,35,37–39], the second category consists of antecedent rainfall conditions [26,28,29,40], and the third category consists of accumulative event rainfall and duration parameters [41]. Although rainfall intensity–duration models have been most commonly used in recent years [21], thresholds for rainfall-induced landslides may define the rainfall, soil moisture, or hydrological conditions that, when reached or exceeded, are likely to trigger landslides [36]. Some research has also suggested that groundwater and soil moisture are factors influencing the initiation of

landslides [42,43], and antecedent rainfall can affect both of these factors. Accordingly, antecedent rainfall can be used to determine when landslides may occur [36]. In research on rainfall thresholds incorporating the antecedent rainfall conditions, large differences exist in the number of days of antecedent rainfall that were employed in each study. For example, daily rainfall was employed in conjunction with 15-day antecedent rainfall [39], both daily and 3-day cumulative rainfall were used [44], and 3-day and 30-day antecedent rainfall were employed [45]. Guzzetti et al. [36] suggested that the large variability in the antecedent rainfall may be attributed to three types of factors concerning the research area: diversity in lithological, morphological, vegetation, and soil conditions; differences in climatic regimes and meteorological circumstances; and the heterogeneity and incompleteness in the rainfall and landslide data used to establish the rainfall thresholds. As a consequence, the local conditions and availability of data in the research area must be assessed when choosing the number of days of antecedent rainfall.

Since the rainfall threshold determined using a single rain gauge for a large area constitutes one value for the entire area, as soon as rainfall reaches or exceeds the threshold, landslides may occur anywhere in that area, and knowing their precise locations is impossible. As a consequence, a denser array of rain gauges can be employed to acquire rainfall data with finer spatial resolution [21], and the research areas can be subdivided into analytical units with a smaller area, which can better account for the spatial variability of rainfall patterns in the analytical units and the spatial resolution of landslide prediction. However, 19.1% of recent studies on this subject failed to subdivide their research areas, and those studies that did subdivide their research areas had resulting analytical units with an average area of 302.0 km<sup>2</sup> [21]. For instance, a research area of 4660 km<sup>2</sup> was subdivided into 12 analytical units with an average area of 388.3 km<sup>2</sup> [39], but excessively large analytical units make it impossible to identify the precise possible locations of landslides. In addition, the subdivision approaches employed in some studies run into the problem of incomplete coverage. For instance, although a 25 km<sup>2</sup> research area was subdivided into eight analytical units, the landslide prediction results only represented the paths of roads in the subdivisions and not the entire subdivisions because most landslides (94%) in the study occurred on roadside slopes [26]. Althuwaynee et al. [28] divided the research area into six circular analytical units with their centers at rain gauges, but the analytical units did not cover the entire research area and also overlapped. Although these studies subdivided their research areas into different analytical units, the units could not provide a landslide probability distribution with a finer spatial resolution because they were excessively large, or experienced problems such as incomplete coverage and overlap. If the method of subdividing a research area into analytical units is improved so that the units are smaller in area, the spatial resolution of the landslide probability estimation results could be improved. There are seven types of analytical units subdivided in research areas: grid cell, terrain unit, unique condition unit, slope unit, geo-hydrological unit, topographical unit, and administrative unit [46,47]. The slope units are suitable for landslide probability analysis because they express topographic features and slope characteristics. In this study, we consequently selected slope units as our analytical unit.

#### **2. Research Area and Materials**

#### *2.1. Environmental Setting of Taipei Water Source Domain*

Taipei Water Source Domain is located in the northeast part of Taiwan and supplies tap water for five million people in the greater Taipei area. The area is characterized by hilly and mountainous topography, as well as the Xueshan Range extending to the northeast and a subrange of Mt. Qilan extending to the northwest, both of which account for the area's high terrain in the south and low terrain in the north. Elevations in the area range from 12 to 2130 m (Figure 1).

*Water* **2020**, *12*, x FOR PEER REVIEW 4 of 17

**Figure 1.** Distribution of elevation, lithology, and rain gauges in the Taipei Water Source Domain. **Figure 1.** Distribution of elevation, lithology, and rain gauges in the Taipei Water Source Domain.

Concerning the distribution of lithology, we followed the classification approach proposed by Lin et al. [48] by dividing the Taipei Water Source Domain into areas underlain by alluvium, loose sandstone and shale, hard sandstone and shale, and slate. Whereas alluvium found at the confluence of rivers and in downstream areas covers only a small part of the research area, hard sandstone and shale as well as slate underlay most of the research area. Of these types of lithology, areas underlain by slate had the highest number of landslides and the greatest landslide area. Wu et al. [49] indicated that the areas underlain by hard sandstone and shale as well as slate in the Kaoping River Watershed had the highest landslide ratios in 2008 and 2009. This indicates that the lithology condition of most areas is fragile. Typhoons and torrential rain events can readily wash away unconsolidated sand and gravel as well as trigger landslides, which deposit large loads of sediment Concerning the distribution of lithology, we followed the classification approach proposed by Lin et al. [48] by dividing the Taipei Water Source Domain into areas underlain by alluvium, loose sandstone and shale, hard sandstone and shale, and slate. Whereas alluvium found at the confluence of rivers and in downstream areas covers only a small part of the research area, hard sandstone and shale as well as slate underlay most of the research area. Of these types of lithology, areas underlain by slate had the highest number of landslides and the greatest landslide area. Wu et al. [49] indicated that the areas underlain by hard sandstone and shale as well as slate in the Kaoping River Watershed had the highest landslide ratios in 2008 and 2009. This indicates that the lithology condition of most areas is fragile. Typhoons and torrential rain events can readily wash away unconsolidated sand and gravel as well as trigger landslides, which deposit large loads of sediment in rivers and reservoirs.

#### in rivers and reservoirs. *2.2. Rainfall Data*

*2.2. Rainfall Data*  The rain gauges employed in this study were located as shown in Figure 1, and rainfall data between 1987 to 2016 from these rain gauges were used. Average daily rainfall for the entire area during the same period as the 2000–2015 landslide inventory is shown in Figure 2. Figure 2 shows that apart from the eight typhoon events causing the corresponding landslide inventory, other events of high daily rainfall occurred without a significant increase in landslides. As a consequence, apart from calculating the exceedance probability that rainfall events will exceed the rainfall threshold, we also calculated the probability of landslides when rainfall events exceed the threshold. In addition, Figure 3 shows the average daily rainfall and standard deviation of the eight typhoon events during the 2000–2015 period in each control area of a rain gauge divided by a modified The rain gauges employed in this study were located as shown in Figure 1, and rainfall data between 1987 to 2016 from these rain gauges were used. Average daily rainfall for the entire area during the same period as the 2000–2015 landslide inventory is shown in Figure 2. Figure 2 shows that apart from the eight typhoon events causing the corresponding landslide inventory, other events of high daily rainfall occurred without a significant increase in landslides. As a consequence, apart from calculating the exceedance probability that rainfall events will exceed the rainfall threshold, we also calculated the probability of landslides when rainfall events exceed the threshold. In addition, Figure 3 shows the average daily rainfall and standard deviation of the eight typhoon events during the 2000–2015 period in each control area of a rain gauge divided by a modified Thiessen polygon method, considering the morphology of the area, proposed by Salvaticic et al. [19].

#### Thiessen polygon method, considering the morphology of the area, proposed by Salvaticic et al. *2.3. Landslide Inventory*

[19]. After selecting eight major typhoon events occurring in the research area during the 2000–2015 period—typhoons Xangsane (2000), Nari (2001), Aere (2004), Sinlaku (2008), Morakot (2009), Parma (2009), Megi (2010), and Soudelor (2015)—we collected satellite images before and after each typhoon event, calculated and classified the normalized difference vegetation index (NDVI) to find the possible locations of landslide sites, and eliminated and revised unlikely landslide sites according to the slope, drainage, and land use maps in the study area. In the process of mapping the source areas of landslides

from the satellite images, we often found that human mapping errors affected interpretation quality. We followed the recommended procedures proposed by Liu et al. [50] to map landslides in the research area. Table 1 shows the dates of the eight landslide events and landslide statistical data. The size of landslides ranged from 16 to 118,108 m<sup>2</sup> and the average area was 2474 m<sup>2</sup> . The resulting distribution of landslides caused by the eight typhoon events was shown in Figure 4, which revealed that landslide *Water* sites were concentrated in the southwestern portion of the research area. **2020**, *12*, x FOR PEER REVIEW 5 of 17 *Water* **2020**, *12*, x FOR PEER REVIEW 5 of 17

**Figure 2.** Average daily rainfall within the Taipei Water Source Domain, 2000–2015. The dots represent the eight typhoon events causing the corresponding landslide inventory. **Figure 2.** Average daily rainfall within the Taipei Water Source Domain, 2000–2015. The dots represent the eight typhoon events causing the corresponding landslide inventory. **Figure 2.** Average daily rainfall within the Taipei Water Source Domain, 2000–2015. The dots represent the eight typhoon events causing the corresponding landslide inventory.

**Figure 3.** Average daily rainfall and standard deviation of the eight typhoon events in each control **Figure 3.** Average daily rainfall and standard deviation of the eight typhoon events in each control area of the rain gauge divided by the modified Thiessen polygon method. **Figure 3.** Average daily rainfall and standard deviation of the eight typhoon events in each control area of the rain gauge divided by the modified Thiessen polygon method.

area of the rain gauge divided by the modified Thiessen polygon method.

*2.3. Landslide Inventory* 

*2.3. Landslide Inventory* 

(2009), Megi (2010), and Soudelor (2015)—we collected satellite images before and after each typhoon event, calculated and classified the normalized difference vegetation index (NDVI) to find the possible locations of landslide sites, and eliminated and revised unlikely landslide sites according to the slope, drainage, and land use maps in the study area. In the process of mapping the source areas of landslides from the satellite images, we often found that human mapping errors

typhoon event, calculated and classified the normalized difference vegetation index (NDVI) to find the possible locations of landslide sites, and eliminated and revised unlikely landslide sites according to the slope, drainage, and land use maps in the study area. In the process of mapping the source areas of landslides from the satellite images, we often found that human mapping errors

#### *Water***2020**, *12*, 937


**Table 1.**Landslide inventory for the eight typhoon events.

was 2474 m<sup>2</sup>

research area.

**Typhoon Event** 

**Date (MM/DD/YYYY)** 

*2.4. Analytical Units and Rain Gauge Control Areas* 

*Water* **2020**, *12*, x FOR PEER REVIEW 6 of 17

affected interpretation quality. We followed the recommended procedures proposed by Liu et al. [50] to map landslides in the research area. Table 1 shows the dates of the eight landslide events and

in Figure 4, which revealed that landslide sites were concentrated in the southwestern portion of the

**Table 1.** Landslide inventory for the eight typhoon events.

**Number of New Landslide Sites** 

Xangsane 11/01/2000 326.67 42 326 19,619 131,148 3123 Nari 09/16/2001 538.05 92 107 68,032 261,650 2844 Aere 08/24/2004 465.57 97 140 27,270 239,856 2473 Sinlaku 09/13/2008 348.18 32 475 21,101 71,111 2222 Morakot 08/07/2009 219.83 173 16 118,108 1,016,448 5875 Parma 10/05/2009 221.79 302 47 49,369 484,785 1605 Megi 10/21/2010 262.35 47 407 27,318 118,874 2529 Soudelor 08/08/2015 478.99 589 257 48,041 1,075,263 1826

We employed slope units as analytical units due to their relatively well-defined topographic boundaries, as well as topographic and geological meaning. We employed the subdivision method used by Xie et al. [51] to divide the watershed into slope units. The original topography could be divided into sub-watersheds, and the combination of sub-watershed units before and after reversal yielded the slope units. We ensured that the smallest area of slope units was larger than the average area of landslides [47], which minimized the chance that any specific landslide site would be a part of different slope units, and thereby confuse the analysis results. We also divided the research area into rain gauge control areas (Figure 3) based on rain gauge locations and using the modified Thiessen polygon method. The rainfall measured by each rain gauge was taken as representative of

. The resulting distribution of landslides caused by the eight typhoon events was shown

**Smallest Landslide Area (m<sup>2</sup> )** 

**Largest Landslide Area (m<sup>2</sup> )** 

**Total Area of Landslides (m<sup>2</sup> )** 

and the average area

**Average Area of Landslides (m<sup>2</sup> )** 

landslide statistical data. The size of landslides ranged from 16 to 118,108 m<sup>2</sup>

**Average Rainfall at the Date (mm)** 

different rainfall distribution characteristics within the research area.

**Figure 4.** Distribution of slope units and landslide sites caused by the eight typhoon events in the Taipei Water Source Domain. **Figure 4.** Distribution of slope units and landslide sites caused by the eight typhoon events in the Taipei Water Source Domain.

#### *2.4. Analytical Units and Rain Gauge Control Areas*

We employed slope units as analytical units due to their relatively well-defined topographic boundaries, as well as topographic and geological meaning. We employed the subdivision method used by Xie et al. [51] to divide the watershed into slope units. The original topography could be divided into sub-watersheds, and the combination of sub-watershed units before and after reversal yielded the slope units. We ensured that the smallest area of slope units was larger than the average area of landslides [47], which minimized the chance that any specific landslide site would be a part of different slope units, and thereby confuse the analysis results. We also divided the research area into rain gauge control areas (Figure 3) based on rain gauge locations and using the modified Thiessen polygon method. The rainfall measured by each rain gauge was taken as representative of the control area in which that gauge was located, and we expected this approach to reflect the different rainfall distribution characteristics within the research area.

#### **3. Methods**

#### *3.1. Analysis of Discrete Rainfall Groups*

The two rainfall parameters considered in this study consisted of daily rainfall (*I*) and effective accumulated rainfall (*Rt*). After selecting rain gauges near the research area with rainfall data for recent years, we obtained daily rainfall data for the 1987–2016 period from the Water Resources Agency and Central Weather Bureau. This study calculated the effective accumulated rainfall based on rainfall for that day and rainfall during the previous 7 days using the method proposed by Jan [52]; this calculation was performed using Equation (1):

$$\mathbf{R}\_{l} = \mathbf{R}\_{0} + \sum\_{i=1}^{7} \alpha^{i} \mathbf{R}\_{i} = \sum\_{i=0}^{7} \alpha^{i} \mathbf{R}\_{i} \tag{1}$$

where *R*<sup>0</sup> is the rainfall amount on that day, *R*<sup>1</sup> is the rainfall amount on the day before that day, and so on, and the weighting coefficient α = 0.7 proposed by Jan [52].

Adopting the concept proposed by Tsai [53], after using daily rainfall data to calculate effective accumulated rainfall (*Rt*), we obtained a group of daily rainfall and effective accumulated rainfall (*I*, *Rt*) for each day. The daily rainfall and effective accumulated rainfall were continuous variables and

would not facilitate subsequent calculation of a joint cumulative distribution function, therefore we rounded off the daily rainfall and effective accumulated rainfall values to the 10th place and made them discrete variables. The group of daily rainfall and effective accumulated rainfall (*I*, *Rt*) for each day was termed as "discrete rainfall group" in this study.

We defined different rainfall events by the continuity of daily rainfall. Consecutive days of non-zero daily rainfall were considered to be the same rainfall event, and the number of the consecutive days varied from event to event. We then calculated the distance (*d*) from each discrete rainfall group to the origin (0, 0), and assumed that the greater the value of *d*, the greater the likelihood of landslides. The discrete rainfall group with the greatest *d* in each rainfall event was used to represent that rainfall event in subsequent analysis.

#### *3.2. Joint Cumulative Distribution Function*

The joint cumulative distribution function was obtained from the joint probability mass function of the foregoing discrete rainfall groups. The probability (*P<sup>I</sup>* ,*Rt* (*I<sup>i</sup>* , *Rtj*)) of each discrete rainfall group (*Ii* , *Rtj*) was defined [54] as shown in Equation (2):

$$P\_{I\_\nu R\_l} \left( I\_{l\nu} \ R\_{tj} \right) = P \left( I = I\_i \cap R\_l = R\_{tj} \right) \tag{2}$$

where *i* = 0, 10, 20, 30, . . . ; *j* = 0, 10, 20, 30, . . . ; the joint probability mass function has a probability value only when *I* and *R<sup>t</sup>* are multiples of 10 and the probability values in other places are 0.

The foregoing joint probability mass function yielded a joint cumulative distribution function using:

$$F\_{I\_{\prime},R\_{\ell}}(I\_{i\prime},R\_{tj}) = \sum\_{0}^{i} \sum\_{0}^{j} P\_{I\_{\prime},R\_{\ell}}\left(I\_{i\prime},R\_{tj}\right). \tag{3}$$

The joint cumulative distribution function was a monotonic increasing function with a range between 0 and 1, and had the form of a three-dimensional curved surface when plotted on coordinate axes. The farther the point (*I<sup>i</sup>* , *Rtj*) from the origin, the greater its probability value. The probability of a discrete rainfall group on the curved surface expressed the cumulative probability of all discrete rainfall groups, which were nearer to the origin than this discrete rainfall group (*I<sup>i</sup>* , *Rtj*).

#### *3.3. Selection of a Rainfall Probability Threshold*

After establishing a joint cumulative distribution function, taking each 0.05 as an interval, we set 20 rainfall probability thresholds ranging from 0.05 to 1.00, and employed the error matrix concept to calculate the true positive rate (TPR), true negative rate (TNR), and positive predictive value (PPV) for each rainfall probability threshold at each rain gauge control area. The rainfall probability threshold was treated as the threshold of cumulative probability of the discrete rainfall groups which was used to predict whether rainfall events could trigger landslides. Here, TPR expresses the ratio of discrete rainfall groups that correctly predicted landslide occurrence to discrete rainfall groups triggering landslides actually, TNR expresses the ratio of discrete rainfall groups that correctly predicted no landslide occurrence to discrete rainfall groups triggering no landslides actually, and PPV expresses the ratio of discrete rainfall groups that correctly predicted landslide occurrence to discrete rainfall groups predicting landslides. To capture the performance of each threshold, PPV and Youden's index were used for comprehensive consideration. The higher the PPV and Youden's index values, the more accurate the rainfall probability threshold at classifying landslide occurrence and landslide occurrence for discrete rainfall groups. The TPR, TNR, PPV, and Youden's index calculations were performed employing Equations (4)–(7).

$$\text{TPR (\%)} = \frac{\text{Number of discrete rainfall groups predicting landslides when landslides actually occurred}}{\text{Number of all discrete rainfall groups largely landslides actually}} \qquad (4)$$


$$\text{PPV} \left( \% \right) = \frac{\text{Number of discrete rainfall groups predicting lands} \text{lides when lands} \text{lides actually occurred}}{\text{Number of all discrete rainfall groups predicting lands}} \quad (6)$$

$$\text{Youden's index} = \text{TPR} + \text{TNR} - 1\tag{7}$$

#### *3.4. Poisson Probability Model*

A Poisson probability model relies on the past frequency of events to predict their occurrence probability in the future. The basic assumption underlying this type of model is that future events will occur with the same frequency as past events. In this model, the probability of at least one event occurring in the time interval (*t*) is given by Equation (8):

$$P(N(t)\geq 1) = 1 - e^{-\lambda t} \tag{8}$$

where *P*(*N*(*t*) ≥ 1) indicates the probability of at least one event occurring within a period of *t* years; this probability is known as the exceedance probability.

We calculated the number of discrete rainfall groups exceeding the threshold at each rain gauge in the past using the optimal rainfall probability thresholds and then divided by the years of the rainfall data to obtain the occurrence frequency (λ), which was used to calculate the exceedance probability. The exceedance probability indicated the probability of at least one rainfall event exceeding the threshold of discrete rainfall groups within any one year.

#### *3.5. Conditional Probability*

We employed the concept of conditional probability in the analysis. We first used the Poisson probability model to calculate the exceedance probability of at least one rainfall event exceeding the threshold of discrete rainfall groups within any one year at each rain gauge control area. We divided the number of landslides occurring in each slope unit by the number of rainfall events exceeding the threshold of discrete rainfall groups to estimate the probability that a landslide would occur in that slope unit when the rainfall exceeded the threshold. Lastly, we multiplied the two probabilities together to obtain the probability that a rainfall event would exceed the threshold of discrete rainfall groups and at least one landslide would also occur in each slope unit within any one year, as shown in Equation (9):

$$P(R \ge RT \cap L) = P\left(R \ge RT\right) \times P(L|R \ge RT) \tag{9}$$

where *R* ≥ *RT* indicates rainfall events exceed the threshold of the discrete rainfall group and *L* indicates the occurrence of a landslide.

#### **4. Results and Discussion**

#### *4.1. Joint Cumulative Distribution Functions of the Rain Gauges*

In this study, we collected multi-year daily rainfall data from each rain gauge and calculated the effective accumulated rainfall (*Rt*) by employing Equation (1), which yielded rainfall and effective accumulated rainfall for each day. We then rounded off the daily rainfall and effective accumulated rainfall values to the 10th place, which yielded discrete rainfall groups including both daily rainfall and effective accumulated rainfall. The next step was establishing frequency tables for different discrete rainfall groups, which we used to show the frequency of the discrete rainfall groups. Figure 5 shows the frequency of discrete rainfall groups at the Bihu rain gauge with daily rainfall and effective accumulated rainfall (*Rt*) ranging from 0 to 100 mm. The depth axis represents daily rainfall, the horizontal axis represents the effective accumulated rainfall (*Rt*), and the vertical axis represents the frequency of a discrete rainfall group. We then calculated the cumulative frequency of each discrete rainfall group on this basis, and this represented the frequency of all discrete rainfall groups with **4. Results and Discussion** 

**4. Results and Discussion** 

*4.1. Joint Cumulative Distribution Functions of the Rain Gauges* 

*4.1. Joint Cumulative Distribution Functions of the Rain Gauges* 

values lower than that of any designated discrete rainfall group. The cumulative frequency was then divided by the total frequency of all discrete rainfall groups, which yielded the cumulative probability of each discrete rainfall group. each discrete rainfall group on this basis, and this represented the frequency of all discrete rainfall groups with values lower than that of any designated discrete rainfall group. The cumulative frequency was then divided by the total frequency of all discrete rainfall groups, which yielded the cumulative probability of each discrete rainfall group. groups with values lower than that of any designated discrete rainfall group. The cumulative frequency was then divided by the total frequency of all discrete rainfall groups, which yielded the cumulative probability of each discrete rainfall group.

represents the frequency of a discrete rainfall group. We then calculated the cumulative frequency of each discrete rainfall group on this basis, and this represented the frequency of all discrete rainfall

represents the frequency of a discrete rainfall group. We then calculated the cumulative frequency of

*Water* **2020**, *12*, x FOR PEER REVIEW 9 of 17

*Water* **2020**, *12*, x FOR PEER REVIEW 9 of 17

In this study, we collected multi-year daily rainfall data from each rain gauge and calculated the effective accumulated rainfall (*Rt*) by employing Equation (1), which yielded rainfall and effective accumulated rainfall for each day. We then rounded off the daily rainfall and effective accumulated rainfall values to the 10th place, which yielded discrete rainfall groups including both daily rainfall and effective accumulated rainfall. The next step was establishing frequency tables for different discrete rainfall groups, which we used to show the frequency of the discrete rainfall groups. Figure 5 shows the frequency of discrete rainfall groups at the Bihu rain gauge with daily rainfall and effective accumulated rainfall (*Rt*) ranging from 0 to 100 mm. The depth axis represents daily

In this study, we collected multi-year daily rainfall data from each rain gauge and calculated the effective accumulated rainfall (*Rt*) by employing Equation (1), which yielded rainfall and effective accumulated rainfall for each day. We then rounded off the daily rainfall and effective accumulated rainfall values to the 10th place, which yielded discrete rainfall groups including both daily rainfall and effective accumulated rainfall. The next step was establishing frequency tables for different discrete rainfall groups, which we used to show the frequency of the discrete rainfall groups. Figure 5 shows the frequency of discrete rainfall groups at the Bihu rain gauge with daily rainfall and effective accumulated rainfall (*Rt*) ranging from 0 to 100 mm. The depth axis represents daily

**Figure 5.** Frequency distribution of discrete rainfall groups at the Bihu rain gauge. **Figure 5.** Frequency distribution of discrete rainfall groups at the Bihu rain gauge. **Figure 5.** Frequency distribution of discrete rainfall groups at the Bihu rain gauge.

The joint cumulative distribution function of each rain gauge was then obtained from the cumulative probability of the discrete rainfall groups, and this function was used to plot a joint cumulative distribution chart. Figures 6 and 7 are joint cumulative distribution functions for the Bihu and Fushan (3) rain gauges, and daily rainfall and effective accumulated rainfall (*Rt*) are shown within a 0–300 mm range. The joint cumulative distribution functions have areas with gentler slopes indicating fewer and more dispersed discrete rainfall groups within a certain interval, and areas with steeper slopes indicating more and more concentrated discrete rainfall groups within a certain interval. The joint cumulative distribution function of each rain gauge was then obtained from the cumulative probability of the discrete rainfall groups, and this function was used to plot a joint cumulative distribution chart. Figures 6 and 7 are joint cumulative distribution functions for the Bihu and Fushan (3) rain gauges, and daily rainfall and effective accumulated rainfall (*Rt*) are shown within a 0–300 mm range. The joint cumulative distribution functions have areas with gentler slopes indicating fewer and more dispersed discrete rainfall groups within a certain interval, and areas with steeper slopes indicating more and more concentrated discrete rainfall groups within a certain interval. The joint cumulative distribution function of each rain gauge was then obtained from the cumulative probability of the discrete rainfall groups, and this function was used to plot a joint cumulative distribution chart. Figures 6 and 7 are joint cumulative distribution functions for the Bihu and Fushan (3) rain gauges, and daily rainfall and effective accumulated rainfall (*Rt*) are shown within a 0–300 mm range. The joint cumulative distribution functions have areas with gentler slopes indicating fewer and more dispersed discrete rainfall groups within a certain interval, and areas with steeper slopes indicating more and more concentrated discrete rainfall groups within a certain interval.

**Figure 6.** The joint cumulative distribution function for the Bihu rain gauge. *Water* **2020**, *12*, x FOR PEER REVIEW **Figure 6. Figure 6.** The joint cumulative distribution function for the Bihu rain gauge. The joint cumulative distribution function for the Bihu rain gauge. 10 of 17

**Figure 7.** The joint cumulative distribution function for the Fushan (3) rain gauge. **Figure 7.** The joint cumulative distribution function for the Fushan (3) rain gauge.

all rain gauges when the rainfall probability threshold was 0.95 are shown in Table 3.

Following the analysis results of the joint cumulative distribution functions of the rain gauges, we used rainfall data from the rain gauges during the eight rainfall events triggering landslides to select rainfall probability thresholds. The rainfall probability threshold was treated as the threshold of cumulative probability of the discrete rainfall groups which was used to predict whether rainfall events could trigger landslides. Starting with a rainfall probability threshold value of 0.05, we set a rainfall probability threshold at each interval of 0.05 until a value of 1.00 was reached, and then calculated the TPR, TNR, PPV, and Youden's index of each rainfall probability threshold. Here, the number of landslide events predicted correctly divided by the number of rainfall events triggering landslides actually equaled TPR, the number of no landslide events predicted correctly divided by the number of rainfall events triggering no landslides actually equaled TNR, and the number of landslide events predicted correctly divided by the number of rainfall events predicting landslides equaled PPV. Table 2 shows the results of these calculations for the Bihu rain gauge. In the analysis results for the individual rain gauges, the rainfall probability thresholds with the highest Youden's index were within the probability interval of 0.85–0.95, and the rainfall probability thresholds with the highest PPV were at the probability of 0.95 in all cases. We consequently opted to use a rainfall probability threshold value of 0.95 for the whole area. The TPR, TNR, PPV, and Youden's index for

#### *4.2. Selection of Rainfall Probability Thresholds of the Rain Gauges*

Following the analysis results of the joint cumulative distribution functions of the rain gauges, we used rainfall data from the rain gauges during the eight rainfall events triggering landslides to select rainfall probability thresholds. The rainfall probability threshold was treated as the threshold of cumulative probability of the discrete rainfall groups which was used to predict whether rainfall events could trigger landslides. Starting with a rainfall probability threshold value of 0.05, we set a rainfall probability threshold at each interval of 0.05 until a value of 1.00 was reached, and then calculated the TPR, TNR, PPV, and Youden's index of each rainfall probability threshold. Here, the number of landslide events predicted correctly divided by the number of rainfall events triggering landslides actually equaled TPR, the number of no landslide events predicted correctly divided by the number of rainfall events triggering no landslides actually equaled TNR, and the number of landslide events predicted correctly divided by the number of rainfall events predicting landslides equaled PPV. Table 2 shows the results of these calculations for the Bihu rain gauge. In the analysis results for the individual rain gauges, the rainfall probability thresholds with the highest Youden's index were within the probability interval of 0.85–0.95, and the rainfall probability thresholds with the highest PPV were at the probability of 0.95 in all cases. We consequently opted to use a rainfall probability threshold value of 0.95 for the whole area. The TPR, TNR, PPV, and Youden's index for all rain gauges when the rainfall probability threshold was 0.95 are shown in Table 3.





#### *4.3. Landslide Probability Analysis Employing a Rainfall Probability Threshold and a Long-Term Landslide Inventory*

After determining a rainfall probability threshold for the rain gauges, we calculated the number of discrete rainfall groups exceeding this threshold at each rain gauge during the 1987–2016 period. We then divided these values by the years of statistics at each gauge, which yielded the λ values in Equation (8). Substituting *t* = 1 year into Equation (8) allowed us to calculate the probability of at least one rainfall event exceeding the threshold of discrete rainfall group within any one year (i.e., *P*(*R*

≥ *RT*) in Equation (9)) under the assumption that future rainfall conditions will be the same as past conditions. Figure 8 shows the exceedance probability value calculated for each rain gauge overlaid on each rain gauge control area. The Quchi rain gauge control area had the highest probability of 0.76502 that at least one rainfall event will exceed the threshold of the discrete rainfall group within any one year, whereas the Bihu rain gauge control area had the lowest probability of 0.43886. *Water* **2020**, *12*, x FOR PEER REVIEW 12 of 17 overlaid on each rain gauge control area. The Quchi rain gauge control area had the highest probability of 0.76502 that at least one rainfall event will exceed the threshold of the discrete rainfall group within any one year, whereas the Bihu rain gauge control area had the lowest probability of 0.43886.

**Figure 8.** The exceedance probability that at least one rainfall event will exceed the threshold of discrete rainfall group within any one year in each rain gauge control area. **Figure 8.** The exceedance probability that at least one rainfall event will exceed the threshold of discrete rainfall group within any one year in each rain gauge control area.

In this study, we also divided the number of landslides occurring in each slope unit during the 2000–2015 period by the number of rainfall events exceeding the threshold of discrete rainfall group at the rain gauges to which the slope units were assigned during the same period to estimate the landslide probability in the slope units when the rainfall exceeded the threshold, which is *P(L*│*R* ≥ *RT)* in Equation (9). The resulting probability distribution is shown in Figure 9. Figure 9 shows that the different slope units within a single rain gauge control area have different landslide probabilities, and these differences should be attributed to different geomorphological conditions in In this study, we also divided the number of landslides occurring in each slope unit during the 2000–2015 period by the number of rainfall events exceeding the threshold of discrete rainfall group at the rain gauges to which the slope units were assigned during the same period to estimate the landslide probability in the slope units when the rainfall exceeded the threshold, which is *P(L*|*R* ≥ *RT)* in Equation (9). The resulting probability distribution is shown in Figure 9. Figure 9 shows that the different slope units within a single rain gauge control area have different landslide probabilities, and these differences should be attributed to different geomorphological conditions in the slope units.

the slope units. Lastly, employing Equation (9), we multiplied the probability *P*(*R* ≥ *RT*) that at least one rainfall event will exceed the threshold of discrete rainfall group within any one year in each rain gauge control area by the landslide probability *P*(*L*│*R* ≥ *RT*) in each slope unit when rainfall exceeds the threshold, which yielded the probability that at least one rainfall event exceeds the threshold of discrete rainfall group at the same time that one landslide will occur in each slope unit during the future one-year period (Figure 10). The two probability maps shown in Figures 9 and 10 were validated by the landslide inventory data respectively. The landslides were mainly distributed in the slope units where the landslide probability values were greater than 0.01. The top 2% of slope units ranked with landslide probabilities included 50.40% of slope units where landslides occurred while the top 6% of slope units ranked with landslide probabilities included 100.00% of slope units where landslides occurred in Figure 10. The results indicated these maps had reasonable landslide probability distributions. Figure 10 reveals that the Fushan (3) rain gauge control area, which is located in the southwest part of the research area, contained relatively many slope units with high landslide probability, and the highest probability value was 0.26. Apart from having fragile lithology consisting of hard sandstone and shale as well as slate, this area has a higher elevation and steeper Lastly, employing Equation (9), we multiplied the probability *P*(*R* ≥ *RT*) that at least one rainfall event will exceed the threshold of discrete rainfall group within any one year in each rain gauge control area by the landslide probability *P*(*L*|*R* ≥ *RT*) in each slope unit when rainfall exceeds the threshold, which yielded the probability that at least one rainfall event exceeds the threshold of discrete rainfall group at the same time that one landslide will occur in each slope unit during the future one-year period (Figure 10). The two probability maps shown in Figures 9 and 10 were validated by the landslide inventory data respectively. The landslides were mainly distributed in the slope units where the landslide probability values were greater than 0.01. The top 2% of slope units ranked with landslide probabilities included 50.40% of slope units where landslides occurred while the top 6% of slope units ranked with landslide probabilities included 100.00% of slope units where landslides occurred in Figure 10. The results indicated these maps had reasonable landslide probability distributions. Figure 10 reveals that the Fushan (3) rain gauge control area, which is located in the southwest part of the research area, contained relatively many slope units with high landslide probability, and the highest probability value was 0.26. Apart from having fragile lithology consisting of hard sandstone and shale as well as slate, this area has a higher elevation and steeper slopes than other control areas, which suggests that elevation and slope have a definite correlation with landslide occurrence.

slopes than other control areas, which suggests that elevation and slope have a definite correlation

with landslide occurrence.

*Water* **2020**, *12*, x FOR PEER REVIEW 13 of 17

**Figure 9.** The landslide probability of slope units in the Taipei Water Source Domain when rainfall exceeds the threshold of discrete rainfall group. **Figure 9.** The landslide probability of slope units in the Taipei Water Source Domain when rainfall exceeds the threshold of discrete rainfall group. **Figure 9.** The landslide probability of slope units in the Taipei Water Source Domain when rainfall exceeds the threshold of discrete rainfall group.

**Figure 10.** The probability that at least one rainfall event exceeds the threshold of discrete rainfall group and one landslide will also occur during the future one-year period within the Taipei Water Source Domain. **Figure 10.** The probability that at least one rainfall event exceeds the threshold of discrete rainfall group and one landslide will also occur during the future one-year period within the Taipei Water Source Domain. **Figure 10.** The probability that at least one rainfall event exceeds the threshold of discrete rainfall group and one landslide will also occur during the future one-year period within the Taipei Water Source Domain.

#### *4.4. Discussion 4.4. Discussion*

*4.4. Discussion*  In comparison with a landslide probability model based solely on the use of landslide inventories, our landslide probability model based on the use of landslide inventories and rainfall factors reflect different basic assumed conditions. The assumption of the landslide probability model incorporating rainfall factors is that the frequency of future rainfall events exceeding the In comparison with a landslide probability model based solely on the use of landslide inventories, our landslide probability model based on the use of landslide inventories and rainfall factors reflect different basic assumed conditions. The assumption of the landslide probability model incorporating rainfall factors is that the frequency of future rainfall events exceeding the threshold and the frequency of landslides occurring when the threshold has been exceeded are the In comparison with a landslide probability model based solely on the use of landslide inventories, our landslide probability model based on the use of landslide inventories and rainfall factors reflect different basic assumed conditions. The assumption of the landslide probability model incorporating rainfall factors is that the frequency of future rainfall events exceeding the threshold and the frequency of landslides occurring when the threshold has been exceeded are the same as in the past. In contrast,

threshold and the frequency of landslides occurring when the threshold has been exceeded are the

the assumption of a landslide probability model based solely on the use of landslide inventories is that the frequency of future landslides occurring is the same as in the past. As a consequence, landslide probability models incorporating rainfall factors possess the following advantages: (1) This model can reflect the differences in landslide probability between the rain gauge control areas that have different rainfall conditions. (2) When rainfall data were added in the analysis, the probability model we obtained yielded more reliable results because the rainfall data were collected from a longer period (29–45 years) than the landslide inventory (16 years). (3) If we know how the probability of at least one rainfall event exceeding the threshold will change in the future, the incorporation of rainfall factors in the landslide probability model will allow the effect of possible rainfall changes on the landslide probability to be assessed.

However, several aspects connected to the application of this landslide probability model still require further investigation: (1) The method of analyzing landslide probability proposed in this study requires a long-term landslide inventory and rainfall data, therefore attention must be paid to the completeness of rainfall data for the research area and handling methods when data are incomplete. (2) Whereas the rainfall factors used in this study reflect daily rainfall and effective accumulated rainfall, the use of different rainfall factors will yield different analysis results, which may be explored further in future research. (3) Apart from the modified Thiessen polygon method, the division of rain gauge control areas can be performed using other methods, such as the height–balance polygon method. A finer division method should yield more precise results of a landslide probability distribution, therefore future research can also compare the applicability of different methods of division into rain gauge control areas. (4) We obtained a long-term landslide inventory consisting of only eight events, therefore all events collected were used in the process of building the model. The landslide inventory covering the period of other events may be collected to verify the predictive ability of this landslide probability model.

#### **5. Conclusions**

In this study, we employed joint cumulative distribution functions to calculate the TPR, TNR, PPV, and Youden's index for different rainfall probability thresholds, selected a threshold of 0.95 as suitable for the research area, and used this rainfall probability threshold to calculate the Poisson probability of at least one rainfall event exceeding the threshold of discrete rainfall groups at each rain gauge within the future one-year period. We then combined this probability with the landslide probability in individual slope units when rainfall exceeded the threshold value, which allowed us to estimate the probability that a landslide will occur in individual slope units during the future one-year period. Many of the slope units with a high landslide probability are located in the Fushan (3) rain gauge control area, and the highest probability is 0.26. Apart from fragile lithology, this area is characterized by high elevations and steep slopes, which indicates that the elevation and slope have a significant influence on the occurrence of landslides. This finding suggests that this area should be a focal area for landslide prevention and mitigation efforts.

The landslide probability model established based on the use of a long-term landslide inventory and rainfall factor had a finer spatial resolution and data for a longer period, which yielded more reliable results and enabled the effect of possible rainfall changes on the landslide probability to be assessed. The effects of the completeness of rainfall data for the research area, the use of different rainfall factors, as well as the different methods of division into rain gauge control areas on the landslide probability analysis results can be significant and still require further investigation.

**Funding:** This research was funded by the Ministry of Science and Technology, Taiwan (MOST 107-2311-B-005-001).

**Conflicts of Interest:** The authors declare no conflict of interest.

**Author Contributions:** Conceptualization, C.-Y.W.; data curation, Y.-C.Y.; formal analysis, Y.-C.Y.; methodology, C.-Y.W. and Y.-C.Y.; supervision, C.-Y.W.; visualization, Y.-C.Y.; writing—original draft, C.-Y.W. and Y.-C.Y.; writing—review & editing, C.-Y.W.; funding acquisition, C.-Y.W. All authors have read and agreed to the published version of the manuscript.

### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **A New Method for Wet-Dry Front Treatment in Outburst Flood Simulation**

**Dingzhu Liu 1,2,3, Jinbo Tang 1,2 , Hao Wang 4, \*, Yang Cao 5 , Nazir Ahmed Bazai 1,2,3 , Huayong Chen 1,2 and Daochuan Liu 6**


**Abstract:** When utilizing a finite volume method to predict outburst flood evolution in real geometry, the processing of wet-dry front and dry cells is an important step. In this paper, we propose a new approach to process wet-dry front and dry cells, including four steps: (1) estimating intercell properties; (2) modifying interface elevation; (3) calculating dry cell elevations by averaging intercell elevations; and (4) changing the value of the first term of slope limiter based on geometry in dry cells. The Harten, Lax, and van Leer with the contact wave restored (HLLC) scheme was implemented to calculate the flux. By combining the MUSCL (Monotone Upstream–centred Scheme for Conservation Laws)-Hancock method with the minmod slope limiter, we achieved second-order accuracy in space and time. This approach is able to keep the conservation property (C-property) and the mass conservation of complex bed geometry. The results of numerical tests in this study are consistent with experimental data, which verifies the effectiveness of the new approach. This method could be applied to acquire wetting and drying processes during flood evolution on structured meshes. Furthermore, a new settlement introduces few modification steps, so it could be easily applied to matrix calculations. The new method proposed in this study can facilitate the simulation of flood routing in real terrain.

**Keywords:** shallow water equations; wet-dry front; outburst flood; TVD-scheme; MUSCL-Hancock method

#### **1. Introduction**

Glacier avalanche [1,2], debris flow [3–5], and landslide [6–8] in mountain areas could trigger the occurrence of river blocking [9–12]. Some of this blocking produces large-scale lakes, which leads to back flooding upstream and may inundate roads and villages. Most dammed lakes breach in a short time after their formation, causing massive water to be released catastrophically [9,13]. Yigong Lake was blocked by catastrophic landslides in 1902 and 2000 [14] and formed outburst floods with peak discharges of around 18.9 × 10 <sup>4</sup> <sup>m</sup>3/s [15] and 12.4 <sup>×</sup> <sup>10</sup> <sup>4</sup> m3/s [8], respectively; the Yarlung Tsangpo gorge was blocked twice in 2018, with a peak discharge of 3.2 × 10 <sup>4</sup> m3/s in the second outburst flood [3,4].

**Citation:** Liu, D.; Tang, J.; Wang, H.; Cao, Y.; Bazai, N.A.; Chen, H.; Liu, D. A New Method for Wet-Dry Front Treatment in Outburst Flood Simulation. *Water* **2021**, *13*, 221. https://doi.org/10.3390/w13020221

Received: 9 November 2020 Accepted: 14 January 2021 Published: 18 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

This kind of dynamic process can impose catastrophic damage to downstream people and infrastructure [16]. Outburst floods may also have significant geomorphic and geologic impacts; they have substantial erosive and transport capacity that can rapidly transform river channels and bedforms [17–19], and may even lead to climate change [20] and a global sea level decrease [21]. Outburst floods and their impacts even appear in the myths and stories of many civilizations, such as the Bible and the Koran [22].

Back analysis of outburst flood is an impressive method to determine risk, which has been used to reconstruct large-scale geomorphological dynamic processes that occurred ten thousand years ago. In general, the submerge area and related velocity determine the risk of outburst floods, and a shallow water dynamic model is a widely used and reliable method to predict it [23–26].

Shallow water equations are popular in long-wave hydrodynamic simulation [27] and are an effective way to analyze outburst flood routing. The Godunov-type finite volume method is an effective and convenient method to calculate flood evolution in complex geometry and is widely used in structured cells and unstructured cells [27]. There are two popular forms for shallow water equations: (1) not consider gravity source term in advection terms [28] and (2) consider the geometry in advection terms [29,30].

A TVD (total variation diminishing) scheme is used to limit numerical oscillations near discontinuity [31–33]. Slope limiters such as the minmod limiter, double limiter, and van-Leer limiter are popularly used to keep the solving scheme that has a TVD property [33]. By using a slope limiter, a monotone upstream-centered scheme for conservation laws (MUSCL) reconstruction in the cell center provides second-order accuracy in space [34,35]. The MUSCL method is one of the most successful high-resolution schemes for hyperbolic conservation laws and is applied widely [24,29,33].

Wet-dry front treatment is a key problem when applying shallow water equations to real geometry. Sharp slope geometry especially can over-predict flux and generate negative flow depth [27,29]. Specific treatments during calculation have been applied to limit flux and the gravity source term or to modify geometry [27,29,36], thus or avoiding extremely high flux in intercells and velocity in the cell center. In the process of variable modifications, the limiter's value of the dry cell would equal zero after modifying the local geometry [27,29,36,37].

Many traditional treatments to the wet-dry front change the elevation of the dry cell equal to the wet cell's free surface elevation as shown in Figure 1a [27,29]. If the dry cell is surrounded by four wet cells with different free surface elevations, four elevation modifications are necessary to achieve a balanced flux in the surrounded four cells (Figure 1b,c), and it is very hard to achieve a matrix calculation during simulation as well. A matrix calculation and less cell modification save time because matrix operators are faster than cell loops [38]. In order to apply shallow water equations to a river with a complex geometry and avoid more elevation modifications, we propose processing dry cells by adopting the first term of the slope limiter function in dry cells to solve the wet-dry front problem and accomplish matrix simulation in the whole calculation area. This method can avoid modifications in the dry cell's elevation and achieve a matrix calculation. This method was tested with many cases and is applicable to a complex geometry for outburst flood analysis.

**Figure 1.** The traditional elevation modification of wet-dry front. (**a**) Modify elevation to the same as wet cell; (**b**,**c**) Two times elevation modification of one dry cell.

#### **2. Governing Equations and Schemes**

#### *2.1. Governing Equations*

Two-dimensional shallow water equations are integral forms of Reynolds-averaged Navier–Stokes equations. This equation presumptively neglects vertical momentum exchange and sets the pressure distribution as hydrostatic [39]:

$$\mathcal{U}\_{,t} + F\_{,x} + G\_{,y} = S\_{,} \tag{1}$$

where *t* represents time direction, *x* and *y* are two Cartesian coordinates, *U* is a variable with vector form, *F* and *G* are fluxes vectors at two directions, and *S* is a vector represents source term. The equation is a conserved equation. For general use, the conserved equation is written as:

$$
\begin{bmatrix} \eta \\ hu \\ hv \end{bmatrix}\_{,t} + \begin{bmatrix} hu \\ hu^2 + g(\eta^2 - 2\eta Z)/2 \\ huv \end{bmatrix}\_{,x} + \begin{bmatrix} hu \\ huv \\ hv^2 + g(\eta^2 - 2\eta Z)/2 \end{bmatrix}\_{,y} = \begin{bmatrix} 0 \\ -\mathfrak{r}\_{bx}/\rho - g\eta Z\_{,x} \\ -\mathfrak{r}\_{by}/\rho - g\eta Z\_{,y} \end{bmatrix}, \tag{2}
$$

$$
\pi\_{\rm bx} = \rho g n^2 \mu \sqrt{u^2 + v^2} h^{-1/3} \,, \tag{3}
$$

$$
\pi\_{by} = \rho g n^2 v \sqrt{u^2 + v^2} h^{-1/3} \,\prime \tag{4}
$$

where *η* = *Z* + *h* is the elevation of the flood free surface, where the specific treatment to initial shallow water equations adds geometry information to the advections [29], *Z* is the elevation of the river bed, *h* is the flow depth, *u* is the flow velocity in the *x* direction, *v* is the flow velocity in the *y* direction, *τbx* and *τby* are the bottom shear stress in the *x* and *y* directions, *g* is gravity acceleration, and *n* is the Manning coefficient.

#### *2.2. Finite Volume Method*

The finite volume method has been used in many areas to solve partial equations [40]. The method is implemented by integrating partial equations over the space area for an arbitrary grid. In this study, shallow water equations are hyperbolic equations, which can be integrated as follows:

$$\frac{\partial}{\partial t} \int\_{\varepsilon} \mathcal{U} d\varOmega + \int\_{\varepsilon} (\frac{\partial F}{\partial x} + \frac{\partial G}{\partial y}) d\varOmega = \int\_{\varepsilon} \mathcal{S} d\varOmega. \tag{5}$$

By using Green's formula, Equation (6) can be described as:

$$\frac{\partial}{\partial t} \int\_{\varepsilon} \mathcal{U} d\varOmega + \int\_{L} (\mathcal{F} + \mathcal{G}) dL = \int\_{\varepsilon} \mathcal{S} d\varOmega,\tag{6}$$

where L is the mesh boundary of the integral line, and *ε* is the integral area, which is a rectangular grid here. By using the integral form equation at mesh (*i*, *j*), the second term becomes:

$$\int\_{L} \mathbf{F}\_{\mathrm{i}} \mathrm{d}L + \int\_{L} \mathbf{G}\_{\mathrm{j}} \mathrm{d}L = (\mathbf{F}\_{\mathrm{i}+1/2} - \mathbf{F}\_{\mathrm{i}-1/2}) \Delta y + (\mathbf{G}\_{\mathrm{j}+1/2} - \mathbf{G}\_{\mathrm{j}-1/2}) \Delta x,\tag{7}$$

$$\mathcal{U}\_{i,j}^{n+1} = \mathcal{U}\_{i,j}^{n} - \frac{\Delta t}{\Delta x} \left( \mathcal{F}\_{i+1/2,j} - \mathcal{F}\_{i-1/2,j} \right) - \frac{\Delta t}{\Delta y} \left( \mathcal{G}\_{i,j+1/2} - \mathcal{G}\_{i,j-1/2} \right) + \Delta t \mathcal{S}\_{i\nu} \tag{8}$$

where *n* is the time, and *i* + 1/2 and *j* + 1/2 are the predicted flux at the interface, predicted by two Riemann states.

#### *2.3. HLLC Riemann Solver for Fluxes Prediction*

In order to solve the Riemann problem approximately, Harten Lax and van Leer proposed the famous HLL Riemann solver in 1983, which is widely used by researchers to solve shallow water equations today. The scheme requires estimations for the fastest signal velocities from the discontinuity at the interface, resulting in a two-wave model including shock waves, rarefaction waves, and discontinuity. Toro modified the scheme to a three-wave model [33], and the solver was suited to calculate cases involving a wet-dry front, so the HLLC (Harten, Lax and van Leer) approximate Riemann solver by Toro is used in this paper.

#### *2.4. Slope Limiter*

The face value of variables required for the MUSCL-Hancock reconstruction step and for the time updating step is:

$$\mathcal{U}\_{i+1/2} = \mathcal{U}\_{i} + r\nabla\mathcal{U}\_{i\prime} \tag{9}$$

where r is the distance vector, and ∇*U<sup>i</sup>* is the gradient vector of variable in space. In order to avoid numerical oscillations, we adopt a single slope limiter in this study. The formula becomes:

$$\mathcal{U}\_{l+1/2} = \mathcal{U}\_{l} + \varphi(r)r\nabla\mathcal{U}\_{l\nu} \tag{10}$$

where *ϕ*(*r*) is a limiter function. We adopted the Minmod limiter in case tests. Special gradients of variables were predicted by:

$$r\_{i,j} = \begin{bmatrix} \frac{\eta\_{i+Fn,j+Gu-\eta\_{i,j}}}{\eta\_{i,j}-\eta\_{i-Fn,j-Gu}}\\ \frac{h\nu\_{i+Fn,j+Gu}-h\nu\_{i,j}}{h\nu\_{i,j}-h\nu\_{i-Fn,j-Gu}}\\ \frac{h\nu\_{i+Fn,j+Gu}-h\nu\_{i,j}}{h\nu\_{i,j}-h\nu\_{i-Fn,j-Gu}} \end{bmatrix}'\tag{11}$$

where *ri,j* is slope in mesh (*i*, *j*), which includes two directions' values. If intercell interpolation is in the *x* direction, *F<sup>n</sup>* = 1 and *G<sup>n</sup>* = 0; if intercell interpolation is in the *y* direction, *F<sup>n</sup>* = 0 and *G<sup>n</sup>* = 1.

#### *2.5. MUSCL-Hancock Method*

In the MUSCL-Hancock reconstruction step, the calculation is limited in a single cell. Thus, it does not use the HLLC Riemann solver to predict the flux at the intercell. The

corrected value in the cell center is *U n*+1/2 *i* , and the flux is calculated based on cell face reconstruction, which is predicted by the cell slope limiter:

$$
\mathcal{U}\mathcal{U}\mathcal{U}\_{i+1/2}^n = \mathcal{U}\_i^n + \frac{1}{2}\varphi(r) \left(\mathcal{U}\_i^n - \mathcal{U}\_{i-1}^n\right), \tag{12}
$$

where *UM<sup>n</sup> <sup>i</sup>*+1/2 is the reconstructed cell boundary vector. The predicted cell center value is calculated by:

$$\mathbf{U}\_{i}^{t+1/2} = \mathbf{U}\_{i}^{t} + k\_{x} \left( \mathbf{F} \left( \mathbf{U} \mathbf{M}\_{i+1/2}^{n} \right) - \mathbf{F}\_{i+1/2} \left( \mathbf{U} \mathbf{M}\_{i-1/2}^{n} \right) \right) + k\_{y} \left( \mathbf{G} \left( \mathbf{U} \mathbf{M}\_{j+1/2}^{n} \right) - \mathbf{G} \left( \mathbf{U} \mathbf{M}\_{j-1/2}^{n} \right) \right) + \frac{\Delta t}{2} \mathbf{S}\_{i} \tag{13}$$
 
$$k\_{x} = \frac{\Delta t}{2 \Delta x}; \; k\_{y} = \frac{\Delta t}{2 \Delta y}.$$

As for the Riemann flux calculation, we use results from the MUSCL-Hancock step to reconstruct the value around the interface. The slope limiter is the same as the MUSCL-Hancock reconstruction step. The formula is:

$$\mathcal{U}\_{i+1/2}^L = \mathcal{U}\_i^{n+1/2} + \frac{1}{2}\varphi(r) \left(\mathcal{U}\_i^n - \mathcal{U}\_{i-1}^n\right). \tag{14}$$

Riemann states in another direction to use the same method.

#### *2.6. Stability Criteria*

The numerical scheme is explicit. The stability is defined by the Courant–Friedrichs– Lewy (CFL) criterion. Since this is a two-dimensional calculation case, the time step is limited by local real-time results:

$$
\Delta t = \min \left( \frac{\mathsf{C} \Delta \mathsf{x}}{|u\_i| + \sqrt{g h\_i}}, \frac{\mathsf{C} \Delta y}{|v\_i| + \sqrt{g h\_i}}, \Delta T \right), \tag{15}
$$

where C is the Courant number, ranging between 0 and 1. In some cases, a stable ∆*T* could give a more stable result. If the export results include a specific time point, ∆*T* should be modified to a smaller time step to match the predicted time point.

#### **3. Intercell Bed Elevation and Dry Cell**

Since the flux calculation should follow the real physics law in the real world, the interface property determines the flux calculation during flow routing in real river geometry. We classified the interface property into four types based on flow depth and surface elevation (as shown in Figure 2): (1) Two cells' flow depth is higher than 0, which would generate flux in these specific two cells. (2) Two cells between the interface are dry cells such that both flow depths are equal to zero. (3) One is a wet cell and another is a dry cell, but the elevation of the wet cell is higher than the dry cell. (4) One is a wet cell and another is a dry cell, but the dry cell is higher than the wet cell.

Based on the physical property, the interface in the first and third type should consider mass and momentum exchanges between the two cells during calculation. It is not necessary to consider this effect for the cell interface in Type B and Type D.

**Figure 2.** Classification of interface property. (**a**) Type A: wet cells at the left and right side, *hL* > 0, *hR* > 0, *hL* and *hR* are flow depth in the left and right side of intercell respectively; (**b**) Type B: dry cells at the left and right side of the intercell face; (**c**) Type C: wet and dry cells are connected through the intercell face, the free surface elevation of the wet cell is higher than the dry cell; (**d**) Type D: wet and dry cells are connected between the intercell face, and the free surface elevation of the wet cell is lower than the dry cell.

Local modification of *Z* at the intercell is adopted. The modification is used based on the physical property of the real condition (as shown in Figure 3); e.g., (1) the reflection boundary would stop the flow from moving forward; (2) the dry cell has no flux. The intercell property in Types A, B and C do not need modifications, and the intercell bed elevation is:

$$Z\_{i+1/2} = (Z\_i + Z\_{i+1})/2,\tag{16}$$

where *Zi*+1/2 is the elevation at the intercell; *Z<sup>i</sup>* and *Zi*+<sup>1</sup> are cell center elevations at the *i*th and (*i* + 1)th cell. Type D of the intercell face's elevation is modified as:

$$Z\_{i+1/2} = \min(\eta\_i, \eta\_{i+1}).\tag{17}$$

**Figure 3.** Modification of the intercell elevation. (**a**,**b**) The intercell does not need modification, which is related to Type A and Type B; (**c**) the intercell elevation is modified to the wet cell's elevation, which is related to Type D; (**d**) the sharp slope cell is modified to the dry cell's bed elevation.

In the Type C intercell property, a sharp slope would produce an overpredicted flux in the intercell. Based on the intercell property, the intercell bed elevation was modified as:

$$Z\_{i+1/2} = \max(Z\_i, Z\_{i+1}).\tag{18}$$

Momentum needs to be modified while the intercell property is Type D. The velocity component that is perpendicular and the limiter of the three variables of the shallow water equations should be set to zero. For rectangular cell simulation, the calculation area could be treated as a matrix. Many simulations are based on circulation to calculate the whole simulated area, and they include a step that checks for cells that do not need flux calculations. We want to skip this step due to the running circulation cost time. The specific form of the shallow water equation includes *η*, and the unbalanced flux would be predicted during our simulation which formed by a complex real geometry if the matrix is used directly, for example (Figure 4):

If the dry cell's slope limiter function, Equation (11), is zero, the calculated flux would be unbalanced:

$$\left(\lg(\eta^2 - 2\eta Z)/2\right)\_{,\mathbf{x}} = \frac{\mathbf{g}\left[\left(\eta\_i^2 - 2\eta\_i Z\_{i-1/2}\right) - \left(\eta\_i^2 - 2\eta\_i Z\_{i+1/2}\right)\right]}{2\Delta\mathbf{x}} \neq \mathbf{g}\eta\_i Z\_{,\mathbf{x}}.\tag{19}$$

In order to achieve a matrix calculation and an automatic flux balance during simulation, we adopted the "zero" slope-limiter function and modified the first term based on the geometry. The elevation of dry cell was modified to:

$$\eta\_i = \frac{(Z\_{i+1/2} + Z\_{i-1/2})}{2},\tag{20}$$

and the slope of the surface elevation of the dry cell was calculated as:

$$r\_{i,j(\eta\_i)} = \frac{(Z\_{i+1/2} - Z\_{i-1/2})}{2\Delta x},\tag{21}$$

where *ri*,*j*(*η<sup>i</sup>* ) is the value of the first term of the slope limiter function, and ∆*x* is the cell length in the x direction.

If the flow depth in the dry cell is zero, *ηi*+1/2 = *Zi*+1/2 in the interface, and cell center's value is given by Equation (20). The specific treatment to the dry cell is shown below (as shown in Figure 5):

**Figure 5.** The dry cell's center elevation is calculated by the average of two intercell elevations. Intercell elevations are predicted from the latest two steps that are based on the intercell type and the real conditions. (**a**,**c**) One side is a wet-dry front and the one side is dry-dry; (**b**) both sides are a wet-dry front; (**d**) both sides are sharp slopes; (**e**) both sides are dry cells; (**f**) flow chart of the method.

The balance in the dry cell is automatically reached:

$$\left(\operatorname{g}(\eta^2 - 2\eta Z)/2\right)\_{,x} = \frac{\operatorname{g}(Z\_{i+1/2}\,^2 - Z\_{i-1/2}\,^2)}{2\Delta\mathbf{x}} = \frac{\operatorname{g}(Z\_{i+1/2} + Z\_{i-1/2})(Z\_{i+1/2} - Z\_{i-1/2})}{2\Delta\mathbf{x}} = \operatorname{g}\eta Z\_{,x} \tag{22}$$

In the reflection boundary, where a higher left dry cell and a lower right wet cell surround the intercell, *<sup>η</sup>i*+1/2 = *<sup>η</sup>i*−1/2 = *<sup>η</sup><sup>i</sup>* and *<sup>η</sup>i*−1/2 = *<sup>Z</sup>i*−1/2. The flux balance is reached automatically:

$$\left(\operatorname{g}(\eta^{2}-2\eta Z)/2\right)\_{,\mathbf{x}} = \frac{\operatorname{g}\left(-\eta\_{i-1/2}\,^{2} + \eta\_{i+1/2}\,^{2} + 2\eta\_{i+1/2}Z\_{i+1/2} - 2\eta\_{i-1/2}Z\_{i-1/2}\right)}{2\Delta\mathbf{x}} = \frac{\operatorname{g}\eta\_{i+1/2}(Z\_{i-1/2} - Z\_{i+1/2})}{\Delta\mathbf{x}} = \operatorname{g}\eta Z\_{,\mathbf{x}}.\tag{25}$$

If the flow velocity at all described cells is zero, the flux balance is controlled by the wet-dry boundary and the dry cells. All the steps of this method are summarized in Figure 5f.

#### **4. Results and Discussion**

*4.1. Steady Condition Calculation of Flood*

A test case was used to test the numerical scheme's C-property. A static lake is kept steady, and there is no disturbance. The calculation area is an 8000 m × 8000 m. In the dry bed, there are two bumps:

$$Z(\mathbf{x}, y) = \max(0, Z\_{\text{B1}}, Z\_{\text{B2}}),\tag{24}$$

$$\begin{cases} Z\_{B1} = 2000 - 0.00032 \left[ \left( \chi - 3000 \right)^2 + \left( y - 5000 \right)^2 \right] \\\ Z\_{B2} = 900 - 0.000144 \left[ \left( \chi - 5000 \right)^2 + \left( y - 3000 \right)^2 \right] \end{cases} \tag{25}$$

The lake elevation is 1000 m, and the lower bump is submerged by the lake. The mesh size is a rectangular mesh of 1 m × 1 m. The calculation time step is 1 s. The finish time is 8000 s.

After 8000 s, the lake remained static, the results in Figure 6 show that this approach follows a C-property, the static keep balance automatically.

**Figure 6.** C-property checking for a static lake. (**a**) Lake geometry; (**b**) results after 8000 s.

#### *4.2. Two-Dimensional Smooth River Bed Test*

A two-dimensional smooth bed test was adopted here. The case has an analytical solution smooth bed. This test was adopted by many researchers to test their algorithm's wetdry treatment and calculation accuracy [27,29,41,42]. The calculation area is a 4 m × 4 m, and the origin of the coordinates is in the center of the calculation area. The mesh size is 0.1 m × 0.1 m. The bed is a parabola rotation:

$$Z(x,y) = h\_0 \left(\frac{x^2 + y^2}{a^2} - 1\right),\tag{26}$$

where *h*<sup>0</sup> is the initial flow depth of the origin of the coordinates, a is the distance between the origin and the elevation equal to zero, and *x* and *y* are coordinate variables. Under this condition, water flows on the smooth bed and cannot stop. The frequency of flow is *ω* = 2*π*/*T* = p 8*gh*0/*a*, in which T is the time of one cycle. In the analytical solution for the process, the moving range is small:

$$\eta(\mathbf{x}, y, t) = \max\left[Z(\mathbf{x}, y), h\_0\left(\frac{\sqrt{1 - A^2}}{1 - A\cos(\omega t)} - \frac{\mathbf{x}^2 + y^2}{a^2} \left(\frac{1 - A^2}{\left(1 - A\cos(\omega t)\right)^2} - 1\right) - 1\right)\right],\tag{27}$$

where *A* = *a* <sup>4</sup> <sup>−</sup> *<sup>r</sup>* 4 0 / *a* <sup>4</sup> + *r* 4 0 , and r<sup>0</sup> is the farthest distance to the center. In the simulation test, we consider the same parameter treatments as Song et al. [42], a = 1 m, *h*<sup>0</sup> = 0.1 m, and r<sup>0</sup> = 0.8 m. We adopted a mesh size of 0.01 × 0.01 m. The initial condition is the same as the analytical solutions in T/6, T/3, T/2 and T (Figure 7).

**Figure 7.** *Cont.*

**Figure 7.** Simulated results compared with real analytical results. (**a**) Geometry of the calculation area and the initial condition; (**b**–**e**) comparison between the simulated results and the analytical solution at T/6, T/3, T/2, T.

#### *4.3. Dam Breach over a Thump*

This test case is a dam break flow over a thump. The experiment was carried at the University of Brussels, Belgium [43]. Many researchers have used this case to test their model on complex geometries [44,45].

The test simulated a sudden dam breach of flood flowing over a triangular hump. The calculation area is a 38 × 1.75 m flume. A hump was set at 15.5 m, and a barrier lake was formed upstream (as shown in Figure 8). The static lake's flow depth is 0.75 m. The peak of the triangular thump is at 28.5 m, with a height and bottom width of 0.4 and 6 m, respectively. In the tail of the obstacle, there is a 0.15 m high gate, where flow depth is also 0.15 m. Downstream, the first gate is the dry bed. Roughness of the calculation area is n = 0.0125 s <sup>×</sup> <sup>m</sup>−1/3. Four downstream monitoring locations were set, named G1, G2, G3, and G4, and the measured data is the flow depth, located at 19.5, 25.5, 26.5, and 28.5 m respectively. The mesh size for the calculation is 0.1 m × 0.1 m.

**Figure 8.** Flume test setup of the experiment.

Figure 9 shows four representative moments of simulation. After 1 s, the flood front arrives at the 19 m point. At 8 s, the flood flows over the obstacle, which causes backwater and imposes disturbance on the tail lake. At 16 s, a higher run-up upstream lake formed at the front of the obstacle, with waves upstream of the hump. A distinct hydraulic jump develops at the tail lake. At 40 s, the water surface before the obstacle is dominated by strong waves, while the tail lake becomes static. The flow upstream cannot flow over the obstacle.

**Figure 9.** Free surface elevation during the flood evolution in the experiment. (**a**) At 1 s, flood flows at the dry bed; (**b**) at 8 s, the flood flows up to the obstacle and has an influence downstream; (**c**) at 16 s, all the upstream water flows to the obstacle and a run-up forms; (**d**) at 40 s, the flow downstream remains static, with waves at the upstream lake.

We extracted surface elevation data from the simulation results for comparison. Simulated results at G4 and G13 fit the monitored data very well, but the predicted water surface at G10 and G11 is slightly lower than the monitored data, G20 is slightly higher than measured data, which has been captured in many cases [44]. At the lower stage, the simulated results were similar to simulated results later. The short-term-simulated higher flow depth did not influence the real flood evolution at a later stage. Compared with the same simulated work did by Tomas and Liao [44,45], our simulated results show similar result in G10, G11, and G20. In G4 and G13, our result is closer to measured data compared with their results, which shows better results (as shown in Figure 10).

**Figure 10.** Monitored data compared with the simulated results at the four locations. (**a**) The simulated result is similar to the measured data at G4; (**b**) initially, the simulated results at G10 is lower but did not influence successive results; (**c**) the same higher simulated flow depth at G11 is similar to G10, a short-term lower elevation; (**d**) the simulated results fit well with the measured data at G13; (**e**) the simulated results fit well with the measured data at G20.

#### *4.4. Dam Break Wave Propagating over Three Humps*

The three humps test is a very famous test case proposed by Kawahara in 1986 [46,47]. Initially, the case was adopted to test the finite element model, which is wildly used. The calculation area in this study is a 75 × 30 m flume, which has three humps. The boundary is a fixed reflection boundary. The centers of the humps are A (30 m, 6 m), B (30 m, 24 m), and C (47.5 m, 15 m). The maximum height of the humps is 1, 1, and 3 m, respectively. In the upstream of x = 16 m, there is a lake with a depth of 1.875 m. The bed roughness is n = 0.018 sm−1/3. The calculation geometry was calculated from the formulas below:

$$\begin{cases} \quad a = 1 - \frac{1}{8} \sqrt{\left(x - 30\right)^2 + \left(y - 6\right)^2} \\ \quad b = 1 - \frac{1}{8} \sqrt{\left(x - 30\right)^2 + \left(y - 24\right)^2} \\ \quad c = 3 - \frac{3}{10} \sqrt{\left(x - 47.5\right)^2 + \left(y - 15\right)^2} \\ \quad Z(x, y) = \max(0, a, b, c) \end{cases} \tag{28}$$

where *a* and *b* are geometric functions of the two lower humps, *c* is the geometry function of the higher humps, and the elevation of the bed bottom is the maximum value of *a*, *b*, and *c*. The mesh size is 0.5 m × 0.5 m.

Figure 11 shows the simulated results of six important moments. At 2 s, the water reached two lower humps and started to flow over them. At 6 s, the flood flowed over the two lower humps and started to reached the higher hump. At 12 s, the flood bypassed the higher hump because it could not completely inundate the higher hump. At 30 s, the flood occupied the calculation area. The formed higher flow depth downstream caused backflow. At 100 s, there was still weak flow in the tank. At 300 s, the flow almost stopped and formed a static lake in the tank, and the peaks of all three humps did not submerge. The numerical model properly simulated complex wetting and drying processes and produced similar results to those of other researchers [29,48].

**Figure 11.** *Cont.*

**Figure 11.** Simulated flood evolution on a complex three-hump condition. (**a**) The flood starts to reach the first two low humps at 2 s; (**b**) the flood flows over the two low humps at 6 s; (**c**) the flood flows downstream of the high humps at 12 s; (**d**) the flood forms a higher flow depth downstream at 30 s; (**e**) there is some weak flow in the tank at 100 s; (**f**) the tank maintains a static condition at 300 s.

#### **5. Conclusions**

We propose a new approach to process dry cells and wet-dry front cells via a Godunovtype finite volume prediction method of flood evolution. Shallow water equations automatically balance the gravity source term. The modification includes four steps: (1) identify four types of intercells based on flow depth and surface elevation difference; (2) based on the physical properties of the intercells, modify the bed elevation of the intercell, so as to avoid non-physical flux predictions and gravity balance; (3) modify the dry cell's center elevation to equal the averaged elevation of the two surrounding intercell elevations; (4) change the first term of the slope limiter at the dry cell equal to the ratio of the elevation difference between two intercell bed elevations dividing two times of mesh size. This method was applied to a second-order MUSCL-Hancock-HLLC scheme in time and space for flux and variable prediction in a real geometry. The intercell flux predicted by the reconstructed method remained balanced with the gravity source term automatically, which was proved by mathematical derivations. Four simulated cases showed that the method has a C-property in a complex geometry and achieves the same results as those of many other researchers. Results in the analytical case and the experiment monitoring cases fit each other very well. During all the processing steps, modification could be finished in one step, such that cells did not need to be checked through circulation. This new method can increase the convenience and efficiency of matrix calculations and has a potential for

faster GPU (Graphics Processing Unit) simulation and parallel computing. It could be used in real world outburst flood simulation with high efficiency.

**Author Contributions:** D.L. (Dingzhu Liu) and H.W. design this research and draft the manuscript. J.T. gave many suggestions on testing cases. Y.C. help with coding the program. N.A.B. help with the language. H.C. and D.L. (Daochuan Liu) help with find checking data. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant no. 41941017; the Applied Fundamental Research Program of Sichuan Province, grant no. 2019JY0387; Key Research Program of Frontier Sciences, Chinese Academy of Sciences, grant no. QYZDY-SSW-DQC006 and the National Natural Science Foundation of China.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study is contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **On Dam Failure Induced Seismic Signals Using Laboratory Tests and on Breach Morphology Due to Overtopping by Modeling**

**Chi-Yao Hung 1 , I-Fan Tseng 1 , Su-Chin Chen 1,2 and Zheng-Yi Feng 1, \***


**Abstract:** Dam models were constructed in an indoor flume to test dam breach failure processes to study the seismic signals induced. A simple dam breach model was also proposed to estimate hydrographs for dam breach floods. The test results showed that when the retrogressive erosion due to seepage of the dam continues, it will eventually reach the crest at the upstream side of the dam, and then trigger overtopping and breaching. The seismic signals corresponding to the failure events during retrogressive erosion and overtopping of the dam models were evaluated. Characteristics of the seismic signals were analyzed by Hilbert–Huang transform. Based on the characteristics of the seismic signals, we found four types of mass movement during the retrogressive erosion process, i.e., the single, intermittent, and successive slides and fall. There were precursor seismic signals found caused by cracking immediately before the sliding events of the dam. Furthermore, the dam breach modeling results coincided well with the test results and the field observations. From the test and modeling results, we confirmed that the overtopping discharge and the lateral sliding masses of the dam are also among the important factors influencing the evolution of the breach. In addition, the widening rate of the breach decreases with decreased discharge. The proposed dam breach model can be a useful tool for dam breach warning and hazard reduction.

**Keywords:** dam breach; seepage; overtopping; seismic signal; flume test; breach model

#### **1. Introduction**

Large landslides induced by rainfall or earthquakes may form landslide dams and inundate upstream areas. If the dam breaches, it will pose a serious threat to the area downstream. Nearly 89% of landslide dam failures are caused by overtopping [1,2]. The large-scale landslide caused by Typhoon Morakot in 2009 in Xiaolin village in southern Taiwan caused over 400 fatalities. It also formed a landslide dam [3–5]. Feng (2012) [6] indicated that the dam breached 1 h and 24 min after its formation according to the seismic signal recorded and the time–frequency spectrum. They estimated the velocity of flood propagation downstream to be 8.3 m/s. The dam breach produced large turbulent flows downstream in a short period of time, causing flooding downstream and the failure of many bridges.

In 1951, heavy rainfall caused a large-scale landslide in Tsaoling, Yunlin County, Taiwan, and a large landslide dam was formed. As a result, 137 army engineers unfortunately sacrificed their lives during the installation of an emergency spillway due to the sudden overtopping failure of the dam [7]. In 1999, a large landslide occurred in Tsaoling again due to the 1999 Chichi earthquake [8]. Five landslide-dammed lakes were subsequently formed, of which three were cleared soon after the landslide. However, the other two were not easily cleared, so were strengthened to improve the stability of the dam and emergency

**Citation:** Hung, C.-Y.; Tseng, I.-F.; Chen, S.-C.; Feng, Z.-Y. On Dam Failure Induced Seismic Signals Using Laboratory Tests and on Breach Morphology due to Overtopping by Modeling. *Water* **2021**, *13*, 2757. https://doi.org/10.3390/w13192757

Academic Editor: António Pinheiro

Received: 22 August 2021 Accepted: 1 October 2021 Published: 5 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

spillways were setup to prevent overtopping erosion [9]. Due to the establishment of emergency spillways that controlled the maximum water storage capacity of the landslide dam, the impacts of four typhoons (Typhoon Bilis in 2000, Torajiin 2001, Nari and Mindulle in 2004) were reduced [10]. Cui et al. (2013) [11] and Zhou et al. (2015) [12] reported that on 8 August 2010, the intense rainfall and cascading failure of landslide dams along two gullies induced a fatal debris flows to Zhouqu County, China, that claimed the lives of 1765 people and damaged infrastructure and many homes. Their preliminary field and experimental studies showed that landslide dam cluster modes (i.e., different dam types and their combination) in upstream gullies accounted for the amplification of the scale of Zhouqu debris flows downstream. Cai et al. (2019) [13] analyzed the cascade dam system using a dam breach analysis model (DB-IWHR) for continuous breaking failure paths. They also created a Bayesian network model to determine the failure probability of the cascade dam system. Rˇíha et al. (2020) [14] also modeled cascade dams and indicated that the peak discharge of a dam cascade system may be underestimated by up to 10% when applying an empirical formula derived for a single dam breach. Shrestha and Nakagawa (2016) [15] studied the large-scale landslide in Nepal that resulted from heavy rainfall on 2 August 2014 and the landslide dam on the Sunkoshi River. The retained water overflowed 36 days after the landslide. However, there was no serious damage downstream and no casualties because an emergency spillway was setup before the overflow and the spillway controlled the overflowing water. From these reviews, it is clear that landslides and dam breaches can cause a large number of casualties and property destruction. Therefore, research on the failure processes of landslide dams and hazard prevention of landslide dams is very important.

Hazard prevention and monitoring of landslide dams are always compulsory. Many scholars have used seismic signals recorded from geophones and/or accelerometers for analyses for the creation of warning systems [16–20]. Because both landslide and dam breach events generate seismic signals, the signals can be faithfully recorded by seismometers, and so can be used for interpreting the processes of landslides and dam breach events. However, the seismic signals of landslide and dam breach events cannot always be successfully recorded due to limitations. Additionally, because natural phenomena cannot be repeated, a series of event data cannot be obtained for analysis. Therefore, researchers have often adopted numerical simulations, outdoor large-scale experiments, and indoor small-scale experiments to conduct research on seismic signals induced by landslide dam failure.

Yan et al. (2020) [21] reconstructed the dynamic behavior of the 2017 landslide event in Xinmo village, China, by using the seismic signal characteristics and discrete element method. They categorized the landslide processes into five stages: stationary, slipping, transition, entrainment–transportation, and deposition stages, according to the characteristics of the seismic signals and time–frequency spectra. They identified the transition stage, which is caused by ancient colluvial materials hindering sliding from upslope. However, as the sliding materials continued to accumulate and produce more downward dragging forces, another larger landslide was triggered. This can be observed from the seismic signal as the amplitude first decreases and then increases at the transition stage. Feng et al. (2017) [22] used PFC coupled with FLAC to simulate the 2009 Xiaolin Village landslide process and compared the results with the seismic signal recorded by a broadband seismometer. They found that the types of movement and terrain significantly affect the seismic signal. Although a numerical simulation can readily reconstruct the failure process and influence zones of a landslide, sometimes it is not easy to select accurate physical parameters; thus, the simulation results may be different from the actual landslide.

Some researchers also choose large-scale outdoor experiments. Yan et al. (2017) [23] monitored the seismic signals generated during an outdoor dam-breach test. According to their results based on time–frequency analysis, the low-frequency band (0–1.5 Hz) was mainly due to dam collapse events; the intermediate-frequency band (1.5–10 Hz) was due to rock slide events; the high-frequency band (10–45 Hz) was a result of water flow and sediment transport. Feng et al. (2020a) [24] conducted a large-scale dam breach test at Huisun Forest Station in Nantou, Taiwan. They discussed the characteristics of seismic signals during the dam breach processes and flooding. The flood speed of the test was also estimated from the seismic signals. They indicated that seismic signals can be applied as a basis for early warnings for floods. As we know, a large-scale outdoor test better reflects natural dam breach behavior than the numerical simulation and the small-scale indoor flume test. However, due to the limitations of outdoor large-scale tests that require a large area, long preparation time, and are relatively more expensive, they are less widely used than indoor flume tests.

Many researchers use small indoor flumes to perform tests for landslide dam breaches [25–28]. Most of the tests explored the erosion of the dam body, including the effects of different flume slopes, dam geometry, and material properties. However, the seismic signals caused by the destruction of the dam are less discussed. Hu et al. (2018) [29] used a small flume to test the seismic signals of internal dam erosions. They found a precursor seismic signal prior to the sliding of dam materials. Seismic signals caused by internal erosion due to seepage were mainly high-frequency. If the dam materials were loosely packed, there were more high-frequency seismic signals induced due to the internal erosion. However, they only discussed the seismic signals of dam failure due to seepage and did not discuss the overtopping dam breach and subsequent flooding. There are seismic precursors detected prior to landslides reported in the literatures, e.g., Poli (2017) [30] and Butler (2019) [31]. Feng et al. (2020b) [32] used an indoor flume to study the seismic signals of landslides caused by riverbank erosion. They also found precursor seismic signals before the riverbank sliding. They classified the river bank sliding into three types: single, intermittent, and successive. The three types correspond to the three different characteristics of seismic signals. They also pointed out that the higher frequency seismic signal decays faster than the lower frequency signal. However, this research did not perform tests for retrogressive erosion of a dam due to seepage and overtopping failure.

This research performed tests for retrogressive erosion of a dam due to seepage and the subsequent overtopping failure of dam models. A theoretical dam breach model was proposed and used to compare the flooding process of the test. The experimental setup was a modified version of the test used by Feng et al. (2020b) [32]. In the tests, accelerometers were installed inside the dam to monitor the seismic signals during the dam failure and to understand the correspondence between the failure processes and characteristics of the seismic signals. Hilbert–Huang transform [33] was used for time–frequency analysis for the seismic signals recorded. The setting of the test conditions in this study is not a simple overtopping failure but is similar to the progressive (retrogressive) failure of an outdoor dam breach test by Takayama et al. (2021) [34]. The progressive failure was mainly induced when the dam body was retrogressively eroded towards the upstream crest by seepage. Initially, only small slides and erosions occurred at the toe of the slope, and then as the phreatic surface of the seeping water gradually rose, an increasing number of slides and erosions occurred from the toe towards the crest. At this point, overtopping occurs and the dam starts to breach with vertical downcutting and lateral erosion. The overtopping flood gradually expands the width of the breach, and then a larger amount of floodwater is discharged downstream.

During overtopping, the breach is widened and deepened by the overflowing water. To model the dam breach process, Wu (2011) [35] listed different model approaches and pointed out that modeling can be classified as: (1) parametric breach models and (2) physically based breach models. Parametric breach models usually use statistical regression equations based on laboratory experiments or field dam failure cases. Physically based breach models were highly developed during the past decades and can simulate the dam breach process in a more complete and detailed way. However, the models require heavy numerical calculation requiring extensive calculation time. In addition, these detailed simulation models can be limited due to a lack of understanding of sediment transport under the flow conditions and require multiple runs to calibrate. Unlike the detailed simulation,

Alhasan et al. (2015) [36] proposed a conceptual model, simplified the three-dimensional problem to a one-dimensional problem, and successfully compared the results with field observations. To simulate the horizontal expansion of the dam breach, Tian et al. (2021) [37] proposed a model to combine a theory of sediment transport for vertical incision and a horizontal expansion model based on geotechnical theory. Similarly, the framework proposed in this research is based on the simplified analytical dam breach model by Capart (2013) [38]. We considered the sediment mass conservation Exner equation [39] and a simple sediment transport law [40] to describe the changing of the dam and channel bed profile. We then use this proposed dam breach model to predict the discharge, the height of the crest, and width of the breach for our test. Comparison and analyses were made between the dam breach model calculations and the test results to verify the feasibility of the model.

The major purposes of this study are to discuss (1) the seismic signal precursors prior to the sliding of the dam, (2) the types of movement of the sliding mass of the dam during the retrogressive erosion due to seepage, and (3) the dam breach model proposed and its comparison with the test results.

In this study, only the most representative test result was chosen for presentation; however, many tests were performed and similar results were obtained.

#### **2. Materials and Methods**

#### *2.1. Test Configuration*

The laboratory flume is shown in Figure 1, which is the same equipment used in Feng et al. (2020b) [32]. The size of the flume is 15 × 0.6 × 0.6 m and the slope of the channel bed is 0.1%. The pump is mainly used to pump water from the underground storage tank to the headwater. Water is introduced from the headwater into the water tank and controlled by a sluice (a valve). The inflow is regulated by a screening device before flowing into the flume channel to enable stable flow conditions. The design of the water supply setup is similar to that of Alhasan et al. (2016) [41] in that the water was stilled/regulated before entering the flume channel. Dimensions of the dam model are listed in Table 1. The slope of the dam is 1:1 (45◦ ) before water impounding. After the construction of the dam model, it was left to sit for 1 h before the test. This study assumes that the right side of the flume is an axis of symmetry; therefore, an overflow notch of 0.05 m depth was set on the right side of the flume. The material used to construct the dam model was sieved uniform sand with a median particle diameter of D<sup>50</sup> = 1.5 mm, D<sup>10</sup> = 0.9 mm, and D<sup>90</sup> = 12.1 mm. The unit weight of the dam material averaged 13.93 kN/m<sup>3</sup> and the density of solid particles ρ<sup>s</sup> = 2583 kg/m<sup>3</sup> . The void ratio was 0.816 and porosity 45%. The initial moisture content of the dam materials was measured as 5–8%. The initial internal friction angle of the dam material was estimated to be 38–40◦ . A sand bed with a length of 3.8 m and a thickness of 0.05 m was placed downstream of the dam (Figure 1). Figure 2 shows the side and front view of the dam model.

The dam model was instrumented with sensors including 4 accelerometers, 4 piezometers, and 2 moisture sensors. Figure 3 shows the configuration of the sensors in the dam model and are numbered for identification. The locations of the sensors were selected so that they are not washed out during the tests. Therefore, they were mostly installed on the left side of the dam, with the exception of PP-3 and PP-4. The piezometers were installed close to the bottom of the dam to reflect pore pressure. Moisture sensors 1 and 2 were installed higher, at 0.2 and 0.3 m above the bottom to detect when the seepage water reached those levels. The accelerometers were of the Type 731A produced by Wilcoxon Sensing Technologies with a response frequency between 0.1 and 450 Hz and sensitivity of 10 V/g. The sampling rate was set at 5.12 kHz for the accelerometers to record seismic signals. The piezometers were of the Type KPE-200KPB made by Tokyo Measuring Instruments Laboratory Co, Ltd., and were installed 3 cm above the bottom of the dam model to trace pore pressure (PP) variation during the test. The moisture sensors were of the Type EC-5

produced by METER Group, Inc., and were installed at two different levels to monitor variation in volumetric water content (VWC).

Three cameras were set up at the right side, front, and top of the dam model to record the test process. Because the shooting angle of the sideview file was skewed, for subsequent analyses we used a projection to estimate the water level changes and dam dimensions during the breach.

Brief test process: When water was released, the upstream water level gradually increased until the maximum water level was reached. The maximum water level was controlled by the sluice and maintained at 0.3 m until overtopping. The pump was turned off at 116 s for better seismic signal quality. At 130 s, a tapping was made to leave a time marker, which was used to match the time axis between seismic signals and the test videos. After water seeped into the dam and outflowed at the downstream toe, retrogressive erosion and landslides then started. When the retrogressive erosion reached the upstream crest of the dam, overtopping occurred. A breach was then formed, down cut, and widened. The detailed test process and results are discussed in Section 3.

**Table 1.** The dimensions of the dam model.


#### **Figure 1.** Layout of the test flume and the dam model.

**Figure 2.** (**a**) The side view of the dam model and (**b**) front view of the dam model.

**Figure 3.** Sensor configuration in the dam model (the numbering of the sensors is marked near each sensor).

#### *2.2. Seismic Signal Processing by Hilbert–Huang Transform (HHT)*

The seismic signals recorded during the tests were processed using Hilbert–Huang transform (HHT, Huang et al. 1998) [33]. HHT includes empirical mode decomposition (EMD) to calculate the intrinsic mode functions (IMFs) and a Hilbert transform (HT) to obtain the corresponding time–frequency spectra from the IMFs. HHT can process unsteady and nonlinear signals and analyze the relationship between time, seismic frequency, and energy distribution of signals. The HHT analyses in this study were performed by Visual Signal Ver. 1.6 software (AnCad, Inc. (2018) [42]). The characteristics of the seismic signals due to various sliding events can be identified more easily with the help of time–frequency spectra. The HHT was also applied in Feng et al. (2020b) [32] and Feng et al. (2020a) [24] to successfully interpret flood and landslide events.

#### *2.3. Dam Breach Model—Overtopping*

As we described in the previous section, the test can be separated into two stages. In the first stage, the seepage water flows out of the downstream surface of the dam, causing retrogressive erosion. Due to the retrogressive erosion, the shape of the dam deforms from a trapezoid to triangle and the breach process leads to the second stage. In the second stage, the water overtops the crest and begins the overtopping process. In the second stage, the outflow from the crest dominates the breach process and reduces the water level in the lake.

To simulate the overtopping incision process and compare it with the test results, we propose a simplified dam breach model based on Capart (2013) [38]. In this model, we neglect the discharge due to seepage and simulate the breaching as a continuous process. As illustrated in Figure 4, we assumed a triangular-shaped dam with upstream slope *RD*, downstream slope *SD*, and initial elevation of the dam *zD*; *zC*(*t*) is the crest level and

*zL*(*t*) is the lake level. The initial crest level *zC*(*t* = 0) is equal to *zD*. The initial lake level

**Figure 4.** Schematic and parameters of the proposed dam breach model.

The Exner equation governs the breach process based on the sediment mass balance (Paola and Voller 2005) [43].

$$b\frac{\partial z}{\partial t} + \frac{\partial f}{\partial x} = 0 \tag{1}$$

where *b* is the channel width, *z* is the bottom elevation of the breach channel, *x* is the streamwise direction, and *J* is the sediment transport rate. In this equation, Paola and Voller (2005) [43] simply demonstrated the mass of bedload balancing in a controlled volume; when sediment influx *J*(*x*) is larger than outflux *J*(*x* + ∆*x*) the elevation of the sediment in the control volume increases. For the sediment transport rate, Visser (1995) [44], Alhasan et al. (2016) [41], and Haddadchi et al. (2013) [45] collected different empirical sediment transport formulas used in sand–dike breach erosion. The formulas were verified with experimental results or field cases. However, the formulas contained too many detailed variables and coefficients (e.g., internal friction coefficient, bed shear velocity), which increases the complexity of the model [46]. In the 1950s, Lane (1955) [40] presented a qualitative law of sediment transport rate, which demonstrated *J* can be generally scaled by the water flux and the channel gradient as:

$$J = KQS = -KQ \frac{\partial z}{\partial x} \tag{2}$$

where *K* is a dimensionless transport coefficient; *Q* is the local discharge (the discharge through the breach); *S* is the channel gradient, which can be written as the derivative of channel elevation in the streamwise direction. By substituting (2) into (1), a variable rate diffusion equation can be obtained. Next, we assumed the outflow channel at the toe of the dam converges to the initial shape of the dam, and the level of the crest level evolves along with the water level of the lake. A zero-sediment flux is assumed at the crest (*J*(*xC*(*t*), *t*) = 0) as the second upstream boundary condition [47,48]. By defining operational time *dτ*(*t*) = *KQ*(*t*)/*b*, the varying rate diffusion equation can be reduced to a standard diffusion equation:

$$
\frac{\partial z}{\partial \tau} - \frac{\partial^2 z}{\partial x^2} = 0 \tag{3}
$$

For this dam breach problem (triangle dam with moving upstream boundary condition), a similar structure of the solution can be found in Capart et al. (2007) [47], Voller et al. (2004) [49], and Lai and Capart (2007, 2009) [50,51], and the detailed derivation can be found in Capart (2013) [38]. By using the boundary conditions, the profile of the dam was solved as:

$$z(\mathbf{x}, \tau) = z\_D - S\_D \mathbf{x} - \frac{(\mathcal{R}\_D + \mathcal{S}\_D)\lambda\_s}{i \text{erfc}(-0.5\lambda\_s)} \sqrt{\tau} \text{ ierfc}\left(-\frac{1}{2}\mathbf{x} / \sqrt{\tau}\right) \tag{4}$$

where *S<sup>D</sup>* and *R<sup>D</sup>* represent the downstream slope and upstream slope of the dam, and *ierfc*(*ξ*) is a special function introduced by Carslaw and Jaeger (1959) [52]:

$$\text{ierfc}(\mathfrak{f}) = \int\_{\mathfrak{f}}^{\infty} \text{erfc}(\mathfrak{x}) d\mathfrak{x} = \frac{1}{\sqrt{\pi}} \exp\left(-\mathfrak{f}^2\right) - \mathfrak{f} \text{erfc}(\mathfrak{f}) \tag{5}$$

where *erfc*(*ξ*) is the complementary error function and *λ<sup>s</sup>* is a constant related to the shape of the dam. By taking the upstream sediment flux boundary condition at the dam crest position, *λ<sup>s</sup>* can be solved numerically in Equation (6):

$$\frac{0.5\lambda\_s \, erfc(-0.5\lambda\_s)}{ierfc(-0.5\lambda\_s)} - \frac{S\_D}{S\_D + R\_D} = 0\tag{6}$$

Following the profile of the dam, focusing on the dam crest, the drop of crest *δ*(*τ*) can also be written as:

$$\delta(\tau) = z\_D - z(\mathbf{x}\_{\mathbb{C}}(\tau), \tau) = R\_D \lambda\_{\mathbb{S}} \sqrt{\tau} \tag{7}$$

We replaced the operational time *τ* with the real time, and the time evolution of the breach drop can be given by the ODE:

$$\frac{d\delta(t)}{dt} = \frac{1}{2} \frac{KQ}{b} \frac{R\_D^2 \lambda\_s^2}{\delta(t)}\tag{8}$$

*V<sup>E</sup>* indicates the erosion volume at the crest during the overtopping process. Here, we find that *V<sup>E</sup>* can be scaled as the drop of the crest and the width of the width *δ* 2 *b*. To include the widening effect and simplify the governing equation, we rewrite the equation as:

$$\frac{dV\_E(t)}{dt} = \frac{d}{dt}\left(\delta^2 b\right) = K\_T Q = (K\_V + K\_L)Q \tag{9}$$

where *K<sup>T</sup>* is the scaled coefficient of the total sediment transport coefficient; *K<sup>L</sup>* and *K<sup>V</sup>* represent the coefficients of the erosion rate of the dam in lateral and vertical directions, respectively. To separate the process of vertical incision and lateral erosion, we applied chain rules to simplify the partial differential equation (PDE) (Equation (9)) into two ordinary differential equations (ODEs):

$$\frac{d\delta(t)}{dt} = \frac{K\_V Q(t)}{2b(t)\delta(t)} \frac{db(t)}{dt} = \frac{K\_L Q(t)}{\delta(t)^2} \tag{10}$$

To simulate the lake drainage, the level-pool routing equation [53] is adopted:

$$A\_L \frac{dz\_L}{dt} = -Q \tag{11}$$

where *A<sup>L</sup>* is the lake area, which we assume constant during breaching. For the outflow discharge *Q*, the broad-crested discharge equation is used:

$$Q = \sqrt{\frac{8g}{27}} b\eta(t)^{3/2} \tag{12}$$

where *η*(*t*) = *zL*(*t*) − *zC*(*t*) represents flow depth at the crest. By substituting the broadcrested-weir discharge equation (Equation (12)) into the level-pooling routing equation, Equation (11) can be rewritten as:

$$\frac{d\eta(t)}{dt} = \frac{d\delta(t)}{dt} - \frac{1}{A\_L} \sqrt{\frac{8g}{27}} b\eta(t)^{3/2} \tag{13}$$

Now, the three ODEs (the two ODEs from Equation (10) and the ODE of Equation (13)) with the three variables, *η*(*t*), *δ*(*t*), and *b*(*t*), were successfully derived. The forward Euler method, a first-order numerical procedure for solving ODEs, was applied to calculate the solution of the dam breach model with the following initial conditions:

$$
\delta(0) = 0, \; \eta(0) = 0, \; b(0) = b\_0 \tag{14}
$$

The water level of the lake is assumed to be the same height of the crest as the initial condition at *t* = 0, and *b*<sup>0</sup> is the initial channel width.

The proposed dam breach model is then successfully derived and can be solved numerically. This model is simple because we only have to solve the simpler ODEs instead of the PDEs. The model results were compared with the field observations from the literature and test result in Section 3.

#### **3. Results and Discussions**

#### *3.1. Measurements of the Test*

In the discussion of the test results hereafter, the term "tank" was used instead of "lake". They both represent the water level at the upstream side of the dam in this study. The test processes included tank level raising, water seeping into the dam, sliding of the dam due to retrogressive erosion, overtopping, breach downcutting, and widening and lateral sliding of the dam. Table 2 lists the timing, test stages, selected important events, and variation of the seismic signals of the test processes. We defined *T*<sup>0</sup> = 76 s as the time when the upstream water reached the toe of the dam. Sliding Events 1–6 occurred between 180.6 and 231.9 s, of which Events 1–3 occurred during the rising of the tank level and Events 4–6 occurred when the tank level was maintained at 0.3 m. Events 1–6 are discussed in detail later in Section 3.2. There were also many slides of different magnitudes that occurred during 260–592 s, but they were not discussed in this study. *T<sup>6</sup>* = 592 s is defined as the timing of overtopping and thus the breach downcutting and widening processes started as Event 7. There are six lateral slides of the dam detected during Event 7. We monitored the test until 930 s.


**Table 2.** Test processes and the selected important events.

Figure 5 shows the tank water level, the signals measured by the accelerometers, piezometers, and water content sensors. The tank level gradually increased from *T<sup>0</sup>* = 76 s (Figure 5a). When the water reached the dam slope, some shallow surface sands started to slide down after 150 s as the water level rose. The slope of the upstream face of the dam was slightly reduced to about 40◦ , but no serious deep sliding occurred. During the test, the upstream face of the dam was still stable. The pore pressure of PP-1 started to increase at about T = 100 s (Figure 5d). The volumetric water content measured by VWC-2 began to increase at T = 176 s (Figure 5c) because the seepage water had reached the level of VWC-2 at 0.2 m. The elevation (0.3 m) of VWC-1 was higher than that of VWC-2 so that there was about 10 s lag at T = 166 s for VWC-1 to detect the seepage water. When overtopping occurred at *T<sup>6</sup>* = 592 s, the pore pressures and volumetric water contents began to gradually decrease simultaneously. Therefore, we confirmed that the piezometers and the moisture sensors can accurately reflect the rising and falling of the water inside the dam.

**Figure 5.** Test measurements: (**a**) water level of the tank, (**b**) seismic signal of Acc. 2, (**c**) volumetric water content, (**d**) pore pressure.

Referring to Figure 6, six side-view images were captured to show the overall test processes: (a) at 72 s (*T0*), the water reached the toe of the dam. The tank level was still zero. (b) At 150 s, the tank level had increased and water seeped into the dam. Once the water seeped out of the downstream surface of the dam, retrogressive erosion commenced and induced slides that gradually eroded the dam towards the upstream crest until overtopping. (c) At 300 s, the tank level was controlled at 0.3 m. Retrogressive erosion continued with many slides at the downstream slope of the dam. (d) At 592 s (*T6*), overtopping occurred and the dam became a triangular shape. (e) At 650s, the tank level was reduced to 0.24 m and the breach was downcut and widened due to overtopping flow. Lateral slides also

occurred. (f) At 930 s, the test was ended. Overtopping flow stopped. The tank level was the same as the crest level.

**Figure 6.** Side-view images at different test stages.

#### *3.2. Seismic Signals Due to Retrogressive Erosion before Overtopping*

While the dam experienced retrogressive erosion, many slides occurred with different types of movements. Based on the seismic signals and with the help of the test videos (Supplementary Materials Videos S1–S5), we identified four types of movements from the test result. In addition, precursor seismic signals were found prior to a slide. These can be useful in categorizing landslide types and prewarning based on the seismic signals in hazard prevention work. There were many slides that occurred during retrogressive erosion; however, we only chose six typical events, Events 1–6 for illustration.

Figure 7 shows two seismic signals (Events 1 and 2) induced by two cracks, Cracks 1 and 2, the corresponding time–frequency spectrum, and the top view of Cracks 1 and 2. The occurrence time of the two signals was 180.6 s (*T1*) to 181.3 s and 182.8 to 183.5 s, respectively. The two signals are recognized as precursor signals prior to a slide, because a large slide, Event 3, occurred immediately after these two signals. The major seismic frequency of Event 1 and 2 was analyzed as 374 Hz, as shown in Figure 7b, and heavier energy traces in dark red can be observed near 374 Hz. This very high frequency is likely due to the particulate sands sliding on or colliding with each other during the crack development. The duration of Event 1 is about 0.5 s corresponding to the shorter crack length of Crack 1, while the duration of Event 2 is longer at 0.7 s corresponding to the longer Crack 2. From these results, we know that seismic signals induced by precursor events can be properly recorded and very useful for application to landslide prewarning.

**Figure 7.** Events 1 and 2, the precursors prior to the Event 3 slide: (**a**) seismic signal, (**b**) time–frequency spectrum, (**c**) top view of the Crack 1 in red dashed line and Crack 2 in orange dashed line.

From the results of the retrogressive erosion process, we categorized four types of mass movements: (1) single slide, (2) intermittent slide, (3) successive slide, and (4) fall. Events 3–6 correspond to these four types of movements, respectively.


(4) A fall—Event 6: A fall is that mass falls down through the air and falls almost vertically. Figure 11 shows the fall, Event 6, which occurred at 309.5 s (*T5*). The duration of Event 6 was short. The amplitudes of the signal were small and the energy traces in the spectrum were also weak owing to the fact that only a small mass fell in Event 6.

The movement types of single, intermittent, and successive slides identified in this study also occurred in the riverbank erosion tests performed by Feng et al. (2020b) [32] and the landslide tests by Feng and Chen (2021) [54]. Their failure types and failure mechanism are consistent with the results found in this study. Besides these three types of movement, we presented the fourth type, fall, which should also be helpful when correlating seismic signals to landslide events. All four types of movements are very common in retrogressive erosion due to seepage out of a dam and can be easily and correspondingly identified from induced seismic signals.

**Figure 8.** Event 3, the single slide: (**a**) seismic signal, (**b**) time–frequency spectrum, (**c**) front and top view of the single slide.

**Figure 9.** Event 4, the intermittent slide: (**a**) seismic signal, (**b**) time–frequency spectrum, (**c**) series of front views the intermittent slide.

**Figure 10.** Event 5, the successive slide: (**a**) seismic signal, (**b**) time–frequency spectrum, (**c**) series of front views of the successive slide.

**Figure 11.** Event 6—the fall (**a**) seismic signal, (**b**) time–frequency spectrum, (**c**) front view images of the fall.

#### *3.3. Comparison of the Dam Breach Model Result with the Breach Events from Literature*

The model-predicted discharge was first verified with field measurements from literature and the test results. We reviewed four field dam breach cases: (1) Tangjiashan landslide dam breach in China [55], (2) Lake Ha! Ha! breakout flood in Canada [56], and (3) two lahar dam breaches from Mapanuepe Lake in the Philippines [57]. The essential information is shown in Table 3.


**Table 3.** Information on dam breach events from literature [38].

To compare the model-predicted results with the field measurements, it is convenient to present the data in dimensionless form. Since it is difficult to identify the point in time when the overtopping reached peak discharge (*TP*) from the field, we adopted the approximate equation from Capart (2013) [38] as Equation (8):

$$T\_P = \frac{3A\_L}{\left(gb^2Q\_P\right)^{1/3}}\tag{15}$$

where *Q<sup>P</sup>* is the field observed peak discharge, *A<sup>L</sup>* is the dammed lake area, and *b* is the breach channel width. The dimensionless hydrographs recorded are shown in Figure 12. The hydrographs from these different field measurements are reasonably close.

For the breach model, there are three critical parameters to control the shape and the magnitude of the hydrograph: *λ*, *KV*, and *KL*. To eliminate the complexity of the model, we used dimensionless hydrographs to compare with that of the test result. In that case, the hydrograph is only controlled by the ratio between the coefficients of lateral erosion (*KL*) and the vertical erosion (*KV*). We varied the ratio (*KL*/*KV*) between 0 and 1. When the ratio was zero, only vertical erosion was considered. When equal erodibility in lateral and vertical directions is considered equal, i.e., their ratio is 1 (unity). The model-predicted results are shown in Figure 12 with different grayscale lines for the different coefficient ratios of erosion *KL*/*KV*. The field observation cases of Table 3 are plotted with lines and symbols for comparison. Two hydrographs are shown for the Tangjiashan event based on the data shown by Liu et al. (2010) [55], in which they used two approaches to estimate the hydrographs. The hydrography estimated from the test is represented by the blue solid curve.

In Figure 12, the predicted hydrograph becomes narrower when the ratio of *KL*/*K<sup>V</sup>* is gradually increased. The narrower curve represents the stronger lateral erosion strength. By comparing the field measurement data, most of the hydrographs showed agreement with the model prediction when the *KL*/*K<sup>V</sup>* ratio ranged from 0.5 to 1. Therefore, we can say that the lateral erosion of the dam should be considered in modeling; the lateral expansion could affect the shape of the hydrograph.

**Figure 12.** Dimensionless discharge hydrographs of the field-observation cases (the lines with symbols) and model-predicted hydrographs with different coefficient ratio of *KL*/*K<sup>V</sup>* (grayscale lines).

#### *3.4. Comparision of the Dam Breach Model Result with the Test Result after Overtopping (Event 7)*

To further verify the performance of the proposed dam breach model, the model result was compared with the test results. Table 4 lists the parameters used in the breach model to simulate the breach morphology of the test. To calibrate the coefficients in the model, we simply assigned the initial values of the channel width, tank level, and crest height, and then used the model to compute the values in the final stage. According to the differences between the model predictions and the test measurements, we adjusted the coefficients that showed the minimum difference. Although the calibration of the coefficients is simple in this study, the predictability of the model on breach evolution is still satisfactory.


**Table 4.** Parameters for the proposed dam breach model for the test dam.

The modeled result is presented in Figure 13 alongside Event 7 of the test result. The videos of Event 7 can be seen in Supplementary Materials Videos S6 and S7. Figure 13a,b displays the seismic signal and its time–frequency spectrum, respectively, after the overtopping (T6 = 592 s) for the test result. Figure 13c shows the spectral magnitude cross-sectional profile of 366 Hz from the spectrum in Figure 13b. The dominant seismic frequency of the signals during 592~930 s was 366 Hz. There were six noticeable amplitude and magnitude peaks, and they are marked by S1–S6 at 607, 616, 632, 651, 670, and 677 s in Figure 13a–c. They were induced by the six lateral slides of the dam during the breach. Note that the magnitude peaks in Figure 13c are more easily identified than the amplitude peaks in Figure 13a,b when corresponded to the six slides. Figure 14 shows the before-and-after photos of the six lateral slides of the dam.

In the early stages of the breach before 651 s, we can observe that the magnitudes of the lateral slides S1 to S4 gradually increased (Figure 13c) with increasing discharge. This indicates that the magnitudes of these lateral slides of the dam became increasingly larger (Figure 14a–d). As a result, vertical downcutting of the breach was more significant than lateral erosion in the early stage of the test such that the toe of the dam in the lateral direction was lowered and induced the subsequent larger lateral slides.

Figure 13d shows changes in lake level *zL*(*t*) and crest level *z<sup>C</sup>* (*t*). Figure 13e shows the variation of the width of the breach *b*(*t*). From the test results in Figure 13d,e, we know that the tank level did not greatly decrease until 630 s, and the lowering of the tank level became prominent after 630 s. However, the lowering rate of the crest level and widening rate of the width were relatively high before 630 s, indicating that vertical downcutting and lateral erosion were quite strong.

The materials of the lateral slides (S1–S6) of the dam had an influence on the width of the breach. The width of the breach was reduced by 4.1, 2, 2.9, 0.8, 0.45, and 0.1 cm, correspondingly. When the slides occurred, the sliding materials partially blocked the breach, causing a reduction in the width of the beach. The breach was gradually opened wider again while the slid materials were taken by the overtopping flow downstream. Based on the test result (Figure 13d,e), the width evolution gradually becomes stable after the final sliding S6 at 677 s. However, the vertical downcutting of the crest was still active and caused the crest level *z<sup>C</sup>* to decrease until 750 s. After 750 s, the crest level became stable.

Generally, if the volume of a lateral slide is larger, the reduction in the width of the breach should be more observable. However, as a result of the test, the reduction of the width of the breach did not necessarily become larger when the volume of the lateral slides became larger. For example, when slide S1 occurred (Figure 14a), although the volume of the slide was not large, the width of the breach was significantly reduced. This is because the overtopping flow was small at that time and the transport of the slid materials was small, resulting in more slid material accumulating in the breach. When slide S3 occurred (Figure 14c), the slid volume was large, but the width change of the breach was not obvious, due to the large discharge and because the transport of the slid materials was significant such that the accumulation of slid materials in the breach was greatly reduced. Therefore, there is no obvious correlation between the change in the width of the breach and the volume of the slid materials in the test. This is mainly because larger discharges will transport more slid materials. Therefore, it may not be accurate to use the width of the breach to estimate the overtopping discharge when many lateral slides of the dam occur. In addition, we can find that after about 645 s, the lowering rate of tank level and crest level gradually decreased. The rate of change in the width of the breach from 651 to 677 s gradually decreased. Additionally, as the volume of the lateral slides gradually decreased, the influence on the width of the breach was also less; e.g., slide S5 caused marginal changes in breach width. After slide S6, the width of the breach was stable and no longer changed, and furthermore, sliding events no longer occurred.

We then compared the morphological evolutions of the breach between the model and test results. From Figure 13d, the lake level and the crest level results of the model and test results are in generally good agreement, with the exception of a slight difference at the early stage before 645 s. The difference is due to the test starting from retrogressive erosion due to seepage and then overtopping. The test dam's strength was weaker than that of the breach model. In other words, many parts of the materials of the test dam model were formed from the very loose slid materials of the retrogressive slides. This situation is not considered in the model. In the model, we only considered the overtopping process. Therefore, the downcutting erosion rate in the test was higher during the early stage than those set in the model.

In Figure 13e, the evolution of the breach channel width of the model results shows a smoothly increasing curve. In contrast, from the test result, the evolution of the breach width was not smooth and the breach width was reduced when the four lateral slides S1–S4 occurred. These discrepancies were caused by the masses of lateral sliding materials not being considered in the model; i.e., the lateral sediment influx was not considered in the model equations. However, the model result fits the trends of the test result qualitatively well with the exception of the breach width reduction kinks in the curves. Additionally, the small pulses from the lateral slides did not affect the continuous evolution of the crest and the tank level. Therefore, to estimate the dam breach discharge, we could use the lateral erosion (or width expansion) to represent the lateral slides, especially for the loose materials.

In this study, due to the complexity of the test measurement, we did not measure the discharge directly but estimated the discharge during the breach by two different approaches. In the first approach, we considered the mass balance in the lake and assumed the lake area was maintained at a constant size during the breach and thus the discharge can be simply estimated using Equation (16) by differentiating the lake level with respect to time and multiplying by the lake area.

$$Q\_{\rmTest}(t) = -A\_L \frac{dz\_L(t)}{dt} \tag{16}$$

The estimated discharge hydrograph of the test is shown with the thin red curve in Figure 13f. The curve is obviously zigzag in shape. This is because the discharge is estimated by the differential of the lake level. Small changes in the tank level cause large changes in the discharge; for example, the significant change in the hydrograph during t = 700~716 s, as shown in Figure 13f.

Therefore, we developed the second approach to estimate the discharge hydrograph for the test. Similar to the model derivation in Section 3, we applied the broad-crestedweir discharge equation again to estimate the discharge hydrograph of the test using Equation (17):

$$Q\_{\rmTest}(t) = c\_D \sqrt{\frac{8g}{27}} b(t) \eta(t)^{3/2} \tag{17}$$

where *c<sup>D</sup>* is a discharge coefficient to be determined. In previous research, Paˇrílková et al. (2012) [58] and Imanian et al. (2021) [59] both pointed out the choice of *c<sup>D</sup>* could be highly affected by the roughness of the crest and different hydraulic head ratios. However, it is difficult to measure the roughness of the crest in the dam breach experiments, and the coefficients in our dam breach tests were not comparable with those dams without breach in the literature [58,59]. To calibrate the coefficients, we considered the tank level becoming stable in the late stage of the test, and thus used the estimated hydrograph of the late stage derived from Equation (16) to calibrate *cD*; *c<sup>D</sup>* was set as 0.75, with *b*(*t*) and *η*(*t*) from the test measurement. The resultant hydrograph is shown in Figure 13f as the thin blue curve. To discuss in further detail, we also considered the moving average of the early stage of the test and estimate *c<sup>D</sup>* as 0.5. The result is shown as the dashed blue curve. However, we found that the peak discharge of the hydrograph obtained by the second approach (Equation (17)) with *c<sup>D</sup>* = 0.75 was close to the peak discharge obtained by the first approach (Equation (16)), i.e., the thin blue curve and thin red curve in Figure 13f, respectively. In contrast, the peak discharge of the hydrograph using *c<sup>D</sup>* = 0.5 was smaller than that obtained by Equation (16) (dashed blue curve and thin red curve, respectively). The hydrograph estimated with a lower coefficient may underestimate the real peak discharge due to the moving averaging process. Overall, the two hydrographs are smoother and more stable than those obtained by Equation (16). To more accurately estimate the discharge, the second approach that applied the broad-crested-weir discharge equation with *c<sup>D</sup>* = 0.75 is preferred.

In Figure 13f, the three hydrographs estimated for the test using the two approaches show an increase in the discharge, maintain at a fairly "stable" discharge, and then a decrease with time, which resembles a trapezoidal shape. In contrast, the modeled discharge hydrograph (thick blue line in Figure 13f) shows a higher peak discharge at about 645 s, and this curve is similar to a bell shape without a stable discharge. The rise and decline of the hydrographs match the general trends of the estimated hydrographs from the test result.

From the perspective of disaster prevention, we hope to determine the timing of the peak discharge as preparation for early warning. Therefore, it is important to know when the peak discharge of a dam breach occurs. The timing of the peak discharge of this model is at around 645 s, which approximately matches the result of the test result. The dam breach model we proposed is simple and its estimation of hydrographs, lake and crest levels, and widths of the breach are equivalent to the test results. Therefore, it has the potential to be extended and applied to dam-breach assessment and early warning in actual situations.

From the perspective of dam breach warning and hazard reduction, the timing and magnitude of peak discharge arrival are both very important factors. From the test results, we found that when the timing of peak discharge was approaching, the lateral slides occurred more frequently and the slid masses increased. If we apply this finding to the real world, the frequency of lateral slides and their magnitudes can be indicated by seismometers and cameras to give early warning on the timing of peak discharge of a dam breach. In addition, the peak discharge and hydrograph can be calculated through the proposed dam breach model with variations of the breach width and flow depth at the crest. This model shows consistency in comparison with the field observation data and test results, and the model can be a useful tool in dam breach warning and hazard reduction.

**Figure 13.** Test and model results of breaching: (**a**) seismic signal of Acc. 2, (**b**) time–frequency spectrum of the seismic signal of Acc. 2, (**c**) spectral magnitude profile of 366 Hz cross-section shown in Figure 13b, (**d**) lake (tank) and crest levels of the model and test results, (**e**) breach width (crest channel width), (**f**) discharge hydrographs of the test and model.

#### **4. Conclusions**

This study constructed test dam models in an indoor flume to examine dam failure processes with seismic signal monitoring. A simple dam breach model was proposed and used to compare the flood process of the test. We explored the seismic signals corresponding to the sliding events during retrogressive erosion due to seepage and breaching. The monitored seismic signals corresponded clearly to the sliding events. As retrogressive erosion continued, the erosion eventually reached the crest at the upstream side of the dam, and then triggering overtopping and breaching. We verified satisfactorily this simple dam breach model by using our test result together with field observations from the literature.

Precursor seismic signals generated by cracking prior to the sliding events of the dam model were detected. Further research is strongly recommended on how to extend this observation for dam safety monitoring and prewarning to the real world. Based on the characteristics of the seismic signals, we found four types of mass movements during the retrogressive erosion process, i.e., single, intermittent, and successive slides, and fall. This result is also very useful when categorizing landslide types using seismic signals.

Overtopping discharge and lateral sliding masses of the dam are also among the important factors influencing the evolution of the breach. The masses of the lateral slides will suddenly reduce the width of the breach, but the overtopping flow will transport the masses downstream, making the width of the breach wider again. Two approaches that apply the lake level data or the broad-crested-weir discharge equation were used to estimate the hydrograph for the test. The hydrographs, obtained by the approach using the broad-crested-weir discharge equation, showed smoother and more stable hydrograph curves than those obtained by the other approach using lake level data.

The proposed simple dam breach model satisfactorily simulated the hydrograph of dam breaching and successfully assessed the vertical and lateral variations of the breach. The model can be a useful tool to help explain the dam breach process and dam breach prewarning. However, in future study, the mass input from the lateral slides can be further considered in the model.

**Supplementary Materials:** The following are available online at https://zenodo.org/record/522055 8#.YR5PwdMzZTY, Video S1: Event 1 and 2, Video S2: Event 3, Video S3: Event 4, Video S4: Event 5, Video S5: Event 6, Video S6: Event 7 side view, Video S7: Event 7 front view.

**Author Contributions:** Conceptualization, Z.-Y.F., C.-Y.H. and S.-C.C.; methodology, Z.-Y.F. and C.-Y.H.; validation, Z.-Y.F., C.-Y.H. and I.-F.T.; formal analysis, Z.-Y.F. and C.-Y.H.; investigation, Z.-Y.F., C.-Y.H. and I.-F.T.; resources, S.-C.C.; data curation, C.-Y.H. and I.-F.T.; writing—original draft preparation, Z.-Y.F. and C.-Y.H.; writing—review and editing, Z.-Y.F., C.-Y.H., I.-F.T. and S.-C.C.; visualization, C.-Y.H. and I.-F.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Ministry of Science and Technology, Taiwan, R.O.C., grant number 109-2625-M-005-009-MY2.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors acknowledge Hallam Atherton for reviewing the manuscript style. **Conflicts of Interest:** The authors declare no conflict of interest.

#### **List of symbols**


### **References**


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