Simulation and Management Impact Evaluation of Debris Flow in Dashiling Gully Based on FLO-2D Modeling

Abstract

Dashiling Gully, located in Miyun District, Beijing, exhibits a high susceptibility to debris flow due to its unique geological and topographical characteristics. The area is characterized by well-developed rock joints and fissures, intense weathering, a steep gradient, and a constricted gully morphology. These factors contribute to the accumulation of surface water and loose sediment, significantly increasing the risk of debris flow events. Following a comprehensive field geological investigation of Dashiling Gully, key parameters for simulation were obtained, including fluid weight, volume concentration, and rainfall. The formation and development conditions of potential mudslides were analyzed, and numerical simulations were conducted using FLO-2D software (version 2009) to assess scenarios with rainfall probabilities of 1 in 30, 50, and 100 years. The simulations accurately reconstructed the movement velocity, deposition depth, and other critical movement characteristics of mudslides under each rainfall scenario. Using ArcGIS, pre- and post-treatment hazard zoning maps were generated for Dashiling Gully. Furthermore, the efficacy of implementing a retaining wall as a mitigation measure was evaluated through additional numerical simulations. The results indicated that mudslide velocities ranged from 0 to 3 m/s, with deposition depths primarily between 0 and 3 m. The maximum recorded velocity reached 3.5 m/s, corresponding to a peak deposition depth of 4.31 m. Following the implementation of the retaining wall, the maximum deposition depth significantly decreased to 1.9 m, and high-risk zones were eliminated, demonstrating the intervention’s effectiveness. This study provides a rigorous evaluation of mudslide movement characteristics and the impact of mitigation measures within Dashiling Gully. The findings offer valuable insights and serve as a reference for forecasting and mitigating similar mudslide events triggered by heavy rainfall in gully mudslides.

1. Introduction

The mountainous regions of Beijing are prone to debris flows and landslides, particularly during the summer months. This susceptibility is attributed to a combination of factors, including complex geological structures, frequent neotectonic activity, anthropogenic influences, and intense monsoon rainfall [1]. As Beijing needs to develop and integrate with the nation’s strategy, there is a growing need for enhanced debris flow management and control strategies. Effective management requires a thorough understanding of debris flow formation conditions, movement patterns, and underlying mechanisms. Numerical simulation techniques offer a valuable tool for accurately recreating the evolution of debris flow, providing crucial insights into their dynamic and kinematic characteristics, as well as informing preventive engineering measures. This study focuses on Dashiling Gully as a case study to investigate debris flow events. Analyzing the dynamic and kinematic characteristics of debris flow in Dashiling Gully, along with determining appropriate preventive engineering measures, is essential for forecasting and mitigating similar events within Beijing’s mountainous terrain.

Debris flows are complex two-phase flows composed of solid and liquid phases, with their movement mechanisms governed by the properties of each phase and their interactions [2]. Dynamics characteristics can vary significantly at different locations within a mudslide [3]. Numerical simulation methods enable the visualization of mudslide movement, providing data on parameters such as velocity, deposition depth, and other relevant attributes. This information is crucial for evaluating the effectiveness of mudslide mitigation strategies. In recent years, extensive research on mudslides has been conducted by scholars worldwide. With the rapid advancements in science and technology during the 21st century, various software tools capable of simulating mudslide dynamics have emerged, including Geoflow, Massflow-2D [4], RAMMS [3], FlO-2D [5], and CFX.

Numerous researchers have utilized ArcGIS [6,7,8] to visualize numerical simulation results, effectively illustrating the dynamics of mudslide events. These visualizations provide a valuable reference for developing mudslide prevention and control strategies. Furthermore, understanding mudslides and mass movements has broader implications, extending to marine environments and the geological record of sediment transport on land and in the oceans [9,10]. This knowledge is relevant for modeling marine instability and landslide processes as well [11,12,13,14]. Several studies have employed numerical simulations to investigate mudslides. Četina et al. [15] simulated the movement of debris flow beneath Stoze, Slovenia. Wu et al. [5] compared the performance of two numerical software packages, FLO-2D and Debris-2D, for debris flow modeling. Kim et al. [16] used FLO-2D to establish a mathematical model of the Umyeon Mountain debris flow. Liu J [17] assessed the effectiveness of debris flow mitigation measures using the Kanako 2D software (Ver.2.00). Hsu et al. [18] employed numerical simulations to delineate debris flow hazard zones. Chau [19] integrated debris flow modeling with GIS to identify potential hazard zones. Wu et al. [20] utilized GIS for three-dimensional debris flow simulations. Nie et al. [21] developed a coupled model for dynamic hazard assessment, considering landslides as material sources for debris flows. Further research has focused on modeling the entire debris flow process, from initiation to deposition. Chen et al. [22] proposed a two-dimensional hybrid numerical method for simulating the complete debris flow progression. Cui et al. [23] investigated debris flow processes using the Arc-SCS model combined with hydraulic methods and empirical formulas to calculate runoff dynamics. Hong et al. [24] presented a unified framework for addressing rainfall-induced debris flow initiation (triggered by landslides) and subsequent propagation. Zhou et al. [25] forecasted debris flow initiation under extremely heavy rainfall conditions. Studies have also explored debris flow risk assessment and mitigation. Jakob et al. [26] evaluated potential losses and damages caused by debris flows. Zhang et al. [27] developed an optimized fluid volume approach for simulating three-dimensional debris flows.

This study employed the FLO-2D numerical simulation method to investigate the Dashiling Gully debris flow in Beijing. The objective was to simulate the movement processes under various rainfall scenarios, both before and after the implementation of mitigation measures, and to evaluate the effectiveness of the implemented gully remediation. A 1:1000 topographic map of Dashiling Gully was obtained through drone aerial photography. High-precision DEM data were acquired using GIS software (10.8), converted into ASCII format, and subsequently used to construct the computational model. Relevant parameters required for the simulation were gathered through field investigations, laboratory experiments, and calculations. The movement characteristics of the debris flow under different pre- and post-treatment conditions were simulated, and the mitigation efficacy of the implemented barrier dam was assessed through comparative analysis. The computation of pertinent kinematic features, such as flow velocity and deposition depth, provides valuable reference data for the management of similar debris flow events. Hazard zones within the Dashiling Gully were identified based on the simulated movement velocity and deposition depth, both before and after the implementation of mitigation measures. Subsequently, the effectiveness of the intervention strategies for debris flow prevention and control was evaluated. The findings of this study offer valuable insights and serve as a reference for managing similar mudslide events. This study aims to identify and assess the hazardous zones in the Dashiling Gully by examining changes in movement velocity and deposition depths before and after treatment interventions. Additionally, we evaluate the effectiveness of these interventions in mudslide prevention and control. The main innovation of this study is to combine the actual engineering projects with numerical simulation, fully consider the impact of three different rainfall frequencies, and reproduce the debris flow movement characteristics under three different rainfall frequencies. Based on the reproduced movement characteristics, a corresponding management plan is proposed, and the feasibility of the scheme is tested again by numerical simulation. The economy can be maximized while meeting the safety requirements.

2. Study Area Overview

Dashiling Gully is situated in the northwest region of Bulaotun Town, Miyun District, Beijing, at longitude 116°56′48.66652″ E and latitude 40°40′20.18105″ N (Figure 1). The gully is located upstream of Dashiling Village, with a steep slope. Dashiling Gully is located upstream of Dashiling Village and is characterized by a steep slope and significant terrain undulation. The catchment area of Dashiling Gully spans approximately 0.427 km², featuring one main gully and five branch gullies arranged in a dendritic pattern. The main gully extends for about 1312.47 m, with its lowest elevation being 429.59 m and its highest elevation being 605.12 m, resulting in a relative elevation difference of 175.53 m and an average longitudinal gradient of 133.74‰. The steep topography, substantial longitudinal gradient, and prevalent weathering, denudation, and collapse phenomena within the main and branch gullies provide favorable conditions for debris flow formation and movement. Additionally, the constricted nature of the gullies facilitates the rapid accumulation of surface water, mobilizing the loose sediment and generating mudslides with significant kinetic energy.

Based on regional geological data and field surveys, the exposed strata in the Dashiling area primarily consist of Cretaceous southern porphyry coarse-grained biotite granodiorite gneiss (K₁N) and Pleistocene alluvial and residual slope deposits. The latter is mainly composed of basalt and volcanic rocks. The Pleistocene alluvial succession largely comprises gravel beds interspersed with large boulders, sand, and other residual slope components. K₁N and Qp² represent the typical deposits of the Cretaceous (southern porphyry coarse-grained biotite granodiorite gneiss) and Pleistocene (alluvial and residual slope deposits) epochs in the Miyun District, respectively.

The Dashiling Gully study area experiences a warm temperate monsoon continental semi-arid climate. The average annual temperature is 10 °C, with an extreme minimum temperature of −27.3 °C. The long-term average annual rainfall is 600 mm, exhibiting a decreasing trend from southwest to northeast.

3. Mudslide Formation Conditions

3.1. Source Conditions

The upper and middle reaches of the Dashiling Gully contain abundant Quaternary loose sediment deposits, along with artificial dry masonry dams. These features provide a substantial source of material for mudslide formation during periods of heavy rainfall (Figure 2 and Figure 3). The primary source area, located in the formation zone, is characterized by higher terrain on the western, northern, and eastern sides, with lower elevations in the southern and central portions. This area exhibits steep slopes with undulating topography, generally forming a “V” shape. The natural slope angle ranges from 30° to 50°, with a vegetation cover rate of approximately 50%. Loose sediments on the mountain slopes constitute the primary source of both eroded material and debris flow. Human activities, particularly farming practices, frequently disturb these loose accumulations on slopes and within gullies. Areas devoid of vegetation and loose material experience rapid rock weathering and joint development, accelerating the rate at which rocks undergo avalanches of rockfall events. The formation zone’s slope area is approximately 51.02 × 10⁴ m². Field investigations indicate an average loose material thickness of about 0.217 m on the slope surface. Based on these measurements, the total static reserve volume of loose material on the slope surface is estimated to be 11.08 × 10⁴ m³.

In mudslide-prone areas, tributary gullies often exhibit steeper slopes and greater vertical drops compared to the main gully. Additionally, larger watershed areas in tributaries increase the likelihood of material contribution to mudslide activity. On-site investigations revealed that the primary sources of loose materials, including alluvial, diluvial, and slope deposits within the channel, consist mainly of sedimentary gravels and loose gravels. Debris flow material displays highly variable particle size distributions and is generally angular and poorly rounded, indicating short transport distances. Considering the source characteristics and the looseness of the channel material, the channel area is estimated to be 5.14 × 10⁴ m², with an average gravel thickness ranging from 1.8 m to 2.0 m. Based on these calculations, the total static reserve of loose material in the channel is estimated to be 10.5 × 10⁴ m³.

During this study, potentially unstable slopes were identified in the mid-section of the Dashiling Gully watershed. These slopes exhibit susceptibility to failure, potentially acting as material sources for debris flows and other mass wasting events. They are characterized by a series of rockfall and rockslide occurrences and have the potential to trigger small-scale debris avalanches with an estimated volume of approximately 200 m³. In terms of storage capacity, these slopes could contribute a dynamic storage volume of 40 m³ and a static storage volume of 200 m³ to potential debris flow events.

3.2. Hydrological Conditions

The primary water source for debris flows in Dashiling Gully is atmospheric precipitation, with heavy rainfall acting as the main triggering factor. Therefore, mudslides in Dashiling Gully are classified as rainfall-induced gully debris flows [1]. The study area is located within a region of high rainfall in the Yanshan Mountains, specifically in the low and middle mountain zones. Influenced by both climatic and topographical factors, precipitation exhibits characteristics of substantial inter-annual variation, significant regional differences, uneven seasonal distribution, and concentration during the flood season (Figure 4). Rainfall is predominantly concentrated in the summer months (June to September), accounting for over 72% of the annual precipitation, with an average annual rainfall of 675.0 mm. The flood season is characterized by intense and heavy rainfall events, which are primary triggers for mudslides in the area.

4. Research Methodology

This study utilized FLO-2D software to simulate the Dashiling Gully mudslide. Developed by O’Brien in 1988, FLO-2D is a two-dimensional numerical simulation tool designed for analyzing and computing flood and debris flow events. The software primarily employs the non-Newtonian model and the central finite difference numerical method. FLO-2D enables the real-time simulation of debris flow movement velocities and deposition depths during events, and it is also effective for evaluating the performance of mitigation structures such as check dams [28].

4.1. FLO-2D Model and Governing Equations

The FLO-2D model utilizes several governing equations to simulate debris flow behavior. These equations include the following.

(1) Continuity equation:

$$\frac{\partial h}{\partial t}+\frac{\partial \left(uh\right)}{\partial x}+\frac{\partial \left(vh\right)}{\partial y}=\mathrm{I}$$

(1)

where $h$ represents the deposition depth; $\mathrm{I}$ denotes the rainfall intensity during the mudslide event; $u$ and $v$ indicate the average flow velocities in the x and y directions, respectively; and t is the time.

(2) Equation of motion:

$$S_{fx}=S_{Ox}-\frac{\partial h}{\partial x}-\frac{\partial u}{g\partial t}-u\frac{\partial u}{g\partial x}-v\frac{\partial u}{g\partial y}$$

(2)

$$S_{fy}=S_{Oy}-\frac{\partial h}{\partial y}-\frac{\partial v}{g\partial t}-u\frac{\partial v}{g\partial x}-v\frac{\partial v}{g\partial y}$$

(3)

where $g$ represents the gravitational acceleration; $S_{fx}$ and $S_{fy}$ are the frictional slopes in the x and y directions, respectively; and $S_{Ox}$ and $S_{Oy}$ are the slopes at the bottom of the channel in the x and y directions, respectively.

(3) Rheological equations:

$$\tau ={\tau }_c+{\tau }_{mc}+{\tau }_v+{\tau }_t+{\tau }_d$$

(4)

where ${\tau }_c$ represents the viscous yield force, ${\tau }_{mc}$ denotes the Mohr–Coulomb shear stress, ${\tau }_v$ indicates the viscous shear stress, ${\tau }_t$ is the turbulent shear stress, ${\tau }_d$ represents the dispersive shear stress, and $\tau$ is the total shear stress.

O’Brien and Julien [29] further refined the equations by introducing an improved slope representation:

$$S_f=S_y+S_v+S_{td}=\frac{{\tau }_y}{{\gamma }_{m}h}+\frac{K\eta u}{8{\gamma }_m{h}^2}+\frac{n^2{u}^2}{h^{4/3}}$$

(5)

$${\tau }_y={\alpha }_2{e}^{{\beta }_2{C}_v}$$

(6)

where $S_f$ represents the total friction slope drop; $S_y$ denotes the yield slope drop; $S_v$ indicates the viscous slope drop; $S_{td}$ is the turbulent-discrete slope drop; ${\tau }_y$ represents the yield stress; ${\gamma }_m$ denotes the relative density of the earth and rock fluid; $h$ indicates the deposition depth; K represents the laminar resistance coefficient; $\eta$ denotes the viscous coefficient; n indicates the Manning’s coefficient; and u is the movement velocity.

4.2. Selection of Simulation Parameters

4.2.1. Fluid Weight

Due to the absence of historical monitoring data for debris flows in Dashiling Gully, the mudslide flow fluid weight was determined through a combination of field investigations and a table look-up method. The mudslide type is categorized as a water–rock flow, with the fluid consisting of a dilute slurry. Following the ”Specification of geological investigation for debris flow stabilization” (DZ/T0220-2006) [30], Appendix H, a mudslide investigation form was completed, and the susceptibility degree was scored according to Appendix G [30], resulting in a score of N = 78. Based on Table G.2 [30], the mudslide fluid weight (γ_c) was determined to be 1.537 (t/m³), and the sediment correction factor was established as 1.50 (γ_h = 2.65).

4.2.2. Selection of Catchment Points

Catchment points represent the initiation points for simulated mudslides, assuming that mudslide events originate from these specific locations. These points are typically situated in areas with dense material sources and favorable conditions for rainwater accumulation. Such locations provide increased gravitational potential energy for mudslide initiation, which is subsequently converted into kinetic energy during mudslide movement [31]. Consequently, catchment points are predominantly located at the interface between the source area and the transportation zone. Figure 5 illustrates the selected catchment point locations based on this rationale. Due to the short lengths of other minor tributary gullies, the establishment of catchment points within them was deemed unnecessary.

4.2.3. Volume Concentration

A mudslide is a two-phase flow composed of solid particles and a fluid, typically water. It is characterized by a high concentration of solid material suspended within the fluid, resulting in a heterogenous, non-Newtonian fluid behavior. The volume concentration represents the proportion of the total volume occupied by the solid phase within the mudslide mixture. Due to the challenges associated with field sampling, the volume concentration for this study was determined to be 0.45, based on a combination of the FLO-2D manual recommendations and field observations. The volume concentration (Cv) can be expressed as the following:

$$C_{\mathrm{v}}=\frac{v_s}{v_w+v_s}$$

(7)

where $V_S$ represents the volume of solids in the mudslide flow mixture and $V_w$ denotes the volume of water in the mudslide flow mixture.

4.2.4. Laminar Flow Coefficient, Yield Stress, and Viscosity Coefficient

Based on the FLO-2D manual recommendations and the characteristics of the Dashiling Gully mudslide, the laminar flow damping coefficient K was determined to be 2300. Yield stress ${\tau }_y$ and the viscous coefficient $\mathsf{\eta }$ are two critical parameters in the rheological model used for numerical simulation calculations, as they influence the flow and deposition processes of the mudslide.

The relationship between yield stress ${\tau }_y$ and volume concentration $C_v$ can be expressed as the following:

$${\tau }_y={\partial }_2{e}^{{\beta }_2{C}_v}$$

(8)

Similarly, the relationship between the viscosity coefficient $\mathsf{\eta }$ and volume concentration $C_v$ is given by the following:

$$\eta ={\partial }_1{e}^{{\beta }_1{C}_v}$$

(9)

For this study, the values of these parameters were selected based on the FLO-2D manual and the specific conditions of Dashiling Gully, resulting in the following: ${\partial }_1$ = 0.811, ${\partial }_2$ = 0.0046, ${\beta }_1$ = 13.72, and ${\beta }_{2 }$ = 11.24.

4.2.5. Manning’s Roughness Coefficient

In FLO-2D simulations, Manning’s roughness coefficient represents the roughness of the surface over which the debris flow travels. Higher values of Manning’s coefficient indicate a greater resistance to flow and a rougher surface. Therefore, the value of (n) needs to be assigned according to the micro-geomorphological characteristics of the mudslide channel. Based on the FLO-2D manual recommendations and the observed conditions in Dashiling Gully, the following values were selected: 0.1 for the transportation zone, 0.3 for the deposition zone, and 0.2 for other areas.

4.2.6. Clear Water Flow Process Line

The clear water hydrograph represents the real-time rainfall runoff during a mudslide simulation. Multiplying the clear water hydrograph by a magnification factor generates the mudslide hydrograph, which accounts for the additional volume and altered flow characteristics due to the presence of sediment.

This study employed a rainfall-runoff method to estimate mudslide discharge, assuming that mudslides and rainstorms occur concurrently and with the same frequency. Under this assumption, the design flood discharge at the catchment outlet, including all designated inflows, is considered to be transformed into mudslide discharge. The calculation process begins by using hydrological methods to determine the design flood discharge for various rainfall frequencies at the sub-basin outlet (refer to hydrology manuals for specific calculation methods). Subsequently, appropriate blockage coefficients are selected, and Equation (10) is used to compute the peak mudslide flow discharge.

$$Qc=(1+\phi )Qp\cdot Dc$$

(10)

where Qc represents the peak debris flow discharge (m³/s) for a given rainfall frequency P; Qp denotes the peak flood discharge (m³/s) for the same rainfall frequency P; $(1+\phi )$ indicates the mudslide sediment correction factor, taken as 1.50 according to Table G.2 [30] in the “Specifications for Engineering Investigations of Mudslide Disaster Prevention and Control”; $\phi$ represents the mudslide sediment correction factor; and Dc denotes the mudslide blockage coefficient, determined based on Table I.1 [30] in the same “Specifications for Engineering Investigations of Mudslide Disaster Prevention and Control”, with a value of 2.0 adopted in this study.

For catchment areas (F) less than 3 km², Equation (11) is used to calculate the peak flood discharge.

$$Qp=\psi \cdot F\cdot S$$

(11)

where $\psi$ represents the stormwater runoff coefficient; F denotes the catchment area (km²); and S indicates the hourly rainfall intensity (mm/h).

Using these equations, the peak flood discharge (Qp) and peak mudslide discharge (Qc) were calculated for each section, as presented in

Table 1. Calculation of peak flood discharge (Qp) in the main gully and tributary gullies for various rainfall frequencies.

Section	Catchment Area (km2)	Rainstorm Intensity (mm/h)			Peak Flood Discharge (m3/s)
		p = 1%	p = 2%	p = 3%	p = 1%	p = 2%	p = 3%
Main gully catchment	0.179062	125	115	100	1.87	1.72	1.49
Tributary gully catchment	0.10916	125	115	100	1.14	1.05	0.91

.

The amplification factor BF, used to convert the peak flood discharge to peak debris flow discharge, is calculated based on the volume concentration (Cv) using Equation (12).

$$BF=\frac{1}{1-C_V}$$

(12)

5. Simulation Results and Analysis

5.1. Computational Modelling Results

Mudslide events with rainfall frequencies of 1 in 30 years, 1 in 50 years, and 1 in 100 years were simulated to determine the corresponding spatial distributions of mudslide velocities and deposition depths. The results of these simulations are presented as distribution maps in Figure 6.

5.2. Analysis and Interpretation of Simulation Results

5.2.1. Movement Velocity Analysis

(1) Overall flow velocity: The simulated mudslide velocities exhibited relative stability across different scenarios. Under typical rainfall frequencies, velocities within the tributary gully generally ranged from 0 to 1.5 m/s, while velocities in the upstream section of the main gully, characterized by a steeper gradient, ranged from 0 to 3 m/s. Peak velocities were observed at the confluence of the tributary and main gullies. Downstream, velocities decreased as the terrain gradient flattened, ultimately leading to deposition at the gully outlet.

(2) Influence of rainfall intensity: Both mean and peak mudslide velocities increased slightly with increasing rainfall intensity. Mudslide velocity is primarily controlled by gully morphology and rainfall conditions. While increases in rainfall intensity resulted in only minor increases in flow velocity, the extended duration of high-velocity flow led to a significant increase in sediment transport capacity, thereby enhancing the destructive potential of the mudslides. Simultaneously, downward and lateral erosion deepened and widened the gully, respectively, replenishing the sediment supply for future mudslide events and further increasing their magnitude and destructive capacity.

5.2.2. Mudslide Deposition Depth Analysis

(1) Deposition depth and velocity: Mudslide deposition depth and velocity are critical factors in hazard assessment. Simulation results indicated that the deposition depths increased significantly with increasing rainfall intensity, particularly at the confluence of the tributary and the main gully, as well as at sharp bends within the gully. The maximum deposition depth was observed at the accumulation zone near the gully outlet.

(2) Influence of rainfall intensity on sediment transport: Under low rainfall intensities, limited clear water flow resulted in weak erosive power and reduced sediment transport capacity. As rainfall intensity increased, the clear water flow became more substantial, enhancing erosion and leading to larger mudslide volumes. At the maximum rainfall intensity, the sediment transport capacity reached a critical threshold, resulting in a dramatic increase in sediment transport and deposition further downstream towards the gully outlet.

(3) Absence of deposition fan: Despite varying rainfall frequencies, no distinct deposition fan was formed at the Dashiling Gully outlet. This is attributed to the narrow channel geometry, which restricts rapid flow, and the presence of two near right-angle bends that impede mudslide movement and significantly reduce flow velocities. Additionally, the gentle slopes downstream of the gully and at the outlet, combined with the limited space at the gully mouth, further contribute to the absence of a well-defined deposition fan.

5.3. Hazard Evaluation

Mudslides pose a significant threat to both human life and the environment due to their destructive potential. Assessing and evaluating mudslide hazards are crucial steps for implementing effective mitigation and control measures. This study employed established mudslide hazard classification criteria (see

Table 2. Mudslide hazard classification based on deposition depth (H) and the product of maximum deposition depth and maximum velocity (HV).

Mudslide Hazard Level	Deposition Depth (H, m)	Logical Relation	HV (m2/s)
high risk	$\mathrm{H} \ge$ 2.5	OR	$\mathrm{HV} \ge$ 2.5
medium risk	$0.5\le$ $\mathrm{H}<2.5$	AND	$0.5\le$$\mathrm{HV}<2.5$
low risk	$0.0<$ $\mathrm{H}<2.5$	AND	$\mathrm{HV}<0.5$

Note: HV represents the product of deposition depth and movement velocity.

), which consider two key parameters—flow velocity and deposition depth—along with an assessment of the Dashiling Gully morphology, to categorize the level of risk [3].

As depicted in Figure 7, the primary high-risk zones are concentrated at the deposition area near the gully outlet, indicating a significantly elevated mudslide hazard in these locations. Therefore, it is crucial to implement regular monitoring and appropriate mitigation measures to protect the lives and property of nearby residents.

6. Calculation of Parameters for Mudslide Mitigation

6.1. Total Mudslide Volume

The design and mitigation measures for Dashiling Gully considered a 100-year return period (p = 1%) rainfall event with an intensity of 125 mm/h. The total mudslide volume (Q) can be determined through either computational or empirical methods. While empirical methods offer higher accuracy, they often lack the necessary data and can only provide rough estimates. Therefore, a computational method based on the mudslide duration (T) and the peak discharge (Qc) was employed, following the formula provided in Appendix I [32] of the “Mudslide Disaster Prevention and Control Engineering Survey Specification” (DT/T0220-2006) [30]. The typical peak duration of a mudslide ranges from 20 to 60 min, with 60 min selected for this calculation.

The total mudslide volume is calculated using Equation (13):

$$Q=KTQc$$

(13)

When F < 5 km², K is equal to 0.202. The calculated total mudslide volume for the main gully section is presented in

Table 3. Calculation of total mudslide volume (Q) in the main gully and tributary gullies of the Dashiling Gully for various rainfall frequencies.

Section	Mudslide duration	Peak mudslide discharge Qc (m3/s)			K	Total mudslide volume Q (104 m3/h)
	(s)	p = 1%	p = 2%	p = 3%	0.202	p = 1%	p = 2%	p = 3%
Main gully catchment	3600	5.60	5.15	4.48		0.4069	0.3744	0.3255
Secondary gully catchment		3.41	3.14	2.73		0.2481	0.2282	0.1985

.

6.2. Sediment Yield from a Mudslide

The total volume of sediment transported by a single mudslide event can be calculated using Equation (14):

$$Q_H=Q({\gamma }_c-{\gamma }_w)/({\gamma }_H-{\gamma }_w)$$

(14)

where $Q_H$ represents the total amount of sediment discharged by a single mudslide event (m³); $Q$ denotes the total mudslide volume (m³); ${\gamma }_c$ indicates the specific weight of solids within the mudslide (t/m³); ${\gamma }_w$ is the specific weight of water (t/m³); and ${\gamma }_H$ is the specific weight of solids in the mudslide (t/m³).

Due to the lack of historical monitoring data for mudslides in this gully, the type and proportion of solids involved in mudslide movement were estimated based on current gully conditions. The specific weight of solids at the main gully catchment was assumed to be 2.5 t/m³, while the specific weight of solids at the tributary gully catchment was assumed to be 2.4 t/m³. The calculated sediment yields for each catchment are presented in

Table 4. Calculation of total sediment volume transported by a single mudslide event at the main gully and tributary gully catchments in Dashiling Gully.

Section	Mudslide Specific Weight γc	Water Specific Weight γw	Solids Specific Weight γH	Sediments Volume QH (104 m3)
	(t/m3)	(t/m3)	(t/m3)
				p = 1%	p = 2%	p = 3%
Main gully catchment	1.537	1	2.5	0.1457	0.1340	0.1165
Tributary gully catchment	1.537	1	2.4	0.0952	0.0875	0.0761

.

6.3. Mudslide Impact Pressure

Mudslide impact force is a critical parameter in the design of mudslide mitigation structures. The overall impact pressure exerted by a mudslide can be calculated using Equation (15), as specified in the “Mudslide Disaster Prevention and Control Engineering Design Specification” (DZ/T0239-2004) [33]:

$$P=\lambda \frac{{\gamma }_c}{g}V{c}^2\sin \alpha$$

(15)

where P represents the overall mudslide impact pressure (kN); $\lambda$ denotes the building shape coefficient, taken as 1.33 for rectangular structures; ${\gamma }_c$ indicates the mudslide specific weight (kN/m³); $Vc$ is the average mudslide velocity across the channel cross-section (m/s); and $\alpha$ represents the angle between the impacted surface of the structure and the direction of mudslide impact, assumed to be 90° in this study. The calculated overall mudslide impact pressures for each section are presented in

Table 5. Calculation of overall mudslide impact pressure at the main gully and tributary gully catchments in the Dashiling Gully.

Location	Mudslide Specific Weight γc (kN/m3)	Average Flow Velocity of Mudslide Section Vc (m/s)			Mudslide Flow Impact Pressure P (kPa)
		p = 1%	p = 2%	p = 3%	p = 1%	p = 2%	p = 3%
Main gully catchment	15.37	1.02	0.46	0.53	2.14	0.44	0.58
Tributary gully catchment	15.37	1.23	0.50	0.87	3.12	0.51	1.56

.

6.4. Mudslide Runup and Maximum Rise Height

When a mudslide encounters an adverse slope, it can exhibit runup, which refers to the phenomenon of the flow continuing upslope due to its momentum. Additionally, when a mudslide encounters an obstacle, its kinetic energy is instantaneously converted into potential energy, causing the debris material to splash upwards, a phenomenon known as mudslide rise height. The maximum rise height and runup height can be estimated using Equation (16):

$$\begin{array}{l}\mathsf{\Delta }H=\frac{V{c}^2}{2g}\\ \mathsf{\Delta }Hc=\frac{bV{c}^2}{2g}\approx 0.8\frac{V{c}^2}{g}\end{array}$$

(16)

where $\mathsf{\Delta }H$ represents the maximum mudslide rise height (m); $\mathsf{\Delta }Hc$ denotes the mudslide runup height (m); $Vc$ indicates the average mudslide velocity (m/s); and b is a coefficient that depends on the slope of the obstacle. The calculated runup and rise heights are presented in

Table 6. Calculated mudslide rise heights and runup heights for the main gully and tributary gully catchments in Dashiling Gully.

Location	Average Velocity of Mudslide Section Vc (m/s)			Mudslide Rise Height ΔH (m)			Mudslide Runup Height ΔHc (m)
	p = 1%	p = 2%	p = 3%	p = 1%	p = 2%	p = 3%	p = 1%	p = 2%	p = 3%
Main gully catchment	1.02	0.46	0.53	0.11	0.02	0.03	0.08	0.02	0.02
Tributary gully catchment	1.23	0.50	0.87	0.15	0.03	0.08	0.12	0.02	0.06

.

6.5. Mudslide Superelevation at Bends

Superelevation, also known as bend overheight, refers to the phenomenon where a mudslide thickens at a bend due to the higher velocity on the outside of the curve (concave bank) and the lower velocity on the inside of the curve (convex bank). This difference in velocity results in a redistribution of the flow, causing it to be thicker on the outside and thinner on the inside. The superelevation at a bend can be estimated using Equation (17):

$$\mathsf{\Delta }h=2.3\frac{V{c}^2}{g}{\log }_{10}\frac{R_2}{R_1}$$

(17)

where $\mathsf{\Delta }h$ represents the superelevation or bend overheight; $R_2$ denotes the radius of curvature of the concave bank; $R_1$ indicates the radius of curvature of the convex bank; $Vc$ is the average mudslide velocity. The calculated superelevation values for each band are presented in

Table 7. Calculated mudslide superelevation at bends in the main gully and tributary gully of Dashiling Gully.

Location	Convex Bank Radius R1 (m)	Concave Bank Radius R2 (m)	Average Velocity of Mudslide Section Vc (m/s)			Mudslide Superelevation $\mathbf{\Delta }\mathit{h} \left(\mathbf{m}\right)$
			p = 1%	p = 2%	p = 3%	p = 1%	p = 2%	p = 3%
Main gully catchment	24	61	1.02	0.46	0.53	0.10	0.02	0.03
Tributary gully catchment	14	32	1.23	0.50	0.87	0.13	0.02	0.06

.

7. Dashiling Mudslide Mitigation Measures

7.1. Mitigation Strategy

Based on the specific characteristics of the Dashiling Gully mudslide hazard, and considering the engineering geology, construction constraints, and other relevant factors, the mitigation strategy focuses on reducing conditions conducive to mudslide initiation, intercepting a significant portion of sediments in the middle and lower reaches of the gully and effectively managing the discharge and routing of smaller volumes of fine-grained sediment. Key engineering measures implemented include demolition, check dam construction, retaining wall construction, drainage channel excavation, cover plate installation, and gully dredging.

A central component of the mitigation strategy is the construction of concrete retaining walls. Specifically, C25 rubble concrete check dams (C25 concrete refers to concrete with a compressive strength of 25 MPa) were installed at the confluence of the main gully and tributary gully, as well as at a major bend in the main gully where dimensions are substantial. These structures, designated as barrage 01 and barrage 02 (barrage 01 and barrage 02 refer to the No. 1 concrete retaining wall and the No. 2 concrete retaining wall, respectively), serve several crucial functions: 1. they hinder the mobilization of sediment sources, thereby reducing the overall volume of material available for mudslide initiation; 2. they intercept and attenuate peak debris flow discharges, decreasing the sediment supply to the downstream gully segment and mitigating the potential for downstream hazards; 3. by regulating peak flows, the check dams alleviate pressure on downstream drainage channels; and 4. they minimize the amount of sediment reaching the gully outlet, ultimately reducing the destructive potential of mudslide events.

7.2. Evaluation of Mitigation Effectiveness

To evaluate the effectiveness of the implemented mitigation measures, mudslide simulations for a 100-year rainfall frequency were conducted while keeping all other computational parameters constant. Prior to running the simulations, the “Create Levee Segment with Polyline” tool within the FLO-2D software was used to incorporate the relevant barrier dam parameters. The resulting simulation outputs are presented in Figure 8, Figure 9 and Figure 10.

Following the implementation of the check dams in Dashiling Gully, the deposition patterns of mudslides exhibited significant changes. In the pre-mitigation scenario, the maximum deposition depth occurred at the accumulation zone near the gully outlet. However, after the implementation of the check dams, the maximum deposition depth shifted to the locations of the two barrier structures. This shift is attributed to the check dams effectively intercepting and retaining the sediment transported by the mudslides. Consequently, post-mitigation deposition depths within the channel were generally below 0.4 m. While the overall mudslide velocities did not change significantly due to the steep gradient of Dashiling Gully, the volume concentration of sediment within the flow decreased substantially, gradually transitioning into a clear water flow that is discharged through the drainage channel. Hazard analysis revealed that the implementation of the check dams successfully eliminated high-risk zones within the gully. The only remaining medium-risk zone is located at the retaining walls themselves. The check dams effectively intercept mudslide events, significantly reducing deposition at the gully outlet and lowering the risk level within the deposition zone [32].

8. Discussion and Conclusions

8.1. Discussion

This study investigated the geological and environmental conditions of the Dashiling Gully debris flow through field geological surveys. The debris flow type was identified as a rainfall-induced gully debris flow, and the formation conditions were analyzed. Numerical simulations were conducted using FLO-2D software to assess debris flow movement characteristics under three different rainfall frequencies (1 in 30 years, 1 in 50 years, and 1 in 100 years). Hazard zones were delineated based on debris flow velocity and deposition depth, with a focus on the 100-year return period event. The necessary parameters for debris flow mitigation were calculated, and a safe and feasible mitigation plan, consisting primarily of check dam construction, was proposed and evaluated. This study employed numerical simulation techniques to investigate the movement velocity and deposition depth of mudslides in Dashiling Gully. However, due to inherent limitations of the FLO-2D software, the model did not account for channel erosion during debris flow initiation and internal water body oscillations within the flow. Future research efforts will aim to incorporate these processes into mudslide modeling. The sudden and unpredictable nature of mudslide events presents challenges for obtaining real-time field data. While numerical simulations offer a valuable tool for hazard assessment, they currently lack comprehensive field data for validation and calibration. Future research will focus on collecting extensive field data to improve the accuracy and reliability of mudslide models. It is important to note that this research has limitations, as it does not explicitly depict the erosive effects of the debris flow on the channel bed and banks, nor does it simulate phenomena such as liquid-phase oscillations and jumping.

Existing mudslide mitigation strategies often fail to achieve a balance between safety and cost-effectiveness, and they may not fully consider the dynamic characteristics of mudslides. Frequently, designs rely on past mudslide events and mitigation parameters, which can lead to either over-engineering or inadequate safety factors. By analyzing the dynamic behavior of mudslides, this study provides a theoretical basis for the design of future mitigation projects in Dashiling Gully, addressing these shortcomings and promoting more effective and efficient mitigation strategies.

8.2. Conclusions

The main conclusions of this study are as follows:

• Field geological surveys were conducted to analyze the geological, topographical, and hydrological conditions contributing to debris flow formation in Dashiling Gully. Key topographic elements (slope, aspect, elevation, and channel bed gradient), geological elements (stratum lithology), and hydrological elements were determined. The basin is characterized by numerous tributary gullies in the basin, and there are sufficient solid sources. The confirmed solid source reserves are about 20 × 10⁴ m³. There is sufficient rainfall in summer, which can easily cause mudslides, seriously threatening the lives and property safety of 13 households in Dashiling Village.
• FlO-2D software was employed to numerically simulate mudslide events in Dashiling Gully under three different rainfall frequencies. The simulations provided critical data on mudslide velocity and deposition depth. Results indicated that mudslide velocity increases with increasing rainfall intensity, and both the extent and depth of deposition also increase with rainfall intensity. Prior to the implementation of mitigation measures, simulations of a 100-year rainfall event revealed a maximum mudslide velocity of 3.5 m/s and a maximum deposition depth of 4.3 m. Hazard zoning classified the gully outlet as a high-risk area under these conditions.
• Following the construction of check dams, additional simulations were conducted for a 100-year rainfall frequency event. The results demonstrated that while mudslide velocities remained relatively unchanged, the check dams effectively trapped a significant volume of sediment. Notably, the maximum deposition depth decreased from 4.3 m to 1.9 m, with maximum deposition now occurring at the check dam locations. Furthermore, post-mitigation deposition depths throughout the gully remained below 0.5 m. Hazard assessments indicated that high-risk zones were eliminated, and apart from a medium-risk area adjacent to the check dams, the entire gully was classified as low-risk. Additional simulations incorporating two more check dams downstream of the gully outlet did not reveal any significant improvement in mitigation effectiveness. Consequently, considering economic and safety factors, check dams were strategically placed at the confluence and bend locations to optimize debris flow mitigation.