Back Analysis of Rainfall-Induced Landslide in Cimanggung District of Sumedang Regency in West Java Using Deterministic and Probabilistic Analyses

Abstract

Rainfall-induced landslides are widespread in Indonesia, particularly in West Java, where volcanic residual soils are typically stable but may become unstable during heavy rainfall. This study aims to back analyze the geotechnical factors contributing to the Cimanggung landslide in 2021. The methods applied in this study include site investigations, laboratory testing, and numerical modeling. We performed deterministic, coupled seepage-slope stability analysis and Monte Carlo probabilistic analysis to assess the slope performance prior to and after rainfall infiltration. The results reveal that the initial water level significantly affects slope stability, and heavy rainfall infiltration triggered the landslide’s initiation. The deep water table (over 20 m below ground level) maintains the slope stability, and increasing the water table to 16 m compromises its stability. Heavy rainfall infiltration reduces suction in the unsaturated zone, decreasing the shear strength and triggering landslides. The heavy rainfall infiltration did not penetrate deep enough to raise the water table; rather, poor urban drainage on the upper slope caused it. Rainfall infiltration caused wetting in the upper zone, weakening the slope and causing loss of support. It is recommended that effective drainage management and integrated slope monitoring be applied to mitigate landslide risks in this region.

1. Introduction

Rainfall-induced landslides are one of the most widespread geo-disasters worldwide. Most rainfall-induced landslide incidents globally take place in tropical regions [1]. The tropical climate has the characteristics of high annual temperatures, high annual rainfall, and distinct wet and dry seasons. During the rainy seasons, the tropical region often experiences intense and prolonged rainfall, particularly during monsoon seasons. Heavy rainfall saturates the soil, reducing its stability and increasing the likelihood of landslides. Rainfall-induced landslides often occur abruptly, causing devastating impacts [2]. Ninety percent of fatalities from landslides were found to be caused by rainfall-triggered landslide disasters. A previous study [3] indicated that the Philippines and Indonesia are landslide fatality hotspots in Southeast Asia, with Indonesia’s fatalities particularly concentrated on the island of Java. Landslides are the second most common disaster in Indonesia, threatening the lives of people and their livelihoods while also causing damage to important infrastructures. A spatiotemporal analysis of landslide occurrences in Java showed that West Java is most prone to landslides, as 67% of incidents took place in West Java, with rainfall being the main triggering factor [4].

Although rainfall is widely known as a triggering factor, heavy rainfall may not always cause a landslide incident. The fundamental slope conditions shall act simultaneously with the triggering factor to cause instability. The susceptibility of a slope sliding depends on its inherent conditions, such as the slope morphology, hydrology, and geological properties. Rainfall can cause a marginally stable slope to become unstable.

In the tropical region, intense weathering broke down volcanic rocks in the hilly area to form residual soil deposits. Volcanic residual soil predominantly occupies the hilly areas of the island of Java and lies well above the groundwater level, thus remaining in an unsaturated state [5]. Residual soil in Java typically remains stable on steep slopes (45–60 degrees), owing to the contribution of its negative pore pressure to its shear strength [6,7]. Instability can occur when the pore water pressure temporarily increases within the slope during heavy rainfall. Landslides in residual soil are typically of a shallow depth, occurring suddenly and rapidly. These events involve the sliding of large soil masses and can result in catastrophic impacts, such as cases in Hong Kong [8], Italy [9], and Indonesia [10], among others. In a subtropical region like Italy, unsaturated, shallow pyroclastic soils often experience disastrous landslides [9,11]. A hydrological analysis showed that antecedent rainfall increased the soil moisture within the unsaturated pyroclastic soil, which led to a detachment of the slope portion and initiated debris flow following a rainstorm [11]. On Java, intensive weathering causes the unsaturated soil to be much thicker, able to extend to 10–20 m thick [5,7]. The increased soil thickness in tropical soils, compared with the shallower pyroclastic soils in subtropical regions, introduces additional heterogeneity which may affect its hydrological response to rainfall infiltration.

In order to evaluate the susceptibility of slope conditions to landslides, geoengineers formally employ analysis of the factor of safety. Previous studies on rainfall-induced landslides on Java employed deterministic coupled seepage-slope stability analyses to analyze the stability of the slope when influenced by rainfall infiltration [5,12,13,14]. Due to complex geological conditions and weathering processes, the residual soil’s physical and mechanical properties are associated with natural uncertainties [15]. These natural uncertainties tend to be overlooked when using conventional deterministic slope analysis. Natural uncertainties are frequently disregarded when using conventional deterministic slope analysis. Probabilistic slope stability analysis incorporates variability and uncertainties related to the geotechnical properties and is capable of slope risk assessment. Earlier studies using probabilistic methods to analyze rainfall-induced landslides were carried out, involving variability in the mechanical and hydrological properties of residual soils [15,16,17,18]. However, a probabilistic analysis of transient residual soil slope stability triggered by rainfall on Java has not yet been conducted.

Sumedang Regency is identified as one of the most landslide-prone regions in West Java [19]. Many landslides have occurred throughout the rainy seasons in the area [13,20,21]. This vulnerability is largely attributed to geological factors, including weathered volcanic rock formations, geological faults, and the climatic condition of significant rainfall during the rainy season [22]. A catastrophic landslide occurred on 9 January 9 2021 in Cimanggung district of the Sumedang Regency, claiming 40 lives following heavy rainfall. Another landslide occurred in the same district in 2022 following a rainfall event, causing damage to houses and the evacuation of the village residents. Landslides in this area occurred suddenly and rapidly, making it a potential hazard threat every year.

Understanding the mechanism of these landslides is essential for developing preemptive warning systems and mitigation measures, ultimately reducing landslide risks in the region. Back analysis is capable of revealing the landslide mechanism from the observed characteristics of previous landslides. Deterministic and probabilistic methods are frequently employed for back analysis of rainfall-induced landslides [17,23], involving slope stability modeling and analysis of slope parameter uncertainty. The empirical approach is also commonly used. For example, the authors of [24] utilized multisource and multilevel investigations based on historical data and primary field investigation to elucidate the landslide-triggering factors using precipitation indexes. The use of machine learning enables the empirical model to cater to more complex parameters and relationships. The authors of [25] used rainfall data, soil moisture, and historical landslides to model the occurrence of landslides at a regional scale for a landslide alert system using a machine learning algorithm. The authors of [26] used the slope morphology, soil type, land cover and its changes as well as precipitation data to understand the contribution of each factor to landslide susceptibility and establish a landslide forecasting model based on several machine learning algorithms. The integration of GIS and geoinformatics with conventional deterministic and probabilistic analyses has been effectively employed for the back analysis of landslides at a regional scale. The authors of [27] integrated a detailed terrain analysis and infinite slope stability analysis (TRIGRS) for back analysis and landslide forecasting at a basin catchment scale. The authors of [28] utilized a probabilistic rainfall landslide modeling integrated into a GIS platform (GIS-FORM) to model the regional landslide susceptibility in Niangniangba, China.

Although landslides occur in the Cimanggung district, the volcanic residual soil slopes generally do not fail even during rainfall storms due to their elevation above the groundwater level. We hypothesize that the increase in groundwater level, working in conjunction with rainfall, is responsible for triggering landslides in this area. A slope at the brink of failure may not necessarily fail immediately, but it remains highly susceptible to collapse when exposed to triggering factors. In the case of the Cimanggung landslide, which was preceded by heavy rainfall, the following section will analyze the impact of rainfall infiltration on slope stability. Rainfall infiltration played a crucial role in triggering the catastrophic landslide, particularly given the slope’s near instability.

In this study, we aim to back analyze the Cimanggung district landslide using a coupled seepage-slope stability model with probabilistic analysis. The specific objectives are to examine the relationship between the factors of safety, the water table, rainfall events, and transient pore water pressure and to assess slope performance during rainfall. The methods employed in this study are field investigation, laboratory testing, and numerical modeling. Topographic mapping, borehole drilling, and cone penetration tests were performed to understand the slope profile and subsurface condition. Laboratory testing of undisturbed samples was carried out to obtain the engineering properties for slope modeling. Numerical modeling was carried out using the Slide2 package to simulate the slope conditions during rainfall infiltration and assess the slope performance. Firstly, steady state groundwater analysis was established to model the initial condition, followed by transient analysis to understand the pore pressure changes during rainfall infiltration. Three rainfall scenarios were selected, representing heavy, very heavy, and extreme rainfall conditions. The pore water pressures generated from groundwater analyses were computed for deterministic and probabilistic slope stability analyses to assess the slope performance subjected to rainfall infiltration.

2. Site Description

2.1. Geological Condition

The study area is administratively located in Bojongkondang village in the Cimanggung district of the Sumedang Regency in West Java from coordinates −6.94 to −6.96 S and from 107.81 to 107.83 E. It is composed of volcanic terrain with a slope of 30–40° and an altitude of 735–780 m (Figure 1a). The topographic data in Figure 1a was obtained from DEMNAS, provided by the Indonesian Geospatial Information Agency (https://tanahair.indonesia.go.id/portal-web/ accessed on 1 August 2024).

The study area is composed of, from old to young, lava of a basaltic composition and scoria (Qyl), undifferentiated young volcanic products (Qyu), and a lake deposit (Ql) [29] (Figure 1b). Young volcanic products consist of tuffaceous sand, lapilli, lava, and agglomerates. In this area, this unit is expressed as a flat or low hill area covered by yellowish-gray to reddish-gray soil. A lake deposit occupies the south low flat area, forming horizontal layers of tuffaceous clay, sandstone, gravel, and conglomerate with occasional limestone concretion, plant remains, and fresh water mollusks. The Cimanggung landslide occurred at undifferentiated young volcanic products overlying the compact basaltic lava. Intensive weathering of the young volcanic rocks formed fine-grained soil, which is a potential water catchment and sliding zone. Geological structures which developed in this area are the Cileunyi-Tanjungsari fault and the Cicalengka fault to the northwest and southeast of the study area, respectively (Figure 1). The Cileunyi-Tanjungsari fault is a NE–SW trending dextral strike-slip fault, and the Cicalengka fault also trends from NE to SW almost parallel to the Cileunyi-Tanjungsari fault [30]. Recent research revealed that this area has low-to-moderate tectonic activity [31].

2.2. Rainfall Events

Saturation of the soil is the critical precursor to landslide initiation. Soil saturation decreases the shear strength of the soil, hence making it prone to slides. In unsaturated soil, precipitation is the main trigger of soil saturation. Rainfall events prior to and during the landslide in Cimanggung district were examined for the landslide event on 9 January 2021. The daily rainfall on the day of the landslide catastrophe on 9 January 2021 was recorded at three stations, namely Kec Jatinangor, Unpad Jatinangor, and Cikancung, where the rainfall data on the day were 142.5 mm/day, 99 mm/day, and 69.8 mm/day, respectively, and the antecedent rainfall was 0–2 mm/day [32]. According to Indonesian Meteorological and Geophysical Agency (BMKG) classification [33], daily rainfall of 50–100 mm/day falls into the heavy rainfall category; 100–150 mm/day is considered very heavy rainfall; and over 150 mm/day is considered extreme rainfall.

A shallow landslide event is often associated with downward rainfall infiltration. In a tropical region, weathered soil is rarely saturated. The void of the soil is also partially filled with air, making the soil unsaturated. Rainfall infiltration increases the water content of the soil and subsequently reduces its shear strength, making the soil prone to sliding. Earlier works established that antecedent rainfall is important in building up pore pressure in unsaturated soils. The range of antecedent rainfall-inducing landslides worldwide varies widely from 24 h to 35 days [8]. The landslide early warning system developed spatially for the 83 sites in Indonesia using infinite slope stability analysis (TRIGRS) suggests that 1–3 days of antecedent rainfall is sufficient for a landslide, provided the rainfall is equal to or larger than 61 mm for 1 day and 91 mm for 3 days [34].

In the absence of recent rainfall data, we analyzed daily rainfall records from the past 15 years (2003–2017) from the nearest, now-defunct stations in Jatiroke (−6.929 S, 107.788 E), Rancaekek (−6.969 S, 107.816 E), and Tanjungsari (−6.902 S, 107.796 E) (Figure 1). By examining the maximum annual daily rainfall over this period (Figure 2), we observed that the daily maximum rainfall patterns from all three stations followed a similar trend. The records indicate that extreme rainfall events were rare, while heavy rainfall was fairly common and very heavy rainfall occurred less frequently. The amount of rain recorded on 9 January 2021 aligned with the local climatic conditions, indicating a less frequent occurrence of very heavy rainfall. From these data, we can estimate the potential rainfall in the region and evaluate its impact on slope stability. For slope stability analysis, we considered three daily rainfall scenarios of 100 mm/day, 142.5 mm/day, and 192 mm/day. The daily rainfall of 100 mm/day and 192 mm/day were taken from Figure 2 to represent the heavy and extreme rainfall category, and 142.5 mm/day was taken from [32] to represent very heavy rainfall.

2.3. Landslide in Cimanggung District

Multiple landslides occurred in the Satria Bumi Gumantara (SBG) Housing Complex in Cimanggung district on 9 January 2021 in Sumedang Regency, West Java, resulting in deaths and great damage to housing and infrastructures. A disaster situation report [35] indicated that three slope failures occurred on that day. The first incidence was at 3:30 p.m. Western Indonesian Time following a rainfall event. The first incidence claimed 12 deaths and buried four residential houses. The second incidence took place at 7:30 p.m., immediately followed by the third landslide just five minutes later. The second and third landslide resulted in more casualties, including the evacuation team. The death toll was 40 people, and 14 houses were destroyed.

According to the landslide susceptibility map released by the Indonesian Geological Agency, Cimanggung District is classified as a high-risk zone for landslides [19]. The area’s terrain is characterized by moderately steep to steep slopes. Following the catastrophic landslide at the SBG Housing Complex, another landslide occurred the following year in the nearby Griya Sampurna Complex. On 18 December 2022, a landslide damaged parts of the Nurul Hasanah mosque, forcing seven households to evacuate [36]. Rainfall events triggered both landslides in Cimanggung District. The persistent landslide threat in this district highlights the need for a deeper understanding of landslide mechanisms to prevent future casualties.

The catastrophic landslide on 9 January 2021 occurred on a steep slope with an inclination between 32 and 42 degrees and a height of approximately 30 m. Figure 3 comprehensively depicts the spatial, geological, and geotechnical aspects of the Cimanggung landslide, integrating detailed observations of the study area. Figure 3a illustrates a 3D satellite view from Google Earth [37] showing the study area at the foothills of Mount Aseupan near the densely populated Rancaekek region in Sumedang, where the landslide area is marked with a red polygon.The flat terrain surrounding the region is heavily urbanized with residential and industrial establishments, whereas the hilly areas are almost entirely vegetated. Meanwhile, Figure 3b presents a 3D geological map showing the distribution of geological formation surfaces, where the landslide predominantly comprises undifferentiated young volcanic products (Qyu). Figure 3c highlights the conditions before the landslide in December 2020, when the Pondok Daud Housing Complex was entirely within the landslide boundary and severely impacted, resulting in the complete destruction of all buildings in the complex. According to [38], the drainage lines of a natural earth ditch crossed the crest of the slope (Figure 3c). In contrast, Figure 3d shows the conditions after the landslide in May 2021, illustrating the main crown, flow track, and depositional area, along with the locations of key geotechnical investigation points, namely CPT-1, CPT-2, CPT-3, and CPT-4. Significant damage was observed at the SBG Housing Complex, where five houses were severely damaged, some of which were carried downslope by the landslide. Figure 3e,f provides cross-sectional profiles of the slope, encompassing subsurface information derived from boreholes S-01 and S-02, alongside the locations of CPT-1 (in Profile A-A’) and CPT-4 (in Profile B-B’), illustrating the distribution of silty sand, silty clay, and clay layers within the slope.

3. Methods

3.1. Slope Profile and Geotechnical Characteristics

In this study, the slope profile and geotechnical characteristics were established from site investigation and a series of laboratory tests. The site investigation included topographic mapping, borehole drilling, cone penetration test, and undisturbed sampling. Borehole drilling was carried out up to a depth of 22 m to obtain undisturbed samples every 2 m in depth. Undisturbed sampling using Shelby tubes was performed along the toe of the failed slope. The soil samples were subjected to geotechnical characterization, composed of the shear strength, moisture content, porosity, grain size, and permeability (

Table 1. Engineering properties of the volcanic soil.

Properties	Silty Sand	Silty Clay	Clay
Specific gravity	2.6	2.56	2.57
Natural moisture content	0.32	0.40	0.40
Porosity	0.41	0.50	0.55
Unit weight	16.8	17.5	18.0
Percentage of sand (%)	59.1	24.8	11.1
Percentage of silt (%)	26.8	49.1	31.5
Percentage of clay (%)	14.1	26.1	57.4
Soil texture	Sandy loam	Silt loam	Clay
Hydraulic conductivity (m/s)	2 × 10−6	5 × 10−7	1.0 × 10−7
Average effective cohesion (kPa)	11.0	23.0	27.0
Average effective angle of friction (°)	29.0	25.0	23.0

). Cone penetration testing and borehole investigation revealed that the slope profile consisted of silty sand (depth: 0–12 m), silty clay (depth: 12–18 m), and clay (depth: 18–22 m) (Figure 3e). The SPT values at the borehole near S-02, which were obtained from a previous study [37], indicated that the silty sand was loose (SPT N value: 2–9), the silty clay was medium-to-highly stiff (SPT N value: 8–25), and the clay was quite stiff (N value: 32).

The geotechnical characteristics of the soils from the laboratory testing are presented in Table 1. Table 1 indicates that the soil in the upper layer (0–12 m) contained 40% fines, with increasing fines contents of 75% and 89% at greater depths. The soil texture classification revealed that the upper 12 m was composed of sandy loam, transitioning to silt loam between 12 and 18 m and clay from 18 to 22 m. Saturated permeability values were obtained through field infiltration and falling head laboratory tests, showing permeability to the order of 10⁻⁶ and 10⁻⁷ m/s, respectively. The average shear strength parameters were determined from the direct shear tests. The average cohesion ranged from 11 to 27 kPa, and the average friction angle was 23–29°.

The soil water characteristic curve (SWCC) and unsaturated hydraulic conductivity function for seepage analysis were estimated using the van Genuchten function in Slide v.6 (Rocscience) [39] groundwater analysis software. The SWCC was estimated from particle size distribution data. Meanwhile, the unsaturated hydraulic conductivity function was predicted from the saturated coefficient of permeability (Table 1) and the SWCC curve for each soil (Figure 4). Figure 4a shows that the soils desaturated quickly when the air entry value (aev) was exceeded, which was 10 kPa for the silty sand and 20–25 kPa for the silty clay and clay. The hydraulic conductivity also decreased when the aev was exceeded. It can be seen that silty sand is more likely to decrease its hydraulic conductivity compared with silty clay and clay (Figure 4b). The groundwater table was not measurable during the soil investigation. A previous study indicated that the groundwater level was found to be quite deep at 8–20 m below ground level [37].

3.2. Coupled Seepage-Slope Analysis and Limit Equilibrium

In this study, we combined deterministic and probabilistic approaches to provide a comprehensive evaluation of slope stability. The analysis began with a deterministic method, specifically the coupled seepage-limit equilibrium analysis, to model the mechanistic processes affecting slope stability under rainfall infiltration. The weathering of volcanic soils in Java is quite extensive, leaving thick residual soils which occupy the hill slopes. The water table is often found quite deep within the residual soils, causing most of the soils to be unsaturated. In unsaturated soils, the void of the soil is partially filled with air and water. Water is attached to the soil grain due to the capillary forces and surface tension, leading to matric suction or negative pore pressure to exist in unsaturated soil. The role of matric suction enhances the shear strength of the soil (τ), as depicted in Equation (1) [40]:

$$\tau =c^{\prime }+\left(\sigma -u_a\right)\tan {\mathrm{\varnothing }}^{\prime }+\left(u_a-u_w\right)\tan {\varnothing }^b$$

(1)

where c′ is the effective cohesion, ∅′ is the effective friction angle in the saturated condition, (σ − u_a) is the net normal stress, (u_a − u_w) is the matric suction, and ∅^b is the friction angle with respect to changes in matric suction.

Rainfall infiltration reduces the negative pore water pressure, hence decreasing the shear strength of the soil and influencing the stability of the slope. A coupled seepage and deterministic slope stability analysis using the Slide2 package [39] was conducted to evaluate the impact of rainfall infiltration on the stability of a volcanic residual soil slope.

Firstly, seepage analysis was conducted using finite element groundwater modeling in Slide v.6. A steady state analysis was first performed to establish the baseline conditions, followed by a transient analysis to evaluate how rainfall infiltration affects pore water pressures within the slope over time. Transient analysis was carried out based on the Richards flow equation (Equation (2)):

$${\displaystyle \frac{\delta }{{\delta }_x}} \left(k_x{\displaystyle \frac{\delta H}{\delta x}}\right)+{\displaystyle \frac{\delta }{\delta y}}\left(k_y{\displaystyle \frac{\delta H}{\delta y}}\right)+q=m_w{\gamma }_w{\displaystyle \frac{\delta H}{\delta t}}$$

(2)

where H is the hydraulic head, k_x and k_y are the hydraulic conductivity in the x direction and y direction, respectively, q is the influx, m_w is the water storage modulus, and γ_w is the unit weight of water. Then, a slope stability analysis using the limit equilibrium method was carried out to determine the factor of safety over time, accounting for the transient pore water pressures resulting from groundwater analysis.

The slope was modeled based on field investigation data from the Cimanggung slope, as shown in Figure 3d, with the material properties listed in Table 1. Since no water table was encountered during the field investigation, we first carried out a sensitivity analysis to understand the slope stability under different water tables. Water tables from 13 to 20 m below the ground surface were simulated to obtain the critical condition of slope stability for the steady state analysis. The head boundaries were assigned below the groundwater table, while the lowest boundary was set as a no-flux boundary (Figure 5). A steady state analysis was performed to establish the initial water table conditions at designated depths. Transient analysis was performed for a marginally stable slope to assess the impact of rainfall infiltration. The transient analysis was conducted by applying vertical infiltration along the slope face. A seepage review was applied to prevent surface ponding on the slope (Figure 5).

In this study, we investigated the slope stability under varying rainfall intensities of 100 mm/day, 142 mm/day, and 192 mm/day. Due to the lack of hourly rainfall data, we assumed an even distribution of daily rainfall across each hour. We simulated scenarios where the total daily rainfall was uniformly distributed over 3, 4, 5, and 24 h periods. The initial condition was set with a water table at 16 m, representing a critical state. The slope performance was modeled over 24 h, with uniform rainfall occurring for 3 h followed by no rain for the remainder of the day. This same approach was applied to all other rainfall intensities except for uniform rainfall for 24 h.

3.3. Monte Carlo Probabilistic Slope Analysis

Following the deterministic approach discussed earlier, which focuses on the mechanistic processes influencing slope stability, this section incorporates Monte Carlo probabilistic slope analysis to address the uncertainties inherent in the soil properties, hydrological conditions, and rainfall events.

The volcanic residual soils covering most of the hilly areas in Java were derived from intense weathering in the tropical region. Weathering of a parent rock is a complex process which may result in varying physical and mechanical properties across a short distance. This variation can influence the likelihood of slope failure. This study utilized probabilistic analysis to account for uncertainties in slope properties, with the unit weight, cohesion, and internal friction angle considered to be random variables. Monte Carlo probabilistic analysis in Slide2 [39] was used to assess the probability of failure (P_f) and the reliability index (β) for the slope performance. The statistical parameters for the cohesion, friction angle, and unit weight of the soil were characterized using the mean value, standard deviation, and coefficient of variation (

Table 2. Statistical parameter for probabilistic slope analysis.

Soil	Mean	Coefficient of Variation (%)	Distribution
Silty sand
Unit weight (kN/m3)	17	2	Normal
Cohesion (kPa)	11	1.5	Normal
Friction angle (°)	29	1	Normal
Silty clay
Unit weight (kN/m3)	18	1.5	Normal
Cohesion (kPa)	23	3	Normal
Friction angle (°)	25	1	Normal
Clay
Unit weight (kN/m3)	20	2	Normal
Cohesion (kPa)	17	2.5	Normal
Friction angle (°)	29	1.5	Normal

). The mean and standard deviation values were derived from laboratory tests conducted in five trials per sample, with three samples taken for each soil type. A normal distribution represents the variation in each parameter.

Monte Carlo simulations provided evaluation of the slope stability by generating a large number of scenarios through random sampling of the input parameters within defined probability distributions. This approach not only provided the factor of safety but also quantified failure probabilities and reliability indices, offering a more realistic and comprehensive assessment of landslide risks. Unlike deterministic methods, which rely on fixed parameter values, Monte Carlo simulations consider a range of possible outcomes, capturing real-world variability. By combining the probabilistic results with the deterministic, coupled seepage-limit equilibrium analysis, this study achieved a robust evaluation of slope stability, balancing mechanistic insights with an understanding of uncertainties. This integration identifies critical thresholds, such as rainfall intensity or water table levels, which could trigger slope failure, thereby providing valuable information for risk management and mitigation strategies.

The probability of failure (P_f) is represented as the ratio of the total number of simulations, where the factor of safety is less than one versus the total number of simulations (N) (Equation (3)). The function indicator (I) is used to count the number of unsuccessful simulations. Therefore, P_f is defined as the ratio of unsuccessful simulations to the total number of simulations (N) [18] as follows:

$$P_f={\displaystyle \frac{1}{N}}{\sum }_i^{N}I(FoS<1)$$

(3)

The reliability index (β) is a numerical value which indicates the safety margin of a slope by comparing the mean factor of safety (μ) and the variability in the factors contributing to instability, represented by the standard deviation of the factor of safety (σ). It is expressed by the ratio of these two values as described in [23], which is expressed as follows:

$$\beta ={\displaystyle \raisebox{1ex}{$(\mu -1)$}\!\left/ \!\raisebox{-1ex}{$\sigma $}\right.}$$

(4)

To evaluate the slope performance, we refer to the broader conditions outlined by USACE (1999) [41], which utilize a combination of Pf and β (

Table 3. Geotechnical performance of slope determined from probability of failure and reliability index [43].

Geotechnical Performance Level	Probability of Failure (Pf)%	Reliability Index (β)
High	0.00003	5
Good	0.003	4
Above average	0.01	3
Below average	0.06	2.5
Poor	2.3	2
Unsatisfactory	7	1.5
Hazardous	16	1

). Additionally, we considered suggested values from a similar approach in [42] for the natural slopes (

Table 4. Suggested value of reliability index and failure probability for natural slopes [42].

Slope Type and Location	Potential Failure Mode	Potential Consequences	Minimum Reliability Index	Maximum Failure Probability
Wooded or forested slopes, moderate-to-steep inclination, colluvium or residual soil cover	Shallow sliding, limited movement, or just slope deformation without overall failure	No elements at risk, no potential for debris flow formation	1	15%
Slopes of low-to-moderate inclination in which high pore water pressures can develop, forested or cleared sloping areas	Slow moving slides, shallow to deep-seated, relatively flat slip surfaces	No potential for catastrophic failure without warning signs, progressive action during successive rainstorms may induce complete failure over time, no elements at risk	1.5	5%
Relatively steep slopes with high relief in forested or cleared areas, slopes near natural gullies, colluvium or residual soil cover	Shallow sliding with rapid movement and potential for large travel distances	Significant potential for debris flow formation during intense storms, considerable travel distance, elements at low-to-moderate risk of damage	2	1%
Slopes in which high pore pressure can develop, near urbanised areas	Sliding with rapid movement, shallow-to-deep slip surfaces with relatively steep inclination	Elements at moderate-to-high risk of damage or destruction from landsliding	2.5	0.5%
Slopes in which high pore pressures can develop, extremely close to properties in urbanized areas	Sliding with rapid movement, shallow-to-deep slip surfaces with relatively steep inclination	Elements at high to extremely high risk of destruction from landsliding	3	0.1%

). Table 4 is considered specifically to address the situation where the natural slope has evolved into an urbanized settlement.

4. Results and Discussion

4.1. Factor of Safety over Increasing Water Table

To investigate the effects of the initial water table on slope stability, we simulated the water table depth based on a previous study [37], starting at 20 m below ground level and progressively raising the level until reaching a critical value. The initial conditions assumed only a phreatic water table, with no rainfall applied. A factor of safety (FoS) greater than 1.1 was deemed satisfactory, and the corresponding probability of failure was also evaluated. Figure 6 presents the simulation results, illustrating the FoSs for different water tables and the relationship between the FoS and the associated probability of failure and reliability index.

As illustrated in Figure 6, with an initial water table of 20 m, the slope was in a stable condition, exhibiting a mean factor of safety (FoS) of 1.22, a probability of failure (P_f) of zero percent, and a high reliability index of six. Even when the water table was raised to 18 m, the slope remained relatively safe, with an FoS of 1.1 and a reliability index of two (Figure 6b). Although the P_f at this level (six percent) was relatively poor according to the classification in Table 3, this does not necessarily indicate hazardous or catastrophic conditions. Instead, the P_f should be interpreted as the likelihood of unsatisfactory performance rather than an imminent failure.

The critical performance of the slope occurred when the water table rose to 16 m. At a water table depth of 16 m, the FoS was 1.05, and the reliability index was 1.135 (Figure 6b). Although the FoS was just slightly above one, the slope performance was considered unsatisfactory (Table 3 and Table 4), as indicated by the high P_f (11.5%) (Figure 6a) and low reliability index. Any further increase beyond this level led to hazardous conditions, as illustrated in Figure 6, where the factor of safety (FoS) dropped below one, the probability of failure (P_f) exceeded 45%, and the reliability index became negative.

The rise in the water table to this level was attributed to drainage pipe leakage from the upslope residential area toward the downslope, as reported by Adiguna et al. (2023) [37] and Inspire (2021) [35]. Our field investigation, based on interviews with local residents, revealed that prior to the catastrophic landslide, the open drainage line near the slope crest (Figure 3a) was unlined. The drainage ditch should have been a concrete-lined rectangular trench, but due to unfinished construction, the remaining ditch at the upslope remained a natural earth ditch. This suggests that water from the open drainage may have traveled downslope over time, raising the phreatic water level, in addition to the leakage from the drainage pipe.

4.2. Influence of Rainfall Events on Transient Pore Pressure

The intensity and duration of rainfall influence the timing of a slope’s failure. This is related to the transient response of pore water pressure to rainfall infiltration. As rainfall infiltrates a slope, the matric suction in the soil reduces, increasing the pore pressure and hence decreasing the shear strength of the soil, causing slope failure. The response of the porewater pressure to rainfall infiltration over time and depths depends on the soil water characteristic curve (SWCC) and hydraulic conductivity. The progression of the wetting front, or the saturation of soil through its depth in various designated rainfall scenarios, is represented by section A at mid-slope, as shown in Figure 5. The results of the transient pore pressure modeling are presented in Figure 7.

The intensity and duration of rainfall significantly affect the timing of slope failure due to the transient response of pore water pressure to infiltration. As rainfall permeates the slope, it reduces the matric suction within the soil, leading to an increase in pore pressure, which consequently lowers the soil’s shear strength and triggers slope failure. The temporal and spatial response of pore water pressure to infiltration is governed by the soil water characteristic curve (SWCC) and hydraulic conductivity. The progression of the wetting front and the degree of soil saturation at varying depths under different rainfall conditions are depicted in section A at the mid-slope in Figure 5. The outcomes of the transient pore pressure for all rainfall scenarios are illustrated in Figure 7.

Figure 7 illustrates the initial water table at 16 m, with the soil above it remaining unsaturated, as indicated by the negative pore pressures above the water table and up to the surface. In the initial condition (t = 0), without rainfall, the maximum matric suction observed at the surface was 12 kPa, slightly exceeding the air entry value for silty sand. During rainfall events lasting 3, 4, and 5 h, the matric suction at the surface was completely diminished at t = 3 h and t = 4 h, followed by a slight recovery once the rain ceased (Figure 7a–i). For rainfall durations extending to 24 h, the suction profile at the surface gradually decreased until the final time step (t = 24 h) (Figure 7j–l).

Rainfall infiltration of 100 mm (Figure 7a), 142 mm (Figure 7b), and 192 mm (Figure 7c) over 3 h resulted in a similar gradual decrease in the matric suction from below the surface up to a depth of 5 m, indicating a consistent response in the soil moisture. However, at a depth of 7.4 m, the pore pressure profiles in Figure 7a,b remained comparable, showing a small increase in pore pressure. In comparison, Figure 7c shows a notable increase in pore pressure, rising from −6.0 kPa (t = 0 h) to −4.6 kPa (t = 24 h), which indicates advancement of the wetting front due to the increased rainfall.

Figure 7d–f illustrates that when the rainfall duration in the respective scenarios of 100 mm, 142 mm, and 192 mm was extended to 4 h, the pore pressure profiles, ranging from below the surface to a depth of 5 m, exhibited similar patterns of pore pressure increases. At a depth of 7.4 m, a slight, gradual increase in pore water pressure can be observed in all three figures (Figure 7d–f), with values rising from −6 kPa (t = 0 h) to −5.4 kPa, −5.10 kPa, and −4.8 kPa, respectively, at t = 24 h. Figure 7f shows the most significant increase in pore water pressure, which corresponded with the higher rainfall intensity.

Figure 7g–i shows that when the total rainfall was 100 mm, 142 mm, and 192 mm for 5 h, a smaller, gradual increase in pore water pressure was found at depths of 1.2 m, 4 m, 5 m, and 7.4 m. The largest increase in pore water pressure was found at a depth of 4 m, where the pore pressure rose from −9.2 kPa (t = 0 h) to −8.66 kPa (Figure 7g), −7.96 kPa (Figure 7h), and −7.5 kPa (Figure 7i) at t = 24 h. When the total rainfall was 100 mm, 142 mm, and 192 mm for 24 h, the wetting at the surface formed slowly, reaching a saturated condition at the end of the rainfall. At a depth of 1.2 m, the most pronounced change in pore water pressure was seen at t = 24 h, rising from −11.5 in the initial condition to −6.09 (Figure 7j), −5.4 kPa (Figure 7k), and 0 kPa (Figure 7l). A saturation zone at a depth of 1.2 m formed.

As rainfall subsides, the wetting front progresses deeper into the slope due to the downward redistribution of water. Across all rainfall scenarios, the wetting front deepened over time, reaching a maximum depth of 7.40 m. At shallower depths (1.2–4 m), the increase in pore water pressure was more pronounced compared with those of the deeper regions. The magnitude of wetting decreased with the depth and effectively halted at 11 m. The presence of negative pore pressure at certain depths suggests that rainfall infiltration does not elevate the initial water table. Instead, infiltration leads to an increase in pore pressure within the unsaturated soil, resulting in a reduction in shear strength due to the loss of matric suction.

4.3. Evolution of Safety Factor During Rainfall Infiltration

Increasing rainfall intensities and durations affect slope stability by reducing the shear strength of the soil. The temporal evolution of the factor of safety during rainfall infiltration under varying intensities and durations is illustrated in Figure 8 and discussed in detail as follows. Figure 8 shows that after rain fell, in all rainfall scenarios, the factor of safety immediately dropped from 1.05 to 1.02. This corresponds to the increase in porewater pressures from the surface up to a depth of 4 m immediately after rainfall started (Figure 7).

Figure 8a illustrates that when rainfall occurred at a rate of 33.33 mm/h for 3 h (totaling 100 mm), the slope experienced a reduction in its factor of safety (FoS) yet did not fail, with the FoS remaining slightly above one. A similar trend was observed in cases where 100 mm of rainfall was distributed over 4 and 5 h (Figure 8b,c). When the same total rainfall was evenly distributed over 24 h, slope failure occurred at 21.8 h. This aligns with the pore pressure profile in Figure 7j, which indicates that the pore pressure developed at the surface and down to a depth of 4 m was higher compared with the scenario where 100 mm of rainfall occurred over just 3–5 h (Figure 7a,d,g).

In contrast, when the rainfall intensity increased to 47.33 mm/h over 3 h (totaling 142 mm), slope failure occurred after 8 h (Figure 8a). Similarly, when 142 mm of rain fell over 4 h at a rate of 35.5 mm/h, failure also occurred after 8 h (Figure 8b). Examining the pore pressure profiles revealed that at t = 8 h, the increase in pore water pressure was comparable between rainfall intensities of 47.33 mm/h and 35.5 mm/h (Figure 7a,d). For the case where 142 mm of rainfall was distributed over 5 h, the slope failed after 10 h (Figure 8c). Finally, when 142 mm of rain fell steadily over 24 h (at a rate of 5.92 mm/h), slope failure was triggered after 19 h (Figure 8d). Figure 7h,k confirms that the increase in pore water pressure leading to failure occurred after t = 8 h.

When a total of 192 mm of rainfall fell for 3 h at an intensity of 64 mm/h, the slope failed after 5 h (Figure 8a). Similarly, with an infiltration rate of 48 mm/h or 192 mm over 4 h, the factor of safety (FoS) dropped below 1.0 after 7 h (Figure 8b). When rainfall occurred at a rate of 38.4 mm/h (192 mm over 5 h), the FoS similarly decreased to below 1.0 after 7.5 h (Figure 8c). Lastly, when 192 mm of rain was distributed evenly over 24 h at a rate of 8 mm/h (Figure 8d), slope failure occurred after 18 h. The pore pressure profiles in Figure 7c,f confirm that significant wetting occurred well before t = 7 h and t = 8 h, whereas Figure 7i,l indicates that this wetting occurred after t = 7 h.

4.4. Analysis of Slope Performance Under Rainfall Infiltration

The slope performance under rainfall infiltration was assessed with probabilistic analysis using the Monte Carlo method. The slope performance was evaluated using the mean factor of safety, probability of failure, and reliability index. For each rainfall scenario, the probabilistic analysis was carried out for the selected time steps, and the results are summarized in

Table 5. Results of Monte Carlo probabilistic slope analysis corresponding to rainfall intensity in each time step.

Rainfall Intensity	Time Step	Mean FoS	Pf	β	Rainfall Intensity	Time Step	Mean FoS	Pf	β
	(h)		(%)			(h)		(%)
Initial Condition	0	1.054	11.5	1.135	Initial Condition	0	1.054	11.5	1.135
100 mm in 3 h	3	1.024	23.8	0.725	100 mm in 5 h	3	1.022	24.9	0.676
	7	1.014	33.4	0.428		7	1.018	29.2	0.537
	12	1.012	36.0	0.350		12	1.016	31	0.473
	24	1.006	42.6	0.166		24	1.008	39.9	0.223
142 mm in 3 h	3	1.003	45.6	0.095	142 mm in 5 h	3	1.012	36.1	0.348
	7	1.000	48.6	0.013		7	1.003	46.1	0.081
	12	0.994	55.7	−0.169		12	0.996	52.8	−0.106
	24	0.986	64.8	−0.405		24	0.959	61.9	−0.345
192 mm in 3 h	3	1.01	37.6	0.304	192 mm in 5 h	3	1.013	34.3	0.401
	7	0.997	52.6	−0.101		7	1.002	46.6	0.067
	12	0.983	57.6	−0.216		12	0.995	54.0	−0.138
	24	0.98	64.3	−0.399		24	0.988	63.1	−0.371
100 mm in 4 h	2	1.021	26.0	0.640	100 mm in 24 h	2	1.02	26.6	0.604
	8	1.014	33.5	0.430		8	1.02	26.4	0.612
	12	1.013	34.8	0.382		12	1.019	27.1	0.590
	24	1.008	40.0	0.229		24	0.988	61.8	−0.344
142 mm in 4 h	2	1.021	26.1	0.634	142 mm in 24 h	2	1.023	24.5	0.693
	8	0.999	50.0	−0.042		8	1.023	24.1	0.71
	12	0.994	56.1	−0.174		12	1.017	34.5	0.75
	24	0.985	65.8	−0.447		24	0.985	65.8	−0.433
192 mm in 4 h	2	1.017	29.9	0.522	192 mm in 24 h	2	1.021	26.3	0.622
	8	0.997	52.6	−0.098		8	1.099	27.4	0.59
	12	0.982	57.0	−0.120		12	1.013	37.0	0.51
	24	0.983	67.6	−0.511		24	0.985	65.9	−0.422

. The range of values for slope performance analysis can be seen in Table 3 and Table 4.

Table 5 indicates that the slope, even in its initial condition, was in an unsatisfactory state, with a failure probability of 11.5% and a reliability index of 1.135. Despite its critical status, slope failure does not occur immediately and requires a triggering factor. Rainfall infiltration serves as the primary trigger for failure, particularly as the Cimanggung slope comprises a thick of unsaturated soil layer (approximately 16–20 m deep). Certain rainfall intensities and durations are capable of destabilizing the slope.

Previous analyses suggest that the wetting in the unsaturated soil layer above the water table triggered the Cimanggung landslide. Rainfall infiltration does not raise the initial phreatic surface but causes a wetting front within the unsaturated soil, therefore lowering its shear strength. Table 5 shows that a rainfall intensity of 100 mm/day over 3, 4, and 5 h did not induce slope failure, though the probability of failure increased progressively from the initial 26% to 42%. Correspondingly, the slope’s reliability index declined steadily, approaching zero over time. When the rainfall intensity reached 100 mm in 24 h, the mean factor of safety fell below one, with a failure probability of 61.8%, indicating that over half of the stability iterations resulted in failure.

When correlating the timings of slope failure in Figure 8 to Table 5, it can be seen that when a failure occurred, the P_f increased to almost 50%, and the reliability index was negative. Assessment of the slope performance based on Table 3 shows that with time, the unsatisfactory initial condition deteriorated into hazardous conditions and, finally, failure. The initial slope condition before rainfall infiltration which fell into an unsatisfactory condition was supposed to be acceptable for natural slopes in wooden or forested areas, where no elements are at risk (Table 4). However, as the area is also inhabited both upslope and downslope, the deterioration of unsatisfactory to hazardous conditions under extreme rainfall events is intolerable. The slope should be recognized as unsatisfactory before a landslide occurs, deeming it unsuitable for habitation and prompt early evacuation. A maximum probability of failure of 0.1% and a minimum reliability index of three is required for slopes in proximity to urbanized areas [42]. Previous analysis showed that when the phreatic water level was 20 m deep, the slope performance was high (P_f = 0% and β = 6).

Steep slopes in Java, composed of volcanic residual soil, generally remain stable, particularly due to the deep phreatic water table [6,44]. The residual soil along the slope above the water table remains in an unsaturated state. The presence of negative pore pressure (or matric suction) within this unsaturated soil increases the shear strength, thereby enhancing the slope’s factor of safety. Extreme rainfall or isolated storm events are highly likely to cause a transient increase in pore water pressure in the slope, causing a landslide [44]. In the case of the Cimanggung landslide, our back analysis indicates that extreme rainfall intensities have the potential to trigger slope failure. However, rainfall infiltration alone was not the sole factor contributing to the landslide. Instead, the primary cause of slope instability was the rising water table, which can be attributed to inadequate drainage management. This rise in water level was influenced by unlined drainage from upslope housing and a damaged drainage pipe [37]. Heavy rainfall further exacerbated this condition by increasing seepage into the unsaturated soil. Due to uncertainties regarding the volume of drainage water infiltrating the soil, we did not model the exact rise in water levels from drainage seepage. Instead, we assumed an incremental rise in the water table from its lowest level observed in previous measurements (see Figure 6a,b) to identify the critical water table height.

Human activities frequently cause landslides in residual soils. Actions such as slope excavation, fill placement, disruption of natural drainage and seepage, and deforestation all contribute to reduced slope stability, heightening the risk of slope failures, particularly in urban areas [44]. In the Cimanggung landslide, inadequate drainage management contributed significantly to slope failure. Landslide risks in this area are heightened by expanding residential construction near the slope’s toe. Java’ rapid population growth has increased settlement in hilly regions, where spatial planning lacks stringent regulation. Inadequate understanding and regulation of urban drainage in hilly regions, combined with recent practices of placing waste rock fill on slopes, may compromise post-landslide stability. To mitigate future hazards, an integrated slope monitoring system is recommended in the study area. This system should incorporate inclinometers and extensometers for measuring slope displacement alongside moisture and water level probes to monitor variations in soil saturation and the water table. At the regional scale, it is essential to develop more detailed land use planning and zoning regulations for hilly and mountainous areas, with clear guidelines on drainage management and construction activities on vulnerable slopes, while also promoting the establishment of conservation zones. Additionally, implementing a regional-scale rainfall-induced landslide analysis using integrated geology, geotechnical data, GIS, and artificial intelligence is essential to support these objectives.

5. Conclusions

This study employed a back analysis approach to assess the geotechnical behavior of the Cimanggung slope under rainfall infiltration, aiming to understand the factors leading to the catastrophic 2021 landslide. Site investigations and laboratory analyses were carried out to characterize the slope properties as the basis for numerical modeling. In the absence of hourly rainfall data, rainfall intensities were estimated using the recorded daily rainfall during the landslide event (142 mm/day) as well as the extreme daily rainfall values from 2003 to 2017 (100 mm/day and 192 mm/day). The simulated rainfall durations included 3, 4, 5, and 24 h. A deterministic, coupled seepage limit equilibrium slope stability approach was employed alongside Monte Carlo probabilistic analysis, enhancing conventional deterministic results and offering new insights into slope performance.

The analysis began with establishing an initial critical water level by simulating different water levels until reaching a critical state. Deterministic analysis indicated that a water level of 16 m resulted in a critical factor of safety (FoS 1.05), and the probabilistic analysis confirmed an unsatisfactory slope condition, reinforcing the deterministic findings. Simulating different rainfall intensities and durations for the initial critical slopes resulted in a reduction in the factor of safety over time and decaying slope performance. The slight variation in FOS values derived from the deterministic limit equilibrium method presents challenges in clearly differentiating between stable and unstable conditions. Probabilistic analysis produces a probability of failure of nearly 50% and a negative reliability index to assist in identifying failure. For rainfall intensities of 100 mm/day sustained over 3, 4, and 5 h, the results showed no immediate slope failure despite deteriorating slope conditions. The findings reveal that variations in extreme rainfall intensity and duration can trigger slope failure within 5–22 h after rainfall onset.

High, steep slopes of residual soils on the island of Java typically maintain stable conditions. However, human activities and extreme precipitation are common causes of landslides. In the case of the Cimanggung landslide, inadequate urban drainage management led to a rise in the phreatic water table, rendering the slope unsatisfactory for stability. Under conditions of heavy rainfall infiltration, the slope stability was further degraded, emphasizing the importance of addressing drainage issues in urbanized regions. The combined deterministic and probabilistic approaches used in this study effectively elucidated the mechanisms of rainfall-induced landslide in the tropical residual soil slope in the study area, particularly by defining the relationship between rainfall infiltration and the porewater pressure response in volcanic residual soils. This methodology also provides a more comprehensive analysis of slope stability during rainfall events, where traditional safety factor assessment alone is inadequate for evaluating slope performance in tropical volcanic residual soils. The benefit of the applied method is its leading to the establishment of site-specific thresholds (rainfall intensity and water level) for landslide early warning systems. This method excels for local conditions, while at a regional scale, integration of GIS and artificial intelligence methods is necessary.