Rainfall duration effect on slope stability of unsaturated silty sand soil

Landslides and slope instability events in Indonesia frequently occur during the rainy season. The relationship between rainfall and landslide activity is closely linked to the ability of rainwater to infiltrate the soil, which in turn affects slope stability. The objective of this study is to assess the duration of water infiltration in unsaturated soil conditions. Soil samples were taken from the western region of Indonesia and classified as silty sand (SM). Advanced laboratory testing was conducted to obtain the unsaturated soil properties, including soil water characteristic curve (SWCC), shrinkage curve, unsaturated permeability, and unsaturated shear strength. Few studies have examined the influence of different rainfall durations on seepage and slope stability. In this study, numerical simulations include rainfall application on the ground surface for three different durations over 1 day, that is, 6-h, 12-h, and 24-h simulations. A groundwater table was located at a depth of 5 m from the surface. The simulation results reveal increases in the groundwater level and in pore-water pressure during infiltration. This event reduces the suction force in unsaturated silty sand soil, thereby decreasing the factor of safety (FoS) in slope stability. The most significant decrease in FoS occurs in the 6-h simulation, while the effect on the safety factor in the 24-h simulation is not significant. This occurs due to the high intensity of rain during the shorter rainy period. After the rainy conditions, the factor of safety gradually rises and stabilizes on the sixth day, reaching an FoS of 1.86. This work identifies areas where silt–sand lithology predominates, along with high rainfall intensity and landslide susceptibility, providing important information to guide mitigation measures.

1 Introduction

Muara Enim, located in South Sumatra, as shown in Figure 1, is a productive region that contributes significantly to various industries, including agriculture, forestry, and mining. The study area is located in Padang Bindu Village, Pahang Enim District, Muara Enim Regency, South Sumatra Province, Indonesia. Geographically, the area forms part of the Bukit Barisan Mountain Range, which was formed by the tectonic collision between the Eurasian Plate and the Indo-Australian Plate. Consequently, the regional topography is highly variable, ranging from coastal morphology to rolling hills and mountainous terrain (Satyanaga et al., 2024). Based on geological conditions, the area is part of the South Sumatra basin, specifically the Lematang Depression, which is surrounded by anticlinorium and the major Northwest–Southeast Sumatran Fault System (Nawawi et al., 1996).

Figure 1

Figure 1. Study area map of Muara Enim (source: Google Earth).

In this study, soil property data indicated a quaternary alluvial deposit (Qa) (Pusat Penelitian dan Pengembangan and Gafoer, 1986), which can be classified as silty sand (SM). A previous study of sand characteristics with unsaturated conditions found that the shear strength is controlled by net normal stress and matrix suction. The lower normal stress has been interpreted as exhibiting peak softening, whereas the high net normal stress showed strain hardening behavior. As the shear strength increases, the friction angle has no relevance to the linear trend, and the ϕb decreases (Schnellmann et al., 2013).

Given the relatively dense population area, environmental safety should be considered, particularly in the residential area near the sloping area. The region is recognized as a landslide-prone area. According to the Regional Disaster Management Agency (BPBD) of Muara Enim, a total of 14 landslide incidents occurred along this provincial road between 2014 and 2023, including seven events in 2022. Although the region is generally classified as flat to gently sloping, landslides were reported in the Lawang Kidul subdistrict on 13 January 2025 and 17 March 2025 (BNPB, 2023). One week prior to the events, weather forecasts indicated precipitation intensities ranging from 100 to 200 mm, which were later confirmed by data from the BMKG (Meteorology, Climatology, and Geophysical Agency) station. The data were collected in January, whereas the rainfall peak was documented in November. The properties of soil in unsaturated conditions have become a focus because it is sensitive to volumetric change driven by water content. Matrix suction is applied at increasingly effective stress levels, where the strength should increase (Fredlund and Rahardjo, 1993). Whenever rain occurs, the volumetric water content at shallower depths increases and successively migrates to the groundwater level, parallel with the increasing matrix suction reduction rate (n%). At the same time, the rainfall intensity affects the infiltration of the soil column (Zhong et al., 2023). On the Loess Plateau, moisture content has remained relatively unchanged for 20 years. The moisture content is 31% at a depth between 1 and 8 m. From this, it can be inferred that long-term infiltration can significantly affect the soil water content below the ground surface. With the continued infiltration, the pore-water pressure increased and consequently weakened the bonds between particles (Gu et al., 2024). The reduction of soil strength creates the potential for landslides in sloping areas. A case study from Yunnan focused on lateritic soil and found that the landslides were induced by prolonged rainfall (Xi et al., 2024).

Recent advances in unsaturated soil mechanics have also demonstrated that matric suction plays a significant role not only in shear strength but also in the bearing capacity and overall stability of geotechnical structures. Several numerical and analytical studies have highlighted the sensitivity of geostructures—particularly shallow foundations and retaining systems—to variations in suction, water content, and environmental loading. For instance, researchers have investigated the combined vertical–horizontal–moment (V–H–M) bearing capacity of footings on partially saturated soils (Fathipour et al., 2023a), as well as the seismic bearing capacity of strip footings using finite element limit analysis and second-order cone programming (Maghferati et al., 2023). Other studies examined the thermo-hydro-mechanical response of unsaturated backfills (Bahmani Tajani et al., 2023), the pseudo-static seismic stability of shallow foundations (Nouzari et al., 2021), and the influence of combined loading on the bearing capacity of unsaturated soils (Afsharpour et al., 2022). Together, these works underscore the importance of accurately capturing suction-dependent behavior and permeability in numerical modeling of unsaturated geomaterials.

Several novel studies have been conducted on the stability analysis of geostructure in unsaturated soil conditions (Adiguna et al., 2023; Fathipour et al., 2022; Fathipour et al., 2020; Fathipour et al., 2023b). However, few studies assess slope stability in the Sumatra region by explicitly incorporating the principles of unsaturated soil mechanics and their effect on rainfall infiltration. This gap is critical because many slopes in Sumatra consist of unsaturated silty sand and are frequently subjected to intense rainfall events. Therefore, this study aims to simulate the effect of rainfall duration on the stability of an unsaturated silty sand slope by performing seepage–stability numerical simulations.

2 Methodology

2.1 Materials and data

The data were acquired from Muara Enim, South Sumatra. The area was interpreted to have a 1:1 slope, which is shown in Figure 2. Laboratory testing was conducted to determine the physical properties of soil, and the SWCC test case was conducted to build a model of water movement that measured the gravimetric and volumetric water content. These data will be used to determine the permeability and unsaturated shear strength assumption. Table 1 presents the material properties of the soil. The groundwater table depth, based on borehole observations, is 5 m below ground surface.

Figure 2

Figure 2. Slope profile.

Table 1

Table 1. Soil laboratory results.

As given data, the soil was classified as silty sand (SM). The effective shear strength parameters, cohesion (c′), and friction angle (ϕ′) are estimated using correlations recommended in AS 4678-2002, based on the soil type and density. The latest rainfall intensity of South Sumatra in 2023 was published on the BMKG website and is presented in Table 2. To be more specific, the data were acquired from the nearest station, as shown in Table 3.

Table 2

Table 2. Precipitation rate.

Table 3

Table 3. Daily rainfall intensity.

2.2 Best fit parameter

The SWCC data were modeled using the mathematical theory suggested by Satyanaga et al. (2017) with the equation shown in Equation 1.

${\theta }_w=\left(\frac{\ln \left(1+\frac{\psi }{{\psi }_r}\right)}{\ln \left(1+\frac{{10}^6}{{\psi }_r}\right)}\right)\times \left[{\theta }_r+\left({\theta }_s-{\theta }_r\right)\left(\beta ·\text{erfc}\left(\frac{\ln \left(\frac{{\psi }_a-\psi }{{\psi }_a-{\psi }_m}\right)}{s}\right)\right)\right],(1)$

where:

β = 0 when ψ ≤ ψ_a; β = 1 when ψ ≥ ψ_a,

θ_w = volumetric water content,

θ_s = saturated water content,

ψ = matric suction under consideration (kPa),

ψ_a = air entry value (kPa),

ψ_m = matric suction at the inflection point of the SWCC (kPa),

ψᵣ = suction corresponding to the residual water content,

s = parameter representing the geometric standard deviation of the SWCC, and

θᵣ = residual water content.

The SWCC corresponding to the gravimetric water content is shown in Figure 3. An iterative non-linear regression procedure provided in Microsoft Excel was used to adjust all parameters to fit the mathematical equation to the SWCC experimental data. The plotted graph shows that the pressure of the air entry value is 4.9 kPa, while in Figure 4, the air entry value is slightly greater, at 5.0 kPa. As the soil dries, the soil moisture content decreases as the suction pressure increases. The performance of the equation in best fitting the SWCC experimental data is evaluated using the R² criteria. R² for fitting the gravimetric water content of SWCC is 0.975, while R² for fitting the volumetric water content of SWCC is 0.981. Both values indicate that the performance of the equation is relatively good in best fitting the SWCC experimental data.

Figure 3

Figure 3. Experimental gravimetric water content SWCC.

Figure 4

Figure 4. Experimental volumetric water content SWCC.

The shrinkage curve is shown in Figure 5. The trend from the graph presents the response during soil drying. As the soil shrinks, the water content decreases. The decrease in water content leads to an increase in matric suction. Meanwhile, Figure 6 shows that unsaturated permeability values increase when the volumetric water content exceeds 0.40. This permeability value will continue to increase as the water content rises and shows a linear trend on a logarithmic scale.

Figure 5

Figure 5. Shrinkage curve of the Muara Enim sample.

Figure 6

Figure 6. Volumetric water content vs. unsaturated permeability.

2.3 Numerical modeling

The numerical simulation was performed utilizing the GeoStudio software, particularly SEEP/W and SLOPE/W. This software is widely used and validated in geotechnical engineering practice for coupled seepage–stability analysis of slopes. The water infiltration process, including the simulation of rainfall duration and its pore-water pressure distribution, was modeled using SEEP/W, while the safety factor of the slope was calculated using SLOPE/W. Because the investigated slope is long and nearly homogeneous along the out-of-plane direction, adopting a two-dimensional representation is adequate for capturing its seepage and stability behavior.

For seepage analysis in SEEP/W, the soil is modeled as an unsaturated porous medium governed by Darcy’s law. The boundary conditions applied for the seepage analysis are shown in Figure 2. The upstream and downstream boundaries along the phreatic surface are constrained by constant total heads of 15 m and 11 m, respectively, to represent the regional groundwater table. A steady-state seepage analysis using these head boundaries is first performed to obtain the initial pore-water pressure distribution prior to rainfall. Transient rainfall simulations are then conducted by applying a flux boundary at the ground surface. The left vertical boundary is defined as a zero-pressure boundary (total head H = 0 m), allowing water to freely exit the model once pore-water pressures become positive.

For stability analysis in SLOPE/W, the constitutive model Mohr–Coulomb with an unsaturated shear strength function was used. The effective shear strength parameters were derived from empirical correlations. The contribution of matric suction, which links shear strength to suction through an unsaturated friction angle (ϕ^b), is incorporated.

Different rain durations were incorporated into three sets of numerical simulations with SEEP/W as the parent analysis and SLOPE/W as the sub-analysis. The pore-water pressure distributions from SEEP/W were used as input in the SLOPE/W analysis. The results of SEEP/W in the form of a transient stage will be simulated in SLOPE/W over time to calculate slope stability.

3 Results and discussion

The rainfall data were simulated for three duration cases: 6-h, 12-h, and 24-h. For reference, the intense precipitation that occurred in March 2025 was recorded to be 153.00 mm/day on 13 March 2025. Therefore, the rainfall intensity was divided into three cases: a 6-h duration of 25.20 mm/h, a 12-h duration of 12.75 mm/h, and a 24-h duration of 6.38 mm/h. The simulation of the rainfall duration shows that longer periods of rain lead to lower rainfall rates.

The rain simulation starts at 5:00 a.m. with light rain for 1 hour, followed by the design rainfall, and ends with light rain. The design rainfall will be converted into meters per second as software input. Light rain is planned to occur at half the intensity of the design rainfall. A 6-h simulation with a design rainfall of 7.08 × 10⁻⁶ m/s will result in light rain of 3.54 × 10⁻⁶ m/s. Meanwhile, the 12-h rain simulation will have a rainfall rate of 3.54 × 10⁻⁶ m/s and a light rain rate of 1.77 × 10⁻⁶ m/s. The final simulation with 24-h rainfall will use a design rainfall value of 1.77 × 10⁻⁶ m/s and light rainfall of 0.88 × 10⁻⁶ m/s. The relationship between time and design rainfall is presented in Figure 7.

Figure 7

Figure 7. Rainfall simulation.

The rain simulation that started at the 6th hour with varying durations and rainfall intensities showed the effect of the slope stability factor of safety (FoS). The rainfall condition results in infiltration of water into the soil, which potentially decreases the factor of safety. The water content in the soil can lead to an increase in pore-water pressure and reduce the suction force in the soil. The suction pressure (or matric suction) in unsaturated soils is a negative pressure that exists within the soil pores, pulling the soil particles together. This suction force is a key factor influencing the behavior of unsaturated soils, increasing the strength and overall stability of the soil slope.

As shown in Figure 8, the 6-h rain simulation reduced FoS from 1.84 to 1.47, while the 12-h and 24-h rain simulations reduced it to 1.49 and 1.54, respectively. The 6-h rain simulation reveals a significant decline in FoS. This reduction occurred because the rainfall intensity was higher than in the other two simulations.

Figure 8

Figure 8. Safety Factor vs. Time (Hours).

The decrease in the factor of safety occurs due to changes in pore-water pressure in the soil, in this case, during rain on sandy clay soil. In the first 6 h before the rain occurred, the pore-water pressure value showed a negative number, which means there was suction in the soil. The negative pore-water pressure values gradually approach 0 as the pore-water pressure increases. According to Figure 8, critical conditions occur in the 6-h simulation; therefore, at the landslide point, the change in pore-water pressure is shown in Figure 9. This phenomenon indicates that a high rainfall rate with a short duration affects slope stability.

Figure 9

Figure 9. Pore-water pressure and factor of safety after 6 h of rainfall.

Three observation points are located in different areas to analyze the water pressure during the rainfall event. Figure 10 reflects the increasing trend of all three points, where at Point A, the water pressure rises to 14.05 kPa. Meanwhile, Point B shows a lower value of 12.70 kPa, and Point C shows a higher value of 15.09 kPa. This condition is possible because the placement of Point C is the first of the three point observations to absorb the effects of rainwater infiltration.

Figure 10

Figure 10. Pore-water pressure with time during rainfall.

The rain event changes the groundwater level and the suction in the soil, which will later affect the factor of safety. The FoS value will gradually increase at different rates in each simulation. However, the FoS value will stabilize at the same time, specifically on the 6th day, as shown in Figure 11.

Figure 11

Figure 11. Safety Factor vs. Time (Days).

Before rainfall (steady state), matric suction in the unsaturated zone above the groundwater table provides an additional strength component, increasing the factor of safety (FoS). During rainfall (transient state), infiltration rapidly reduces matric suction, thereby lowering the safety factor of the slope. The 6-h event (highest intensity) produces the sharpest suction loss and the largest positive pore-water pressure increments near the surface; the 12-h event shows an intermediate response; the 24-h event yields a deeper wetting front yet lower peak pore-water pressure. Accordingly, the transient safety factor is lowest for the 6-h event, higher for the 12-h event, and highest for the 24-h event. After the rainfall event, drainage restores suction from the surface downward, pore-water pressure dissipates over several days, and the safety factor recovers toward a steady state.

4 Conclusion

The study on the effect of rainfall duration on slope stability in unsaturated silty sand soil revealed that similar daily rainfall amounts lead to varying decreases in the FoS value. The simulation shows that the rain with the shortest duration has the largest FoS rate decrease. The higher rainfall intensity over a short period of time on silty sand causes a greater drop in suction as a result of increasing pore-water pressure, which is represented by the steep line.

The decrease in FoS value is only noticed during rainy conditions, and the FoS progressively increases to a stable value on approximately the 6th day after the rain stops. There is a slight difference in the rate of increase in FoS values between the three simulations. Therefore, there is no difference in the duration of the rain infiltration effect on slope stability.

The most fascinating aspect about the return of the FoS value is that the stability number is higher than the initial value. The initial value before the rain occurred was 1.84, while the stable FoS value on the 6th day was 1.86. It indicates that there are long-term residual effects on the soil due to changes in water pressure.

The present analysis focuses on detailed unsaturated hydraulic properties (SWCC, shrinkage curve, and hydraulic conductivity), while the effective shear strength parameters were estimated in accordance with AS 4678-2002. Future studies should therefore include direct shear or triaxial tests on unsaturated samples to obtain more reliable strength parameters and extend the present two-dimensional analyses to three-dimensional finite element models (e.g., using ABAQUS) to capture possible end effects, spatial variability of soil properties, and more complex boundary conditions. A parametric study of groundwater table depth variations should also be conducted to quantify the effect on the factor of safety.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding authors.

Author contributions

BP: Conceptualization, Formal analysis, Investigation, Methodology, Writing – original draft. FR: Data curation, Investigation, Software, Writing – original draft. GA: Writing – review and editing, Data curation, Formal analysis. AH: Conceptualization, Funding acquisition, Project administration, Supervision, Writing – original draft. EB: Investigation, Methodology, Supervision, Validation, Writing – original draft. MW: Conceptualization, Methodology, Software, Writing – original draft. WP: Funding acquisition, Project administration, Resources, Validation, Writing – review and editing. WR: Investigation, Methodology, Validation, Visualization, Writing – review and editing. NG: Resources, Validation, Visualization, Writing – review and editing. ED: Data curation, Formal analysis, Validation, Writing – review and editing. AS: Methodology, Resources, Supervision, Validation, Writing – review and editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. This research was funded by the Directorate of Research and Development, Universitas Indonesia, under Hibah PUTI 2024 (Grant No. NKB-539/UN2.RST/HKP.05.00/2024).

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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