Parametric Study of Rainfall-Induced Instability in Fine-Grained Sandy Soil

Abstract

This study investigates the stability of fine-grained sandy soil slopes under varying rainfall intensities, durations, and geotechnical properties using a parametric analysis within GeoStudio. A total of 4416 unique parameter combinations were analyzed, incorporating variations in unit weight, cohesion, friction angle, slope inclination, slope height, rainfall intensity, and duration. Results reveal that rainfall intensity is the most influential variable on the factor of safety (FS), with higher intensities (e.g., 360 mm/h) on steeper slopes (e.g., 45°) leading to critical FS values below 1, indicating an imminent risk of failure. Under moderate conditions (e.g., 9 mm/h rainfall on slopes of 26.6°), the FS remains above 2. This dataset provides a valuable foundation for training machine learning models to predict slope stability under diverse environmental conditions, contributing to the development of early warning systems for rainfall-induced landslides.

1. Introduction

Rainfall-induced slope failures represent a significant threat to both human safety and infrastructure stability worldwide [1,2]. The occurrence of landslides not only results in tragic loss of life but also causes substantial economic damage and disruption to essential services [3,4]. The increasing frequency of intensity of rainfall events due to climate change has further exacerbated this issue, leading to a rise in slope failures in regions that were previously considered stable [5,6], this is important because, from 2004 to 2016, rainfall triggered 79% of non-seismic landslides, resulting in a total of 55,997 deaths [7]. Understanding the mechanisms through which rainfall triggers slope instability is therefore crucial for developing effective mitigation strategies.

Slopes consisting of unsaturated soils are particularly vulnerable to rainfall-induced failures. As rainfall infiltrates the soil, it reduces the matric suction, leading to a decrease in shear strength and increase in pore water pressure [8,9,10,11,12,13]. This process can eventually lead to a condition where the factor of safety (FS) drops below 1, indicating imminent slope failure, making rainwater the most important triggering factor in the instability of slopes [14]. The complexity of these interactions between rainfall and slope stability highlights the need for sophisticated analysis and predictive tools.

Recent advancements in artificial intelligence (AI) and machine learning (ML) offer promising avenues for improving slope stability analysis [15,16,17,18,19]. By leveraging large datasets and powerful computational algorithms, AI can assist in the early detection of potential slope failures, thereby providing critical lead time for emergency response and risk management. However, the development of reliable predictive models requires extensive datasets that accurately capture the diverse range of conditions under which slopes may fail [20].

The primary objective of this study is to generate a comprehensive dataset through a systematic parametric analysis of fine-grained sandy soil slope stability under varying rainfall conditions. Using numerical modeling with GeoStudio [21], this research examines the influence of key soil and geometric parameters such as unit weight, cohesion, friction angle, slope inclination, slope height, rainfall intensity, and rainfall duration on slope stability. The resulting dataset will serve as a valuable resource for training and validating machine learning models aimed at predicting slope failures [22]. Ultimately, this work seeks to contribute to the development of an early warning system that can mitigate the risks associated with rainfall-induced slope failures by enabling timely and accurate predictions.

2. Parametric Study

For this study the stability of the slope was assessed through the factor of safety; and the factors affecting the stability of the slope are considered to be the unit weight, cohesion, friction angle, slope inclination, slope height, rainfall intensity, and rainfall duration. Figure 1 shows the slope geometry used for the parametric study, with boundary conditions representing rainfall intensity through water flux (mm/h), which are selected over the lines 3–6 with potential seepage review, the lines 7–8 that represent the ground water table with a maximum matric suction of 75 kPa for fine-grained sandy soil [23,24] and the lines 1–2, 3–8, and 6–7 for no flow boundary (Q = 0 m³/s) to prevent any water from entering or leaving through the sides and the bottom, simulating impermeable conditions. For the ground water table depth (Hw) of 5 m and inclination of 7° was chosen based on Rahardjo et al. (2007) [25].

For fine-grained sandy soils, the mechanical behavior is influenced by the percentage of fines, which affects cohesion, friction angle, and unit weight. These parameters are essential in assessing slope stability and soil behavior under different environmental conditions. The cohesion (c) in fine-grained sandy soils tends to increase with the increase in fines content, particularly at fine contents up to 10–15%. Values of cohesion for sandy soils with fines content within this range are reported to be between 5 and 20 kPa [26,27]. Studies involving clayey sands and sand–clay mixtures reveal that as fine content increases, the soil’s cohesion also increases due to better particle interlocking [28]. For the friction angle (θ) typically decreases with the addition of fines. For sandy soils with 5–15% fines, the friction angle ranges between 28° and 35° [27,28]. As shown in direct shear tests, the reduction is more significant beyond 10% fines, with values ranging from 30° to 35° at lower fines and dropping to approximately 28° as the fine content increases toward 15% [26,29]. For the unit weight (γ) of fine-grained sandy soils is influenced by the fine content and compaction. For sandy soils containing 5–15% fines, the dry unit weight generally ranges from 15.5 to 18 kN/m³. This trend aligns with results from studies of sand–clay mixtures, where the addition of fines increases soil density up to a certain threshold [27,28,29]. The final properties for the analysis are for the cohesion (c) for 5 to 13 kPa, for the friction angle (θ) for 28 to 34° and for the unit weight (γ) for 13 to 19 kN/m³.

For the slope geometry, three slope inclinations (β = 26.6, 33.7, 45°) and four slope heights (5, 10, 15, 20 m) were chosen for the study. For the rainfall conditions, four rainfall intensities (9, 50, 80, 360 mm/h), and four rainfall durations (12, 24, 36, 48 h) were considered. A sensitivity analysis was performed to determine how each of these parameters influence slope stability, thereby identifying the most critical factors affecting the factor of safety (FS) under various environmental and geotechnical conditions.

3. Unsaturated Soil

In unsaturated soils, the matric suction, or negative pore-water pressure, plays a crucial role in providing additional shear strength. As water infiltrates during rainfall, matric suction decreases, resulting in a reduction of effective stress and shear strength, which can lead to slope instability [10]. Matric suction also acts as a stabilizing force by resisting deformation and limiting slope movement. This aspect is particularly relevant for fine-grained sandy soils, which exhibit distinct hydraulic behaviors due to their high permeability and rapid response to changes in water content [30]. Understanding the balance between suction, infiltration, and slope stability is crucial for assessing failure risks in unsaturated soils under varying rainfall conditions [31].

3.1. Shear Strenght

The shear strength of unsaturated soil depends on both the effective stress and the matric suction. For the fine-grained sandy soil used in this study, the base parameters adopted were soil density γ = 16 kN/m³, cohesion c = 9 kPa, and friction angle θ′ = 31°. These values align with typical values for fined- grained sandy soils and were selected based on geotechnical recommendations [25]. The relationship between matric suction and shear strength was modeled using the Vanapalli et al. (1996) [32] equation, which is expressed as:

$$\tau =c^{\prime }+\left(\sigma -u_a\right)tan{\varphi }^{\prime }+\left(u_a-u_w\right)\left[{\displaystyle \frac{{\theta }_w-{\theta }_r}{{\theta }_s-{\theta }_r}}tan{\varphi }^{\prime }\right]$$

(1)

where τ is the shear strength, c′ is the effective cohesion, (σ − u_a) is the net normal stress, (u_a − u_w) is the matric suction, ϕ′ is the effective angle of internal friction, θ_w represents the volumetric water content, θ_s is the saturated volumetric water content, and θ_r is the residual water content. This equation was implemented in the SEEP/W software (2024) for parametric analysis.

3.2. Soil Water Characteristics Curve (SWCC)

The soil water characteristic curve (SWCC) describes the relationship between matric suction and water content in the soil. The SWCC for the fine-grained sandy soil was modeled using the Fredlund and Xing (1994) [33] equation, which is widely applied in unsaturated soil mechanics for estimating the volumetric water content based on the soil’s suction potential. The SWCC provides essential insights into the hydraulic behavior of the soil, which influences the infiltration process during rainfall events, and subsequently, the slope stability. In this study, the parameters of the SWCC were determined from empirical relationships, using soil-specific values for air-entry suction and residual water content.

$${\Theta }_w=C_{\psi }{\displaystyle \frac{{\Theta }_s}{{\left\{ln\left[e+{\left(\frac{\Psi }{a}\right)}^n\right]\right\}}^m}}$$

(2)

where ${\Theta }_w$ is the volumetric water content, $C_{\psi }$ is the correction function, ${\Theta }_s$ is the saturated volumetric water content, e is the natural number (2.71828), $\Psi$ is the negative pore water pressure, and a, n and m are curve fitting parameters. $C_{\psi }$ = 1 [34].

3.3. Hydraulic Conductivity

Hydraulic conductivity in unsaturated soils varies as a function of the matric suction and water content. For this study, the permeability function was derived from the equation proposed by Leong and Rahardjo (1997) [35], was used. Fine-grained sandy soils generally exhibit higher hydraulic conductivities, allowing for rapid infiltration and redistribution of water, which directly affects slope stability under rainfall conditions [36]. The measured hydraulic conductivity for this analysis was k_s = 1 × 10⁻⁴ m/s, which was used in numerical simulations to assess the infiltration dynamics and their impact on slope stability.

$$k_w=k_s\ast {\Theta }^p$$

(3)

where k_w is the coefficient of permeability with respect to water for unsaturated soil, k_s is the saturated coefficient of permeability, Θ is equal to θ_w/θ_s, and p is the fitting parameter corresponding to the slope of the permeability function. The fitting parameters for the soil water characteristics curve are shown in

Table 1. Soil Water Characteristic Curve (SWCC) and hydraulic conductivity parameters for fine-grained sandy soil.

Fine-Grained Sandy Soil	SWCC				HydraulicConductivity
	a  (kPa)	m	n	θs	ks  (m/s)	p
	10	1	1	0.45	1 × 10−4	4

. Figure 2 shows the hydrological properties for the fine-grained sandy soil used in the analysis.

4. Analysis

The analysis of the models examined the effects of various factors on slope stability, particularly under the influence of rainfall. A sensitivity analysis was conducted using GeoStudio, leveraging both SEEP/W for transient seepage analysis and SLOPE/W for stability analysis. The Morgenstern–Price method was employed as the primary limit equilibrium method, chosen for its robustness in satisfying both moment and force equilibrium [37].

The Morgenstern–Price method, which employs a mathematical function to estimate the interslice shear forces, was applied in this study with the interslice force function assumed as constant (f(x) = 1) (similar to the Spencer method). This approach is particularly well-suited for analyzing complex geotechnical problems involving varied parameters, such as soil cohesion, friction angle, unit weight, slope angle, and external factors like rainfall intensity and duration. The method iteratively solves for both horizontal and vertical force equilibrium, ensuring that the computed factor of safety (FS) is both accurate and reliable across multiple slices of a potential sliding mass. The equation used to relate the interslice shear force (X) and normal force (E) is:

$$X=E \lambda f\left(x\right)$$

(4)

For the analysis, key parameters such as cohesion, friction angle, and unit weight were systematically varied, alongside geometrical properties like slope height and angle, and rainfall characteristics including intensity and duration. This structured approach enabled the isolation of the impact of each variable on slope stability, specifically its effect on the FS. By running simulations where one parameter was varied while others were held constant, the sensitivity of the FS to each parameter was identified. The results indicate how the FS declines under different parameter combinations, particularly under higher rainfall intensities and steeper slopes, highlighting the critical variables that influence slope stability.

4.1. Numerical Model Validation

In order to validate the numerical model developed for analyzing slope stability under rainfall, the results from Rahardjo et al. (2007) [25] are used as a benchmark. Rahardjo’s study focused on the instability of homogeneous soil slopes under varying rainfall intensities, soil properties, and slope geometries, which provides a solid basis for comparison with the results of this research. Both studies focus on fine-grained sandy soil subjected to rainfall, and the parameters and boundary conditions were replicated to assess the performance of my model (see Figure 3).

In this test, rainfall was sustained for 24 h, during which the factor of safety (FS) progressively decreased over time, reaching a minimum before beginning to increase. This increase typically occurs as rainfall ceases or stabilizes, allowing excess pore water pressures or seepage forces within the soil to gradually dissipate [38]. As the soil regains stability, matric suction may also recover, particularly in unsaturated soil layers above the water table. These recovery mechanisms—dissipation of pore pressures and the restoration of matric suction—effectively elevate the FS after it reaches its minimum, signifying a transition back to more stable conditions following the critical period of rainfall infiltration.

4.2. Effect of Soil Properties

The results for the sensitivity analysis considering the soil properties (unit weight, cohesion and friction angle) are presented in this section, for demonstration purposes the results shown in this section are only for a 10 m slope height.

4.2.1. Unit Weight

To assess the effect of unit weight on slope stability, cohesion and friction angle were held constant at 9 kPa and 31°, respectively. The parametric study evaluated the factor of safety (FS) across three slope inclinations—26.6°, 33.7°, and 45°—under various rainfall intensities (9 mm/h, 50 mm/h, 80 mm/h, and 360 mm/h) and durations (see Figure 4). The results clearly show a consistent relationship between increasing unit weight and decreasing FS, with the exception of a slight stabilization under extremely high rainfall intensity (360 mm/h).

For the 26.6° slope, FS values generally decreased as unit weight increased from 13 to 19 kN/m³ across all rainfall intensities. For lighter rainfall (9 mm/h), FS ranged from 3.012 to 2.563, indicating stable conditions. However, under 360 mm/h rainfall, FS dropped significantly to values between 1.351 and 1.389, reflecting a much higher risk of slope failure. Interestingly, there is a slight increase in the FS as unit weight rises, suggesting that denser soils may offer temporary resistance to rapid infiltration at extreme rainfall intensities. This highlights how rainfall infiltration progressively reduces matric suction and increases pore water pressure, ultimately reducing the shear strength of the soil and leading to instability [39].

A similar pattern was observed for the 33.7° slope. Under 9 mm/h rainfall, the FS decreased from 2.61 to 2.2 as unit weight increased. However, under 360 mm/h rainfall, the FS ranged from 1.065 to 1.095, showing a slight increase in the FS with higher unit weights, similar to the behavior observed for the 26.6° slope. This indicates that for moderate slopes, heavier soils provide marginally better stability under intense rainfall, likely due to their greater compaction and reduced infiltration rates. This demonstrates that while soil density plays a crucial role, rainfall intensity and duration also significantly contribute to slope instability by increasing pore water pressure and reducing the soil’s effective stress [38].

In contrast, for the 45° slope, the behavior under 360 mm/h rainfall differed. While the FS values were already lower due to the steeper slope, the FS decreased consistently with increasing unit weight. For example, under 360 mm/h rainfall, the FS values dropped from 0.974 at 13 kN/m³ to 0.874 at 19 kN/m³. This indicates that for very steep slopes, the higher unit weight exacerbates the driving forces of slope failure under extreme rainfall, likely overwhelming any beneficial effects of soil compaction. The reduced FS at higher unit weights shows that the steeper inclination amplifies the destabilizing forces due to gravity, making these slopes highly vulnerable under extreme rainfall conditions. This confirms the significant role of rainfall in triggering slope failure on steep terrains, as the saturated conditions further reduce soil shear strength, leading to rapid reductions in the FS [40,41].

Across all slope inclinations, increasing unit weight generally reduced FS, with the most severe declines occurring under high-intensity rainfall. Notably, while the 26.6° and 33.7° slopes exhibited a slight increase in the FS under extreme rainfall conditions (360 mm/h) with higher unit weights, the 45° slope showed a consistent decrease in the FS with increasing unit weight under the same conditions. Additionally, the significant impact of rainfall on slope stability is consistent with findings from previous studies, which emphasize the role of water infiltration in reducing shear strength and increasing the likelihood of landslides [42].

4.2.2. Cohesion

Cohesion is a critical factor in resisting shear forces within a slope, which directly impacts stability. In this study, the factor of safety (FS) was examined for slope inclinations of 26.6°, 33.7°, and 45°, with cohesion values varying from 5 to 13 kPa. Rainfall intensities ranged from 9 mm/h to 360 mm/h, with durations spanning from 12 to 48 h. Friction angle and soil density were held constant across the analysis to focus on the effects of cohesion (see Figure 5).

For the 26.6° slope, as cohesion increased, the FS demonstrated a consistent rise across all rainfall scenarios. Under the lowest rainfall intensity (9 mm/h), the FS ranged from 2.54 at 5 kPa cohesion to 2.95 at 13 kPa, indicating stable conditions even at the lower cohesion levels. In more extreme rainfall scenarios (360 mm/h), the FS values dropped but remained above 1, ranging between 1.13 and 1.62. This indicates that higher cohesion values help mitigate instability, even under severe rainfall conditions, but cannot completely prevent reductions in the FS. Despite the stabilizing effect of cohesion, rainfall infiltration leads to the reduction of shear strength due to rising pore water pressures, a common occurrence in unsaturated soils [43].

The 33.7° slope exhibited similar behavior, with the FS increasing as cohesion rose. Under mild rainfall (9 mm/h), the FS ranged from 2.18 to 2.56 across the cohesion values, reflecting relatively stable conditions. However, at 360 mm/h, the FS dropped more significantly, starting at 0.95 for the lowest cohesion and rising to 1.40 at 13 kPa. This shows that while increased cohesion improves slope stability, moderate slopes are more vulnerable to critical failures as rainfall intensity increases.

The 45° slope, being the steepest, showed the greatest susceptibility to instability, particularly under extreme rainfall. For low-intensity rainfall (9 mm/h), the FS values increased from 1.74 to 2.10 as cohesion increased. However, under 360 mm/h rainfall, the FS values were consistently low, starting at 0.74 at 5 kPa and reaching 1.16 at 13 kPa. Despite the increase in cohesion, this slope remained close to or below the critical FS threshold of 1, underscoring the heightened vulnerability of steeper slopes to rainfall-triggered failures, even when cohesion is relatively high. Rainfall-induced slope failures are primarily driven by the saturation of soils, which diminishes the effective stress and reduces the contribution of cohesion to shear strength [44].

The results reveal that cohesion plays a key role in improving slope stability, with higher cohesion values yielding greater FS across all rainfall conditions. However, as rainfall intensity increases, the beneficial effect of cohesion is diminished, especially for steeper slopes. This observation aligns with existing literature, which emphasizes the role of rainfall in saturating the soil, reducing matric suction, and decreasing the overall shear strength of the slope [45,46,47,48].

4.2.3. Friction Angle

The friction angle (θ) is a key parameter influencing the shear strength of soil, particularly in the context of slope stability. Its impact on the factor of safety (FS) was evaluated for slope inclinations of 26.6°, 33.7°, and 45°, with friction angles ranging from 28° to 34°. Rainfall intensities varied from 9 mm/h to 360 mm/h, with durations between 12 and 48 h, while cohesion and soil density were held constant across all tests to isolate the effect of friction angle on stability (see Figure 6).

For the 26.6° slope, as the friction angle increased, there was a noticeable and consistent rise in FS across all rainfall scenarios. Under the mildest rainfall condition (9 mm/h), the FS increased from 2.48 at a friction angle of 28° to 3.02 at 34°. As rainfall intensity increased, the FS decreased but still showed a positive correlation with friction angle, reaching values of 1.28 to 1.47 for the most severe rainfall event (360 mm/h). These results demonstrate that an increase in friction angle significantly enhances slope stability, especially under lower rainfall conditions, although the stabilizing effect diminishes under higher rainfall intensities. Studies have shown that while higher friction angles improve stability by increasing shear strength, the reduction of effective stress caused by rainfall infiltration still compromises stability under high rainfall conditions [49,50].

The 33.7° slope exhibited similar trends, with FS values rising as friction angle increased. For the 9 mm/h rainfall intensity, the FS ranged from 2.14 at a 28° friction angle to 2.60 at 34°. When subjected to extreme rainfall (360 mm/h), FS values dropped more significantly but still ranged from 1.10 to 1.26. This suggests that while friction angle enhances slope stability, its effect is diminished under saturated conditions, where high pore water pressure reduces the effectiveness of frictional resistance [51].

The 45° slope, being the steepest, exhibited lower FS values overall, especially under intense rainfall conditions. Under 9 mm/h rainfall, the FS increased from 1.75 to 2.10 as the friction angle rose from 28° to 34°. However, in the most extreme rainfall scenario (360 mm/h), FS values dropped below 1, ranging from 0.83 to 0.93 across the same range of friction angles. These results align with studies indicating that frictional resistance is significantly reduced when the soil becomes saturated [38].

4.2.4. Effect of Rainfall Intensity and Duration

The rainfall intensities considered for this parametric study were 9, 50, 80, and 360 mm/h. According to the World Meteorological Organization (WMO) 2023 [52], these intensities range from moderate, heavy and extreme rainfall, with classifications of slight (<2.5 mm/h), moderate (2.5–10 mm/h), heavy (10–50 mm/h), and violent (>50 mm/h). The interaction between rainfall intensity and soil permeability is crucial for understanding water flow through the slope. When rainfall intensity surpasses the soil’s permeability, runoff occurs as the soil cannot absorb the water quickly enough. This runoff effect was a key consideration in selecting rainfall intensities for this study.

The results, focused on a slope height of 10 m, show that the factor of safety (FS) decreases as rainfall intensity increases. The Figure 7 show the effect of rainfall intensity and duration on slope stability shows a clear trend, where the factor of safety (FS) decreases as both rainfall intensity and duration increase. Across all slope inclinations, lower rainfall intensities, such as 9 mm/h and 50 mm/h, exhibit relatively stable FS values over time. For these lower intensities, the FS remains close to the initial values, decreasing gradually as rainfall duration increases. For example, at 9 mm/h, the FS drops only slightly, from approximately 2.8 to 2.7 after 12 h, while at 50 mm/h, the FS declines more noticeably, reaching around 2.4 at the end of 12 h. This suggests that for moderate rainfall intensities, the destabilization of slopes is less pronounced, and the FS remains above critical thresholds.

In contrast, the effect of higher rainfall intensities, such as 80 mm/h and 360 mm/h, is much more severe. As the rainfall duration increases, the FS drops significantly, indicating heightened instability. For the 80 mm/h intensity, the FS decreases from initial values around 2.4 to as low as 1.7 after 12 h. The 360 mm/h intensity shows the most dramatic reduction, with the FS falling from about 2.1 to values close to 1.2 by the end of the 12-h period. This pronounced decrease highlights the critical role of high-intensity rainfall in reducing slope stability, especially when rainfall is sustained over several hours.

Additionally, steeper slopes exhibit lower initial FS values and more substantial decreases under high-intensity rainfall. While moderate rainfall results in only slight reductions in FS, intense rainfall accelerates the destabilization process, leading to critically low FS values, particularly after extended rainfall durations. These results emphasize the importance of considering both rainfall intensity and duration in slope stability assessments, as higher intensities and prolonged rainfall significantly increase the risk of slope failure due to the progressive build-up of pore water pressure and reduced soil shear strength.

The results demonstrate that both rainfall intensity and duration are critical factors in slope stability. As the duration of rainfall increases, the FS decreases significantly, particularly for steeper slopes and higher rainfall intensities. These findings emphasize the importance of considering both rainfall duration and slope inclination when assessing the risk of slope failure under prolonged rainfall conditions.

4.2.5. Effect of Slope Height

The parametric study was conducted for four different slope heights, and for demonstration purposes, the results obtained from the analysis of 9 mm/h and 50 mm/h rainfall intensities will be shown to compare how the slope height affects the stability of slopes with different inclinations. Figure 8 shows that across all inclinations, the results show that as the slope height increases, the FS decreases. This behavior is consistent with the principles of slope stability, as taller slopes have more mass, which generates greater gravitational driving forces, increasing the likelihood of failure [53].

The results reveal that as the slope height increases, the factor of safety (FS) consistently decreases across all slope inclinations and rainfall intensities. Under a rainfall intensity of 9 mm/h, the FS significantly drops as the height changes from 5 m to 20 m. For the 26.6° slope, the FS declines from 4.173 at 5 m to 2.286 at 20 m, showing the highest initial FS and steepest decline among all cases. Similarly, the FS for the 33.7° slope reduces from 3.673 to 1.928, while for the 45° slope, the FS decreases from 3.181 to 1.564, indicating a more pronounced effect on steeper slopes under the same rainfall conditions.

When subjected to a higher rainfall intensity of 50 mm/h, the FS experiences a similar downward trend with increasing slope height. For the 26.6° slope, the FS drops from 3.682 at 5 m to 2.176 at 20 m, which, while lower than the 9 mm/h case, follows the same pattern. The 33.7° slope sees a reduction in the FS from 3.219 to 1.805, and the 45° slope shows the most significant drop, from 2.715 to 1.424 as the slope height increases. The steeper the slope, the more dramatic the effect of height on stability, particularly at higher rainfall intensities.

This analysis highlights the critical role that both slope height and inclination play in influencing slope stability, with higher slopes and steeper inclinations resulting in significantly lower FS, particularly under high rainfall intensity.

5. Results and Dataset

The parametric study conducted in this research focused on understanding the behavior of fine-grained sandy soil slopes under varying conditions of slope height, slope angle, soil unit weight, cohesion, friction angle, rainfall intensity, and rainfall duration. A total of 4416 unique combinations of these parameters were evaluated, providing a comprehensive dataset that captures a wide range of potential slope stability scenarios. This dataset will serve as the foundation for training machine learning algorithms to predict slope stability under diverse geotechnical and environmental conditions.

The results demonstrate that each factor—slope height, inclination, soil properties (unit weight, cohesion, friction angle), and rainfall conditions—has a pronounced effect on the factor of safety (FS). Higher slope heights and steeper inclinations generally lead to lower FS values, particularly when combined with higher rainfall intensities and extended durations. These findings align with established geotechnical principles, where gravitational forces increase with slope height, and rainfall infiltration reduces soil shear strength by saturating the slope and increasing pore water pressures.

For example, the results indicate that for slopes with moderate inclinations (e.g., β = 26.6°), the FS remains above 2.0 under lower rainfall intensities (e.g., 9 mm/h) and shorter durations. However, as rainfall intensity and duration increase, particularly under conditions such as 50 mm/h for 12 h, the FS declines significantly. For steeper slopes (e.g., β = 45°), the FS drops below 1.5, even under moderate rainfall conditions, indicating potential failure under higher slope heights and intense rainfall events.

This dataset, generated using a sensitivity analysis in GeoStudio, provides a robust platform for machine learning model development aimed at predicting slope failure risks. The diversity of conditions simulated in this study offers a strong basis for training algorithms capable of rapid slope stability assessments. While this study focuses on fine-grained sandy soils, future research will expand the dataset by incorporating fine-grained silty and clayey soils, which exhibit different behaviors in terms of permeability and plasticity. This will enhance the dataset’s versatility and improve the predictive accuracy of machine learning models for a broader range of geotechnical scenarios.

6. Conclusions and Discussion

The parametric study carried out in this research provided significant insights into the factors affecting the stability of fine-grained sandy soil slopes. By analyzing the influence of various geotechnical and environmental parameters—slope height, slope inclination, unit weight, cohesion, friction angle, rainfall intensity, and rainfall duration—on the factor of safety (FS), it is possible to highlight key factors that play a dominant role in determining slope stability [54,55,56,57,58,59,60,61]. These parameters are essential inputs for an early warning system aimed at predicting slope failures.

The results indicate that rainfall intensity and slope inclination have the greatest impact on the factor of safety. Slopes subjected to high rainfall intensities (e.g., 360 mm/h) exhibited a sharp decline in the FS, particularly for steeper slopes (β = 45°), where the FS dropped below 1, indicating an imminent risk of slope failure. Steep slopes with high rainfall intensities represent the most critical scenarios for slope instability, especially when combined with longer rainfall durations (e.g., 12 h), which further exacerbates the reduction in the FS. Rainfall, by increasing pore water pressures and reducing effective stress, causes a significant reduction in shear strength, leading to slope failure.

In terms of slope height, the study demonstrated that taller slopes generally experience lower FS values, particularly when combined with steep inclinations and higher rainfall intensities. For example, slopes of 20 m with an inclination of 45° and subjected to rainfall intensities of 50 mm/h or higher showed critical FS values below 1.5, signaling potential instability. Therefore, slope height becomes a critical parameter when assessing the overall risk of failure, especially for large engineering projects involving embankments or cut slopes.

Soil cohesion and friction angle also contributed significantly to the stability of the slopes, but their effects were more pronounced at lower rainfall intensities. Higher values of cohesion and friction angle provided greater resistance to slope failure, as indicated by the gradual increase in the FS for stronger soils. However, once the rainfall intensity exceeded 80 mm/h, even highly cohesive soils showed a marked reduction in the FS, emphasizing that rainfall remains the dominant destabilizing factor under extreme conditions.

For unit weight, the factor of safety showed a consistent reduction as soil density increased, particularly under high rainfall intensities. This suggests that heavier soils, while offering greater resistance to movement under dry conditions, are more susceptible to failure when saturated during intense rainfall. This highlights the need to carefully evaluate soil properties when designing slopes in regions prone to heavy rainfall events.

In summary, rainfall intensity emerged as the most influential parameter on slope stability, particularly when combined with slope inclination and slope height. For steep slopes (greater than 33.7°), the combination of high rainfall intensities (above 80 mm/h) and prolonged durations (12 h) led to FS values below 1, indicating that these conditions are likely to trigger slope instability. As a guideline, for slopes with inclinations of 45° or more, it is recommended to maintain the FS above 1.5 to avoid instability, especially in regions with frequent intense rainfall.

These findings provide valuable guidance for future slope design and stability assessments, emphasizing the need for comprehensive geotechnical evaluations in regions with significant rainfall. The generated dataset serves as a critical tool for training machine learning models that can predict slope failures under various environmental and soil conditions. Further studies will expand the dataset to include silty and clayey soils, which will allow for more robust predictive modeling across a wider range of geotechnical contexts.