Sensitivity Analysis of the Influence of Heavy-Intensity Rain Duration on the Stability of Granular Soil Slopes Under Unsaturated Conditions

Abstract

This study investigates slope stability under rainfall infiltration using numerical modeling in Plaxis 2D, comparing poorly graded sand (6.5% fines) and well-graded sand (11.9% fines) under high-intensity rainfall of 30 mm/h for durations of 8, 12, 18, and 24 h. The results indicate that, as rainfall duration increases, soil saturation rises, leading to reduced suction, lower shear strength, and decreased safety factors (S.F.s). Poorly graded sand shows minimal sensitivity to infiltration, with the S.F. dropping by only 4.3% after 24 h, maintaining values close to the initial 1.126. Conversely, well-graded sand demonstrates significant sensitivity, with its S.F. decreasing by 25.4% after 8 h and 73.7% after 24 h, due to higher water retention capacity and suction. This highlights the significant contrast in stability behavior between the two soil types. The findings emphasize the critical role of soil hydro-mechanical properties in assessing slope stability, especially in regions with intense rainfall. This study establishes a methodology for correlating safety factor variations with rainfall duration and soil type, offering valuable insights for modeling and mitigating landslide risks in rainy climates, considering the hydraulic and mechanical parameters of the soil.

1. Introduction

The stability of slopes affected by rainfall is a crucial topic in geotechnical engineering and soil mechanics, with significant implications for infrastructure safety, urban planning, and the mitigation of natural disasters. Slope failures can result from various factors, such as earthquakes and external loads. However, rainfall is the most common cause of failure [1,2,3,4,5,6]. As noted in [7], the initial volumetric water content of the soil, its hydraulic characteristics, and the intensity and duration of rainfall are variables that significantly affect pore pressure in slope soils and, consequently, their instability. In regions prone to heavy precipitation, intense and prolonged rainfall can considerably impact slope stability, especially when these slopes are in unsaturated conditions [8].

Infiltration occurs when rainwater or irrigation water penetrates vertically into the soil, with some portion running off the surface, allowing gravitational downward flow to become part of the soil water [9]. This infiltration of rainwater can alter the hydro-mechanical behavior of the soil, generating changes in pore pressure, reducing the material’s shear strength, and, therefore, affecting the safety factor, potentially leading to failure in these slopes [10,11,12,13,14,15]. Each year, thousands of lives and USD millions are lost due to landslides [16], underscoring the need to study these failure mechanisms in depth and to develop effective prevention, mitigation, and numerical modeling strategies.

Although there are numerous studies similar to the present one, most have focused solely on variations in intensity or on fully saturated conditions [17,18]. However, few works jointly address the effect of key hydro-mechanical variables such as suction, degree of saturation, and their direct impacts on the global safety factor in unsaturated soils. This study aims to fill that gap by integrating these parameters to achieve a more comprehensive slope behavior assessments under intense and prolonged rainfall conditions.

Numerous authors have analyzed the impact of rainfall intensity on slope stability [11,19,20,21]. Most have concluded that high-intensity rainfall [22] poses the greatest stability challenges for slopes, as it generates higher pore pressure, reduces soil cohesion, and decreases the internal friction angle compared to low-intensity rainfall [11,19,23]. For this study, a rainfall intensity of 30 mm/h was considered, classified as high-intensity [24,25,26].

This study differs from others by focusing on the comparative analysis of soils with different gradation characteristics, such as poorly graded sand (SP-SM) and well-graded sand (SW-SM), under rainfall conditions with a constant intensity of 30 mm/h. Unlike other studies that vary rainfall intensity, this study maintains a constant intensity while varying the rainfall duration, soil type, and their hydro-mechanical properties. This approach provides a more precise understanding of how different soil properties influence slope stability under rainfall conditions.

Numerical modeling was performed in Plaxis 2D using the Mohr–Coulomb constitutive model. Although both the Mohr–Coulomb and hardening soil models share the same failure criterion and yield similar evaluations of ultimate soil strength [27,28], the former was selected due to the study’s focus. Since the analysis does not aim to capture deformation behavior or strain accumulation, the Mohr–Coulomb model offers a simpler and more efficient solution for this purpose.

The unsaturated soil condition considers matric suction and water content in terms of volumetric water content or the degree of saturation as a basis for evaluating slope failures [14,29,30] in unsaturated conditions. In this context, suction curves are essential as they describe the relationship between suction and soil water content or degree of saturation. These curves represent the soil’s water retention capacity and hydraulic behavior under unsaturated conditions. These curves can be modeled using various hydraulic models. This study used the van Genuchten hydraulic model [31,32,33], available in Plaxis 2D. Proper parameterization of these elements enables a more realistic and detailed analysis of how rainfall infiltration affects slope stability [34].

Two soil types were selected for modeling the slope: poorly graded sand with 6.5% fines, classified as SP-SM [32], and well-graded sand with 11.9% fines, classified as SW-SM [33]. The choice of these materials is based on their differentiated behavior in terms of permeability, compaction, and stability under rainfall conditions. Poorly graded sand (SP-SM), with a low proportion of fines, exhibits high permeability and reduced cohesion, making it potentially more vulnerable to infiltration and slope instability [32,33]. In contrast, well-graded sand (SW-SM), with higher fine content, shows better apparent cohesion, reducing permeability and increasing erosion resistance [32,33]. This selection enables a comparative evaluation of the effect of gradation properties and fine content on slope stability under rainfall conditions.

This study aims to investigate the effect of rainfall on the stability of unsaturated soil slopes, specifically under high-intensity rainfall with varying durations, to obtain the safety factor (S.F.) as a comparative value for each proposed case. The safety factor analysis was conducted using the “Strength Reduction Factor” (SRF) method [35], available in Plaxis 2D. This method progressively reduces soil strength parameters, such as cohesion and friction angle, until failure occurs.

The findings of this study highlight that SW-SM soil, due to its higher fines content and water retention capacity, experiences a significant reduction in its safety factor under prolonged rainfall, making it more susceptible to instability [36]. In contrast, SP-SM soil, with lower fines content and higher permeability, shows less sensitivity to infiltration, maintaining a relatively constant safety factor. These results emphasize the critical impact of soil hydro-mechanical properties on slope stability under intense rainfall conditions [15].

This study is limited by the simplification of real-world conditions, as it models specific scenarios of intense rainfall (30 mm/h) on two soil types without accounting for external factors such as seismic activity or vegetation. It is well known that vegetation has a significant impact on infiltration capacity [37,38], but this is beyond the scope of the present research.

Additionally, the results depend on the parameters assumed in Plaxis 2D, which could limit their applicability to more complex contexts.

Rainfall intensity is a determining factor in slope stability, especially in areas prone to heavy precipitation. This study modeled a slope with a 45° inclination for two soil types under the influence of rainfall with an intensity of 30 mm/h. Different scenarios with rainfall durations of 24, 18, 12, and 8 h were analyzed to evaluate their impact on slope stability. These results provide insight into how the combination of slope angle, soil type, and rainfall duration affects the safety factor of slopes.

2. Materials and Methods

2.1. Research Method

Figure 1 presents a flowchart outlining the structure of this research. This diagram illustrates the key stages of the study, from the literature review and selection of soil parameters to the numerical modeling in Plaxis 2D and the analysis of results.

In this regard, a literature review was conducted, consulting various relevant scientific and technical articles. Studies were selected that investigated the influence of rainfall intensity and duration on slope stability [11,12,19,20], the behavior of unsaturated soils under water infiltration conditions [9,39,40], and oil types and geometries susceptible to failure due to rainfall on slopes [41,42,43]; publications providing specific geotechnical parameter values, such as permeability, cohesion, friction angle, elasticity modules, and the hydraulic parameters of the van Genuchten model (Sres, Ssat, ga, gn, gl) for the soil types studied, were also included [32,33,44,45].

These articles were selected based on their importance for understanding the physical behavior of slopes, the analytical methodologies used, such as the finite element method, and their presented conclusions regarding critical factors influencing slope stability, such as rainfall intensity and duration [11,19]. This literature review provides a solid foundation for developing a robust methodological approach for numerical modeling using Plaxis 2D. Plaxis 2D was selected as the modeling tool for this study because of its ability to model the complex behavior of slopes under rainwater infiltration conditions, using the Fully Coupled Flow Deformation analysis [46]. This finite element software is widely recognized in geotechnical engineering for its ability to simulate the combined effect of infiltration and soil mechanical properties, as highlighted by several previous studies [11,12].

2.2. Constitutive Model

Numerical methods are commonly used in slope stability analyses to address complex geometries, material anisotropy, and nonlinear behavior [46]. This study will use the Mohr–Coulomb constitutive model with the Fully Coupled Flow Deformation analysis [47] in Plaxis 2D software, 2024 version. The Mohr–Coulomb model is selected to adequately represent the soil’s elastic–plastic behavior, considering key parameters such as cohesion, friction angle, and deformation modulus. Additionally, the Fully Coupled Flow Deformation analysis enables precise simulation of the interactions between water flow and soil deformation, which is crucial for evaluating slope stability under intense rainfall conditions. This comprehensive methodology accurately represents the combined effects of water infiltration and the soil’s mechanical properties, providing more precise and reliable results for slope design and risk mitigation.

2.3. Soil Properties

Two soil classifications were selected for the study: SP-SM [32] and SW-SM [33].

Table 1. Soil properties.

Properties	SP-SM	SW-SM
Saturated unit weight [kN/m3]	18.9	18
Unsaturated unit weight [kN/m3]	15.7	16
Deformation modulus [kN/m2]	30,000	15,000
Poisson’s ratio	0.3	0.35
Friction angle [°]	38	36
Cohesion [kN/m2]	5	10
Sand percentage	93.5	87.8
Fines percentage	6.5	11.9
Gravel percentage	0	0.3
Initial degree of saturation	70	70

presents the properties of both soils used in the numerical model.

The friction angle and cohesion values assigned to each soil were defined based on their USCS classification, fines content, and the typical behavior of granular soils. Various sources indicate that for well-graded and poorly graded sands, the friction angle generally ranges between 30° and 40°, and cohesion may vary between 0 and 20 kN/m² depending on the degree of compaction and fines content [48]. In this case, representative values within these ranges were assigned: 38° and 5 kN/m² for the SP-SM soil, and 36° and 10 kN/m² for the SW-SM soil.

The selection of these two soil types aims to analyze how different granulometric and hydraulic properties influence slope stability under intense rainfall. Poorly graded sand (SP-SM), with 93.5% sand and 6.5% fines, represents a highly permeable soil with low cohesion (5 kN/m²), making it susceptible to rapid infiltration. In contrast, well-graded sand (SW-SM), with 87.8% sand and 11.9% fines, has higher cohesion (10 kN/m²) and lower permeability, allowing for greater water retention. This analysis was conducted in Plaxis 2D.

2.4. Hydraulic Model

In this study, the Van Genuchten model [31] was used to describe the hydraulic behavior of the soil, under the following Equation (1):

$$\theta ={\theta }_r+{\displaystyle \frac{\left({\theta }_s-{\theta }_r\right)}{{[1+{\left(\alpha h\right)}^n]}^m}}$$

(1)

$$m=1-{\displaystyle \frac{1}{n}}$$

In the Plaxis 2D software, the variables are defined using different names and symbols, which are presented in Equation (2):

$$S\left(\Psi \right)=S_{res}+\left(S_{sat}-S_{res}\right)g_a{[1+{\left(g_a\left|\Psi \right|\right)}^{g_n}]}^{g_c}$$

(2)

$$g_c={\displaystyle \frac{1-g_n}{g_n}}$$

where ($\Psi$) represents the degree of saturation, $S_{res}$ represents the residual saturation, $S_{sat}$ represents saturation under fully saturated conditions, $\Psi$ represents the matric suction, $g_a$ is a fitting parameter related to air entry into the soil, and $g_n$ is a fitting parameter related to water extraction from the soil once the air entry value is exceeded [31,49].

It is also worth noting that, regarding the parameters of the original van Genuchten equation and its adaptation within Plaxis 2D, the following equivalences are established:

$$S_{res}={\theta }_{res}$$

$$S_{sat}={\theta }_{sat}$$

$$g_a=\alpha$$

$$g_n=n$$

$$g_c=-m$$

Additionally, Equation (3) represents the effective saturation:

$$S_{eff}={\displaystyle \frac{S_r\left(\psi \right)-S_{res}}{S_{sat}-S_{res}}}$$

(3)

where $S_{eff}$ is the effective saturation, $S_r\left(\psi \right)$ is the degree of saturation as a function of suction, $S_{res}$ is the residual saturation, and $S_{sat}$ is the total saturation.

Using the effective saturation and total water pressure, the effective water pressure can be determined with Equation (4):

$$p_{active}=S_{eff}·p_w$$

(4)

where p_active is the effective water pressure.

With the effective water pressure, the effective stress of the soil can be calculated using Equation (5), as shown below:

$${\sigma }^{\prime }=\sigma -p_{active}$$

(5)

where ${\sigma }^{\prime }$ is the effective stress and σ is the total stress.

To analyze the behavior of flow and strength in partially saturated soils, Plaxis 2D describes the evolution of water pressure as a function of suction level, represented by the following differential Equation (6):

$${\displaystyle \frac{dS\left(p_w\right)}{d_{p_w}}}=\left(S_{sat}-S_{res}\right)\left[{\displaystyle \frac{1-g_n}{g_n}}\right]\left[g_n{\left({\displaystyle \frac{g_a}{{\gamma }_w}}\right)}^{g_n}·p_w^{\left(g_n-1\right)}\right]{\left[1+{\left(g_a·{\displaystyle \frac{p_w}{{\gamma }_w}}\right)}^{g_n}\right]}^{\left({\displaystyle \frac{1-2g_n}{g_n}}\right)}$$

(6)

Finally, in the context of partially saturated soils, soil permeability changes with water content, as suction affects the amount of water in the pores, influencing the soil’s ability to allow water flow. The following formula represents this modification:

$$k_{rel}\left(S_r\right)=max\left[{S_{eff}}^{gl}{\left(1-{\left[1-{S_{eff}}^{{\displaystyle \frac{g_n}{g_n-1}}}\right]}^{\left({\displaystyle \frac{g_n}{g_n-1}}\right)}\right)}^2,{10}^{-4}\right]$$

(7)

Regarding the suction curves, these were obtained from previous research conducted by various authors. The suction curve for SW-SM soil was taken from the work of A.A.S. Kaushalya et al. [33], while the suction curve for SP-SM soil was derived from the research of D. Lizana Olarte et al. [32]. Therefore, the parameters necessary to construct these curves were also derived from the data and models proposed in these studies, ensuring the accuracy and representativeness of the suction properties for each soil type in this study. Likewise, based on the characteristics of the soils considered in the analysis, representative permeability values available in the literature were adopted. In particular, the value assigned to the SW-SM soil was taken from E. Kardena [44], while the value corresponding to the SP-SM soil was based on data reported by G.F.N. Gitirana Jr. and D.G. Fredlund [45], to accurately represent the hydraulic behavior of each material under infiltration conditions.

The aforementioned values are presented below in

Table 2. Van Genuchten parameters.

Parameters	SP-SM	SW-SM
Permeability [m/day]	1.572	0.864
Sres	0.050	0.025
Ssat	1.000	1.000
ga	5.411	0.085
gn	2.449	1.561
gl	−0.592	−0.359

for each soil type.

Figure 2 presents the suction curves corresponding to each soil as follows:

2.5. Rain Characterization

This study selected a rainfall intensity of 30 mm/h, which is considered high intensity. Such rainfall tends to cause slopes’ most significant instability issues [11,19,23]. Duration of 8, 12, 18, and 24 h were considered to evaluate how this intensity affects slope stability. This approach enables the assessment of how the duration of intense rainfall affects the behavior of the two selected soil types. It also facilitates the identification of high-risk landslide scenarios and the soils’ sensitivities under such conditions.

2.6. Slope Geometry and Boundary and Flow Conditions

Figure 3 shows the geometry and dimensions of the evaluated slope. Regarding the slope geometry, a medium–high inclination angle of 45° was chosen [42,43,50]. Additionally, a slope height of 12 m was considered. This allows for the analysis of slope stability under conditions of high inclination and significant height.

It is worth noting that, for the strength parameters used in the materials, a 45° slope represents an aggressive condition from a stability standpoint. However, the unsaturated condition of the soil—particularly due to matric suction—contributes significantly to maintaining the slope’s stability in its initial state, prior to rainfall infiltration.

For the analysis, control points were established at H = 12 [m], H = 9 [m], H = 6 [m], H = 3 [m], and H = 0 [m]. Figure 4 specifies the position of the points where the analysis for this research was conducted. This choice allows for a precise observation of variations in the soil properties and responses along the slope structure, improving the accuracy of the study on stability and material behavior.

Additionally, the boundary conditions of the numerical model are shown. At the lower boundary of the model, complete deformation restriction is imposed, meaning the soil cannot deform in any direction. At the lateral boundaries, deformation is allowed only along the Y-axis. Meanwhile, at the upper boundaries of the model, full deformation is permitted in both the Y and X axes.

Regarding flow conditions, it was determined that rainwater infiltration would occur at the upper boundary under the Infiltration condition in Plaxis 2D. In contrast, water flow would be allowed at both the lateral and lower boundaries under the Seepage condition.

3. Results and Discussion

3.1. Effect of Rainfall Duration on the Degree of Saturation

In Figure 5 and Figure 6, due to rainfall infiltration into the slope, a significant increase in the degree of saturation was observed in both soils. Initially, the slope’s degree of saturation was 70%. However, as rainfall infiltrates, this saturation progressively increases, reaching values close to 100% at the upper part of the slope. This increase in saturation is not limited to the surface layers; in cases of longer-duration rainfall, the increase in saturation propagates deeper into the slope.

As shown in Figure 6 (see red arrow), an overload is observed on the slope face for the same rainfall durations of 18 and 24 h in SW-SM soil. This overload represents the accumulation of rainwater that could not infiltrate and instead flows over the slope surface [11,12,20].

Figure 7 and Figure 8 present the graphs of effective saturation versus time at the control points of the model (see Figure 4). These graphs provide insight into how saturation varies over time at each specific slope height. This analysis was crucial for observing the increase in saturation as time progressed, offering a detailed understanding of the slope’s behavior under different levels of water infiltration.

This graph shows how the effective saturation of the SP-SM soil varies at different depths of the slope (12 m, 9 m, 6 m, 3 m, and 0 m) as a function of rainfall duration. Each curve represents a specific elevation within the soil profile, where the progressive advancement of infiltration from the top of the slope toward the base can be observed. The data should be interpreted from the top to the bottom of the slope: the higher the elevation, the earlier saturation occurs; the lower the elevation, the more the effect is delayed or almost negligible, highlighting how water progressively moves through the soil profile.

This graph, like the previous one, shows how the effective saturation varies—this time for the SW-SM soil—at different depths of the slope (12 m, 9 m, 6 m, 3 m, and 0 m) throughout rainfall. Each curve represents a specific elevation within the soil profile, where the progressive advancement of infiltration can be observed, although this occurs more slowly and gradually compared to the SP-SM soil. The data should be interpreted from the top to the bottom of the slope: the upper zones become saturated first; meanwhile, at deeper levels, the increase occurs later and more gradually, highlighting the greater water retention capacity of the SW-SM soil.

The slope analyzed with SP-SM soil (see Figure 7) shows that water infiltration initially occurs at the upper levels. At a height of 12 m, saturation increases rapidly, stabilizing at 93.5% in 1.2 h. At 9 m, the process is delayed, beginning to saturate at 6 h and reaching 94% at 9.6 h. At 6 m, saturation starts later, at 14.4 h, stabilizing between 93–94% at 18.6 h. At lower levels, such as 3 m, saturation progresses more slowly, significantly increasing only at 21.6 h, with a maximum of slightly above 80%. Finally, at the base of the slope (0 m), saturation remains at the initial condition consistently throughout the analysis period, indicating that infiltration does not significantly reach this level.

On the other hand, the slope with SW-SM soil (see Figure 8) exhibits slower saturation due to the higher fines content, which reduces soil permeability. At a height of 12 m, the upper level reaches 100% saturation at 9.6 h, showing a more gradual increase compared to SP-SM. At 9 m, saturation begins at 2.4 h and stabilizes at 100% at 16.8 h. At 6 m, the process starts at 7.2 h, reaching 100% at 24 h, while at 3 m, saturation begins at 12 h and reaches 94% within the same period. At the base of the slope (0 m), the increase in saturation is minimal, starting at 19.2 h and reaching only 75%. This demonstrates that infiltration is more gradual and limited in depth due to the low permeability of SW-SM soil.

In Figure 7 and Figure 8, it is observed that, in terms of saturation speed, SP-SM soil responds quickly to infiltration, achieving a stable saturation of approximately 93.5% at the slope’s top (H = 12 m) in just 1.2 h. This is attributed to its low fine content, facilitating rapid drainage and less water storage. In contrast, SW-SM soil shows a slower saturation process due to its higher fines content, reaching 100% at the same level of H = 12 m after 9.6 h. This behavior reflects the influence of SW-SM’s lower permeability, which retains water in the soil profile for a longer time.

Regarding the maximum saturation reached, it can be observed that, in SP-SM soil, saturation stabilizes between 93.5% and 94% throughout most of the profile without achieving full saturation. This is explained by the granular structure of poorly graded sand, which allows the formation of preferential pathways that facilitate water flow and reduce pore retention capacity [51]. On the other hand, in SW-SM soil, water infiltrates more slowly. Still, it achieves full saturation (100%) in the upper layers, demonstrating a higher water retention capacity due to its fine content and compact structure. However, in the lower layers (H = 0 m), this maximum saturation is not reached, stabilizing around 75%, indicating a limitation in the depth propagation of infiltration due to the soil’s low permeability.

In summary, the analysis of the increase in the degree of saturation highlights significant differences between the two soil types studied. Due to its granular structure and lower fine content, SP-SM soil exhibits a rapid initial response to infiltration, stabilizing between 93.5% and 94% across most of the profile without achieving full saturation, reflecting a limited water retention capacity. In contrast, SW-SM soil shows a slower and more progressive process, reaching 100% saturation in the upper layers. It demonstrates its higher water storage capacity due to its better gradation and fines content. However, in the deeper layers, both soils exhibit limitations in saturation propagation, with SW-SM reaching only 75% at the base of the slope. These results underscore how the hydro-mechanical properties of soils influence infiltration dynamics and their distribution within the slope.

3.2. Effect of Rainfall Duration on Matric Suction

In Figure 9 and Figure 10, it can be observed that, as soil saturation increases, matric suction decreases significantly. Additionally, the longer the rainfall duration, the greater the depth affected on the slope, further reducing matric suction.

Figure 11 and Figure 12 present graphs of matric suction versus time, measured at the control points shown in Figure 4.

Figure 11 shows how the effective suction of the SP-SM soil varies over time at five levels of the slope (12 m, 9 m, 6 m, 3 m, and 0 m). Each curve represents a specific elevation, highlighting the reduction in suction as a consequence of the advancing infiltration. The data should be interpreted from the top to the bottom of the slope: the higher the elevation, the earlier the loss of suction occurs, reflecting the progressive movement of water through the soil profile.

Figure 12, like the previous one, shows how the effective suction varies—this time for the SW-SM soil—over time at five levels of the slope (12 m, 9 m, 6 m, 3 m, and 0 m). Each curve represents a specific elevation, showing a progressive decrease in suction as infiltration advances, although in a more gradual manner compared to the SP-SM soil. The data should be interpreted from the top to the bottom of the slope, reflecting the gradual movement of water in a soil with higher retention capacity and lower permeability, such as SW-SM.

Significant differences in suction behavior are observed between the two soil types. This reflects the fines content [19] and the well-graded or poorly graded granulometry.

For SP-SM soil, the curves show a rapid loss of suction in the upper areas of the slope (H = h and H = 0.75 h) within the first 4.8 h, reaching very low suction values in a short time. In the slope’s intermediate and lower areas, the suction loss is more gradual, indicating a limited water retention capacity in this soil due to its lower fines content.

In contrast, SW-SM soil initially exhibits higher suction values (around 120 kN/m²) and a more gradual decrease in the upper areas. Effective suction decreases significantly within the first 5.6 h at heights H = 0.5 h and H = 0.75 h but remains elevated in the lowest zone (H = 0) until the end of the analysis, around 100 kN/m². This behavior indicates a greater suction retention capacity, attributable to its higher silt content, allowing it to store and retain moisture better than SP-SM soil.

In summary, SW-SM soil retains suction for a longer period. It demonstrates a greater ability to limit saturation in the lower areas of the slope, which could result in greater stability under prolonged infiltration conditions. On the other hand, SP-SM soil experiences a rapid loss of suction, especially in the upper areas, which could reduce slope stability under rainfall conditions. These behaviors illustrate how gradation and fine content affect slope water and suction retention capacity.

3.3. Effect of Rainfall Duration on the Safety Factor

Table 3. Safety factors obtained for SW-SM and SP-SM soils.

	Safety Factor (S.F.)
	SW-SM	SP-SM
No rainfall	4.329	1.126
Rainfall duration 8 [h]	3.229	1.123
Rainfall duration12 [h]	2.229	1.085
Rainfall duration18 [h]	1.427	1.063
Rainfall duration24 [h]	1.140	1.078

and Figure 13 illustrate how rainfall infiltration causes a reduction in the slope’s safety factor. This behavior is explained by the interaction between the increase in soil saturation and the decrease in suction, which weakens the soil’s internal structure and reduces its ability to resist shear stresses.

For SW-SM soil, a reduction of up to 73.7% in the safety factor (S.F.) is observed as rainfall duration increases. Initially, without rainfall, the S.F. is 4.329, indicating high stability. However, with 8 h of rainfall, the S.F. decreases to 3.229 and continues to drop progressively, reaching 1.140 after 24 h of rainfall. This suggests that, although SW-SM soil can retain stability under moderate infiltration conditions, its S.F. significantly decreases with prolonged rainfall, increasing the risk of slope failure.

For SP-SM soil, the initial safety factor without rainfall is considerably lower (1.126), indicating limited stability even without rainfall conditions. When analyzing the effects of rainfall, there is less variation in S.F. compared to SW-SM soil. After 8 h of rainfall, the S.F. remains almost constant at 1.123 and slowly decreases to a minimum of 1.063 after 18 h of rainfall, stabilizing at 1.078 after 24 h. This low sensitivity to infiltration is due to SP-SM soil’s limited suction retention capacity; however, its generally low S.F. indicates that the slope is inherently less stable and remains at risk even with short-duration rainfall.

This differentiated evolution of the factor of safety between the two soils can be mainly attributed to the effects of grain size distribution on permeability. Recent studies have shown that grain size distribution and the coefficient of uniformity directly influence the soil’s ability to allow water flow, altering pore connectivity and the hydraulic behavior of the soil profile [52,53]. The SW-SM soil, due to its better gradation and higher fines content, has lower permeability, which favors greater moisture accumulation at depth, decreases effective suction, and gradually reduces the S.F. In contrast, the SP-SM soil, with a more uniform grain size distribution and lower fines content, facilitates faster but shallower infiltration, maintaining higher suction in deeper zones and, therefore, more consistent stability over time—though there is a generally lower S.F. value. This behavior highlights the critical influence of grain size distribution on infiltration dynamics and overall slope stability.

Overall, SW-SM soil, while initially more stable due to its higher fine content and cohesion, experiences a significant reduction in S.F. with prolonged rainfall. In contrast, though less affected by rainfall, SP-SM soil consistently exhibits low S.F., making it more vulnerable overall. Both soil types display distinct behaviors in response to saturation, emphasizing the importance of considering soil composition and exposure duration to water in slope stability analysis.

4. Conclusions

This research analyzed slope stability behavior under rainfall infiltration conditions using two types of soil: a poorly graded sand with 6.5% fines (SP-SM) and a well-graded sand with 11.9% fines (SW-SM). Numerical models were developed in Plaxis 2D to simulate the effect of water infiltration on slopes, considering different rainfall durations with an intensity of 30 mm/hr and evaluating the impact on the safety factor for each soil type.

The results revealed that SW-SM soil, with its higher fine content and better gradation, exhibited a more significant decrease in its safety factor as rainfall duration increased, reaching levels close to instability after 24 h of continuous precipitation. This is due to its greater suction retention capacity and water accumulation, which increase saturation and reduce the material’s shear strength. In contrast, SP-SM soil showed lower sensitivity to infiltration, maintaining its safety factor relatively stable even during prolonged rainfall. This low sensitivity is attributed to its lower fine content and more permeable structure, allowing rapid infiltration dissipation without drastically affecting the soil’s internal suction.

Additionally, the analysis of initial safety factors without rainfall showed that slopes composed of SW-SM soil were significantly more stable in the absence of rainfall than those with SP-SM soil, due to its higher cohesion and lower saturated unit weight. However, under rainfall conditions, SW-SM soil experienced greater suction loss and reduced its safety factor, making it more prone to instability during prolonged rainfall events.

This study provides important contributions to the practice and theory of slope stability under rainfall infiltration conditions. In practical terms, the results provide a detailed approach to evaluate the impact of rainfall on slopes with soils of different mechanical and hydraulic characteristics, which can be applied in geotechnical designs and risk mitigation strategies in regions prone to heavy rainfall. At the theoretical level, the analysis reinforces understanding how soil properties, such as cohesion, fines content, and permeability, interact with rainfall conditions to influence the safety factor and slope stability.

However, this study has some limitations. The simulations were performed under ideal conditions without considering external factors such as vegetation, subsurface drainage conditions or seismic events, which could significantly influence the results. In addition, the analysis focused only on two soil types and did not include broader variations in mechanical or hydraulic properties.

Future studies could build upon this work by expanding the range of soil types considered, including silty and clayey sands, and by performing sensitivity analyses on key hydro-mechanical parameters such as initial suction, permeability, and van Genuchten parameters (e.g., α, n, θr, θs). These analyses would help quantify the influence of soil-water retention behavior on pore pressure evolution and safety factor variation. Additionally, future research could explore the effect of slope geometry, such as changes in inclination and height, on stability under different rainfall scenarios. A promising direction also involves integrating soil–vegetation interactions through coupled hydro-mechanical models that account for root reinforcement and evapotranspiration, offering a more realistic representation of natural slopes. Moreover, the adoption of stochastic or probabilistic rainfall models could improve the identification of threshold conditions for failure. Collectively, these methodological enhancements would improve the generalizability, accuracy, and practical relevance of slope stability assessments in areas exposed to intense or prolonged precipitation.