Integrated Limit Equilibrium and Finite Element Modelling of Slope Stability Under Hydro-Mechanical and Stratigraphic Controls

Slope stability analysis is a critical aspect of geotechnical engineering. It directly influences the safety, economic feasibility, and long-term performance of civil engineering projects such as embankments, cut slopes, dams, and transportation infrastructure. The stability of slopes is commonly evaluated using the Factor of Safety (FOS), representing the ratio between resisting and driving forces acting along a potential failure surface [1]. Failure of natural or engineered slopes can lead to catastrophic consequences, including loss of life, and infrastructure damage. It may also result in significant economic losses. These risks highlight the necessity for reliable stability assessment methods [2-4].

A variety of analytical and numerical techniques have been developed to evaluate slope stability. Among the most widely used approaches are the Limit Equilibrium Methods (LEMs). These include the Bishop, Morgenstern–Price, Ordinary (Fellenius), and Janbu methods. These methods evaluate stability by satisfying equilibrium conditions along assumed slip surfaces [5-7]. In contrast, the Finite Element Method (FEM) evaluates slope behavior by simulating stress–strain relationships within the soil mass. It also captures progressive failure mechanisms. This approach provides a more realistic representation of soil response, particularly under complex loading and hydraulic conditions [8]. Both approaches have been widely applied in slope stability studies [9-11].

Slope stability depends on both internal and external factors. Internal factors are related to the inherent properties of soil and rock masses. These include geological conditions, stratigraphy, slope geometry, soil type and shear strength parameters [12-14]. External factors include rainfall infiltration, groundwater fluctuations, and applied surface loads. These factors act as triggering mechanisms that reduce soil shear strength and increase driving forces. As a result, slope failure may occur. In recent years, data-driven approaches have been explored. These include machine learning techniques. They have been used to predict slope FOS based on soil properties, providing tools for rapid assessment [15]. Rainfall is one of the most critical external factors affecting slope stability. Rainfall infiltration increases pore water pressure and reduces effective stress within the soil mass. This process weakens soil shear resistance [16-20]. Previous studies have shown that both rainfall intensity and duration play a key role in slope stability. Prolonged or intense rainfall events are often associated with landslide occurrence [21, 22]. In addition, probabilistic and machine learning approaches have been applied to assess slope reliability under varying environmental conditions [23].

Slope stabilization measures are commonly to improve slope safety. These include modifying slope geometry, increasing soil strength, and controlling groundwater conditions [24-26]. However, their effectiveness depends on the interaction between soil properties, slope geometry, loading conditions, and hydraulic behavior. Recent studies have emphasized the importance of integrating numerical modeling with advanced analytical methods. This integration improves the understanding of slope behavior and enhances design practices [27, 28]. In Iraq, particularly in Mosul, slope instability has received increasing attention. This is due to urban expansion, infrastructure development, and changing climatic conditions. Previous studies have used numerical methods to evaluate slope stability under different scenarios [29, 30]. However, many of these studies consider a limited number of parameters or rely on a single analysis method. This limitation may not fully represent the combined mechanical and environmental effects.

This study addresses this limitation by presenting a comprehensive comparative analysis using both LEM and the FEM. It evaluates the influence of key parameters on the FOS. These parameters include soil strength, slope geometry, unit weight, external loading, groundwater level, rainfall infiltration, and soil layering. The study also aims to clarify the strengths and limitations of each method and to provide practical insights into their applicability under different engineering conditions. The findings are intended to support engineers in slope design and stability assessment.

3.1 Effect of shear strength coefficients

Slope stability analyses were conducted by varying the internal friction angle (22°, 25°, and 28°) while maintaining a constant soil cohesion of 25 kPa and a wet unit weight of 18 kN/m³. The slope angle was gradually increased from 29° to the critical value of 54.2°. Both LEM-Ordinary, Bishop, Janbu, and Morgenstern–Price- and the FEM were employed to evaluate the influence of shear strength parameters on slope stability. The results indicate that increasing the internal friction angle leads to a consistent increase in the FOS across all applied methods. This quasi-linear trend reflects the direct contribution of the friction angle to enhanced soil shear resistance along the potential failure surface, thereby improving resistance to sliding [40, 41]. Although all limit equilibrium approaches capture this behavior, variations in the predicted safety factors were observed due to differences in their underlying equilibrium assumptions. The Bishop and Morgenstern–Price methods generally exhibited higher sensitivity to changes in friction angle (Table 2).

Table 2. Safety factor values for a slope with a variable internal friction angle (ϕ) and slope angle (β)

Conversely, increasing the slope angle produces a pronounced destabilizing effect. As the slope inclination increases from 29° to 54.2°, the FOS decreases substantially, indicating that slope geometry plays a dominant role in controlling stability by amplifying the driving shear stresses acting along the potential slip surface.

The influence of soil cohesion was also examined by varying cohesion values while keeping other parameters constant. The FOS increased with higher cohesion values in both the limit equilibrium and finite element analyses (Table 3), which can be attributed to the enhanced shear strength provided by cohesive resistance [42, 43]. However, at the critical slope angle of 54.2°, the stabilizing effect of increased cohesion was significantly diminished, and the FOS decreased markedly. This observation confirms that under near-critical geometric conditions, slope geometry may override the beneficial effects of improved soil strength and the associated shear resistance, which amplify the vertical loads acting on the soil mass.

Table 3. Safety factor values for a slope with a variable cohesion (C) of soil and slope angle (β)

3.2 Effect of dry weight unit

The dry unit weight is recognized as one of the key factors influencing the calculation of the FOS [44]. As shown in Table 4, for a slope characterized by an internal friction angle of 22°, a cohesion of 25 kPa, and dry unit weight values of 13, 14.9, 16.76, and 18.6 kN/m³. The results indicate that an increase in dry unit weight leads to a consistent reduction in the FOS across all applied methods.

Table 4. Safety factor values for a slope with a variable dry unit weight (γ_d) of soil and slope angle

Specifically, the Morgenstern–Price method indicates a decrease ranging from 12.4% to 17.3%. The Bishop method shows a reduction of approximately 12.3% to 19.8%. Similarly, the Janbu and Ordinary methods exhibit decreases of about 14.7%–17% and 14.2%–17.3%, respectively. The FEM also reflects a comparable decline in the FOS, ranging from 13.2% to 15.7%.

The reduction in the FOS is attributed to the increase in soil self-weight and the associated shear forces. These forces amplify the vertical loads acting on the soil mass, thereby increasing the driving forces relative to the available shear resistance.

In other words, as the dry unit weight increases, the mobilized shear strength becomes insufficient to counterbalance the enhanced gravitational forces. This leads to a progressive reduction in overall slope stability [45, 46].

3.3 Effects of the methods of analysis

Slope stability analyses were performed using the SLOPE/W software. Several (LEM)-namely Ordinary, Bishop, Janbu, and Morgenstern–Price were applied alongside the FEM to evaluate the FOS. The results show that the Bishop method consistently yields the highest FOS values. The Morgenstern–Price and Ordinary methods yielded slightly lower values, while the Janbu method produced the lowest FOS values, as illustrated in Figures 2(a)-(c).

The higher FOS values obtained using the Bishop method are attributed to its consideration of both moment equilibrium and inter-slice forces, as well as all vertical forces acting on the slices. This more comprehensive treatment of force equilibrium accounts for its slightly higher FOS, which deviates by 0.2% from the Morgenstern–Price method, 6.3% from the Janbu method and 4.2% from the Ordinary method.

The Morgenstern–Price method, which satisfies all equilibrium equations irrespective of force or moment assumptions, also produces relatively high FOS values, deviating by 6.1% from the Janbu method and 4% from the Ordinary method. In contrast, the Ordinary method yields lower FOS values because it does not fully satisfy horizontal and vertical force equilibrium and partially neglects lateral forces acting on the slices boundaries. Its FOS deviates by approximately 2.1% from that of the Janbu method, as it primarily considers slice weight and partial moment effects.     

The Janbu method produces the lowest FOS values because it neglects moment equilibrium and shear forces, considering only inter-slice force equilibrium.

(a)

(b)

(c)

Figure 2. Relationship between the Factor of Safety (FOS): (a) Friction angle, (b) Cohesion, and (c) Dry unit weight using Limit Equilibrium Methods (LEM) and Finite Element Method (FEM)

In comparison with the LEM, the FEM provides a more realistic evaluation of slope stability. FEM identifies the critical sliding surface as the weakest zone within the soil mass, where shear resistance is minimal, and evaluates slope behavior based on stress–strain relationships under its governing assumptions. The deviations between the FOS values obtained from FEM and those from the LEMs are relatively small, amounting to 0.29% with respect to the Morgenstern–Price method, 0.05% relative to the Bishop method, 4.3% relative to the Ordinary method, and 6.3% relative to the Janbu method [47, 48].

3.4 Effect of slope angle (β)

The relationship between slope angle (β) and the FOS was evaluated using both LEM and the FEM, as illustrated in Figure 3. The slope angles considered in this study were 29°, 39.8°, 48°, and 54.2°, for slopes characterized by the properties summarized in the previous tables under normal conditions (i.e., without external loading). The results indicate that the FOS values obtained using the Bishop and Janbu methods are closely consistent, whereas the Morgenstern–Price, Ordinary, and FEM approaches produce comparable results. As the slope angle increases from 29° to 54.2°, the FOS decreases by approximately 53.4% for the Bishop and Janbu methods and by about 52.1% for the remaining methods. This decline in FOS follows a nonlinear trend, indicating that slope stability is highly sensitive to variations in slope angle [49, 50].

The reduction in the FOS with increasing slope angle is attributed to the increase in soil self-weight, which amplifies the vertical and shear components of the driving forces acting along the slope. As the slope becomes steeper, the available shear resistance becomes progressively smaller relative to the driving forces, thereby increasing the likelihood of sliding and potential failure [51, 52]. These findings highlight the critical role of slope geometry in controlling overall stability and emphasize that reducing slope inclination is an effective measure for enhancing slope safety.

Figure 3. Relationship between the slope angle (β) and the Factor of Safety (FOS) using Limit Equilibrium Methods (LEM) and Finite Element Method (FEM)

3.5 Effect of external loads

External loads, such as those imposed by buildings or infrastructure, can be represented as applied forces defined by their magnitude and area of application, which determine the resulting stresses within the soil mass. In urban environments, slope stability may be significantly affected by human activities, including excavation, construction, and modifications to drainage conditions. Modern analytical approaches, such as advanced computational models and real-time monitoring techniques, provide effective tools for evaluating the influence of these factors on slope behavior [53].

Figure 1 shows the application of an external surcharge load of 250 kPa positioned 2 m from the slope crest. The impact of this load on the slope FOS is summarized in Figures 4–6. For slopes with internal friction angles between 22° to 28°, the application of the external surcharge load reduces the FOS decreases from 2.103, corresponding to an approximate 42% decrease (Figure 4). For slopes with cohesion values ranging from 16 and 30 kPa, the initial FOS of 1.714 decreases by approximately 38.9% under the same loading condition (Figure 5). Similarly, for slopes with dry unit weights from 13.6 to 18.6 kN/m³ and a slope angle of 29°, the external load causes a reduction in FOS of about 51.2%, as shown in Figure 6.

The reduction in the FOS under external loading primarily attributed to the increase in the vertical component of the sliding mass, which may exceed the available soil shear resistance. Additionally, the applied loads can elevate pore water pressure within the soil mass, further decreasing effective stress and shear resistance, thereby reducing the FOS [54]. Under unloaded conditions, slopes with an inclination of 54.2° are already close to failure; however, the application of external loads can trigger failure even at a reduced slope angle of 39.8°.

Figure 4. Relationship between the Factor of Safety (FOS) and the internal friction angle for a slope with and without external load using the Finite Element Method (FEM)

Figure 5. Relationship between the Factor of Safety (FOS) and cohesion for a slope with and without external load using the Finite Element Method (FEM)

Figure 6. The connection between the Factor of Safety (FOS) and the dry unit weight for a slope with and without an external load using the Finite Element Method (FEM)

3.6 Effect of changing water level within the slope

Water is a critical factor affecting the stability of earthen slopes, especially under seasonal variations such as rainfall infiltration, snowmelt, or proximity to surface and groundwater sources [55]. Figure 7 shows the variation in the FOS with increasing groundwater levels for slopes analyzed under both unloaded and externally loaded conditions. To assess this effect, groundwater levels measured from the slope base at 5, 7, 9, 11, and 13 m were considered. Two slope scenarios were analyzed: one without external loading and another subjected to an external surcharge load of 250 kPa. Identical soil properties were adopted for both cases (ϕ = 22°, γ_m = 12 kN/m³, and C = 25 kPa).

Figure 7. Effect of groundwater level on slope Factor of Safety (FOS) under unloaded and externally loaded conditions

Under dry conditions, the FOS was 2.103. As shown in Figure 7, a progressive reduction in the FOS was observed with increasing groundwater levels. Specifically, the FOS decreased by approximately 3.8% when the water table reached 5 m and by up to 26.6% when it rose to 13 m, indicating a trend toward unstable conditions. When the same groundwater levels were combined with an external surcharge load of 250 kPa, the destabilizing effect became more pronounced, leading to slope failure at a water level of 13 m.

The reduction in slope stability is primarily due to increased pore water pressure resulting from elevated groundwater levels. This increase decreases effective stress within the soil, thereby reducing its shear resistance. additionally, water infiltration weakens interparticle bonding by dissolving cementitious materials and surrounding soil particles, leading to reductions in both cohesion and internal friction. When an external surcharge load of 250 kPa is applied, these destabilizing effects are amplified. The combined increase in pore water pressure and the total weight of the soil mass enhances the driving forces relative to resisting forces, further reducing the FOS. Consequently, the simultaneous presence of elevated groundwater levels and external loading constitutes a critical condition for slope instability and potential failure [56, 57].

3.7 Effect of rainfall on the slope stability

Rainfall-induced landslides are among the most frequent and destructive natural hazards. Infiltrating rainwater penetrates the slope body rather than remaining on the surface, making rainfall a dominant triggering factor for slope failure [58, 59]. The influence of rainfall on slope stability was evaluated by considering two slope scenarios: one representing a natural slope without external loading and another subjected to an external surcharge of 250 kPa. Both scenarios employed identical soil properties, with an internal friction angle (ϕ) of 22°, a wet unit weight (γ_m) of 12 kN/m³, and cohesion (C) of 25 kPa. Rainfall intensities of 10, 30, and 50 mm/day were applied over periods ranging from 10 to 60 days, as depicted in Figure 8. This set up allowed for a systematic assessment of rainfall intensity and duration on slope stability under both unloaded and externally loaded conditions.

Under dry conditions, the initial FOS was 2.103. As rainfall intensity and duration increased, a progressive reduction in FOS was observed (Figure 9). At a low rainfall intensity of 10 mm/day, the FOS showed a moderate decrease during the early stages of infiltration before stabilizing, reflecting limited saturation depth and partial dissipation of matric suction. In contrast, higher rainfall intensities of 30 and 50 mm/day caused a rapid and substantial reduction in the FOS, particularly during the first 10–30 days of infiltration. After this period, the FOS tended to stabilize as the soil approached near-saturated conditions, indicating that the rate of stability reduction decreases once the soil reaches high moisture content.

Figure 8. Effect of rainfall intensity on the stability of a natural slope under unloaded conditions

Figure 9. Variation of the Factor of Safety (FOS) with rainfall intensity and duration for a natural slope without external loading

When the same rainfall scenarios were applied to the slope subjected to an external surcharge load of 250 kPa, the destabilizing effect became considerably more pronounced. Figure 10 illustrates the loading condition, which amplified the reduction in the FOS shown in Figure 11. Even under low rainfall intensity 10 mm/day, the FOS experienced a noticeable decrease during the initial rainfall period. For higher rainfall intensities of 30 and 50 mm/day, the combined effect of prolonged infiltration and external loading caused a rapid reduction in the FOS, with values approaching critical or failure conditions within 10–40 days of rainfall.

Figure 10. Effect of rainfall intensity and duration on the Factor of Safety (FOS) for a slope subjected to an external load of 250 kPa (Geostudio 2012 simulation)

Figure 11. Variation of the Factor of Safety (FOS) with rainfall intensity and duration for a slope subjected to an external load of 250 kPa

The observed reduction in slope stability is primarily due to the hydromechanical interactions between rainfall infiltration and soil behavior. As rainfall continues, matric suction gradually diminishes and eventually vanishes when the soil becomes saturated. This leads to increased groundwater levels and pore water pressure, reducing effective stress and soil shear strength. The presence of an external load further these effect by increasing both the total driving forces and pore pressures within the slope, making soil mass susceptible to instability and potential failure [60-62].

3.8 Effect of two layers on the slope

Natural slopes frequently consist of multiple soil layers formed through long-term sedimentation, and such stratification can substantially influence slope stability behavior [63, 64]. In this study, both LEM and FEM were employed to systematically investigate the effect of soil layering on slope stability. The focus was placed on the mechanical role of layer sequencing rather than solely reporting numerical differences. Based on the soil properties summarized in Table 5, a second layer classified as silty soil (ML) was add to the original single-layer clay slope (CH). Using LEM, Figure 12 compares the stability of single-layer and two-layer slopes under varying slope angles. The results indicate that the introduction of the silty layer enhances the FOS, increasing values by approximately 63.3% to 70.6% relative to the single-layer slope, which exhibited values ranged from 1.97 to 2.102. As slope angle increases, the FOS values for different configurations tend to converge.

Table 5. Geotechnical properties of the second soil layer (ML) used as input parameters in the numerical slope stability analysis

Figure 12. Comparison of the Factor of Safety (FOS) between single-layer and two-layer slope configurations under unloaded conditions using the Limit Equilibrium Method (LEM)

The FEM analysis, presented in Figure 13, corroborates the LEM findings, showing an improvement of approximately 68.9% in the FOS for the two-layer slope. To further evaluate the influence of layer arrangement, the lower silty layer was replaced with a clayey layer characterized by significantly higher cohesion (c = 87 kPa). This modification resulted in a substantial increase in the FOS, as illustrated by the LEM results in Figure 14 and the FEM results in Figure 15. The observed improvement is primarily attributed to the enhanced cohesiveness and shear resistance of the clay layer, which reinforces the soil mass and effectively limits deformation and potential failure development.

Figure 13. Comparison of the Factor of Safety (FOS) between single-layer and two-layer slope configurations under unloaded conditions using the Finite Element Method (FEM)

Figure 14. Comparison of the Factor of Safety (FOS) between single-layer and two-layer slope configurations under external loading using the Limit Equilibrium Method (LEM)

Figure 15. Comparison of the Factor of Safety (FOS) between single-layer and two-layer slope configurations under external loading using the Finite Element Method (FEM)

A key insight from these analyses is that slope stability is strongly governed by the vertical sequence of soil layers. Configurations in which a stronger, more cohesive clay layer underlies a weaker silty layer consistently yield higher FOS values than the reverse arrangement. This finding highlights the importance of accurate subsurface characterization in engineering practice, as the mechanical interaction between soil layers plays a decisive role in controlling slope performance and failure mechanisms.