Comparative Analysis of Slope Stability using Finite Element Method (FEM) and Limit Equilibrium Method (LEM)

The design of slopes in open pit mines requires an in-depth understanding of the ground behavior to predict the potential failure mechanism and to better determine the stabilization measures. This study compares the critical slip surface defined by the limit equilibrium method (LEM), the limit analysis (LA), and the finite elements method (FEM) for the stability analysis to better approach the stability on a multi-layered slope. The safety factor, the size, and the location of the critical slip surface obtained from the applied methods are considered in the comparisons. This study highlights some features that affect the slope stability and presents a procedure for addressing the evaluation challenges in a multi-layered formation. Moreover, it presents some aspects of the upper-bound computation on the safety factor of a layered slope subjected to the effects of pore water pressures. Based on the obtained results, the critical slip surface defined by the limit equilibrium method compares well with the slip mechanism suggested by the limit analysis and the finite element approach. In view of the differences in the shape and location of the critical slip surface, as well as the values obtained for the safety factor, it is recommended that an engineer should analyze critical slopes using the finite element method in combination with the limit equilibrium or limit analysis method as a cross reference. The authors propose that in defining the potential failure mass, consideration must be given to the conducted field research and monitoring.

Rapid Draw-Down (RDD) in an earthfill dam has serious implications for dam safety regarding slope stability issues. The evaluation of reservoir draw-down impact on slope stability was carried out with the Limit Equilibrium Method (LEM) and stress-based Finite Element Method (FEM), using GeoStudio. The time-dependent Factor of Safety (FOS) and nonlinear behavior were evaluated considering 8 h of RDD. The resulting FOS values of 1.28 and 1.27 using LEM and stress-based FEM were classified as unsafe. The minimum allowable draw-down factor of safety value is 1.3, as per the guideline. The suggested two designs, with upstream horizontal filters and increased upstream dam permeability, provided an adequate FOS. However, the nonlinear analysis with coupled FEM has shown that the upstream slope is unstable in all three cases (i.e., as-built design, increased upstream dam shell permeability, and suggested application of horizontal filter layers) considering 8 h of RDD. Several gradual draw-down rates were also tested and it has been found that the FOS increases with decreased draw-down rates. FOS charts, pressure fluctuation, and flow measurements in the upstream dam shell have revealed that slope stability is highly influenced by pore water pressure and draw-down rate. The safe allowable draw-down rate of 20 h was identified, considering the as-built design of the dam.

This paper compares the results of different probabilistic approaches and emphasizes the necessity of probabilistic analyses in slope stability studies. To do that, Limit Equilibrium Method (LEM) and Finite Element Method (FEM) are utilized and their outputs are compared in terms of probability of failure (PF), reliability index (RI), factor of safety (FS) and the failure surface. Lastly, concept of Random Finite Element Method (RFEM) is studied and effects of spatial correlation distance are investigated.

Influence of 3D subsurface flow on slope stability for unsaturated soils

This paper develops a new numerical procedure for the slope stability analysis, by combining the slice method in the limit equilibrium method with the lower-bound approach in the limit analysis method. The procedure provides an appropriate lower-bound solution subject to the collapse mechanism represented by a potential slip surface. First, the safety factor for the shear strength is calculated for the case in which the position of the slip surface is known beforehand. The problem is formulated as an optimization problem for finding a stress field which minimizes the safety factor within the limitations of satisfying the lower-bound conditions. The formulated problem is solved numerically by the mathematical programming technique. The obtained stress field appears physically reasonable. Several case studies have shown that the simplified Janbu method based on the critical slip surface tends to underestimate the safety factor on the safety side, compared with the lower-bound solution by the proposed procedure. Subsequently, the assumption used in each of the representative slice methods, which are necessary to render the stability problem to a statically determinate, is verified by the use of the stress field determined by the proposed procedure. Finally, a procedure for locating the critical noncircular slip surface which minimizes the safety factor within the lower-bound conditions is developed. Many important properties in the slope stability analysis are clarified through the development of this procedure.

In the assessment of slopes, factor of safety values still remain the primary indexes for determining how close or far slopes are from failure. Limit equilibrium and finite elements methods are among the most popular methods of slope analysis. Both methods were used to analyze homogeneous and inhomogeneous slopes. However, Limit equilibrium methods are relatively simple and suffer from many assumptions compared with finite element analysis. Recently, as computational techniques advance, more and more attention has been paid to the slope stability evaluations using finite element methods (FEM). This article demonstrates a finite element approach to analyze the response of homogeneous and layered slopes. A detailed parametric analysis is presented to study the effect of surcharge (it can be an imposition of building load….etc.) on the stability of the slope. In regard with these results it is seen that the factor of safety increases with increase in soil properties, groundwater depth, slope length, distance from the crest of slope. However, it decreases with increase in surcharge intensity, increase of weak soil layer thickness and increase of slope angle and slope height.

Slope stability analyses are usually carried out using deterministic methods, which aim the calculation of a single safety factor assuming the values of the shear strength parameters as representative and fixed. These methods fail to assess the uncertainties in soil properties and do not indicate the proportion of influence that each resistance parameter has on the final value of the safety factor. The probabilistic methods, based on probability, reliability and statistical theories, allow the estimation of the influence of these uncertainties on the deterministic calculations, with the possibility to broadly predict the risk of failure associated with a geotechnical slope stability project. This dissertation studies the application of three probabilistic methods (Monte Carlo, Latin Hypercube, and Alternative Point Estimates) in the evaluation of slope stability, with aid of limit equilibrium methods for the calculation of safety factors. In order to infer the impact of random variables on the estimates of probability and reliability, as well as the importance of an adequate quantification of the standard deviation values, comparisons are made among the results obtained with probabilistic and deterministic methods (limit equilibrium method, finite element method), discussing the main advantages, difficulties and limitations in their application to soil slope stability problems.

Despite extensive research on landslides globally, there is a notable knowledge gap on mechanisms influenced by combined rainfall and earthquake events to induce landslides in non-tropical coastal areas, and how to mitigate such failures. This study assessed the factors governing landslide susceptibility in the non-tropical coastal regions under the combined influence of rainfall and earthquake, and further proposes a novel slope protection work that can potentially mitigate such hazard. Adopting datasets from two distinct coastal regions in the United States, this study employed both the Limit Equilibrium Method (LEM) and the Finite Element Method (FEM). Hazard analysis was conducted using Factor of Safety (FoS) from LEM and Strength Reduction Factor (SRF) from FEM on the identified slopes to gain insights into combined rainfall- and earthquake-induced landslides. The results indicate that LEM exhibits limitations in reliability of slope stability analysis with complex failure mechanisms, and is primarily suitable for simple slopes without the influence of non-anthropogenic activities. Contrarily, FEM demonstrated relatively superior applicability for stability analysis of the slopes with complex failure mechanisms and under the influence of environmental stressors in coastal regions. FEM-based assessment of slopes under the dry state and the combined state (earthquake and rainfall) conditions revealed high susceptibility to failure in non-tropical coastal areas under the combined state conditions. Coupled earthquake and rainfall influence on soil mass slopes in non-tropical coastal areas induced shear strain propagation and matric suction reduction along shallower depths, leading to decreased slope stability. Further, we proposed a novel slope protection work that demonstrated higher efficiency in reducing shear strain and increasing SRF (+ 16%), presenting a potentially viable slope protection strategy for non-tropical coastal areas.

Seismic slope instability poses a major hazard in earthquake-prone regions, where ground shaking can cause sudden slope failures resulting in severe damage and loss of life. Reliable assessment of seismic slope performance is therefore essential for geotechnical design. This study compares the Limit Equilibrium Method (LEM) and the Finite Element Method (FEM) in evaluating slope stability under pseudo-static and dynamic loading. The analysis investigates the effects of horizontal (kh) and vertical (kv) seismic coefficients, soil constitutive models, mesh refinement, and earthquake loading types on the Factor of Safety (FoS). Pseudo-static results show a clear reduction in stability with increasing seismic intensity. As the horizontal coefficient increases from kh=0.0 to kh=0.20, the FoS decreases from 1.706 to 0.945 in LEM and from 2.018 to 1.123 in FEM. Vertical acceleration further reduces FoS, especially when kv approx 0.75 kh. FEM consistently predicts higher stability than LEM, typically by 17-19%, due to its ability to model stress redistribution and deformation compatibility. Analyses of constitutive models and mesh refinement indicate close agreement between Mohr-Coulomb and Hardening Soil Small models, with differences generally within 1-3%, while finer meshes reduce FoS by 2-7% due to improved strain localization. Dynamic simulations show that time-history loading produces slightly higher FoS than pseudo-static analysis, whereas harmonic cyclic loading yields the lowest stability. These results highlight the importance of advanced numerical modeling and realistic seismic input in achieving reliable assessments of seismic slope stability.

The applicability of the dynamic programming method to two-dimensional slope stability analyses is studied. The critical slip surface is defined as the slip surface that yields the minimum value of an optimal function. The only assumption regarding the shape of the critical slip surface is that the surface is an assemblage of linear segments. Stresses acting along the critical slip surface are computed using a finite element stress analysis. Assumptions associated with limit equilibrium methods of slices related to the shape of the critical slip surface and the relationship between interslice forces are no longer required. A computer program named DYNPROG was developed based on the proposed analytical procedure, and numerous example problems have been analyzed. Results obtained when using DYNPROG were compared with those obtained when using several well-known limit equilibrium methods. The comparisons demonstrate that the dynamic programming method provides a superior solution when compared with conventional limit equilibrium methods. Analyses conducted also show that factors of safety computed when using the dynamic programming method are generally slightly lower than those computed using conventional limit equilibrium methods of slices; however, as Poisson's ratio approaches 0.5, the computed factors of safety from the dynamic programming method and the limit equilibrium method appear to become similar.Key words: dynamic programming, slope stability, stress analysis, optimization theory, limit equilibrium methods of slices.

The performance of the stability chart (SC), limit equilibrium (LE), and finite element (FE) methods for stability analysis of weathered volcanic rock slopes under static and earthquake loads is not fully understood. This research aimed to evaluate the performance of the SC, LE, and FE methods for slope stability analyses by studying a case of a weathered volcanic rock slope at the Leuwikeris Dam diversion tunnel in Indonesia. Site characterisations were carried out to obtain the input parameters for the static and pseudostatic slope stability analyses. The results showed that using various search methods of failure surface and the suggested optimum number of finite elements, multiple non-circular failure surfaces were predicted from the LE and FE methods that were not anticipated in the initial slope design based on the SC method. The location and shape of the failure surfaces from the LE method agreed with those from the FE method. The difference between the Fs values from the static LE analysis and those from the static FE analyses was less than 14%, but the discrepancy increased up to 78% in the pseudostatic analyses. This study highlights the importance of validating the results from one method with the other methods to prevent slope failures.

Natural slopes are non-homogeneous in nature, which behave differently than homogeneous slopes. The non-homogeneity in slopes exist in various ways, which include change in stratifications and/or shear strength parameters (cohesion, friction angle) with depth, presence of saturated–unsaturated zones, etc. This study is performed to show the effect of non-homogeneity due to different types of soils on the stability of two-layered slopes. Homogeneous and two-layered non-homogeneous models of soil slope are prepared with three different fine-grained and coarse-grained types of soils. Both the limit equilibrium method and finite element methods were used to evaluate the stability of the slopes and the results are presented in terms of safety factors along with the corresponding critical slip surfaces. Slopes with coarse-grained soil showed translational type of failure, while rotational failure was observed for fine-grained slopes.

Slope stability has been a long-standing problem in geotechnical practice. The difficulty in analyzing slope stability may be attributed to geological complexity and versatile environments, but the limitations of analysis methods should not be ignored. In this work, the conventional limit equilibrium methods and the FE stress-based limit equilibrium methods with special emphasis on their limitations are reviewed, and the advantages of the finite element method with the capability of strength reduction are pointed out and illustrated by using some slope examples. Particularly, a flowchart of decision tree on selecting single-grid or two-grid search scheme is proposed for the shear strength reduction finite element method of slope stability analysis. Based on some slope examples, it is demonstrated that the automatic selection or switch between the single-grid scheme and the two-grid scheme can be remarkably superior to the single mesh scheme from the perspectives of computational cost and software development.

Slope stability represents an area of geotechnical analysis in which finite element method provides a lot of benefits over limit equilibrium. In this paper, the authors apply a finite element code, PLAXIS, on slope stability analysis with various conditions to state out sensitivities of not only the soil parameters, slope configuration and groundwater condition but also numerical condition that one would encounter when making a FE slope design. It demonstrates that slightly conservative safety factor is obtained using FEM over the ones from limit equilibrium method. Intensity of mesh for simulation domain shall be selected as a fine level for an acceptable accuracy and economical computation time. Element nodes slightly affect the result of safety factor and final deformation of the slope.

This paper deals with the soil slope stability analysis along the road section (National Highway-05) near Luhri area, Himachal Pradesh, India. The area constantly experiences local as well as regional slides which enhances the siltation, reduce carrying capacity of the Sutlej river with time and further increases the water level on the banks of the slope. High traffic congestion puts the area at high risk zone and therefore, stability analysis was done using probabilistic as well as deterministic approach under static conditions through limit equilibrium method (LEM) and finite element method (FEM). FEM was used for stability analysis, mainly to obtain deformational characteristics, under static conditions and compared with LEM results. The results of both the methods help in identifying the zones of vulnerability in the case study. Further, the values of safety factor obtained from both the methods are in close approximation. The study also reveals that the slope is critically stable and a remedial measure has been suggested by modifying the geometry of the slope, which needs proper protection from any external factors like rainfall and earthquakes that may cause unforeseeable circumstances.