Slope reliability assessment using an innovative critical failure path approach

A GIS-based method for locating the critical 3D slip surface in a slope

This paper presents a new approach to determine the minimum factor of safety and the associated critical line segment pseudostatic slip surface. The new technique is called Alternating Variable Local Gradient (AVLG) that it is based on Univariat method. The slip surface shape is line segment (or non-circular). The safety factor is calculated using Janbu function. This procedure can truly convert the initial slip surface to critical slip surface with the different conditions of slope and soil properties. The critical slip surface obtained in this method provides both minimum factor of safety and more accordance with reality in nature. Resultant critical slip surface is reasonable also comparative study of numerical examples indicate the efficiency and accuracy of proposed method.

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.

The Various methods of optimization or random search have been developed for locating the critical slip surface of a slope and the related minimum safety factor in the limit equilibrium stability analysis of slope. But all these methods are based on a two-dimensional (2D) method and no one had been adapted for a search of the three-dimensional (3D) critical slip surface. In this paper, a new Monte Carlo random simulating method has been proposed to identify the 3D critical slip surface, in which assuming the initial slip to be the lower part of an ellipsoid, the 3D critical slip surface in the 3D slope stability analysis is located by minimizing the 3D safety factor of limit equilibrium approach. Based on the column-based three-dimensional limit equilibrium slope stability analysis models, new Geographic Information Systems (GIS) grid-based 3D deterministic limit equilibrium models are developed to calculate the 3D safety factors. Several practical examples, of obtained minimum safety factor and its critical slip surface by a 2D optimization or random technique, are extended to 3D slope problems to locate the 3D critical slip surface and to compare with the 2D results. The results shows that, comparing with the 2D results, the resulting 3D critical slip surface has no apparent difference only from a cross section, but the associated 3D safety factor is definitely higher.

The various methods of optimization or random search have been developed for locating the critical slip surface of a slope and the related minimum safety factor in the limit equilibrium stability analysis of slope. However, all these methods are based on a two-dimensional (2D) method and not one had been adapted for a search of the three-dimensional (3D) critical slip surface. In this paper, a new Monte Carlo random simulation method has been proposed to identify the 3D critical slip surface, in which assuming the initial slip to be the lower part of an ellipsoid, the 3D critical slip surface in the 3D slope stability analysis is located by minimizing the 3D safety factor of limit equilibrium approach. Based on the column-based 3D limit equilibrium slope stability analysis models, new geographic information systems (GIS) grid-based 3D deterministic limit equilibrium models are developed to calculate the 3D safety factors. Several practical examples, of obtained minimum safety factor and its critical slip surface by a 2D optimization or random technique, are extended to 3D slope problems to locate the 3D critical slip surface and to compare with the 2D results. The results shows that, comparing with the 2D results, the resulted 3D critical slip surface has no apparent difference only from a cross-section, but the associated 3D safety factor is definitely higher.

Finding the critical slip surface and estimating the landslide volume are of primary importance for slope seismic design. However, this may be difficult due to the uncertainty of ground motions. To address this problem, a new method for calculating uncertainties is recommended in this paper, especially for the critical slip surface and landslide volume under random earthquake ground motions. Firstly, a series of intensity–frequency nonstationary random earthquake ground motions were generated based on an improved orthogonal expansion method. A given number of potential slip surfaces were set in a soil slope. Subsequently, the factor of safety (FOS) of each slip surface for all ground motions was calculated and the minimum FOS curves were obtained. It was found that the critical slip surfaces and failure times are uncertain under different earthquakes. The Monte Carlo method was used to verify the accuracy of probability density evolution method (PDEM), and the results of the PDEM and the Monte Carlo method are consistent, meaning that the PEDM has higher computational efficiency. Moreover, the distributions of earthquake-triggered landslide volume and landslide depth were analyzed by considering equivalent extreme events. Both landslide volume and depth exhibit a normal distribution for a homogeneous soil slope. The framework of this study is meaningful for slope seismic design in engineering, for example, the location of critical slip surface can be used for slope reinforcement, and the distribution of sliding volume can be used for disaster assessment.

This paper discusses the second-order reliability-based design optimization (SORBDO) of unsaturated finite slopes. An efficient search algorithm is proposed to locate the most probable slip surfaces using the Morgenstern–Price method of slices. The variability of fitting parameters of the soil water characteristic curve (SWCC) and shear strength parameters have been taken into account for evaluating the reliability of unsaturated finite slopes. Six unsaturated shear strength (USS) models are considered for the analysis of unsaturated soils. The most conservative model for the optimum design of finite slopes is recommended. Moreover, the results indicate that the mean and standard deviation of the fitting parameters of SWCC have a significant effect on the critical centers, critical slip surfaces, and reliability index of the unsaturated finite slopes. The results demonstrate a significant change in the critical centers associated with critical slip surfaces due to the change in the mean and coefficient of variation of the fitting parameters of SWCC. Statistical analysis of the experimental data shows that a positive correlation exists between fitting parameters of SWCC related to air entry value (af) and residual water content (mf). Negative correlations are found between the fitting parameters of SWCC related to air entry value (af) and slope (nf). Similarly, the SWCC fitting parameters related to residual water content (mf) and slope (nf) have negative correlations for clayey soils. It is observed that the correlated value of the reliability index is overestimated with reference to the uncorrelated value for clayey soil slopes. The proposed design charts are beneficial for engineers and practitioners for the sustainable design of unsaturated finite slopes. Overall, the developed rigorous SORBDO framework offers a more rational approach for assessing critical failure surfaces and critical centers, considering the interdependency of random variables.

Assessment of Embankment Factor Safety Using Two Commercially Available Programs in Slope Stability Analysis

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 most devastating factor for slope failures is rainfall infiltration. Surficial slope failures in residual soil slopes are a common sight. In general, slope angles vary considerably from being flat to steep in natural conditions, which govern the hydrological regime of the slope. Further, different types of soils behave differently under rainfall condition in terms of rainfall infiltration and the associated changes in their mechanical behaviour, particularly under different slope inclinations. This paper presents a study on the effect of slope inclination on stability of different soil slopes under rainfall conditions. Two-dimensional numerical models were prepared with three different soils having different hydraulic and mechanical properties to investigate the stability of the unsaturated soil slopes. Seepage analysis is performed in the finite element framework, and stability analysis for the slopes is performed in limit equilibrium framework using numerical package SLIDE. The water table in the slope rises high for flat slopes, which is contrary to levels observed in steep slopes. From the results, it was observed that flat slopes allowed more infiltration leading to the rapid reduction in negative pore pressure thereby decreasing the safety factor. Both the initial factor of safety and minimum factor of safety decreased nonlinearly with slope angle. The critical slip surface becomes shallower (shifts towards the slope surface) with increase in angle of the slope. There was very little influence of slope inclination on the stability for slopes higher than 55°.

Slope stability analysis is a crucial task in the design of geotechnical structures. In many computational methods, such as those combining displacement-based finite element methods and strength reduction techniques, no assumptions are made a priori about the shape or position of the failure mechanism. This is usually considered to be a positive feature but there are situations where the ability to control the search domain for the critical slip surface might be of interest. These are the cases where the critical slip surface converges towards a local (unintended) one, or when it is necessary to determine the factor of safety for slopes with varying inclinations such as the upstream and downstream slopes of embankment dams. This article presents the Finite Element Limit Equilibrium Method (FELEM), which integrates stress states computed by the finite element method along a predefined trial slip surface to determine the factor of safety. This method is combined with a swarm-based metaheuristic optimization algorithm to identify the critical slip surface with the lowest factor of safety. The combined approach is tested on two numerical examples, addressing issues such as discretization error, optimization procedure settings, and non-associated plastic flow. Finally, the combination of FELEM and the optimization algorithm is applied to a boundary value problem of a newly designed embankment dam. Slope stability is evaluated independently for both the upstream and downstream slope, each with a different inclination. Computations are performed for the hydrostatic and steady-state seepage conditions.

The impact of deep excavation to the stability of adjacent slope is evaluated based on the slip line theory. Stress field of slope under various excavation conditions is simulated by finite element method, while slip line field is determined by non-associated flow rule. Factor of safety is obtained by integrating the skid-resistance and the shear stress on each slip line, and the slip line with minimum factor of safety corresponds to the critical slip surface. Two typical displacement constraint boundaries are considered. The results indicate that the critical slip surface moves towards to the slope surface and develops downwards. The factor of safety decreases with the excavation process. For flexible displacement constraint boundary, large deformation of supporting pile causes obvious variation of critical slip surface and factor of safety. In terms of the stiff displacement constraint boundary with internal supports, deep excavation only has limited effect on the slope stability.

It is difficult to accurately simulate the deformation and failure process of accumulation slope because of its inherent discontinuity, in-homogeneity and aeolotropism properties. Discrete element method (DEM) is adopted in this paper for preliminary study of the deformation and failure process of accumulation slope. Strength reduction method is introduced into the DEM for the study of slope safety factor and the critical slip surfaces; the whole progressive failure process of accumulation slope is also investigated from a microscopic view. Particle friction coefficient and bond strength are set as variables in the process of strength reduction in PFC. Cumulative displacement of slope crest and slope toe and numerical results of particle unbalance force are recognized as a comprehensive index of slope failure. The failure process and safety factor of accumulation slope are obtained by DEM simulation. For comparison, limit equilibrium method (LEM) and finite element method (FEM) are used for the same example. The results show that discrete element strength reduction method outstands in the study of discontinuous medium. The progressive failure mechanism of the accumulation slope is revealed. The safety factor obtained by sole use of DEM is basically the same with that obtained by combined use of FEM and LEM, indicating the safety factor obtained is reliable.

Extension of Hassan and Wolff method for system reliability analysis of soil slopes

Quantitative risk assessment of landslides induced by slope failure is an important precondition for formulating effective disaster prevention, mitigation measures, and establishing a landslide risk warning system. In general, the location of the critical slip surface and the failure mode is unlikely to be predicted due to the spatial variability in soil. It remains a challenging task to effectively identify the critical slip surface and conduct the efficient risk assessment based on a three‐dimensional (3‐D) slope with spatial variability. Based on Monte Carlo simulation and the random field method, a quantitative risk evaluation method for slope failure considering the spatial variability of soil parameters is proposed in the study. Compared with a uniform soil slope, the landslide volume, the critical slip surface, and the factor of safety considering the spatial variability of soil are all uncertain; thus, the soil spatial variability has a significant effect on the failure mode and stability of the slope. By using the random finite element method, the critical slip surface of the slope is accurately identified, the corresponding landslide volume and slide distance are calculated, and the modified risk index for a landslide is further enriched, which can provide the reference basis for predicting the landslide deformation, quantitatively evaluating the landslide risk, and mitigating the landslide disaster.