General Slip Surfaces Research Articles

An efficient method for calculating system reliability of soil slope with general shape slip surface

An efficient method for calculating system reliability of soil slope with general shape slip surface

Direct Search for Critical General Slip Surface of Slopes with Nonlinear Strength Envelope

Direct Search for Critical General Slip Surface of Slopes with Nonlinear Strength Envelope

Pseudo-static seismic analysis of reinforced soil slopes using the horizontal slice method

In this paper, the horizontal slice method (HSM) is employed to examine the stability of reinforced soil slopes. In this method, the soil mass is divided into a series of horizontal slices, and then the stability of each slice is examined. Unlike the previous studies, the formulation presented in this paper is able to analyse any type of the sliding surface. In addition to the log-spiral slip surface, the general slip surface is also examined. The genetic algorithm (GA) optimization method is employed to find the critical slip surface. Furthermore, the distribution of reinforcements along the depth is assumed to be uniform or non-uniform. Seismic effect is considered through the pseudo-static method. The HSM is implemented through a computer program written in MATLAB. After solving the problem, the critical slip surface, the amount of force and the length of reinforcements for the purpose of slope stabilization are obtained. Finally, the results are compared with other studies. These comparisons indicate that the method presented in this paper provides accurate results. The results also demonstrate that the general sliding surface is more critical than log-spiral sliding surface, thus leading to a larger amount of required reinforcement.

System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines

A data driven multivariate adaptive regression splines (MARS) based algorithm for system reliability analysis of earth slopes having random soil properties under the framework of limit equilibrium method of slices is considered. The theoretical formulation is developed based on Spencer method (valid for general slip surfaces) satisfying all conditions of static equilibrium coupled with a nonlinear programming technique of optimization. Simulated noise is used to take account of inevitable modeling inaccuracies and epistemic uncertainties. The proposed MARS based algorithm is capable of achieving high level of computational efficiency in the system reliability analysis without significantly compromising the accuracy of results.

Reliability Analysis of Earth Slopes Considering Spatial Variability

The paper presents a computational procedure for reliability analysis of earth slopes considering spatial variability of soils under the framework of the Limit Equilibrium Method. In the reliability analysis of earth slopes, the effect of spatial variability of soil properties is generally included indirectly by assuming that the probabilistic critical slip surface is the same as that determined without considering spatial variability. In contrast to this indirect approach, in the direct approach, the effect of spatial variability is included in the process of determination of the probabilistic critical surface itself. While the indirect approach requires much less computational effort, the direct approach is definitely more rigorous. In this context this paper attempts to investigate, with the help of numerical examples, how far away are the results obtained from the indirect approach from that obtained from the direct approach. In both the approaches, it is required to use a model of discretization of random fields into finite random variables. A few such models are available in the literature for one-dimensional (1D) as well as two-dimensional (2D) spatial variability. The developed computational scheme is based on the First Order Reliability Method (FORM) coupled with the Spencer Method of Slices valid for limit equilibrium analysis of general slip surfaces. The study includes bringing out the computational advantages and disadvantages of the three commonly used discretization models. The sensitivity of the reliability index to the magnitudes of the scales of fluctuation has also been studied.

Probabilistic Stability Analysis of the Bois Brule Levee Considering the Effect of Spatial Variability of Soil Properties Based on a New Discretization Model

The paper presents a computational procedure for reliability analysis of earth slopes for which the probabilistic critical slip surfaces have been determined considering spatial variability of soils. The effect of spatial variability has been taken into account based on a newly developed discretization model which is free from the shortcomings of the discretization models available in the literature and all these shortcomings are demonstrated numerically in this paper. The developed algorithm is based on the First Order Reliability Method coupled with the Spencer Method of Slices valid for limit equilibrium analysis of general slip surfaces. A case study of the Bois Brule Levee has been reanalyzed using the developed technique and several observations have been discussed. The result obtained in this study clearly shows that the proposed model is considerably more conservative than other available models.

Imperialistic Competitive Algorithm: A metaheuristic algorithm for locating the critical slip surface in 2-Dimensional soil slopes

In this study, Imperialistic Competitive Algorithm (ICA) is utilized for locating the critical failure surface and computing the factor of safety (FOS) in a slope stability analysis based on the limit equilibrium approach. The factor of safety relating to each trial slip surface is calculated using a simplified algorithm of the Morgenstern-Price method, which satisfies both the force and the moment equilibriums. General slip surface is considered non-circular in this study that is constituted by linking random straight lines. To explore the performance of the proposed algorithm, four benchmark test problems are analyzed. The results demonstrate that the present techniques can provide reliable, accurate and efficient solutions for locating the critical failure surface and relating FOS. Moreover, in contrast with previous studies the present algorithm could reach the lower value of FOS and reached more exact solutions.

Probabilistic Critical Slip Surface for Earth Slopes Based on the First Order Reliability Method

The paper presents a computational procedure for reliability analysis of earth slopes in which the probabilistic critical slip surface is located using a mathematical programming formulation similar to that used to search for the deterministic critical slip surface in a conventional slope stability analysis. The procedure is based on the First Order Reliability Method (FORM) in conjunction with the Spencer method for evaluation of factor of safety of general slip surfaces and the Sequential Quadratic Programming (SQP) technique of optimization. When applied to two benchmark illustrative examples, the procedure yields the probabilistic critical slip surfaces which are reasonable and the values of the associated minimum reliability indices are close to or lower than those reported by different investigators using different methodologies, and compare well with those from the direct Monte-Carlo simulation method (MCS). Further, the developed procedure has been made use of to investigate another important aspect of reliability analysis, namely, how the results of reliability analyses vary with the probability distributions assumed for the basic random variables. Three most commonly assumed distributions, namely, normal, lognormal and truncated normal distributions have been considered. The results indicate that the lognormal assumption used solely to ensure non-negativity of the basic variables might lead to non-conservative prediction of probability of failure. Whether the effect of such distributional assumption is consistent when the coefficients of variation (COVs) of the basic random variables vary within their respective ranges has also been investigated.

Stability assessment of earth slope using modified particle swarm optimization

This paper has proposed an effective method to determine the minimum factor of safety (FS) and associated critical failure surface in slope stability analysis. The search for the minimum FS based on limit equilibrium methods is a complex optimization problem as the objective function is non-smooth and non-convex. Recently, particle swarm optimization (PSO) as a meta-heuristic optimization algorithm has been developed with success in treating various types of problems. In the current study, a new approach of PSO is proposed to calculate the safety factor of earth slopes. The safety factors of the general slip surfaces are calculated using Spencer method of slices, and each new slip surface is randomly generated by straight line technique. The reliability and efficiency of the proposed algorithm are examined by considering a number of published cases. The results indicate that the new method can predict a more critical failure mechanism with a lower FS and can outperform the other methods in the literature as well as standard PSO. Finally, the proposed method will be validated by considering an existing slope failure in Ulu Klang, Malaysia.

Locating the general failure surface of earth slope using particle swarm optimisation

In this study, a new particle swarm optimisation (PSO) approach is proposed for evaluating the factor of safety (FS) in a slope stability analysis based on the limit equilibrium method. The safety factors of the general slip surfaces are calculated using a concise algorithm of the Morgenstern–Price method, which satisfies both the force and the moment equilibriums. Each new slip surface is randomly generated by a straight-line technique. The performance of the proposed algorithm is evaluated using a set of three benchmark functions and three slope stability problems from the literature. The results indicate that the new method can provide high-quality, accurate and efficient solutions for computing the FS. Moreover, this method can predict a more critical failure mechanism of earth slope and outperform both the other methods in the literature and the standard PSO.

Quasi-Three-Dimensional Slope Stability Analysis Method for General Sliding Bodies

A quasi-three-dimensional procedure has been developed for computing the stability of earth slopes and waste containment facilities along general slip surfaces. The procedure, termed the Resistance-Weighted procedure, is an extension of existing quasi-three-dimensional procedures, which utilize results from two-dimensional slope stability analyses to estimate three-dimensional stability. As a part of this procedure, a scheme has been developed for modeling realistic three-dimensional sites and efficiently generating input data for two-dimensional analyses. This scheme enables Resistance-Weighted calculations to be performed using existing commercial spreadsheet and two-dimensional slope stability software. The method can also be incorporated into existing two-dimensional slope stability software with relatively little development effort. The Resistance-Weighted procedure and geometric modeling scheme are presented in this paper. Application of the procedure to a case history and results of a series of analyses to validate the procedure are described. The results of the analyses show that the Resistance-Weighted procedure produces results that compare favorably with more rigorous three-dimensional procedures. Although the Resistance-Weighted procedure is approximate, it serves as a simple means for estimating the magnitude of three-dimensional effects when a more rigorous three-dimensional procedure is not available.

Generalised framework of limit equilibrium methods for slope stability analysis

A generalised framework is proposed in this paper incorporating almost all of the existing limit equilibrium methods of slices for slope stability analysis with general slip surfaces. The force and moment equilibrium equations are derived in terms of the factor of safety and the initially assumed normal stress distribution over the slip surface, multiplied by a modification function involving two auxiliary unknowns. These equations are then analytically solved to yield explicit expressions for the factor of safety. Various assumptions regarding the interslice forces can be transformed into a unified form of expression for the normal stress distribution along the slip surface. An iterative procedure is developed to expedite the convergence of the solution for the factor of safety. Experience to date indicates that the process generally converges within a few iterations. Computation schemes are suggested to avoid numerical difficulty, especially in computing the factor of safety associated with the rigorous Janbu method. The present framework can be readily implemented in a computer program, giving solutions of slope stability associated with a number of conventional methods of slices.

Generalised framework of limit equilibrium methods for slope stability analysis

A generalised framework is proposed in this paper incorporating almost all of the existing limit equilibrium methods of slices for slope stability analysis with general slip surfaces. The force and moment equilibrium equations are derived in terms of the factor of safety and the initially assumed normal stress distribution over the slip surface, multiplied by a modification function involving two auxiliary unknowns. These equations are then analytically solved to yield explicit expressions for the factor of safety. Various assumptions regarding the interslice forces can be transformed into a unified form of expression for the normal stress distribution along the slip surface. An iterative procedure is developed to expedite the convergence of the solution for the factor of safety. Experience to date indicates that the process generally converges within a few iterations. Computation schemes are suggested to avoid numerical difficulty, especially in computing the factor of safety associated with the rigorous...

Discussion of “Global Search Method for Locating General Slip Surface Using Monte Carlo Techniques” by Abdallah I. Husein Malkawi, Waleed F. Hassan, and Sarada K. Sarma

Discussion of “Global Search Method for Locating General Slip Surface Using Monte Carlo Techniques” by Abdallah I. Husein Malkawi, Waleed F. Hassan, and Sarada K. Sarma

Closure to “Global Search Method for Locating General Slip Surface Using Monte Carlo Techniques” by Abdallah I. Husein Malkawi, Waleed F. Hassan, and Sarada K. Sarma

Closure to “Global Search Method for Locating General Slip Surface Using Monte Carlo Techniques” by Abdallah I. Husein Malkawi, Waleed F. Hassan, and Sarada K. Sarma

Effect of reinforcement force distribution on stability of embankments

The effect of reinforcement force distribution on the stability of reinforced embankments is studied. The stability of reinforced embankments is analyzed using the extended generalized method of slices by incorporating the effect of reinforcement. The proposed method is capable of handling features such as a tension crack in the embankment, a varying soil strength profile in the foundation soil and a general slip surface. The method allows the tensile force distribution along the reinforcement to be varied. The stability analysis of reinforced embankments is solved using a spreadsheet optimization tool. The versatility of the proposed method is demonstrated through several cases of reinforced embankments. The results obtained from the proposed method are in good agreement with those obtained from other analytical or numerical methods. The assumed force distribution along the reinforcement appears not to affect the embankment stability in undrained condition. In drained condition, it has some effect on the location of the critical slip surface, but small effect on the factor of safety.

Closure to “Unified Formulation for Analysis of Slopes with General Slip Surface” by R. D. Espinoza, P. L. Bourdeau, and B. Muhunthan

Closure to “Unified Formulation for Analysis of Slopes with General Slip Surface” by R. D. Espinoza, P. L. Bourdeau, and B. Muhunthan

Discussion of “Unified Formulation for Analysis of Slopes with General Slip Surface” by Stephen G. Wright and James Michael Duncan

Discussion of “Unified Formulation for Analysis of Slopes with General Slip Surface” by Stephen G. Wright and James Michael Duncan

Discussion: Unified Formulation for Analysis of Slopes with General Slip Surface

Discussion: Unified Formulation for Analysis of Slopes with General Slip Surface

Slope System Reliability with General Slip Surfaces

The main requirements for assessing the system reliability of slopes are outlined briefly and a comprehensive procedure is presented based on potential slip surfaces of arbitrary shape. The evaluation of system reliability of soil structures such as slopes is important because of the spatial variability of geotechnical parameters within any soil layer and also the fact that slopes are frequently associated with multi-layered soil deposits. The performance function for the stability of a slope, defined in terms of a ‘factor of safety’, is usually inexplicit and non-linear. A ‘rigorous’ method of slope stability analysis such as the Generalised Procedure of Slices may be used as the basis of a reliability analysis. A complete analysis should include the search for a critical slip surface and the calculation of reliability index or the probability of failure associated with it. System reliability bounds are evaluated by considering the probabilities of failure associated with a number of slip surfaces including the critical slip surface. It is shown that the upper bound of the system failure probability can be significantly higher than the failure probability associated with the critical slip surface. This finding is significant for slope design and for geotechnical risk assessment generally.