Abstract
Although the finite element method (FEM) has been used extensively to analyse the slope stability problems, the computational precision and definition of failure are still two main key concepts of finite element algorithms that attract the attention of researchers. In this paper, the modified Euler algorithm and the explicit modified Euler algorithm with stress corrections are used to analyse two dimensional (2D) slope stability problems with the associated flow rule, based on the shear strength reduction method. The rounded hyperbolic Mohr-Coulomb (M-C) yield surface is applied. Effects of the element type and various definitions of failure on the computational precision of 2D slope stability problems are evaluated. Conclusions can be drawn that the modified Euler scheme is applicable when the factor of safety (FOS) is small; however, the explicit modified Euler algorithm with stress corrections is more precise if the factor of safety is relatively large. The fully integrated quadrilateral isoparametric element is better than the triangular element in terms of the precision. With respect to the definition of failure, the displacement mutation of the characteristic point combining with the continuums of the plastic zone can be regarded as a reliable definition of failure and can be widely used to perform and analyse numerical simulations of slope stability problems.
Highlights
E finite element (FE) approach in analyzing slope stability problems can be catalogued to the realm of elastic-plastic mechanics
The assumption of the perfectly plastic material or nonhardening plastic-rigid body, which was indispensable for limit analysis, was no longer a must for the FE method [15]. e FE approach in terms of incremental plasticity has been widely applied to the slope stability problems [16,17,18,19,20,21,22,23,24,25]
Abbo [29] improved the scheme proposed by Sloan by giving a method of stress corrections. eir algorithms are suitable for analyzing typical boundary value problems in geotechnical engineering. e numerical simulations of slope stability problems have been performed by using the triangle element [20, 23] and the isoparametric element [16,17,18,19]. ey identified that a dense mesh can result in an increase in precision, with a sacrifice of computing time
Summary
Following Sloan [10] and Abbo [29], the explicit modified Euler, which is a family of explicit methods, is used in this study. is method is associated with the shear strength reduction scheme to present a systematic analysis on three definitions of failure in slope stability problems. Is method is associated with the shear strength reduction scheme to present a systematic analysis on three definitions of failure in slope stability problems. E explicit modified Euler integration scheme requires determination of the intersection with the yield surface when the stresses experience a transition from an elastic state to plastic state (e.g., [10, 29, 30]). E aim of this approach is to compute the stress-strain response over each substep by integrating the elastic-plastic constitutive matrix Dep. In order to determine the portion of the stress increment that lies within the yield surface, a scaler α must be found. Abbo [29] has given a stress correction method, and details of this method can be found in his publication Both the two integration algorithms are used to perform the stress-strain relations in the present study. All of the three definitions of failure will be analysed throughout this paper
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