Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming

Abstract

In this paper, the development and application of a new upper bound limit method for two- and three-dimensional (2D and 3D) slope stability problems is presented. Rigid finite elements are used to construct a kinematically admissible velocity field. Kinematically admissible velocity discontinuities are permitted to occur at all inter-element boundaries. The proposed method formulates the slope stability problem as an optimization problem based on the upper bound theorem. The objective function for determination of the minimum value of the factor of safety has a number of unknowns that are subject to a set of linear and nonlinear equality constraints as well as linear inequality constraints. The objective function and constrain equations are derived from an energy–work balance equation, the Mohr–Coulomb failure (yield) criterion, an associated flow rule, and a number of boundary conditions. The objective function with constraints leads to a standard nonlinear programming problem, which can be solved by a sequential quadratic algorithm. A computer program has been developed for finding the factor of safety of a slope, which makes the present method simple to implement. Four typical 2D and 3D slope stability problems are selected from the literature and are analysed using the present method. The results of the present limit analysis are compared with those produced by other approaches reported in the literature.Key words: limit analysis, upper bound, rigid finite element, nonlinear programming, sequential quadratic algorithm, slope stability.

Three-dimensional slope stability problem with a surcharge load

“…Chen et al (2003) overcome this limitation by the use of many small rigid elements and nonlinear programming technique for the minimization analysis, but this method requires very long computer time in the optimization process, and the location of the global minimum is not easily achieved.…”

Limit Analysis of Slope Stability by Rigid Finite-Element Method and Linear Programming Considering Rotational Failure

“…Element rotation has been ignored by previous RFEM-based limit analyses by Chen et al (2003Chen et al ( , 2004Chen et al ( , 2005 and Zhang (1999), and the main purpose was to maintain the condition of no gap or overlap between neighboring elements. Although it appears to be reasonable for the translation-dominant type of slope failure, the assumption proves to be inadequate to describe cases where the rotation may be a contributing factor.…”

“…Importantly, the physical discontinuities in discontinuous media can be reasonably treated as interfaces between the adjacent rigid elements in RFEM. Based on RFEM, lower bound (Zhang and Qian 1993;Zhang 1999) and upper bound (Chen et al 2003(Chen et al , 2004(Chen et al , 2005Yang and Yang 2010) limit analysis methods have been developed.…”

“…In existing studies by RFEM, the constraint of compatibility between rigid elements has been imposed in a simplified way, which leads to the ignorance of rotational components of the centroid velocity of each rigid element (Zhang 1999;Chen et al 2003Chen et al , 2004Chen et al , 2005. This may essentially lead to the exclusion of the rotational or toppling failure mode in numerical limit analysis, which, in some cases, may cause erroneous predictions as mentioned before.…”

2D and 3D stability analysis of slurry trench in frictional/cohesive soil

“…1, in which the failure surface is assumed to pass through the toe of the slurry trench. The log-spiral slip surface is used for problems of slope stability (Chen et al, 2003;Loukidis et al, 2003;Zhu et al, 2003;Jiang et al, 2009) and foundation stability (Kumar and Ghosh, 2007;Han et al, 2012b). The region ABC rotates as a rigid body around the center of rotation O with the materials below the logarithmic surface AC remaining at rest.…”