Upper-bound solutions of three-dimensional passive earth pressures

Abstract

This paper presents a novel approach to the determination of passive soil pressures: using the upper-bound method within the framework of limit analysis theory. It is based on a three-dimensional, kinematically admissible, rotational, hyperbolical failure mechanism. The failure mechanism is composed of the central and two lateral bodies, which are connected by a common velocity field. This approach is similar to two-dimensional stability analyses, where the log spiral potential failure surface is considered. The front surface of the central body interacts with the retaining wall; the upper surface can be loaded by surcharge loading; and the log spiral segment defines the curved failure surface of the central part. The cross sections of the lateral bodies are in agreement with the cross section of the central body. On the outer side, they are laterally bounded by a curved and kinematically admissible hyperbolic surface, which is defined by enveloping the hyperbolical half cones and part of the case surface of the leading half cone. The results give values for the passive soil pressure coefficients that are for most cases lower than the values determined by the upper-bound method of limit analysis for a translational failure mechanism, as published in the literature.Key words: limit analysis, earth pressure, passive pressure, failure surface, soil–structure interaction.