Theoretical studies and applications of an upper-bound stability analysis method based on the failure mode of inclined slices

Abstract

This paper provides an in-depth study of the upper-bound slope stability analysis method proposed by Donald and Chen using inclined slices to simulate the sliding mass (Energy Method Upper-bound, abbreviated to EMU). After a brief review of the theoretical background and numerical method of the EMU, the authors present a weightless slope subjected to a vertical ultimate load to demonstrate its theoretical background. It has been proven that the analytical formulation of the EMU is identical to the closed-form solution given by the slip line method (SLM) for this selected example. Conversely, using its computer program, EMU has produced several closed-form solutions selected from Sokolovski. Thus, the potential for applications in practical engineering problems is demonstrated. With its theoretical background and numerical feasibility, EMU is extended to the area of bearing capacity of strip footings whose theoretical background is based on the slip line theory by Prandtl but involves various semi-empirical factors accounting for the effect of the soil weight, inclined and eccentric loading, and multi-layer foundations. This paper presents a preliminary investigation of semi-empirical approaches to the factors accounting for soil weight. Alternatively, the authors present a computer program Bearing-IWHR at the web, which is an Excel/VBA coded spreadsheet to perform numerical bearing analysis without the need for the semi-empirical factors.