New bounds for the height limit of a vertical slope

Abstract

Using the finite element method, the static and kinematic methods of limit analysis provide tools to solve many stability problems in mechanics of continuous media. The classic problem of the height limit of a Tresca or Mises vertical slope subjected to the action of gravity stems naturally from this theory in plane strain. Although the exact solution to this problem remains unknown, the present work has produced precise bounds using the static and kinematic approaches conjointly: the height limit is now between 3·760 and 3·786 C/ γ, γ being the weight per unit volume and C the soil cohesion. These tests also show that both methods, used on current workstations with industrial optimization codes such as XPRESS or OSL, are capable of solving any plane problem of limit loads in geotechnics or in structural calculus. Copyright © 2000 John Wiley & Sons, Ltd.