UPPER BOUND LIMIT ANALYSIS OF SOIL WITH NON-LINEAR FAILURE CRITERION

Abstract

The paper discusses the effects of non-linearity in the failure criterion of soil on the upper bound solution procedure. By considering the inherent non-linearity of the failure criterion, it is demonstrated that the upper bound procedure yields not only the minimum value of and the external load and the failure mechanism, but also the stress distribution along the slip surface. The stress distribution so obtained satisfies a Kotter type differential equation and guaranties the global equilibrium of the sliding mass. This result is valid for both linear and non-linear failure criteria. When the failure criterion is linear, it is demonstrated that for a simple failure mechanism the classical solution procedure provides only a partial solution which does not include the normal stress distribution. This is due to the different consequence of the normality requirement in the linear and non-linear cases.