Mohr Envelope Elastoplasticity

Abstract

An often-used tool for describing the strength of geotechnical materials is the Mohr strength envelope, which has been used for more than 100 years. For simple problems, analytical bearing capacity solutions can be found and numerical methods exist for finding bearing capacities for more complicated geometries and nonlinear Mohr envelopes. Despite their long history, Mohr envelopes have never been used in elastoplastic calculations, meaning that displacement magnitudes cannot be found. This paper presents the implementation of nonlinear Mohr envelopes in an elastoplastic numerical framework. This allows the use of materials with plasticity behavior described by Mohr envelopes to be used on an equal basis with materials whose plasticity behavior is described by the traditional yield surfaces and plastic potentials. This opens up its use with both failure load calculation and displacement estimates. Mohr envelope elastoplasticity is particularly useful with the use of safety factors as in shear strength reduction methods, where no simple, consistent methods so far exist for nonlinear yield criteria formulated in Cartesian stresses. Several computational examples are given.