Observations on Mohr-Coulomb plasticity under plane strain

Linear elastic-perfect plasticity using the Mohr-Coulomb yield surface is one of the most widely used pressure-sensitive constitutive models in engineering practice. In the area of geotechnical engineering, a number of problems, such as cavity expansion, embankment stability, and footing bearing capacity, can be examined using this model together with the simplifying assumption of plane strain. This paper clarifies the situation regarding the direction of the intermediate principal stress in such an analysis and reveals a unique relationship between hydrostatic pressure and the principal stress ratio for Mohr-Coulomb and Tresca perfect plasticity under those plane-strain conditions. The rational relationship and direction of the intermediate principal stress are illustrated through both material-point and finite-element simulations. The latter involves the analysis of a rigid strip footing bearing onto a weightless soil and the finite-deformation expansion of a cylindrical cavity