A smooth hyperbolic approximation to the Generalised Classical yield function, including a true inner rounding of the Mohr-Coulomb deviatoric section

Abstract

A new yield function recently introduced by Lagioia and Panteghini (2016), herein referred to as the Generalised Classical (GC) yield function, combines a series of criteria commonly used in geotechnical analysis into a single equation, including those of Tresca, Mohr-Coulomb and Matsuoka-Nakai. This makes for efficient implementation of multiple criteria into finite element software, and in this paper two key improvements are made to further enhance the usefulness of the GC yield function. The first is the development of a new expression for the shape parameter γ, corresponding to the so-called ‘Inner Mohr-Coulomb’ option, which ensures that a true inner rounding of the hexagonal Mohr-Coulomb deviatoric section is always obtained. The second is the introduction of a hyperbolic rounding to eliminate a discontinuity which can occur at the tip in the meridional section of the GC yield surface. The resulting yield surface is at least C2 continuous everywhere, provided a rounded criterion is selected, and can thus be used in consistent tangent finite element formulations. The results of finite element analyses carried out for two benchmark problems (a thick cylinder and a rigid strip footing) demonstrate the benefits of the rounding techniques in the new yield surface. Comparisons are made with the original yield surface and also the Hyperbolic Rounded Mohr-Coulomb (HRMC) yield surface originally developed by Abbo and Sloan (1995).