A C2 continuous approximation to the Mohr–Coulomb yield surface

In spite of the development of more sophisticated constitutive models for soil, the Mohr–Coulomb yield criterion remains a popular choice for geotechnical analysis due to its simplicity and ease of use by practising engineers. The implementation of the criterion in finite element programs, however, presents some numerical difficulties due to the gradient discontinuities which occur at both the edges and the tip of the hexagonal yield surface pyramid. Furthermore, some implicit techniques utilising consistent tangent stiffness formulations are unable to achieve full quadratic convergence as the yield criteria is not C2 continuous. This paper extends the previous work of Abbo and Sloan (1995) through the introduction of C2 continuous rounding of the Mohr–Coulomb yield surface in the octahedral plane. This approximation, when combined with the hyperbolic approximation in the meridional plane (Abbo and Sloan, 1995), describes a yield surface that is C2 continuous at all stress states. The new smooth yield surface can be made to approximate the Mohr–Coulomb yield function as closely as required by adjusting only two parameters, and is suitable for consistent tangent stiffness formulations.