Linearization of elasto‐plastic consolidation equations

Abstract

In the framework of the finite element method, the problem of elasto‐plastic consolidation gives rise to a system of non‐linear, coupled residual equations which satisfy the conditions of balance of momentum and balance of mass. In determining the roots of these equations it is necessary that the coupled equations be linearized. To this end, the concept of ‘consistent linearization’ proposed by Simo and Taylor for a single‐phase system is applied to the two‐phase soil‐water system. The roots of the coupled residual equations are solved iteratively by employing Newton's method. It is shown that in non‐linear consolidation analyses, the use of a tangent coefficient matrix derived consistently from the integrated constitutive equation defining the characteristics of the solid skeletal phase results in an iterative solution scheme which preserves the asymptotic rate of quadratic convergence of Newton's method. Numerical examples involving combined radial and vertical flows through an elasto‐plastic soil medium are presented to demonstrate the computational superiority of the above technique over the method based on standard ‘elasto‐plastic continuum formulations’ adopted in most finite element codes.