Numerical Implementation of the Transformed Stress Method for 3D Generalization of Soil Constitutive Models

Abstract

Conducting three‐dimensional (3D) numerical simulation is of great importance for accurately analyzing the stress and deformation of complex geotechnical structures. The transformed stress (TS) method provides an ingenious theory for the 3D generalization of soil constitutive models, but studies on its numerical implementation are limited. This paper first illustrates the basic idea of the TS method by showing how to obtain a 3D yield surface from the triaxial compression yield locus. According to the evolution trend of the Matsuoka‐Nakai yield locus on the deviatoric plane, a revised expression is proposed to determine the TS tensor when tensile stress appears. As an example, the Modified Cam‐clay model is generalized to be 3D, and its stress integration is implemented using the closest point projection method. Partial derivatives of the TS are efficiently calculated by the implicit differentiation method, while various singularity problems in special cases are overcome. Single‐element testing under different loading conditions and tunnel excavation simulation demonstrate that the proposed stress integration algorithm has high accuracy and strong convergence. Based on this work, the potential capability of the TS method in geotechnical structure analysis is displayed.