Study on Nonlinear Viscoelastic Constitutive Equations for Rock

Abstract

Numerical simulation is one of the effective tools for the long-term stability assessment of underground structures. The reliability improvement of the numerical simulation requires precise constitutive equations to reproduce time-dependent behavior of rock such as loading-rate dependence, creep, and relaxation. These time-dependent behaviors of rock have nonlinearity between stress and strain rate and are influenced by surrounding environment. A number of constitutive equations have been proposed in previous studies; however, the equations based on the theory of linear viscoelasticity have difficulty reproducing accurately the time-dependent behavior of rock, and most of the equations based on the theory of viscoplasticity have been applied to the limited loading condition such as creep. In this article, nonlinear viscoelastic constitutive equations for rock proposed by the authors were introduced, and their exact solutions and application to experimental results were summarized. These equations can reproduce nonlinear time-dependent behavior and not only brittle but also ductile failures of rock and can be applied to the behavior under various loading conditions and experiment environment. In the equations, compliance or inelastic strain is assumed to be increased with time, but the functions and their combinations are of great variety. Hence, the differences of the solutions and applicability of the equations were detailed, and in addition future subjects were presented.