A unified and rigorous solution for quasi-static cylindrical cavity expansion in plasticity constitutive models

Abstract This paper presents a unified and rigorous solution for the quasi-static cylindrical cavity expansion problem in all existing plasticity constitutive models. Rigorous three-dimensional definitions of p’ and q are used as proposed by Chen & Abousleiman. Then, the p-q stress space is transformed to the three stress components in a cylindrical coordinate system. The governing partial differential equations (PDEs) for cylindrical cavity expansion, including the stress equilibrium equation, the constitutive equation, the consistency equation, the continuity equation, and the drainage conditions, are written with respect to the three stress components in a cylindrical coordinate system. The PDEs are subsequently reduced to ordinary differential equations (ODEs), which can be summarized in unified matrix form by means of a similarity transformation. A rigorous semi-analytical solution can immediately be obtained by numerically solving the ODEs using commercial ODE solvers, such as MATLAB. The proposed solution procedure is general and can be applied to both the drained and undrained conditions in all plasticity constitutive models. Finally, the partially drained effect was discussed through numerical analysis, and empirical equations considering the partially drained effect were proposed for calculating the limit effective radial stress and excess pore pressure at the cavity wall.