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.

本文针对所有现有的塑性本构模型中的准静态圆柱腔扩张问题提出了统一而严格的解决方案。Chen和Abousleiman提出了严格的p ^'和q三维定义。然后，p - q应力空间在圆柱坐标系中转换为三个应力分量。针对圆柱坐标系中的三个应力分量，编写了圆柱孔扩张的支配偏微分方程（PDE），包括应力平衡方程，本构方程，一致性方程，连续性方程和排水条件。 。随后将PDE简化为常微分方程（ODE），可以通过相似性变换将其归纳为统一矩阵形式。通过使用商用ODE求解器（例如MATLAB）对ODE进行数值求解，可以立即获得严格的半解析解。拟议的求解程序是通用的，并且可以应用于所有可塑性本构模型中的排水和不排水条件。最后，通过数值分析讨论了局部排空效应，并提出了考虑局部排空效应的经验方程式，以计算极限有效径向应力和孔壁处的过大孔隙压力。