This paper presents analytical solutions for the finite expansion problems of a spherical or cylindrical cavity, using a simple yet novel graphical approach recently proposed by Chen & Abousleiman in 2022, in both original Cam Clay (OCC) and modified Cam Clay (MCC) soils under undrained conditions. It is shown that, for a soil mass subjected to isotropic in situ stress conditions, the stress paths in the deviatoric plane for the spherical and cylindrical cavity expansions turn out to be two straight lines, which correspond to Lode angles equal to $\frac{11\pi }{6}$ and $\frac{5\pi }{3}$, respectively. The desired limiting cavity pressure therefore can be directly and accurately evaluated through simple numerical integration with respect to the mean effective stress, while the relationship between the internal cavity pressure and the cavity radius, the cavity expansion curve, may be equally conveniently determined. Numerical results obtained from the current graphical method, for a range of the values of over consolidation ratio considered, compare extremely well with those from the conventional semianalytical formulations of the undrained cavity problem that involve solving a system of coupled governing differential equations. It is interesting to note that the representative and approximate solution developed by Collins & Yu in 1996 indeed is a correct one for the spherical cavity expansion problem, and, with minor modifications, will be applicable for the accurate calculation of the responses of the cylindrical cavity as well.

中文翻译：

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重新审视临界状态土壤中不排水的空腔膨胀问题：一种简单的基于图形的方法

本文使用 Chen 和 Abousleiman 最近在 2022 年提出的一种简单而新颖的图形方法，在原始凸轮粘土 (OCC) 和改良的凸轮粘土 (MCC) 土壤中提出了球形或圆柱形腔的有限膨胀问题的解析解。不排水的条件。结果表明，对于承受各向同性地应力条件的土体，球形和圆柱形空腔膨胀的偏平面中的应力路径结果是两条直线，对应的 Lode 角等于$\frac{11\pi }{6}$和$\frac{5\pi }{3}$， 分别。因此，通过对平均有效应力的简单数值积分，可以直接准确地评估所需的极限型腔压力，同时可以同样方便地确定内部型腔压力与型腔半径之间的关系，即型腔膨胀曲线。从当前图形方法获得的数值结果，对于所考虑的一系列过固结比值，与不排水空腔问题的传统半解析公式（涉及求解耦合控制微分方程组）的结果进行了非常好的比较。有趣的是，Collins & Yu 在 1996 年开发的具有代表性的近似解确实是解决球形空腔膨胀问题的正确解，并且，