This paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in non-associated Mohr-Coulomb soil under non-hydrostatic initial stress field (i.e., arbitrary K_0 values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen & Wang in 2022 for the special in situ stress case with K_0 = 1. The new generalized, graph-based theoretical framework contains two essential components: the geometrical analysis to track the stress path trajectory/evolution in different sectors of the deviatoric plane; and a full Lagrangian formulation of both the constitutive relationship and radial equilibrium equation to analytically determine the representative soil particle responses at the cavity surface. It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K_0 being involved. The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr-Coulomb plastic regions. The analytical closed-form solutions developed herein can be regarded as a definitive one for the undrained cavity expansion problem in classical Mohr-Coulomb materials without the approximations and simplifications in previous solutions, and will be of great value for the interpretation of pressuremeter tests in cohesive-frictional soils.

中文翻译：

---

K_0 固结莫尔-库仑土中不排水圆柱孔洞膨胀的完整图形解

本文通过展开独特且有效的图形，针对非静水初始应力场（即土压力系数的任意 K_0 值）下非关联莫尔-库仑土中的不排水圆柱形空腔膨胀问题开发了一个通用且完整的解决方案Chen & Wang 最近在 2022 年针对 K_0 = 1 的特殊原位应力情况提出了求解程序。新的广义的、基于图形的理论框架包含两个基本组成部分：跟踪不同部门的应力路径轨迹/演化的几何分析偏平面的；以及本构关系和径向平衡方程的完整拉格朗日公式，用于分析确定空腔表面的代表性土壤颗粒响应。有趣的是，对于涉及 K_0 的所有不同情况，空腔膨胀偏应力路径总是由一系列分段直线组成。目前通用图形方法的显着优势/特征在于它可以推导出全封闭形式的空腔膨胀响应，但不受垂直应力中介假设的限制和传统分区方法存在的困难这涉及对不同的 Mohr-Coulomb 塑性区域进行繁琐的连续测定。本文开发的解析解可被视为经典莫尔-库仑材料中不排水空腔膨胀问题的权威解决方案，无需先前解决方案中的近似和简化，