This paper develops a complete analytical solution for the drained (or dry) cylindrical cavity expansion in non-associated Mohr-Coulomb soil, by using the graphical approach and Lagrangian formulation of the cavity boundary value problem (through tracing the responses of a single soil particle at the cavity wall). The novelty of the new solution lies not only in the relaxation of the strict intermediacy assumption for the vertical stress as usually adopted in the previous analyses, but in the comprehensive consideration of arbitrary values of K_0, the coefficient of earth pressure at rest, as well. The essence of the so-called graphical method, i.e., the unique geometrical analysis and tracking of the deviatoric stress trajectory, is fulfilled by leveraging the deformation requirement that during drained expansion the progressive development of the radial and tangential strains must maintain to be compressive and tensile, respectively. With the incorporation of the radial equilibrium condition, the problem is formulated to solve a single first-order differential equation for the internal cavity pressure with respect to a pivotal auxiliary variable, for all the distinct scenarios of K_0 being covered. Some selected results are presented for the calculated cavity expansion curve and limit cavity pressure through an example analysis.

中文翻译：

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Mohr-Coulomb 岩土材料中圆柱形空腔膨胀的图形理论框架

本文通过使用空腔边界值问题的图形方法和拉格朗日公式（通过跟踪单个土壤颗粒的响应），为非相关莫尔-库仑土壤中的排水（或干燥）圆柱空腔膨胀开发了一个完整的解析解在空腔壁上）。新解的新颖之处不仅在于放宽了以往分析中通常采用的竖向应力的严格中介假设，还在于综合考虑了静止土压力系数K_0的任意取值，以及. 所谓图解法的本质，即对偏应力轨迹的独特几何分析和跟踪，通过利用变形要求来实现，即在排水膨胀期间，径向和切向应变的逐渐发展必须分别保持压缩和拉伸。结合径向平衡条件，针对关键辅助变量求解内部空腔压力的单个一阶微分方程，涵盖 K_0 的所有不同情况。通过实例分析，给出了计算出的型腔膨胀曲线和极限型腔压力的部分结果。该问题被制定为针对关键辅助变量求解内腔压力的单个一阶微分方程，涵盖了 K_0 的所有不同场景。通过实例分析，给出了计算出的型腔膨胀曲线和极限型腔压力的部分结果。该问题被制定为针对关键辅助变量求解内腔压力的单个一阶微分方程，涵盖了 K_0 的所有不同场景。通过实例分析，给出了计算出的型腔膨胀曲线和极限型腔压力的部分结果。