This paper presents an analytical solution for combined vertical and torsional shear loading of a cylindrical cavity in undrained modified Cam‐Clay. The governing partial differential equations for the cylindrical cavity are established in the polar coordinate. The problem is formulated as a set of first‐order differential equations by using the axisymmetric condition, equilibrium equations, and elastic‐plastic constitutive relationship. The influence of the second shear loading on the initial shear strain is considered in the plastic state. Then the stress‐strain distributions can be calculated by integrating within the elastic and plastic zones around the cavity. A finite element method simulation of the cavity under combined shear loading is established to verify the proposed approach, and the results are in good agreement with the proposed analytical solution. Parametric analyses are carried out on the effects of clay overconsolidation ratios and in situ stress coefficients under different loading paths and loading ratios. The results show that the combined shear loading on the cavity wall has a significant effect on the stress distribution of the surrounding soil, and the influence of the loading path cannot be neglected.

中文翻译：

---

不排水改性 Cam-Clay 中圆柱形空腔的垂直和扭转剪切联合载荷的解析解


本文提出了不排水改性 Cam-Clay 中圆柱形空腔的垂直和扭转剪切联合载荷的解析解。在极坐标下建立了圆柱腔的控制偏微分方程。利用轴对称条件、平衡方程和弹塑性本构关系将问题表述为一组一阶微分方程。在塑性状态下考虑第二次剪切载荷对初始剪切应变的影响。然后可以通过在型腔周围的弹性和塑性区域内积分来计算应力应变分布。建立了联合剪切载荷下空腔的有限元模拟来验证所提出的方法，结果与所提出的解析解非常吻合。对不同加载路径和加载比下粘土超固结率和地应力系数的影响进行了参数分析。结果表明，空腔壁的联合剪力载荷对周围土体的应力分布有显着影响，且加载路径的影响不可忽视。