Abstract This paper presents a semi-analytical solution for undrained cylindrical cavity expansion in modified Cam-clay soils under biaxial in-situ stresses based on the small strain and large strain assumptions in the elastic and plastic regions, respectively. The cylindrical cavity expansion problem is treated as a boundary value problem and formulated by solving a system of first-order differential equations with four stress components as basic unknown variables. The validity of the proposed solution is examined by comparing with the existing solution, where the in-situ stress is uniform. Extensive parametric studies are conducted to investigate the effects of biaxial in-situ stresses on the stress distribution, the expansion process and the shape and size of elastic-plastic boundary. The results indicate that the elastic-plastic boundary is in the shape of an ellipse due to the shear stress induced by biaxial in-situ stresses. The major axis of the elliptical elastic-plastic boundary is in accordance with the direction of the larger in-situ stress. The present solution is free of the limitation that the cavity expands under the uniform in-situ stress, therefore it is expected to provide a more general method for practical geotechnical and petroleum problems.

中文翻译：

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改性凸轮粘土中不排水圆柱腔膨胀：考虑双轴地应力的半解析解

摘要 本文分别基于弹性和塑性区域的小应变和大应变假设，提出了双轴原位应力下改性凸轮粘土中不排水圆柱空腔膨胀的半解析解。圆柱腔膨胀问题被视为边值问题，并通过求解具有四个应力分量作为基本未知变量的一阶微分方程组来表示。通过与原位应力均匀的现有解决方案进行比较来检验所提出的解决方案的有效性。进行了广泛的参数研究，以研究双轴原位应力对应力分布、膨胀过程以及弹塑性边界的形状和尺寸的影响。结果表明，由于双轴原位应力引起的剪切应力，弹塑性边界呈椭圆形。椭圆形弹塑性边界的长轴与较大的地应力方向一致。本方案不受均匀地应力作用下空腔膨胀的限制，有望为实际岩土和石油问题提供更通用的方法。