饱和结构性黄土不排水柱孔扩张问题弹塑性解

Elastic-plastic Solution for Undrained Expansion of Cylindrical Cavity in Saturated Structured Loess

摘要:

为导出饱和黄土中不排水柱孔扩张问题严格解，采用结构性黄土修正剑桥模型描述黄土力学特性。在弹性区采用小变形假设求解孔周土体应力与变形，同时将塑性区柱孔扩张边值问题转化为3个以应力分量为基本未知量的一阶非线性常微分方程求解问题。以弹塑性界面上应力分量作为初始条件求解控制方程，得到孔周塑性区应力分布，然后对径向平衡方程积分求得孔隙水压力。通过算例分析验证了该方法的正确性。结果表明：退化解与已有数值解完全吻合，并且黄土结构性对孔周应力、超静孔压以及弹塑性半径等影响显著。

Abstract:

To derive a rigorous solution for undrained expansion of cylindrical cavity， the modified Cam-clay model of structured loess was employed to describe the mechanical properties of loess. The small deformation assumption was used to solve the soil stress and deformation in the elastic zone around the cavity. Besides， the boundary value problem of cylindrical cavity expansion can be transformed into three first-order nonlinear ordinary differential equations with the stress component as the basic unknown quantity in the plastic region. The governing equation was solved by using the stress component on the elasto-plastic interface as the initial condition to obtain the stress distribution in the plastic zone around the cavity， then the pore water pressure was derived by integrating the radial equilibrium equation. The correctness of the method in this paper is verified by parameter analysis. The results show that the degenerate solution is completely consistent with the existing numerical solution， and the soil structure has a significant effect on the stress component， the specific volume， the excess pore water pressure， and elastic-plastic radius.