饱和粘土中球孔扩张问题弹塑性解析

Elastic-plastic solution of sphere cavity expansion in saturated clay

为了研究静力触探试验及沉桩扩孔等工程问题,基于修正剑桥模型,推导了不排水条件下球孔扩张问题的半解析解.将扩张球孔周围土体分为临界状态区、塑性区以及弹性区三个区域.弹性区内,利用弹性理论得到应力和孔隙水压力的解答;临界状态区及塑性区内,利用相关联的流动法则、拉格朗日分析法建立了关于应力的一阶非线性常微分方程组,以弹塑性界面处的应力分量作为初值,求解微分方程组可得到应力和孔隙水压力的解答.研究结果表明:各向同性超固结比对扩孔压力、土体应力、超孔隙水压力以及塑性区范围均具有显著影响,且扩孔过程中土体剪切模量并非常量,其随扩孔半径、各向同性超固结比的变化而变化;同时通过与已有解答进行比较,对本文方法的可靠性进行了验证.

An exact semi-analytical solution in the undrained cavity expansion can be obtained on the basis of the MCC model to research the cone penetration test and the pile driving. The field around the cavity can be divided into three zones： critical zone, plastic deformation zone and elastic deformation zone. In the elastic zone, an analytical solution for the distributions of stress and excess pore pressure is deduced according to the elastic theory. In the critical and plastic zone, a set of first-order nonlinear ordinary differential equations concerning stress can be obtained according to the associated flow rule and the lagrangian analysis method. The stressss and pore pore pressure can be solved as an initial value problem starting at the elastic-plastic boundary. The results show that the isotropic over consolidation ratio has a significant influence on the stresses and the excess pore pressure.The shear modulus vary significantly with the cavity radius and the isotropic over consolidation in the course of cavity expansion.