非饱和土中圆柱孔扩张问题不排水解答及吸力影响效应分析  

Critical cylindrical cavity expansion in unsaturated soil under undrained conditions incorporating suction effects

作　　者：张亚国[1] 翟张辉 梁发云[3] 李同录[2] ZHANG Ya-guo;ZHAI Zhang-hui;LIANG Fa-yun;LI Tong-lu(School of Civil Engineering,Chang'an University,Xi'an 710061,China;School of Geological Engineering and Surveying,Chang'an University,Xi'an 710054,China;Department of Geotechnical Engineering,Tongji University,Shanghai 200092,China)

机构地区：[1]长安大学建筑工程学院,陕西西安710061 [2]长安大学地质工程与测绘学院,陕西西安710054 [3]同济大学地下建筑与工程系,上海200092

出　　处：《岩土工程学报》2021年第4期734-742,共9页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金青年基金项目(41807242);中央高校基本科研业务费专项项目(300102281202)。

摘　　要：圆柱孔扩张理论为沉桩挤土及旁压试验分析等提供了理论基础,然而已有研究多是针对饱和土展开,在非饱和土相关工程中并不适用。基于修正剑桥临界状态模型,对非饱和土中不排水条件下的圆柱孔扩张问题进行求解。在考虑非饱和土吸力效应的情况下推导土体应力–应变关系式,并引入反映吸力与比体积之间关系的液相本构方程。在此基础上联立圆柱孔周围土单元平衡微分方程,最终将非饱和土中的圆柱孔扩张问题归结为求解一阶偏微方程组的问题。通过引入辅助变量将所有方程转至拉格朗日系下,以弹塑性边界上的应力及比体积作为初值条件对其进行求解。结果表明:当非饱和吸力增大时,圆柱孔周围土体应力和扩孔压力均随之增大,说明土体出现了吸力硬化效应;对于初始比体积较小的土体,随着塑性区内的径向位置增加,比体积和吸力会出现先增大后减小的变化特征,说明圆柱孔在不排水扩张过程中局部土体发生了剪胀。所采用的本构关系较为简洁,参数易于确定,便于在非饱和土相关的工程问题得到实际应用。The cylindrical cavity expansion theory provides the theoretical basis for analysis of pile installation and pressuremeter tests. However, most of the studies are conducted on cavity expansion in saturated soil, and are unsuitable for solving the engineering problem in unsaturated soil. Therefore, based on the critical state soil model, the cylindrical cavity expansion in unsaturated soil under undrained conditions is solved. The stress-strain relationship is derived considering suction effects. Meanwhile, a constitutive equation for the relationship between the suction and the void volume is introduced. Combing the radial equilibrium equation, the formulation of the problem is reduced to solving a system of the first-order ordinary differential equations. Introducing an auxiliary variable, all of the differential equations are transferred to the Lagrangian description and solved by taking the values at the elasto-plastic boundary as the initial value. The results show that the soil stresses and the cavity expansion pressure increase as the suction increases, which can be regarded as the suction-stiffening effects. For the soil with low initial ratio volume, the partial volume and the suction in the plastic zone firstly increase, and then decrease, which implies that the shear dilatancy occurs during the cavity expansion. The results have a potential application in the related projects owing to the simple constitutive relation and available parameters.

关 键 词：非饱和土 不排水条件 圆柱孔扩张 吸力 弹塑性解 

分 类 号：TU431[建筑科学—岩土工程]