基于统一状态参数模型的砂中柱孔扩张分析

An analysis of cylindrical cavity expansion in sand based on a unified state parameter model

目前关于不同初始状态砂土砂中柱孔扩张的研究结果还缺乏更深层次的分析,并且由于没有考虑砂土屈服面形状因素的影响,造成许多研究成果难以在不同类型砂土中推广。采用统一状态参数模型(clay and sand model,CASM)和Rowe剪胀方程来描述砂的弹塑性变形特点,结合大变形理论并引入辅助变量,推导了基于拉格朗日描述的弹塑性区内砂土体积和有效应力的一阶偏微分方程组,在此基础上结合弹塑性区的边界条件和柱孔扩张弹性解,建立了饱和砂中的排水柱孔扩张半解析解。结果表明,CASM可以通过改变应力状态参数n和间距比r*的值使砂的屈服面形状发生改变,进而使文中解答能够用于不同类型饱和砂中的排水柱孔扩张计算,其中n、r*值越大,松砂初次屈服时的偏应力和后续砂中的扩孔压力越大,但中密、密实砂土中的情况与松砂完全相反。极限扩孔压力随砂土初始状态参数的减小而增大,相应的砂土体积也从一直剪缩变为先剪胀后剪缩,弹塑性区半径先减小后增大,硬化行为从一直硬化变为先软化后硬化。静止侧压力系数增大时,极限扩孔压力也增大,但对砂的体积变化规律影响不大。本研究可为相关岩土工程问题分析提供可靠理论支持。

The current studies of the cylindrical cavity expansion in sand still lack a deeper analysis for the results obtained in sands with different initial states.In addition,most of previous studies have not considered the influence of the shape of yield surface of sand,which made their results difficult to be popularized in different types of sand.In order to obtain a general solution to expansion of cylindrical cavity in sand under the drained condition,a unified state parameter model-clay and sand model(CASM)with Rowe’s stress–dilatancy relation is used to describe the characteristics of elastic-plastic deformation of sand.By employing that large strain occurs in sand and introducing an auxiliary variable,several partial differential equations to calculate the effective stress and specific volume of sand in the elastoplastic zone are derived on the basis of the Lagrangian description.Under the elastic-plastic boundary conditions and the elastic solution of cylindrical cavity expansion,a semi-analytical solution for drained cylindrical cavity expansion in sand is obtained by solving the governing equations numerically.The results show that the solution of cylindrical cavity expansion established in this paper can be used in many types of sand by changing the values of stress-state parameter n and spacing ratio r*to select an appropriate shape of yield surface of sand,and the greater the values of n,r*are,the greater the initial yield deviatoric stress of loose sand and the subsequent expansion pressure,but these situations will reverse in medium dense and dense sand.The ultimate expansion pressure increases with the decreasing initial state parameter of the sand,and together with the volume variation rule of sand changes from always contraction into dilatation first and then contraction,the radius of the elastic-plastic zone decreases first and then increases,and the hardening response of sand changes from always hardening into softening first and then hardening.The ultimate expansion pressure increases with the increasing coefficient of earth pressure at rest of sand,but the volume change law of sand has little change.This study provides a reliable theoretical support for the analysis of related geotechnical engineering problem.