考虑非饱和土吸力效应的圆柱孔扩张有效应力解析  

Effective Stress Solution for the Cylindrical Cavity Expansion in Unsaturated Soil Considering Suction Effect

作　　者：翟张辉 张亚国[2] 李同录[1] 黄沛[2] ZHAI Zhanghui;ZHANG Yaguo;LI Tonglu;HUANG Pei(School of Geological Eng.and Surveying,Chang’an Univ.,Xi’an 710054,China;School of Civil Eng.,Chang’an Univ.,Xi’an 710061,China)

机构地区：[1]长安大学地质工程与测绘学院,陕西西安710054 [2]长安大学建筑工程学院,陕西西安710061

出　　处：《工程科学与技术》2020年第3期100-106,共7页Advanced Engineering Sciences

基　　金：国家自然科学基金项目(41807242,51608042);中央高校基本科研业务费专项项目(300102289102)。

摘　　要：为探究吸力效应对圆柱孔周围土体应力应变的影响,推导了非饱和土中的圆柱孔扩张有效应力析解。在弹性区和塑性区分别采用Hooke定律和修正剑桥模型,将非饱和吸力作为硬化参数,建立圆柱孔周围土体的应力应变控制方程。通过引入辅助变量,将欧拉坐标系下的平衡微分方程转至拉格朗日坐标系,非饱和圆柱孔扩张问题转换为以弹塑性边界为边值条件求解1阶常微分方程组的问题。以弹塑性边界上的应力和初始比体积作为初值,对非饱和土中圆柱孔扩张问题进行分析。结果表明:受扩孔压力作用,圆柱孔周围土体将从弹性状态进入塑性屈服状态,土体初始吸力的变化对塑性区应力状态影响显著。随着初始吸力的增加,圆柱孔周围相同位置处的土体各应力分量增大,极限扩孔压力也随之增大。对于初始孔隙比较大的疏松土体,吸力增大使得圆孔周围塑性区范围缩小;塑性区土体比体积沿径向呈单调减小,吸力越大,比体积减小越明显。对于初始孔隙比较小的密实土体,吸力变化对塑性区范围大小影响不明显;塑性区内土体比体积沿径向先增大后减小。这是因为在弹塑性边界附近处出现了剪胀现象,且吸力越大,剪胀现象越明显。最后,通过与原位旁压试验和已有数值模拟结果对比,对本文方法的可靠性进行了验证。To investigate the suction effect on the stress and strain of soil around cylindrical cavity,the analytical solution of effective stress in unsaturated soils was derived.In the elastic and plastic regions,the Hooke’s law and the modified Cam-Clay model were respectively employed.Taking suction as a hardening parameter,the governing equations about stress-strain around the cylindrical cavity were established.By introducing the auxiliary variable,the equilibrium differential equation in Eulerian system was transformed into Lagrangian system.The cylindrical cavity expansion in unsaturated soils was analyzed by solving the first-order ordinary differential equations where the elastic-plastic boundary was the initial conditions.Taking the values of stress and specific volume at the elastic-plastic boundary as initial values,the effects of suction and initial specific volume on the distributions of stress and strain were calculated and analyzed.The results showed that the soil around the cylindrical cavity changed from elastic state to plastic state due to the cavity expansion,and the suction had a significant effect on the stress state of plastic region.With the suction increase,three stress components,as well as the ultimate cavity pressures increased.For loose soils with larger void ratio,the ranges of plastic region reduced with the suction increasing.The specific volume decreased monotonously along the radial direction,which tended to be obvious as the suction increasing.However,for dense soils with smaller void ratio,the effect of suction on the ranges of plastic region was so small that could be ignored.The specific volume near the elastic-plastic boundary increased due to the dilatancy occurring.The larger the suction were,the more obvious of the dilatancy appeared.Finally,the reliability of the proposed method was verified by comparing with the data from lateral pressure test and calculation by the finite element method.

关 键 词：非饱和土 吸力 圆柱孔扩张 修正剑桥模型 旁压试验 

分 类 号：TU473[建筑科学—结构工程]