一个基于微观力学分析的散粒体应力–剪胀关系  

Micromechanics-based stress-dilatancy relationship for granular materials

作　　者：刘洋[1] 于鹏强 张铎 王肖肖 LIU Yang;YU Peng-qiang;ZHANG Duo;WANG Xiao-xiao(Department of Civil Engineering,University of Science and Technology Beijing,Beijing 100083,China;Underground Space Engineering Technology Center,Central South Architectural Design Institute Co.,Ltd.,Wuhan 430071,China)

机构地区：[1]北京科技大学土木工程系,北京100083 [2]中南建筑设计院地下空间工程技术中心,湖北武汉430071

出　　处：《岩土工程学报》2021年第10期1816-1824,共9页Chinese Journal of Geotechnical Engineering

基　　金：国家自然科学基金项目(51178044)。

摘　　要：从微观力学角度出发,基于真应力张量推导了散体中平均接触力与平均接触位移的计算公式,并通过宏–微观能量守恒得到了考虑散体各向异性组构及其演化的应力–剪胀关系;详细分析了剪胀参数的物理意义及对剪胀性的影响,并与经典的剑桥流动法则、Rowe剪胀方程以及室内试验结果进行了比较分析。研究结果表明,提出的应力–剪胀关系宏微观物理意义明确,考虑了材料密实状态和微观各向异性组构及其演化对应力–剪胀关系的影响,可以很好地模拟散粒体的初始剪胀(缩)行为,并可反映峰值应力比滞后于最大剪胀比的现象。同时提出的应力–剪胀方程还可以描述材料在相变点处应力比不等于临界应力比的现象,与已有室内试验结果一致,能够较好地预测散体材料三轴条件下的各向异性应力–剪胀关系。From the perspective of micromechanics,the formulas for the average contact force and contact displacement in the granular are derived based on the true stress tensor,then the stress-shear dilatancy relationship considering the fabric anisotropy and its evolution is obtained through the macro-micro energy conservation.In addition,the physical meaning of dilatancy parameters and their influence on dilatancy are analyzed.Finally,the proposed formulation is compared with the classical Cambridge flow law,Rowe dilatancy equation and test results to calibrate its reasonableness and applicability.The proposed stress-dilatancy relationship with clear physical meaning can describe the initial dilatancy(contraction)behavior for granular materials,considering the anisotropic evolution of fabric and the influence of the density on the dilatancy.Moreover,the proposed stress-dilatancy equation can reflect that the stress ratio at the phase transition point is less than the critical stress ratio and the peak stress ratio emerges behind the maximum dilatancy ratio.It is in good agreement with the test results and can better predict the anisotropic stress-dilatancy relationship of granular materials.

关 键 词：应力–剪胀关系 微观力学 组构演化 能量守恒 

分 类 号：TU431[建筑科学—岩土工程]