粗粒土三维细观组构与本构关系研究

STUDY OF MICROFABRIC AND CONSTITUTIVE RELATION OF GRANULAR MATERIAL

运用数学统计方法研究具有方向和大小的粗粒土组构、接触力、枝矢量等与粗粒土本构之间的多尺度关系。通过统计概率的方法进行分析含有一定项数单位向量的多项式接触方向概率分布密度函数(组构张量)和矩张量;运用最小二乘法来确定组构张量展开成3种不同形式多项式表达式系数,建立3种形式组构张量与已知数据统计表达式之间的联系,通过正交分解使展开式各项相互独立,构建粗粒土细观参数组构、接触力、枝矢量与粗粒土应力的表达式。对比钢珠三轴试验和数值计算的宏细观应力,二者结果基本一致,且二阶颗粒接触法向接触密度分布函数能较好描述颗粒接触组构。研究得到的粗粒土细观参数应力表达式为三维条件下粗粒土应力–接触力–组构数值模拟奠定理论基础。

Coarse aggregate multi-scale study is mainly to establish the connection between fabric,contact forces,branch vector and constitutive relation,through probability statistics method for the direction and magnitude of the coarse aggregate orientational tensor. It gets a certain number of unit vector directional of contact probability distribution density function（fabric） and moment tensor by the method of statistical probability. The fabric tensor spread out three different forms polynomial expressions using least-square method to determine correlation coefficients. Three types of fabric tensor and the known data expression of statistics the relationship are set up. Orthogonal decomposition is used to make expansion independent with each other. Coarse aggregate stress expressions which included microstructure parameters fabric,contact force and branch vector are built. Compared with steel balls triaxial test and numerical calculation contrast macro-mesoscopic stress,two results are consistent. The simulation results indicate that second-rank contact normal density distribution function give reasonable approximations. A theoretical basis has been established for numerical simulation and the stress expressions for coarse aggregate microscopic parameters under the condition of three dimensional stress-contact force-fabrics.