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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。
Mathematical statistical methods are used to study the multi-scale relations between coarse grained soil structure, contact force, branch vector, and coarse grained soil with direction and size. Through the method of statistical probability, the polynomial contact direction probability distribution density function (tensor tensor) and moment tensor of a unit item vector with a certain number of elements are analyzed. The least square method is used to determine the structure tensor and expanded into three different forms of polynomial expressions The coefficients of the three kinds of formal tensions and the statistical expressions of the known data are established. The orthogonal expansions make the expansions independent of each other, and the microstructure parameters of the coarse grained soil are constructed. The contact force, the branch vector The expression of stress with coarse grained soil. Comparing the three-axis test of the steel ball and the numerical calculation of the macro-scale stress, the results of the two are basically the same, and the second-order particle contact normal contact density distribution function can better describe the particle contact structure. The micromechanical parameters of the coarse-grained soils, which are obtained from the study, lay a theoretical foundation for numerical simulation of the stress-contact force-structure of coarse grained soils under three-dimensional conditions.