The paper combines experimental and numerical analyses to study the relation between small strain stiffness and micro-structure of an idealized granular material under isotropic and anisotropic stress conditions. Results from the resonant column device on glass ballotini show that the relation between the maximum shear modulus and anisotropic stress components strongly depends on the applied stress path. Discrete element simulations (DEM) are performed to investigate the material behaviour along isotropic compression, triaxial compression and constant $$\hbox {K}_0$$ deformation. The DEM analysis reveals that each stress path is associated with a characteristic evolution of the coordination number, i.e., the average number of contacts per particle. In turn, the maximum shear modulus is found to be a direct function of the coordination number. In order to include the micro-structure interpretation in the analytical description, a modified version of Hardin’s relation is proposed as a function of coordination number, void ratio and mean pressure.

中文翻译：

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颗粒材料中的各向异性应力状态和小应变刚度：RC 实验和 DEM 模拟

本文结合实验和数值分析，研究了理想化颗粒材料在各向同性和各向异性应力条件下小应变刚度与微观结构之间的关系。玻璃ballotini 上共振柱装置的结果表明，最大剪切模量和各向异性应力分量之间的关系在很大程度上取决于施加的应力路径。执行离散元模拟 (DEM) 以研究沿各向同性压缩、三轴压缩和恒定 $$\hbox {K}_0$$ 变形的材料行为。DEM 分析表明，每个应力路径都与配位数的特征演变有关，即每个粒子的平均接触数。反过来，发现最大剪切模量是配位数的直接函数。