DEM simulations of the small strain stiffness of granular soils: effect of stress ratio

Abstract

DEM (discrete element method) simulations are carried out to evaluate the small strain stiffness (i.e. Young’s modulus and shear modulus) of a granular random packing with focus on the effect of stress ratio (SR). The results show that the Young’s modulus in a given direction generally depends on the stress component in that direction. The Young’s modulus normalized by the related stress component remains nearly constant when SR is less than a threshold value $SR_\mathrm{th}$. When SR is larger than $SR_\mathrm{th}$, the normalized Young’s modulus decreases, particularly in the minor principle stress direction. Moreover, the Young’s modulus during unloading is always smaller than the one during loading at the same stress state, which indicates that the microstructure of the specimen has been modified by the historical shearing process. The shear modulus mainly depends on the mean effective stress and shows similar evolution trend as the Young’s modulus. This study finds that the macroscopic stiffness of the specimen is closely related to the evolutions of particle contact number and contact force during shearing. When SR is less than $SR_\mathrm{th}$, the specimen only adjusts the distribution of contact forces to resist the external load, without any apparent change of contact number. When SR is larger than $SR_\mathrm{th}$, however, the specimen has to adjust both contact number and contact forces to resist the external load. The study also illustrates that there is a good relationship between the macroscopic stiffness anisotropy and fabric anisotropy, and therefore the stiffness anisotropy may be used as an indicator of fabric anisotropy.