A homogenization equation for the small strain stiffness of gap-graded granular materials

Sandstone usually disintegrates into gap-graded granular materials with a matrix-sustained structure due to weathering factors. This paper presents an investigation on the small strain stiffness of this type of granular materials based on Discrete Element Method (DEM) simulations. Our numerical results indicate the percentage of sliding contact is negligibly small within the small strain range, and the small strain stiffness of fines is well consistent with the widely recognized Hardin's equation. Both findings confirm the validity of DEM simulations on the study of small strain response of granular materials. The simulation results are further analyzed based on mixture theory. A structure variable is introduced to correlate with the evolution of inter-aggregates structure. This variable is found to increase with the volume fraction of coarse aggregates but is rather independent of the confining stress and the initial void ratio of the fine matrix. Based on the insights drawn from DEM simulations, a homogenization equation is proposed for the small strain stiffness of gap-graded granular soils to reproduce the small strain stiffness of gap-gaped materials observed in our numerical simulations and is further validated by laboratory test data from the literature. The equation can be conveniently incorporated into classical elastoplastic models to model gap-graded granular materials.