Mesoscale modeling of quartzite and sandstone under shock loading: Influence of porosity and pressure-dependent quartz stiffness on macroscopic behavior

In this paper, quartzite and sandstone are numerically investigated under planar shock loading. Those geologic materials consist of cemented quartz grains. Quartzite has a compact structure whereas sandstone has a porosity of typically around 20%. A mesoscale (grain scale) model is developed in order to catch inter-granular interactions and porosity crushing under shock loading. For this purpose, quartz grains are explicitly resolved in a Finite-Element model such that their shape and orientation are represented. The quartz grains are modeled as elastic crystals with a pressure-dependent, anisotropic stiffness matrix. Using parameter variations, we study the effect of porosity and pressure-dependency of the quartz stiffness on the macroscopic behavior of quartzite and sandstone. Descriptors of the macroscopic behavior are macroscopic longitudinal stress and shock wave speed. These quantities are determined via a homogenization methodology.