Propagation of impact-induced shock waves in porous sandstone using mesoscale modeling

Generation and propagation of shock waves by meteorite impact is significantly affected by material properties such as porosity, water content, and strength. The objective of this work was to quantify processes related to the shock-induced compaction of pore space by numerical modeling, and compare the results with data obtained in the framework of the Multidisciplinary Experimental and Modeling Impact Research Network (MEMIN) impact experiments. We use mesoscale models resolving the collapse of individual pores to validate macroscopic (homogenized) approaches describing the bulk behavior of porous and water-saturated materials in large-scale models of crater formation, and to quantify localized shock amplification as a result of pore space crushing. We carried out a suite of numerical models of planar shock wave propagation through a well-defined area (the sample) of porous and/or water-saturated material. The porous sample is either represented by a homogeneous unit where porosity is treated as a state variable (macroscale model) and water content by an equation of state for mixed material (ANEOS) or by a defined number of individually resolved pores (mesoscale model). We varied porosity and water content and measured thermodynamic parameters such as shock wave velocity and particle velocity on meso- and macroscales in separate simulations. The mesoscale models provide additional data on the heterogeneous distribution of peak shock pressures as a consequence of the complex superposition of reflecting rarefaction waves and shock waves originating from the crushing of pores. We quantify the bulk effect of porosity, the reduction in shock pressure, in terms of Hugoniot data as a function of porosity, water content, and strength of a quartzite matrix. We find a good agreement between meso-, macroscale models and Hugoniot data from shock experiments. We also propose a combination of a porosity compaction model (ea model) that was previously only used for porous materials and the ANEOS for water-saturated quartzite (all pore space is filled with water) to describe the behavior of partially water-saturated material during shock compression. Localized amplification of shock pressures results from pore collapse and can reach as much as four times the average shock pressure in the porous sample. This may explain the often observed localized high shock pressure phases next to more or less unshocked grains in impactites and meteorites.