Impact-driven compaction is a proposed mechanism for the lithification of primordial bimodal granular mixtures from which many meteorites derive. We present a numerical-experimental mesoscale study that investigates the fundamental processes in shock compaction of this heterogeneous matter, using analog materials. Experiments were performed at the European Synchrotron Radiation Facility generating real-time, in-situ, X-ray radiographs of the shock's passage in representative granular systems. Mesoscale simulations were performed using a shock physics code and set-ups that were geometrically identical to the experiments. We considered two scenarios: pure matrix, and matrix with a single chondrule. Good agreement was found between experiments and models in terms of shock position and post-shock compaction in the pure powder setup. When considering a single grain embedded in matrix we observed a spatial porosity anisotropy in its vicinity; the compaction was greater in the region immediately shockward of the grain, and less in its lee. We introduced the porosity vector, C, which points in the direction of lowest compaction across a chondrule. This direction-dependent observation may present a new way to decode the magnitude, and direction, of a single shock wave experienced by a meteorite in the past.