Through stochastic-numerical microstructure-based experiments, the plastic consolidation under compression of porous brittle solids, with porosities from 0.25 to 0.75 and a large variety of microstructural characteristics, has been investigated. This was made possible by generating microstructures from Gaussian random fields in order to obtain stochastic ensembles of structures with prescribed properties, which are then simulated within the material point method. Below a critical imposed strain rate, the consolidation behavior is found to be very weakly affected by the degree of heterogeneity and anisotropy. Structures where the solid phase takes up more space than the void phase have a consolidation response approximately independent of the structural geometry and dimensionality (comparing two- and three-dimensional structures). Finally, we show that the consolidation of two-dimensional structures collapses on a single master curve that can be described by a simple function similar to one presented for a completely different system, namely a system of interacting discrete cohesive disks. In this function, we report a universal parameter largely independent of material specifications.