The evolving representative elementary volume size in crystalline and granular rocks under triaxial compression approaching macroscopic failure

Abstract

SUMMARY Determining the size of the representative elementary volume (REV) for properties of fracture networks, such as porosity and permeability, is critical to robust upscaling of properties measured in the laboratory to crustal systems. Although fractured and damaged rock may have higher porosity and permeability than more intact rock, and thus exert a dominant influence on fluid flow, mechanical stability and seismic properties, many of the analyses that have constrained the REV size in geological materials have used intact rock. The REV size is expected to evolve as fracture networks propagate and coalesce, particularly when fracture development becomes correlated and the growth of one fracture influences the growth of another fracture. As fractures propagate and open with increasing differential stress, the REV size may increase to accommodate the larger fractures. The REV size may also increase as a consequence of the increasing heterogeneity of the fracture network, as many smaller fractures coalesce into fewer and longer fractures, and some smaller fractures stop growing. To quantify the evolving heterogeneity of fracture networks, we track the REV size of the porosity throughout eleven triaxial compression experiments under confining stresses of 5–35 MPa. Acquiring X-ray tomography scans after each increase of differential stress provides the evolving 3-D fracture network in four rock types: Carrara marble, Westerly granite, quartz monzonite and Fontainebleau sandstone. In contrast to expectations, the REV size does not systematically increase toward macroscopic failure in all of the experiments. Only one experiment on sandstone experiences a systematic increase in REV size because this rock contains significant porosity preceding loading, and it subsequently develops a localized fracture network that spans the core. The REV size may not systematically increase in most of the experiments because the highly heterogeneous porosity distributions cause the REV to become larger than the core. Consistent with this idea, when the rock does not have a REV, the fractures tend to be longer, thicker, more volumetric, and closer together than when the rock hosts a REV. Our estimates of the REV for the porosity of the sandstone are similar to previous work: about two to four times the mean grain diameter, or 0.5–1 mm. This agreement with previous work and the <15 per cent change in the REV size in two of the sandstone experiments suggests that when a system composed of sandstone does not host a localized, system-spanning fracture network, estimates of the REV derived from intact sandstone may be similar to estimates derived from damaged sandstone. Using the existing REV estimates derived from intact sandstone to simulations with more damaged crust, such as the damage zone adjacent to large crustal faults, will allow numerical models to robustly simulate increasingly complex crustal systems.