A pore crack model for the mechanical behaviour of porous granular rocks in the brittle deformation regime

Abstract A model is developed for predicting and simulating the mechanical behaviour and failure mode of brittle porous granular rocks loaded in compression. It is based on a fracture mechanics analysis applied to cracks emanating from the surface of cylindrical pores in two-dimensional, which is well suited to the microstructure of such rocks. It is also consistent with the usual experimental procedure used for biaxial compression tests since the numerical scheme is implemented under the assumption of imposed axial strain. The model takes into account interactions between neighbouring cracks, which grow when their stress intensity factor reaches the fracture toughness of the rock. The simulation of crack growth from cylindrical holes, associated with a failure criterion based on the coalescence of interacting cracks, allows one to calculate the critical stress at rupture and to derive theoretical stress–strain curves. The present model is then used to compare theoretical results with laboratory data obtained on four sandstones with porosity ranging between 13% and 25.5% which were deformed under conventional triaxial compression conditions at confining pressures between 0 and 35 MPa. The comparison shows that by using a small number of parameters (pore size, pore density, fracture toughness, and elastic moduli), the model is able to predict the rock behaviour during the compression tests and the stress level at rupture in a quite accurate way, when the microstructural parameters introduced are consistent with the observations.