Micromechanical model for hysteresis in fluid-saturated porous rocks under hydrostatic loading

This research aims to show that frictional microcracks cause the dependence of rocks' elastic properties on both the perturbation amplitude and the loading history. These relationships are essential for estimating wave velocities and, thus, for analysing laboratory experiments on fluid-saturated rocks under varying stress levels. The first step towards achieving this objective is to propose a microstructural prototype in which hydrostatic remote loading induces local deviatoric stress. This stress is essential for triggering the slip of microcracks once they are closed. The prototype's geometry is based on the classical spherical assemblage of Hashin (J. Appl. Mech., 1962) and includes a fluid-filled central pore. Surrounding this pore is a spherical shell composed of a homogenised medium that is pervasively microcracked, according to the non-interactive model proposed by Kachanov (Mech. Maters., 1982). The properties of the homogeneous material surrounding the central pore are determined by solving the boundary-value problem with the confining pressure applied to the outer boundary of the shell. The second step is to enhance this microstructural model by incorporating a distribution of crack aspect ratios within the spherical shell. We demonstrate how oscillations in loading, with decreasing amplitudes, enable the evaluation of dynamic elastic properties, ultimately leading to the determination of wave velocities. The third step complements these findings by providing experimentalists with a numerical tool to help them improve their methods for evaluating the arrival time of shear waves in tri-axial laboratory experiments. To achieve this, we propose a coupled numerical approach that captures the transformation of the voltage applied to a piezoelectric actuator into an S-wave. This approach also accounts for the propagation of the wave through the testing machine and specimen, as well as the generation of voltage at the receiver, where a complex wave pattern is detected.