Alvin Trévis Biyoghé , Yves Marie Leroy, Lucas Xan Pimienta, Robert Zimmerman

A micro-mechanical model is proposed to predict the stress-strain hysteresis during the cyclic hydrostatic loading of fluid-saturated rocks under drained or undrained conditions. A spherical pore is surrounded by a cracked shell where local deviatoric stress develops despite the remote hydrostatic loading. The effective properties of the material composing the shell are constructed with the crack non-interactive scheme and the overall properties thanks to the spherical assemblage approach.
The fluid pressure in both drained and undrained conditions is assumed uniform throughout the assemblage. A new analytical solution is proposed assuming all cracks to be closed and slipping either forwardly or reversely. It is shown with numerical simulations for drained conditions that this assumption is indeed respected for sufficiently small crack friction angles. However, for reasonable friction values, the closed cracks during the unloading phase could slip in either direction: reversely close to the pore and still forwardly away from the pore. Moreover, at critical radii, the slip could occur in either direction depending on their orientation. A similar micro-structural response is observed for undrained conditions, although the remote confining stress required to close the cracks is much larger.
The model's predictions compare favourably with recent
experimental data on dry sandstones and carbonates presented in a study of the strain amplitude influence on the transition between static and dynamic properties. The crack density and matrix elasticity modulus are sufficient fitting parameters to accurately predict the hysteresis loops, especially for porosity levels above 10%.