Unified phenomenological model for the mechanical behavior of rocks

Abstract

Various types of experiments are used to interrogate the mechanical behavior of rocks. The whole experimental spectrum covers many orders of magnitude in frequency (roughly ten orders of magnitude) and in strain (approximately eight orders of magnitude). These experimental studies have established unambiguously a certain number of robust results, namely, frequency dependence, dependence on stress-strain level (nonlinearity), eventually the presence of hysteresis (stress is not an analytic function of strain), and dependence on the direction of observation (anisotropy). These four behaviors are synthesized in a single model. The model allows direct comparison of the magnitude of the different phenomena (dispersion, nonlinearity, anisotropy) and their combinations in rocks. The frequency dependence of the mechanical properties should not be neglected, but another fundamental parameter, namely, the strain level, is important to explain the mismatch between the “static moduli,” measured with a press in rock mechanics, and the “dynamic moduli,” measured with ultrasonic devices in rock physics, which commonly is not appreciated. Such a unified model helps to make the link between different communities (e.g., rock physics, seismology, applied seismics, and rock mechanics) by using the same mathematical tool, and it could contribute to mutual fertilization among these communities.