Microcrack‐induced elastic wave anisotropy of brittle rocks

TLDR

Brittle rock failure during compression is preceded by anisotropically oriented microcrack formation, growth, and coalescence, which reduce elastic wave velocities while the fourth‑rank crack density tensor contributes little to these changes. The study aims to obtain off‑axis wave velocity measurements to fully quantify the fourth‑rank crack density tensor’s contribution. The authors model crack‑induced anisotropy using second‑ and fourth‑rank crack density tensors and compare the predictions with ultrasonic compressional and shear wave velocity measurements on Berea sandstone under increasing axial stress at constant confining stress. Velocity inversion shows microcracks propagate parallel to maximum compressive stress, and the data fit well with only the second‑rank crack density tensor despite partial crack contact at high confining stress, consistent with White’s partially contacting fracture model.

Abstract

The failure of brittle rocks during compression is preceded by the formation, growth, and coalescence of microcracks. Elastic wave velocities are reduced in the presence of open microcracks and fractures and may therefore be used to monitor the progressive damage of the rock. In general, these microcracks are not randomly oriented, and the rock displays an elastic anisotropy. The elastic anisotropy due to cracks can be expressed in terms of a second‐rank and fourth‐rank crack density tensor. For open cracks the contribution of the fourth‐rank crack density tensor to the elastic wave velocities is small. These results are compared with recent measurements of the ultrasonic compressional and shear wave velocities for propagation parallel and perpendicular to an increasing axial stress applied at constant confining stress to Berea sandstone. Inversion of the velocity measurements indicates that the microcracks propagate parallel to the maximum compressive stress, in agreement with current rock mechanics theory. A reasonable fit to the data is obtained using only the second‐rank crack density tensor even though, at high confining stress, the cracks are expected to be in partial contact along their length. This is consistent with the model of elastic wave propagation in a medium containing partially contacting fractures published by White. However, measurements of off‐axis wave velocities are required to fully quantify the contribution of the fourth‐rank crack density tensor.