Elastic properties of anisotropic rocks using an stepwise loading framework in a true triaxial testing apparatus

Abstract

Directional dependence of mechanical properties, or waves propagating in geomaterials, known as anisotropy, is important in accurately predicting their response to stresses in various engineering applications. These measurements are generally conducted on cylindrical samples under conventional uniaxial or triaxial loading conditions where two or three samples that are prepared at different directions to the plane of symmetry would be required. To avoid using several samples and the variability that might exist in the specimens, this paper explores laboratory testing of anisotropic shale rock samples under true triaxial test (TTT or polyaxial testing) conditions. Herein, two cubic shale samples (A and B) of different lithotypes, were subjected to an step-wise loading path that was increased gradually on each side of the sample. At the same time, compressional and shear wave velocities were measured in three separate directions when isostatic stress conditions are achieved. As a result, independent components of the stiffness tensor of a transversely isotropic media (static elastic modulus and Poisson's ratio) are calculated from the directional stress-strain curve, while dynamic mechanical parameters are determined from directional ultrasonic wave velocities. The results showed strong dependence of these parameters to the direction of measurements with respect to the plane of symmetry, differing between these two lithotypes, confirming transversely isotropic behavior of the samples with varying magnitudes. Petrographic analysis of the samples revealed this is due to the internal structure and orientation of minerals and foliation, particularly muscovite and clay. Moreover, dynamic mechanical parameters were found larger than the static ones and a robust relationship between them was established. Additionally, Young's modulus, Poisson's ratio along axis of symmetry, as well as the P and S wave velocities traveling perpendicular to the bedding were found smaller compared to those parallel to the bedding. Collectively, this approach made us independent from running tests on several samples and avoid the bias that can exist in testing shale samples with high structural complexity when samples should be prepared in several directions.