Identification of higher symmetry in triclinic stiffness tensor: Application to high pressure dependence of elastic anisotropy in deep underground structures

Abstract

We present an approach of identifying anisotropy axes and the type of symmetry from ultrasonic measurements of 21 elastic constants of the complete stiffness tensor characterizing anisotropic materials. The approach is applied to examine anisotropic elasticity of two crystalline rock samples from two underground research laboratories : (1) the migmatized gneiss from Bukov in the Czech Republic; and (2) the Aare Granite from Grimsel in Switzerland. The full stiffness matrix is measured at selected pressure levels from 0.1 to 100 MPa. We demonstrate that the Bukov migmatized gneiss is orthorhombic , whereas the Grimsel granite is transversely isotropic under atmospheric pressure. The degree of anisotropy of both rocks decreases with applied confining pressure due to closing of preferentially oriented cracks. While the Grimsel granite is very sensitive to pressure and becomes almost isotropic at high pressures, a great portion of anisotropy in the Bukov migmatized gneiss remains even under high pressures due to its texture. The dependence of Young's and shear moduli with pressure emphasizes the importance of taking the pressure into account for underground projects.