Osam Sano

Experimental determination of elastic constants of Oshima granite, Barre granite, and Chelmsford granite

Employing polyhedral specimens, longitudinal and shear wave velocities were measured in various directions of propagation and polarization. Sound velocities showed orthorhombic elasticity in all of the rocks. With the assumption of orthorhombic elasticity the nine stiffness constants of all samples were determined by the sound velocities under atmospheric pressure and Kelvin-Christoffels equation. Twenty-one stiffness constants of Oshima granite, determined without assuming any symmetry, also showed orthorhombic features. Directions of the symmetry axes agreed well with the orientation of the preexisting cracks. Akaikes Information Criterion showed that the orthorhombic model with nine nonzero elastic stiffnesses was better than the model having 21 nonzero elastic stiffnesses for Oshima granite. The polyhedrons of two granitic rocks were loaded under hydrostatic pressure. All components of the stiffness constants increased with pressure. Under pressure of more than 120 MPa, two granitic rocks were approximately isotropic. The results show that oriented microcracks are mainly responsible for the orthorhombic elasticity of the granitic rocks and also indicate that dry oriented cracks can not be a cause for the anisotropic elasticity of granites at depths of more than 6–8 km.

A Model for Time-dependent Microcrack Growth Due to Stress Relief and Residual Stress.

Relaxation of rock after removal from in situ state consists of an elastic (instantaneous) component and an anelastic (time-dependent) component. Technique using anelastic strain recovery (ASR) have been aimed to determine the direction and magnitude of in situ principal stresses by measuring changes in geometry of recovered core with time immediately after retrieved from deep boreholes. Timedependent microcrack growth has been suggested as a possible mechanism for the strain recovery process, although it has been modeled by using viscoelastic theories. Time-dependent microcrack growth driven by the tensile residual stress as well as an instantaneous microcracking by the relaxation of the stresses was modeled by considering an homogeneous inclusion containing mocrocracks that grow due to subcritical crack growth. The inclusion having circular cross section was embedded in coaxial himogeneous matrix which was less stiffer than the inclusion. The model was able to predict the dependence of the time-strain curve of the inclusion on the initial stress level and agreed with the observed ASR data.