It is well-known that granite has anisotropy due to the preferred orientation of micro-cracks. Therefore, it is important to investigate the orientation of micro-cracks in granite to discuss the anisotropy. It has been postulated that the orientation of micro-cracks in rock can be determined by DSCA (Differential Strain Curve Analysis). In the case of DSCA, however, it is necessary to use a lot of specimens to determine the orientation of micro-cracks precisely. Additionally, it is impossible to evaluate the orientation of micro-cracks if the rock contains few oriented micro-cracks.
The seismic wave velocity shows the extreme values in the direction of principal axes of elasticity. Therefore, it is possible to obtain the information of the orientation of micro-cracks in rock by the measurement of the wave velocities. In this study, longitudinal wave velocities in various directions were measured to determine the orientation of micro-cracks in granite by using polyhedral specimens.
From the measurement of the longitudinal wave velocities, the three-dimensional distribution of the velocities in granite could be obtained. By using the associated Legendre function, it was shown that the three-dimensional distribution of the longitudinal wave velocity could be approximated within 2nd order terms of the associated Legendre function. This result means that the wave distribution function can be expressed with the quadric surface and the coefficients can be expressed as the symmetric tensor of the 2nd rank. This shows the existence of the principal axes and the principal values which can be expressed with the eigen values and the eigen vector same as the cases of the stress and the strain. It is concluded that the directions of the principal axes and the values of the longitudinal wave velocities in granite can be determined by the calculation as evaluating the principal stress or the principal strain from the stress tensor or the strain tensor.