Investigations on the compression-shear coupled stress waves propagating in heterogeneous rock

In order to investigate the heterogeneous responses in complex rocks, a compression-shear coupled constitutive relationship with four coupled parameters is established and a generalized wave equation is obtained. Based on the generalized self-consistent theory, the approach to determine the four coupling parameters related to local stress and strain state in the heterogeneous rock with multiphase components is proposed. A meso finite element model (meso-FEM) is employed to calibrate the calculation process according to four load paths. Based on the generalized wave equation, three characteristic wave velocities of 3-D plane waves are derived to describe the compression-shear coupled effect on wave propagation. These wave velocities (e.g. the primary wave and secondary wave) are different from those of the conventional compression wave and shear wave due to the coupled effects. As an example, the theoretical method is further employed to investigate wave velocities in the heterogeneous granular medium due to particle rotation. It indicates that wave velocities in the looser medium are related to local rotation and local strain. Particle rotation has significant effects on the wave velocities, which causes severe heterogeneity and compression-shear coupling effect in particle material. Both the heterogeneous distribution of internal materials and particle rotation affect wave velocities. The results provide a profound theoretical explanation for the heterogeneity of rock and are expected to provide a comprehensive understanding of the physical mechanism of the effect of heterogeneity on wave velocity.