Effects of a set of parallel joints with unequal close-open behavior on stress wave energy attenuation

Rock joints with unequal close-open behavior have significant influences on stress wave propagation across them. A stress wave of sufficiently large amplitude does not only mobilize the nonlinear deformation of joints, but also force the joints to close and open. In the present study, the Bandis-Barton model and the Coulomb-slip model are adopted to describe the normal and tangential behavior, respectively, of the closed joints. However, when the joints are open, both sides of the joints behave as two free surfaces. The improved time-domain recursive method is employed to derive wave propagation equations for three cases, i.e. the joint is closed but does not slide, the joint is closed and slides, and the joint is open. Then, the normal and tangential relative displacements of joints, as well as the energy attenuation coefficient, are calculated. A comparison of transmitted waves based on different methods is conducted to verify the validity of the present approach. Eventually, parametrical studies show that the higher in-situ stress causes the smaller energy attenuation coefficient, and the wave energy attenuation is also dependent on the frequency and amplitude of the incident wave, the incident angle, the joint spacing and the joint number.