Blast wave interaction with a parallel jointed rock mass

The present investigation is concerned with the interaction between the blast wave and a rock mass with a set of parallel joints by using a time-domain recursive method. According to the displacement field of a rock mass with a set of parallel joints, the interaction between four plane waves (two longitudinal-waves and two transverse-waves) and a joint is analyzed first. Considering the displacement discontinuity method and the time shifting function, the wave propagation equation based on the recursive method in time domain for obliquely longitudinal- (P-) or transverse- (S-) waves across a set of parallel joints is established. The joints are linearly elastic. The analytical solution by using the proposed method is compared with the existing results for some special cases, including incidence obliquely across a single joint and normally across a set of parallel joints. By verification, it is found that the solutions by the new method match very well with the existing methods. Finally, a blast wave with different waveform propagating across a single or a set of parallel joints is then analyzed. The wave propagation equation derived in the present study can be straightforwardly extended for different incident waveforms to calculate the transmitted and reflected waves without mathematical methods such as the Fourier and inverse Fourier transforms.