Theoretical study on propagation characteristics of P-wave in oblique joints rock mass

In order to investigate the propagation characteristics of P-wave in nonlinear oblique joints rock mass, a comprehensive approach integrating theoretical analysis, comparative validation and numerical calculation was employed. Initially, the hyperbolic joint constitutive model featuring normal nonlinear deformation and tangential linear deformation was presented. Based on the interaction relationship between stress waves and a linear single joint, the propagation equation for P-wave incident on oblique joints was derived according to superposition principle. Then, by using the parameters of the incident P-wave and the conditions of jointed rock mass reported in literature, the transmission and reflection coefficients were calculated and found to be in close agreement, verifying the accuracy and feasibility of the theoretical model. Furthermore, the auxiliary function of δ function was selected as the incident P-wave to analyze the influence rule of waveform, duration and joint stiffness on the propagation characteristics of P-wave in oblique joints rock mass through parameter study. The results demonstrate that the phenomenon of amplitude reduction, amplitude-time delay and duration extension is pronounced when the auxiliary function of δ function incident on oblique joints, which can better reflect the abrupt change characteristics and nonlinear attenuation behavior of P-wave in a short time. The duration of the incident P-wave in oblique joints rock mass can significantly enhance the transmission performance of P-wave and slightly reduce the reflection characteristics of P-wave and S-wave. As the initial normal stiffness and the shear stiffness of joint increase, the reflection coefficient of S-wave decays in a concave surface shape, while the transmission coefficient of P-wave increases in a convex shape. The transmission performance of P-wave is closely related to the normal stiffness of joints, whereas the reflection characteristics of S-waves are significantly influenced by the second joint in the oblique joints. These research findings offer valuable insights into the mechanical properties and dynamic response of natural jointed rock mass.