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

In order to explore the propagation characteristics of P wave in nonlinear oblique joints rock mass, the method combing theoretical analysis, comparative verification and numerical calculation is adopted. Firstly, the hyperbolic joint model with normal nonlinear deformation and tangential linear deformation is introduced. Based on the interaction relationship between stress wave and linear joint, the propagation equation of P wave incident oblique joints is deduced according to the wave theory, Snell theorem, conservation principle of wave front momentum, displacement discontinuity theory and superposition principle. Then, based on the parameters of incident P wave and the conditions of jointed rock mass in literature, the transmission and reflection coefficients are calculated and found to be very close, which verified the accuracy and feasibility of the theoretical model. Furthermore, the auxiliary function of δ function is selected as the incident P wave to analysis influence rule of waveform, duration and joint stiffness on the propagation characteristics of P wave in oblique joints rock mass through parameter research. The results indicated that the phenomenon of amplitude reduction, amplitude-time delay and duration extension is significant when the auxiliary function of δ function incident on oblique joints, which can better reflect the mutation characteristics and nonlinear attenuation feature of P wave in short time. The duration of incident P wave in oblique joints rock mass can significantly improve the transmission performance of P wave and slightly reduce the reflection characteristics of P wave and S wave. But the increase of duration is very weak impact on the transmission of S wave. P waves are prone to transmission but difficult to reflection and S waves are prone to reflection but difficult to transmission when P wave transmit to oblique joints. As kn0 and ks increase, the reflection coefficient Rsc decay in concave surface shape, while the transmission coefficient Tpc increase in convex surface shape. The transmission performance of P wave is closely related to the normal stiffness of joint, while the reflection characteristics of S wave is significantly affected by the second joint in the oblique joints. The research results are beneficial for developing the mechanical properties and dynamic response of natural jointed rock mass.