Analysis of P-wave propagation in filled joints based on the g-λ model

The propagation law of stress waves in joints, as weak structural planes in rock masses, plays a pivotal role in assessing the dynamic stability of rock mass. In particular, the wave propagation characteristics become complicated in filled joints due to their thickness and the properties of the filling materials. Current theoretical investigations on wave propagation in filled rock joints remain scarce, with insufficient consideration of nonlinear deformation characteristics at contact interfaces. Therefore, this paper adopts the g-λ model to characterize nonlinear normal deformation behavior at filled joint interfaces. Taking into account the influence of the filling layer, the propagation equation of stress waves in filled joints is established by the improved time-domain recursive analysis method. Moreover, a parametric analysis is conducted on the transmission and reflection coefficients of P waves.Through theoretical analysis, it is found that the parameter λ is related to the cohesion and internal friction angle of the joints, with increasing λ amplifying nonlinear stiffness enhancement rates. The transmission and reflection coefficients of stress waves are quite sensitive to changes in the incident angle. As the incident angle increases, the reflection coefficient of P waves first decreases and then increases. The transmission coefficient of P waves remains relatively stable as the incident angle increases, but drops sharply when the incident angle continues to increase. Overall, changes in the initial normal stiffness of the joint have a significant impact on the transmission and reflection coefficients of P waves, while changes in the tangential of the joint have dominant influence on the transmission and reflection coefficients of S waves.The results provide a theoretical basis for the propagation law of stress waves in the rock masses with filled joints.