Characteristics of Compressive Stress Wave Propagation Across a Nonlinear Viscoelastic Filled Rock Joint

Filled joints significantly influence the dynamic response of rock masses, exhibiting coupled nonlinear compression-hardening and viscous deformation. However, the combined effects of these mechanisms on wave propagation remain unclear. This study develops a theoretical model based on a nonlinear viscoelastic formulation, in which a compression-hardening spring (governed by the Bandis–Barton model, with its initial compressive stiffness and maximum allowable closure) is connected in series with a viscous dashpot. Using the displacement discontinuity method and the method of characteristics, we analyze the transmission of compressive stress waves across a filled joint. The results show that the transmission coefficient increases with incident wave amplitude but decreases with frequency, whereas reflection exhibits the opposite trends. The initial compressive stiffness has a minimal impact on transmission but induces a nonlinear decrease in reflection. Increasing the maximum allowable closure slightly reduces transmission but sharply increases reflection, whereas higher viscous stiffness enhances transmission and slightly suppresses reflection. Energy attenuation grows rapidly with amplitude before stabilizing. The initial compressive stiffness is most influential at low amplitudes, the maximum allowable closure is most significant at moderate amplitudes, and viscous effects remain consistent across all amplitudes. Increases in frequency lead to a nonlinear decrease in attenuation, with the initial compressive stiffness and maximum allowable closure dominating at high frequencies, and viscous effects prevailing at low frequencies. This work systematically reveals the coupled roles of nonlinear compression-hardening and viscosity in wave propagation across filled joints, providing theoretical support for dynamic hazard mitigation and geophysical exploration.