Analysis of P-wave propagation in filled jointed rock mass with viscoelastic properties

Stress wave propagation in filled jointed rock mass is an important basis for the analysis of rock dynamic stability. The presence of small cracks in rock mass often causes the rock to exhibit viscoelastic behavior, resulting in the amplitude attenuation and time delay of the stress wave. In view of the incomplete understanding of stress wave propagation in viscoelastic media, this study presents an analysis on stress wave propagation in filled jointed rock mass with viscoelastic properties based on the time-domain recursive analysis method. By introducing the quality factors of stress wave in viscoelastic medium, the propagation equation of plane P-wave in filled jointed rock mass with viscoelasticity is established. Subsequently, the transmission and reflection characteristics of P-wave are accordingly analyzed. The results indicate that the transmission and reflection coefficients of P-wave through the filled joint decrease obviously due to the attenuation effect of rock viscoelasticity on wave amplitude, but the coefficients gradually stabilize as the quality factor increases. As the propagation distance of the P-wave increases in viscoelastic rock masses, the transmission and reflection coefficients decrease gradually. The normal stiffness of joint contact interface has a decisive influence on the wave propagation. Specifically, a higher normal stiffness leads to stronger transmission and poorer reflection. The larger the thickness of filled joint, the more obvious the attenuation of P-wave becomes. Additionally, the viscoelasticity of filling layer further aggravates the influence of joint thickness on the attenuation of P-wave. The study comprehensively takes into account the effect of viscoelasticity of both the rock mass and the filling layer on transmission and reflection of waves. The research results provide certain theoretical support for the dynamic response and stability analysis of rock mass containing structural planes.