An equivalent 1D dynamic continuum model for rock mass with parallel joints

Based on viscoelastic theory, an equivalent one-dimensional dynamic continuum model is proposed for rock mass with parallel joints. The model includes two portions, one is the viscoelastic medium model and the other is the concept of "virtual wave source(VWS)". The time retardation and attenuation of longitudinal wave propagation across jointed rock mass are considered in the viscoelastic medium model; and the concept of VWS is adopted to account for the wave reflections between joints. The parameters in the equivalent viscoelastic model are derived analytically based on existing solution for longitudinal wave propagation across a single rock joint. The proposed model is then verified by applying identical incident waves to the discontinuous and equivalent dynamic media at one end and receiving output waves at the other end, i.e. by comparing two results from the displacement discontinuity method and the present equivalent medium method. The results show that the proposed model can simplify the simulation of stress propagation effectively.