Stress wave propagation through viscous-elastic jointed rock masses using propagator matrix method (PMM)

The reflection-transmission coefficients of the stress wave propagating through a jointed rock mass are of great concern in many fields, for example seismology, exploration geophysics and geotechnical engineering. For a natural jointed rock mass, both the rock material and the joints should be treated to be viscous-elastic in the practical dynamic analysis. In this paper, Kelvin viscous-elastic model is adopted to describe the rock deformation behaviour; the viscouselastic behaviour of the unfilled wet joints is reproduced by the displacement and velocity discontinuity model, which also behaves as Kelvin viscous-elastic deformation behaviour. Based on the propagator matrix method (PMM), the reflection-transmission coefficients after P-wave propagating through the rock masses with a single joint and multiple parallel joints are studied, respectively, taking account for the normalized joint elastic stiffness (K), normalized joint viscous stiffness (eta'), the rock quality factor (Q), the incident angle (a), the dimensionless joint spacing (xi) and the joint number. The results show that the increment of eta' has double effect. That is not only can it increase the effective joint stiffness (positive effect), but also can cause energy loss (negative effect). For a certain K, the transmission coefficients first decrease to a minimum, then increase with increase of eta', while the reflection coefficients always decrease. There exists a critical value of eta' which makes energy loss achieve a maximum value. The change trend of the reflection-transmission coefficients that varies with alpha is similar to that of pure elastic joints except that the value of eta' has an effect on the magnitude of these coefficients. In the case of the multiple parallel joints, only transmission coefficients are studied. Both eta' and Q has an important effect on the interlayer multiple reflections, which makes the variation of transmission coefficients very different from the purely elastic results. Finally, to proof the reliability of PMM adopted in this paper, the corresponding numerical models with 2-D universal distinct element code have been carried out, and the comparisons indicates that the two results have good consistent, and PMM is reliable.