S U M M A R YRock joints are often filled with weak medium, for example, saturated clay or sand, of viscoelastic nature. Their effects on wave propagation can be modelled as displacement and stress discontinuity conditions. The viscoelastic behaviour of the filled joint can be described by either the Kelvin or the Maxwell models. The analytical solutions for wave propagation across a single joint are derived in this paper by accounting for the incident angle, the nondimensional joint stiffness, the non-dimensional joint viscosity and the acoustic impedance ratio of the filled joint. It is shown that the viscoelastic behaviour results in dissipation of wave energy and frequency dependence of the reflection and transmission coefficients. Based on curve fitting of the experimental data of P-wave propagation across a single joint filled with saturated sand, both the Kelvin and Maxwell models are found to reproduce the behaviour of the filled joint, in terms of the amplitude and frequency contents. Then, wave transmission across a filled joint set is studied with the virtual wave source method and the scattering matrix method, where multiple wave reflections among joints are taken into account. It is shown that the non-dimensional joint spacing and the number of joints have significant effects on the transmission coefficients.
Different methods are presently available for the analysis of wave propagation across jointed rock masses with the consideration of multiple wave reflections between joints. These methods can be divided into two categories. One is based on the displacement discontinuity model for representing rock joints, where the displacements across a joint are discontinuous and the tractions are continuous, and the other is the equivalent medium method. For the first category, there are three methods, i.e., method of characteristics (MC), scattering matrix method (SMM) and virtual wave source method (VWS). MC solves the equation of motion by using the theory of characteristic curves. SMM is based on the definition of the scattering matrix in which the reflection and transmission coefficients of a set of joints are stored. VWS method replaces the joints in the rock mass with a virtual concept. For the second category, equivalent medium model treats the problem in the frame of continuum mechanics and simplifies it from an explicit wave propagation equation. The objective of this paper is to review and compare these theoretical methods. The comparison shows that the four solutions agree very well with each other. Some additional considerations about the advantages and disadvantages of these methods are also given in the paper.
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