Different analytical models and methods to study wave propagation across rock joints

The effects of joints of on wave propagation are of considerable fundamental significance and engineering interest. This paper presents an overview of different analytical models to describe the joints and methods to take into account multiple wave reflections among joints. Four different models are described in detail, which include the layered medium model, the displacement discontinuity model, thewave scattering model and the equivalent medium model. In order to take into account multiple wave reflections among joints, three different methods, i.e., the method of characteristics, the recursive method and the virtual wave source method, are presented. The differences and connections of these models and methods are also presented.