Wave propagation in discontinuous media, which is of interest for design analysis of underground structures and geotechnical works in general, is studied in this paper with the scattering matrix method. This method determines the response of a system, i.e. the discontinuous medium, excited by an elastic wave. Both P, SV or SH waves can be applied to the model with any oblique angle of incidence. The scattering matrix is composed of reflection and transmission coefficients of a single joint or a set of parallel joints. The analytical solution is obtained in the frequency domain and allows one to consider multiple wave reflections between joints. Reflected and transmitted waves are calculated for one and more joints in dry or fluid filled conditions. The solutions obtained are compared with analytical and numerical solutions available in the literature or obtained independently by using the Distinct Element Method.
This paper deals with wave propagation in discontinuous media. Typical discontinuous media are rock masses that are characterized by the presence of joints/discontinuities. Many efforts have been made so far to understand the effects of these planes of weakness on wave propagation based on analytical and numerical methods and laboratory tests. Analytical methods, to study the problem of wave propagation in discontinuous media, have been developed by Schoenberg (1980), Myer et al. (1990), and Pyrak-Nolte et al. (1990). The displacements across a joint/discontinuity are considered to be not continuous. In fact a displacement discontinuity, or slip, is introduced and is considered to be linearly related to both the normal and shear stress, which are instead assumed to be continuous across the discontinuity. The analytical approach was extended by Myer et al. (1990) and Pyrak-Nolte et al. (1990) to the case of fluid saturated discontinuities using rheological models (e.g. Kelvin and Maxwell models).