Subsurface characteristics of the Rayleigh wave

Abstract

An isotropic elastic half-plane is used as a model for studying theoretically and experimentally the transmission of stresses associated with Rayleigh waves. Solutions of the equations of motion of plane elastodynamics which represent arbitrary progressing Rayleigh waves are derived and then associated with Rayleigh waves produced by a concentrated line load on the boundary of the half-plane through previously established results for the tangential normal stress at the boundary. Mathematically, the problem of establishing the complete Rayleigh wave field is analogous to a well known problem in potential theory. Dynamic photoelastic fringe patterns, associated with the Rayleigh wave generated by a surface charge on a two-dimension model were also obtained as an experimental solution to the problem. The two sets of results compare very favorably. Where discrepancies do occur, explanations are given. In both studies, the maximum stress is found to occur at the boundary, but the stress field below the surface is still significant. For example, the maximum subsurface value of the principal stress difference, which occurs at a fixed depth, is about 75 per cent of the maximum boundary value.