Elastic wave interaction with a stressed half-space containing voids

This study explores the reflection characteristics of plane shear vertical (SV) waves incident upon the free surface of an initially stressed, isotropic elastic half-space containing voids. Using Biot's theory of incremental deformations and the generalized theory of porous elastic media, the governing equations are formulated and analytically solved under two-dimensional plane strain conditions. The presence of initial stress and voids modifies the propagation behavior of elastic waves. It is found that the incident SV-wave gives rise to two distinct reflected waves: a compressional (P) wave and a rotational (SV) wave. The analysis reveals that the reflected SV-wave is influenced solely by the initial stress, whereas the reflected P-wave is significantly affected by both initial stress and the void parameters. Closed-form expressions for the reflection coefficients are derived analytically and evaluated numerically to examine their variations with incident angle, void parameters, and frequency are examined. The results offer insight into wave behavior in porous geological media and stress-loaded materials.