Dynamic response of a graded cracked half-plane with embedded sources

In this work, an efficient boundary integral equation method is developed based on an analytically derived Green’s function for the graded half-plane with buried point sources. The problem under investigation is the dynamic field which develops in an elastic, isotropic, and graded half-plane with an embedded, inclined Griffith crack as it is enveloped by time-harmonic waves radiating from buried monopoles and dipoles. Following numerical verification, the methodology is used to perform a series of parametric studies to investigate the dependence of the displacement and stress concentration wave fields on the following key parameters: (a) the material gradient which exhibits a quadratic type of variation with depth; (b) the type and characteristics of the source; (c) the position and geometrical configuration of the embedded geological crack, and (d) the dynamic interaction phenomena between the propagating wave in the material, the crack, and the free surface of the geological continuum.