Influence of an impulsive source on shear wave propagation in a mounted porous layer over a foundation with dry sandy elastic stratum and functionally graded substrate under initial stress

Abstract

The present paper articulates a mathematical model for the propagation of horizontally polarised shear (SH) wave in an initially stressed composite layered structure under the influence of an impulsive line source. The initially stressed composite structure is comprised of a transversely isotropic fluid saturated porous layer over a foundation with dry sandy elastic stratum and functionally graded substrate (semi-infinite medium) in which the bonding between the interfaces of the layers and semi-infinite medium are considered to be imperfect. Green's functions are derived for the composite layered structure by taking a line force/charge density (Dirac delta function) at the lower interface of intermediate stratum into the account. An efficient analytical treatment involving Green's function technique along with Fourier's transform has been employed to establish the closed form of dispersion equation for the propagating wave. As a special case of the problem, the closed form of dispersion equation has been deduced for a structure with a single layer overlying a semi-infinite medium. These deduced results are validated with pre-established results and classical Love wave equation. Numerical computation has been carried out to demonstrate graphically the effect of various affecting parameters, viz. wave number, initial stress, porosity, sandiness parameter, width ratio, imperfect bonding parameters and functional gradient parameters on the phase velocity of shear wave. Some remarkable results regarding the propagation behaviour of shear wave in the considered composite layered structure due to various affecting parameters serve as the major highlights of the present work which has significant relevance to field of geophysics, earthquake engineering and civil engineering.