Response of fluid-saturated elastic porous media to excitations of multiple energy sources

Abstract

This paper studied the behaviour of elastic waves in porous media consisting of fluid and solid. For analytically quantifying the wave motions of a fluid-saturated porous medium subjected to the excitations of multiple energy sources, a new methodology is developed with the establishment of an analytical wave model. Displacements of both the fluid and solid are considered in the development of the wave model such that the elastic waves propagating in the isotropic and homogeneous porous media can be quantitatively analysed. Solutions of the governing wave equations are developed on the basis of the moving-coordinate method with utilization of Hankel function. Employing the model established, relative displacements between the fluid and solid of a porous medium can be quantified. The wave field in the medium can thus be quantitatively determined for the wave propagation under given multiple energy sources. For demonstrating the application of the theoretical wave model developed, numerical simulations of the elastic waves propagating in a porous medium under multiple energy sources are performed.

Three-dimensional shear and compressional wave propagation of multiple point sources in fluid-saturated elastic porous media

“…As such, the equations needed for describing all the characteristics of the compressional wave propagation governed by equations ( 16) are thus completely developed. The above derivations can also be verified by Wang et al 13 and Han and Dai. 18 Now consider equation for the shear waves, eliminating V by V ¼ À 12 22 v from equation (13b), equation (13a) can be converted to…”

“…The above derivation can be verified in Wang et al 13 and Han and Dai. 18 However, in their works, the shear wave effect has not been fully disclosed yet.…”

“…The wave sources considered in Wang et al 13,14 were uniformly distributed along a vertical line at the center of the cylindrical coordinate system. The wave in such systems is generated by a line source which is perpendicular to the direction of wave propagation.…”

“…where the same parameters are followed as that introduced by the former works of Wang et al 13,14 and Han and Dai. 18 All the parameters are accordance to Biot's 11 as well…”

“…For understanding the relative motion between the fluid and solid, a theoretical and systematical investigation on the relative motion between the fluid and solid of a porous medium is necessary. Wang et al 13,14 developed the equations in terms of the displacements in cylindrical coordinates. The wave sources considered in their work are taken as straight lines which can be merely expanding in a two-dimensional (2D) plane and are insufficient to disclose the spatial wave propagation characteristics in reality.…”