Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range

Abstract

The theory of propagation of stress waves in a porous elastic solid developed in Part I for the low-frequency range is extended to higher frequencies. The breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes. As in Part I the emphasis of the treatment is on cases where fluid and solids are of comparable densities. Dispersion curves for phase and group velocities along with attenuation factors are plotted versus frequency for the rotational and the two dilational waves and for six numerical combinations of the characteristic parameters of the porous systems. Asymptotic behavior at high frequency is also discussed.

Homogenizing the acoustic properties of the seabed: Part I

“…This case was considered previously by Biot [7,8], Sanchez-Hubert [22], Sanchez-Palencia [24,23], Levy [ 181, Buchanan-Gilbert-Lin [9,10,16].…”

“…to work of Biot [7,8], and Stall [25,26]. Biot's work was rather heuristic; hence, several authors have sought to put this on a more solid footing, namely Sanchez-Palencia [23] (Chapter S), [6,24], Levy Burridge and Keller [12].…”

Three-dimensional poro-elasto-plastic model for wave-induced seabed response around submarine pipeline

“…In general, the three-dimensional poro-elasto-plastic computer program DYNE3WAC [16] is based on the fully implicit u-p approximation of the Biot formulation [3]. The dynamic governing equations for the u-p approximation of the Biot formulation are basically the momentum equations for the soil-fluid "mixture" and the mass balance of the flow.…”

“…where F represents the viscous drag forces, assuming the Darcy seepage law can be written as k ij F j ¼ w i , where k is the permeability of soil with the dimensions of [length] 3 [time]/ [mass], which can be expressed by the usual soil mechanics convention k 0 , with k ¼ k 0 =ρ 0 f g 0 , where ρ 0 f and g 0 are the fluid density and gravitational acceleration, respectively, at which the permeability is measured. (3) Conservation of mass of fluid phase:…”

“…To further investigate dynamic response of three-dimensional poro-elasto-plastic model for seabed around submarine pipeline under wave loading, a finite element program DYNE3WAC (DYNamic Earthquake Analysis Program 3D Window Version for ACadiemic) [16] is used in this paper. The 3D poro-elasto-plastic model is based on the fully implicit u-p approximation of the Boit formulation [3]. The fully coupled Boit dynamic equations were employed, together with the u-p approach (skeleton displacement u and pore pressure p), in which the fluid acceleration relative to the solid skeleton is negligible.…”