Abstract:
Recently, a displacement (u,U) finite element model for the three-dimensional poroelasticity problem has been developed by Panneton and Atalla [J. Acoust. Soc. Am. 98, 2976(A) (1995)]. This model, while accurate, has the disadvantage of requiring cumbersome calculations for large finite element models and spectral analyses. To overcome this difficulty, this paper presents a mixed displacement-pressure (u,P) finite element model. First, the classical Biot--Allard equations are rewritten in terms of the solid phase macroscopic displacement vector and the fluid phase macroscopic pressure. The new coupled equations have the advantage of writing the poroelasticity equations in the form of the coupling between an equivalent elastodynamic equation for the solid phase and an equivalent Helmholtz equation for the fluid phase. In particular, the equivalent fluid model is transparent in the developed equations. Next, the associated variational formulation is presented together with its numerical implementation. Also the acoustic--poroelastic, elastic--poroelastic, and poroelastic--poroelastic coupling conditions are derived. Several examples are presented to show the accuracy and effectiveness of the proposed model and its coupling with elastic and acoustic media. In particular a systematic comparison is made with the (u,U) finite element formulation. [Work supported by Canadair, CRSNG, and FCAR.]