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A semianalytical solution for one‐dimensional transient wave propagation in a saturated single‐layer porous medium with a fluid surface layer
Author(s) -
Shan Zhendong,
Ling Daosheng,
Xie Zhinan,
Jing Liping,
Li Yongqiang
Publication year - 2019
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2978
Subject(s) - eigenfunction , porous medium , mechanics , attenuation , perfectly matched layer , poromechanics , mathematical analysis , permeability (electromagnetism) , boundary value problem , porosity , eigenvalues and eigenvectors , materials science , geometry , mathematics , geology , physics , geotechnical engineering , optics , chemistry , biochemistry , quantum mechanics , membrane
Summary One‐dimensional transient wave propagation in a saturated single‐layer porous medium with a fluid surface layer is studied in this paper. An analytical solution for a special case with a dynamic permeability coefficient k f → ∞ and a semianalytical solution for a general case with an arbitrary dynamic permeability coefficient are presented. The eigenfunction expansion and precise time step integration methods are employed. The solution is presented in series form, and thus, the long‐term dynamic responses of saturated porous media with small permeability coefficients can be easily computed. We first transform the nonhomogeneous boundary conditions into homogeneous boundary conditions, and then we obtain the eigenvalues and orthogonal eigenfunctions of the fluid–solid system. Finally, the solutions in the time domain are developed. As the model is one dimensional, geometric attenuation is absent, and only the attenuation in the saturated porous medium is considered. We can apply this model to analyse the influences of different seabed types on the propagation of acoustic waves in the fluid layer, which is very important in ocean acoustics and ocean seismic. This solution can also be employed to validate the accuracies of various numerical methods.