Dynamic Analysis of Porous Media Using Finite Element Method
The mechanical behavior of porous media is governed by the interaction between its solid skeleton and the fluid existing inside its pores. The interaction occurs through the interface of gains and fluid. The traditional analysis methods of porous media, based on the effective stress and Darcy's law, are unable to account for these interactions. For an accurate analysis, the porous media is represented in a fluid-filled porous solid on the basis of the Biot theory of wave propagation in poroelastic media. In Biot formulation, the equations of motion of the soil mixture are coupled with the global mass balance equations to describe the realistic behavior of porous media. Because of irregular geometry, the domain is generally treated as an assemblage of fmite elements. In this investigation, the numerical formulation for the field equations governing the dynamic response of fluid-saturated porous media is analyzed and employed for the study of transient wave motion. A finite element model is developed and implemented into a computer code called DYNAPM for dynamic analysis of porous media. The weighted residual method with 8-node elements is used for developing of a finite element model and the analysis is carried out in the time domain considering the dynamic excitation and gravity loading. Newmark time integration scheme is developed to solve the time-discretized equations which are an unconditionally stable implicit method Finally, some numerical examples are presented to show the accuracy and capability of developed model for a wide variety of behaviors of porous media.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062974Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1478
 M. A. Biot, "Theory of propagation of elastic waves in fluid-saturated porous solid", Journal of acoustical society of America, vol. 28, pp. 168-291, 1956.
 M. A. Biot, "Theory of finite deformations of porous solids," Indiana University. Mathematical Journal, vol. 21, pp. 597-620, 1972.
 J. Prevost, "Consolidation of inelastic porous media," Journal of engineering mechanics division, vol. 107, pp. 169-186, 1980.
 O. C. Zienkiewicz and T. Shiomi, "Dynamic behaviour of saturated porous media: The generalized Biot formulation and its numerical solution," International Journal for numerical and analytical methods in geomechanics, vol. 8, pp. 71-96, 1984.
 J. Prevost, (1985) "Wave propagation in fluid-saturated porous media: An efficient finite element procedure," Soil dynamics and earthquake engineering, vol. 4, pp. 183-2020, 1985.
 R. de Boer, "Development of porous media theories: A brief historical review," Transport in porous media, vol. 9, pp. 155-164, 1992.
 R. de Boer, W. Ehlers and L. Zhangfang, "One-dimensional transient wave propagation in fluid-saturated incompressible porous media," Archive of applied mechanics, vol. 63, pp. 59-72, 1993.
 R. de Boer and Z. Liu, "Plane Waves in a Semi-Infinite Fluid Saturated Porous Medium", Transport in Porous Media, vol. 16, pp. 147-173, 1994.
 Y. Zheng, R. Burridge and D. Burns, "Reservoir simulation with the finite element method using Biot poroelastic approach," 2005.
 Y. Bao, "A Biot formulation for geotechnical earthquake engineering applications," Ph.D. dissertation, Department of Civil, Environmental, and Architectural Engineering, University of Colorado, 2006.