Generalized biot's Theory and mandel's problem of multiple-porosity and multiple-permeability poroelasticity

Amin Mehrabian, Younane N. Abousleiman

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67 Scopus citations


This paper finds in Biot's theory of poroelasticity a complete and consistent extension to the general case of multiple-porosity and multiple-permeability, fluid-saturated, and linearly elastic media. The constitutive stress-strain relations for a medium identified with this extension are presented, and the coefficient matrix of mechanical properties associated with these relations is derived from the corresponding intrinsic properties of its single-porosity constituents. The closed form analytical solution to Mandel's problem is upgraded to the case being considered in this study. This problem addresses the transient consolidation of a porous elastic slab of rectangular geometry, when confined from the top and bottom. A numerical example solution for shale with laboratory setup of Mandel's problem is provided. Results are compared for the cases of single-, double-, and triple-porosity solutions.

Original languageEnglish (US)
Pages (from-to)2745-2763
Number of pages19
JournalJournal of Geophysical Research: Solid Earth
Issue number4
StatePublished - Apr 2014

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Geochemistry and Petrology
  • Earth and Planetary Sciences (miscellaneous)
  • Space and Planetary Science


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