Analysis of stress partitioning in biphasic mixtures based on a variational purely-macroscopic theory of compressible porous media: Recovery of terzaghi's law

Roberto Serpieri, Francesco Travascio, Shihab S Asfour, Luciano Rosati

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The mechanics of stress partitioning in two-phase porous media is predicted on the basis of a variational purely-macroscopic theory of porous media (VMTPM) with compressible constituents. Attention is focused on applications in which undrained flow (UF) conditions are relevant, e.g., consolidation of clay soils and fast deformations in cartilagineous tissues. In a study of the linearized version of VMTPM we have recently shown that, as UF conditions are approached (low permeability or fast loading), Terzaghi's effective stress law holds as a general property of rational continuum mechanics and is recovered as the characteristic stress partitioning law that a biphasic medium naturally complies with. The proof of this property is obtained under minimal constitutive hypotheses and no assumptions on internal microstructural features of a particular class of material. VMTPM predicts that such property is unrelated to compressibility moduli of phases and admits no deviations from Terzaghi's expression of effective stress, in contrast with most of the currently available poroelastic theoretical frameworks. This result is presently illustrated and discussed. Simulations of compressive consolidation tests are also presented; they are obtained via a combined analytical-numerical integration technique, based on the employment of Laplace transforms inverted numerically via de Hoog et al.'s algorithm. The computed solutions consistently describe a transition from drained to undrained flow which confirms that Terzaghi's law is recovered as the limit UF condition is approached and indicate a complex mechanical behavior.

Original languageEnglish (US)
Title of host publicationCOUPLED PROBLEMS 2015 - Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering
PublisherInternational Center for Numerical Methods in Engineering
Pages35-46
Number of pages12
ISBN (Print)9788494392832
StatePublished - Apr 1 2015
Event6th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2015 - Venice, Italy
Duration: May 18 2015May 20 2015

Other

Other6th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2015
CountryItaly
CityVenice
Period5/18/155/20/15

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Keywords

  • Consolidation
  • Effective stress
  • Porous media
  • Terzaghi's law
  • Variational poroelasticity

ASJC Scopus subject areas

  • Computational Mathematics
  • Engineering(all)
  • Applied Mathematics

Cite this

Serpieri, R., Travascio, F., Asfour, S. S., & Rosati, L. (2015). Analysis of stress partitioning in biphasic mixtures based on a variational purely-macroscopic theory of compressible porous media: Recovery of terzaghi's law. In COUPLED PROBLEMS 2015 - Proceedings of the 6th International Conference on Coupled Problems in Science and Engineering (pp. 35-46). International Center for Numerical Methods in Engineering.