The solid phase stress tensor in porous media mechanics and the Hill-Mandel condition

William G. Gray, Bernhard A. Schrefler, Francesco Pesavento

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


An assessment of the stress tensors used currently for the modeling of partially saturated porous media is made which includes concepts like total stress, solid phase stress, and solid pressure. Thermodynamically constrained averaging theory is used to derive the solid phase stress tensor. It is shown that in the upscaling procedure the Hill conditions are satisfied, which is not trivial. The stress tensor is then compared to traditional stress measures. The physical meaning of two forms of solid pressure and of the Biot coefficient is clarified. Finally, a Bishop-Skempton like form of the stress tensor is obtained and a form of the total stress tensor that does not make use of the effective stress concept.

Original languageEnglish (US)
Pages (from-to)539-554
Number of pages16
JournalJournal of the Mechanics and Physics of Solids
Issue number3
StatePublished - Mar 2009


  • Bishop parameters
  • Elasticity
  • Hill-Mandel condition
  • Porous media
  • Skempton stress

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics


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