Poroelasticity and strength of fully or partially saturated porous materials
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To begin with, a mathematical framework for upscaling and averaging operations is proposed. The classical strategies for the definition of the mechanical loading applied to the representative elementary volume in terms of boundary conditions are recalled. This framework is first applied to a saturated porous medium in which the solid phase is linear elastic. This yields Biot’s poroelasticity theory together with estimates of the poroelastic coefficients and of the average strain level in the solid phase. The situation of a non linear elastic solid is then considered with the help of non linear homogenization techniques. A non linear theory of poroelasticity is derived as an application of the secant method which also allows to investigate the macroscopic strength. The existence of macroscopic effective stresses controlling the non linearity of the secant poroelastic coefficients and the strength criterion is discussed under various assumptions on the solid properties.To finish with, the capillary and surface tension effects are incorporated into a micromechanical approach to the poroelastic behavior and the strength of partially saturated porous media.
KeywordsRepresentative Elementary Volume Macroscopic Stress Macroscopic Strain Deviatoric Strain Microscopic Stress
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- J. Bear and Y. Bachmat. Introduction to the modelling of transport phenomena in porous media. Kluwer Academic Publishers, 1990.Google Scholar
- L. Dormieux, E. Lemarchand, D. Kondo, and E. Fairbairn. Elements of poromicromechanics applied to concrete. Concrete Sc. Eng. Mater. Struct., 265:31–42, 2004.Google Scholar
- F. Gilbert. Description thermomécanique de milieux plusieurs constituants et application aux milieux poreux saturés. PhD thesis, Paris VI, 1987.Google Scholar
- J. Mandel. CISM Lecture notes No. 97, chapter Plasticité classique et viscoplasticité. Springer, 1972.Google Scholar
- P. Ponte-Castaneda. Non linear composites: effective constitutive behavior and microstructure evolution. In P. Suquet, editor, Continuum micromechanics. Springer, 1997.Google Scholar
- P. Suquet. Effective behavior of non linear composites. In P. Suquet, editor, Continuum micromechanics. Springer, 1997.Google Scholar
- A. Zaoui. Matériaux hétérogènes et Composites. Cours de l’Ecole Poly technique, 1996.Google Scholar