Constitutive Relationships Governing Thermo-Poroelastic Processes

A. P. S. Selvadurai; A. P. Suvorov

doi:10.1017/CBO9781316543832.003

2 - Constitutive Relationships Governing Thermo-Poroelastic Processes

Published online by Cambridge University Press: 10 November 2016

A. P. S. Selvadurai and

A. P. Suvorov

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A. P. S. Selvadurai: Affiliation:
McGill University, Montréal
A. P. Suvorov: Affiliation:
McGill University, Montréal

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Summary

We consider a poroelastic material consisting of a linear elastic porous skeleton and accessible pore space that is fully saturated with a non-viscous liquid. The solid phase of the porous skeleton is a linear elastic solid material, which can be compressible. The liquid that saturates the pores of the poroelastic material is also assumed to be compressible. The porosity of the porous elastic material is defined as the ratio of the volume of the pores (or the volume of the liquid) to the total volume and is denoted by ϕ. Typical examples of such a porous medium are soil and rock saturated with water.

For poroelastic materials, the linear elastic stress–strain relation can be expressed in terms of the elastic constants of the fully drained poroelastic body or the porous skeleton without any pore fluid. Under drained conditions, the fluid is allowed to flow in to and out of the accessible pore space, but in the fully drained state the pressure remains independent of time (Rice and Cleary, 1976). For example, the fully drained conditions can be reached when, in the loaded poroelastic body, the pore fluid pressure dissipates with time and eventually becomes equal to zero. The overall mechanical properties and the overall thermal expansion coefficient of such a “drained” poroelastic medium will be equivalent to those of the elastic skeleton with empty or unoccupied pores. (Note, however, that, even when the pressure is zero, the liquid is technically present in the pore space of the medium since the medium remains fully saturated.) Normally, if drainage in the poroelastic body is allowed, fully drained conditions of the body subjected to various loadings prevail in the long term, i.e., as time goes to infinity.

We also define undrained conditions as those that arise when change in the mass of fluid is equal to zero. Typically, the undrained response of the poroelastic material is an instantaneous or initial response of the body to applied mechanical, hydraulic or thermal loadings. It is clear that the linear elastic stress–strain relation for a poroelastic body can also be expressed in terms of the elastic moduli of the undrained poroelastic material.

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Type: Chapter
Information: Thermo-Poroelasticity and Geomechanics , pp. 45 - 59

DOI: https://doi.org/10.1017/CBO9781316543832.003 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2016

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