REEXAMINATION OF THE EQUATIONS OF POROELASTICITY

For the mechanical behavior of poroelastic media, the method of homoge nization has been applied to derive effective equations on the macrosc ale, for a matrix with a periodic structure on the microscale. In exis ting theories the resulting effective equations are linear, which not only confirm the phenomenological theory of Blot [J. Appl, Phys. 12, 1 55-165 (1941)], but also provide a theoretical framework for calculati ng the constitutive coefficients. We point out that all past authors a pplied the continuity of displacement and stresses at the initial and undeformed solid-water interface. this implies that the solid displace ment, due either to global or local strain, must be much smaller than the granular or pore size. Here we shall allow the matrix displacement corresponding to the global strain to be comparable to the granular s ize, and show that the resulting effective equations are non-linear in general. The constitutive coefficients of the non-linear terms nevert heless vanish under two conditions: (i) when the global-scale deformat ion is also much smaller than the granular size, and (ii) when the glo bal-scale deformation is comparable to the granular or pore size, but the microcell geometry is symmetric with respect to three orthogonal p lanes. The first limit is trivial and is no different from the existin g theories. The second limit is not trivial and shows the robustness o f the linearized equations. The result suggests that the linear effect ive equations may be adequate even for practical problems involving no t-too-small deformation or loading, as long as the microscale geometry is isotropic in the statistical sense. (C) 1997 Elsevier Science Ltd.