Multi‐porous extension of anisotropic poroelasticity: Linkage with micromechanics

Abstract

We attempt to formalise the relationship between the poroelasticity theory and the effective medium theory of micromechanics. The assumptions of these two approaches vary, but both can be linked by considering the undrained response of a material; and that is the main focus of the paper. To analyse the linkage between poroelasticity and micromechanics, we do not limit ourselves to the original theory of Biot. Instead, we consider a multi‐porous extension of anisotropic poroelasticity, where pore fluid pressure may vary within the bulk medium of interest. As a consequence, any inhomogeneities in the material are not necessarily interconnected; instead, they may form isolated pore sets that are described by different poroelastic parameters and fluid pressures. We attempt to incorporate the effective methods inside Biot‐like theory and investigate the poroelastic response of various microstructures. We show the cases where such implementation is valid and the others that appear to be questionable. During micromechanical analysis, we derive a particular case of cylindrical transverse isotropy—commonly assumed in conventional laboratory triaxial tests—where the symmetry is induced by sets of aligned cracks.

Multi‐porous extension of anisotropic poroelasticity: Consolidation and related coefficients

“…24 Second, the poroelastic coefficients can be obtained from micromechanical derivations, as presented in our parallel paper. 33 In the planned future developments, we will perform the experiments proposed in Sections 4-5.…”

“…Thus, one can choose between macroscopic single-porosity description (𝑛 = 1), more accurate-but still somewhat idealized-mesoscopic dual-porosity description (𝑛 = 2), or even more accurate mesoscopic triple-porosity description (𝑛 = 3), and so on (𝑛 ≥ 4), till fully microscopic description is reached (𝑛 = total number of pores). 33 Naturally, the choice of the model is a trade-off between scale refinement and the accuracy of the estimation-if at all possible-of the parameters.…”

“…Further, one can also search for the micromechanical link to the theory (pore geometry); such linkage is discussed in our parallel paper. 33 We subjectively distinguish three types of porous structures, where our extension is pertinent: hierarchical porosity, complex porosity, and clustered porosity formed by spatially-distributed pore sets. Each type is presented in Figure 2 and discussed below.…”

“…The equations for all isolated sets are given and discussed explicitly in our parallel paper. 33 So far, we have presented two versions of strain-stress relations for a multiple-porosity system. Equations ( 5) used coefficients 𝑎 (𝑝) 𝑖𝑗 and 𝑏 (𝑝) 𝑖𝑗 , whereas Equations ( 22)-( 23) utilized more tangible Skempton-like and storage coefficients.…”