Two-step Homogenization of Poroelastic Properties of a Limestone

Abstract

This study aims at deriving the effective poroelastic properties of the oolitic limestones based on the Hashin composite sphere assemblage (CSA) micromechanical theory. The microstructure of oolitic limestones generally exhibits an assemblage of grains (oolites) surrounded by a matrix. Grain and matrix are linked via the interfacial transition zone (ITZ). Pores exist in these three material phases (oolite, ITZ and matrix). A two-step homogenization method is proposed. The first step consists of upscaling the properties of each porous phase (i.e. porous oolite, porous ITZ and porous matrix) in which each phase contains two sub-phases including pore and solid. The differential self-consistent scheme is used for the first step. At the second step, the three different porous constituents (oolite, ITZ and matrix) are assembled in a CSA model. A mathematical analogy between thermoelasticity and poroelasticity is used to obtain the effective poroelastic properties. A comparison between the proposed model and test data on the oolitic limestone from Bourgogne (France) helps to calibrate the model parameters and to highlight the role of ITZ phase.