Prediction of the anisotropic effective moduli of shales based on the Mori-Tanaka model and the digital core technique

Abstract

Abstract Natural rocks belong to the polymineral composite material with complex microstructures. Such a strong heterogeneity of rocks makes it difficult to estimate the effective moduli by traditional models in theory. In the present study, a Mori-Tanaka (MT) model considering the shape and orientation of inclusion minerals obtained by the micro-CT is established, and then it is applied to evaluate the anisotropic parameters of shales. In the MT model, the principal radii and Eulerian angles of the ellipsoidal inclusion are obtained by solving its inertia matrix through the micro-CT. According to these inclusion information, we make statistics on the ratio of average principal radii and the distribution of Eulerian angles of inclusions with different minerals. In what follows, the effective elastic stiffness matrix of shale samples is predicted by the MT model, and the corresponding digital core is input for finite element method (FEM) analysis to verify the accuracy of the theoretical results. It is shown that the anisotropy of the elastic stiffness matrix predicted by the MT model and FEM is consistent under two sizes of representative volume elements. These findings are potential for applications in rock mechanics, civil engineering and oil exploitation, etc.