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