Multi-scale approach for modeling the transversely isotropic elastic properties of shale considering multi-inclusions and interfacial transition zone

• Multiscale models for shale with multi-inclusions and interfacial transition zones (ITZs) are presented.
• A new multilevel micromechanical homogenization scheme is presented in an explicit form considering the multi-inclusion and ITZ effects.
• With the increase of the ITZ modulus, the equivalent inclusions and the shale rock enjoy higher effective mechanical properties.
• The volume fractions and properties of the multi-inclusions, such as quartz, calcite and dolomite, play important roles in determining the macroscopic properties of shale rocks.

Multiscale approach based explicit analytic predictions are obtained for the transversely isotropic properties of shale rock considering the multi-inclusion and interfacial transition zone (ITZ) effects. Representative volume elements (RVEs) are utilized to describe the material’s hierarchical microstructures from the nanoscale to the macroscale. A new multilevel micromechanical homogenization scheme is presented to quantitatively estimate the material’s transversely isotropic properties with the multi-inclusion and ITZ effects. The ITZ is characterized by the interphase material, whose effects are calculated by modifying the generalized self-consistent model. Furthermore, the explicit form solutions for the transversely isotropic properties are obtained by utilizing the Hill polarization tensor without numerical integration and the standard tensorial basis with the analytic inversions of fourth-rank tensors. To verify the proposed multiscale framework, predictions obtained via the proposed model are compared with experimental data and results estimated by the previous work, which show that the proposed multi-scaling approaches are capable of predicting the macroscopic behaviors of shale rocks with the multi-inclusion and ITZ effects. Finally, the influences of ITZ and inclusion properties on the material’s macroscopic properties are discussed based on the proposed multiscale framework.