The influence of grain shape and volume fraction of sheet silicates on elastic properties of aggregates: Biotite platelets in an isotropic matrix

Abstract

Elastic anisotropy of sheet-silicate-rich rocks such as shales and slates strongly depends on the orientation distribution of platelet-shaped minerals, as well as shape and orientation of pores. Bulk elastic anisotropy of the rock results in the anisotropy with respect to the propagation of elastic waves, and consequently, the fastest P-waves can travel with velocities exceeding the slowest velocities by a factor of two or even greater. An important factor is the sheet-silicate’s grain shapes. We approached a model system of biotite platelets in an isotropic matrix with different methods: A mean-field self-consistent method that considered ellipsoidal particles in an effective anisotropic matrix, and a full-field method based on fast Fourier transforms that considered the microstructure, the topology of the polycrystal, and local interactions. Both methods provided numerically very close results. Using these results, we predicted that the aggregate with more oblate grain shape (thinner platelets) was elastically more anisotropic than the material with grains of less oblate shape, but only for small volume fractions of oriented platelets. For large fractions of platelets, the opposite was true. This switchover in the elastic anisotropy depended on texture strength, platelet shape, and elastic properties of the isotropic matrix.