Determination of 12 orthotropic elastic constants for rocks

Abstract The deformation properties of rocks ultimately become anisotropic depending on the orientations of mineral particles and sedimentary structures . Characterization of deformation anisotropy is important for accurate understanding of the deformation characteristics of structures constructed inside rocks (e.g., rock foundation and tunnel). The simplest anisotropic elastic model is transversely isotropic elasticity, and in recent years, many methods for rationally specifying this elastic constant have been proposed. Although the most general linear elastic model for describing deformation anisotropy is orthotropic elasticity, no efficient method currently exists for determining the orthotropic elastic constants because the number of elastic constants required for the model description is extremely large. A rational determination method for orthotropic elasticity is necessary when considering application at construction sites and coupling with other phenomena such as differences in water content. In this study, a new method was developed for obtaining all 12 constants of orthotropic elasticity by three uniaxial compression tests on specimens sampled in three directions orthogonal to each other. For each specimen, the strain tensor was measured, and the strains in the elastic region were added and analyzed to identify the principal orientation of orthotropic elasticity. Thereafter, nine elastic constants are specified using the stress–strain relationship of each specimen. The methodology is described herein. The validity of the proposed method was evaluated on the basis of results from verification experiments performed with Neogene soft sedimentary rocks.