Identification of elastic constants of transversely isotropic rocks using strain measurements from a single inclined specimen

The elastic behavior of transversely isotropic rocks is governed by five independent constants. Conventional methods for measuring these elastic constants typically involve uniaxial compression tests on three specimens sampled at different inclinations with respect to the isotropy plane. However, this approach may introduce errors due to specimen heterogeneity. In this study, three sets of simple inversion formulas are derived to determine five elastic constants from strain data obtained during hydrostatic compression followed by an increment of axial stress applied to a single inclined specimen. Each of these three sets includes an identical equation for the shear modulus and a distinct matrix equation for the remaining four elastic constants. Although these matrix equations differ in appearance, they are mathematically equivalent and yield identical solutions. To facilitate coordinate transformation, the Mehrabadi-Cowin notation was employed, in which the strain and stress states are represented as first-order tensors in a six-dimensional space, and the corresponding compliance matrix is treated as a second-order tensor in the same space. The input data for the proposed inversion formulas consist of strain measurements taken in a coordinate system aligned with the strike and dip directions of the isotropy plane. If the orientation of the isotropy plane can be inferred from the strain data, then strain measurements obtained in an arbitrary coordinate system can also be used as input. Illustrative examples are provided to demonstrate the accuracy and practical relevance of the proposed approach.