A novel method to determine five elastic constants of a transversely isotropic rock using a single-orientation core by strip load test and strain inversion

Abstract

This study proposes a novel method to determine the five elastic constants from a single-orientation core of a transversely isotropic rock using strip loading and strain inversion. The proposed method can be performed under two test conditions: 1) strip load test and strain inversion (single strip load method) and 2) strip load test combined with Brazilian test and strain inversion (strip load and Brazilian method). Strain inversion was carried out by finite element modeling to determine the elastic constants by minimizing the difference between the measured and numerically modeled strains. The method was validated by numerical and laboratory experiments in comparison with the conventional method that uses two uniaxial compression tests with multiple coring directions. In the numerical validation, elastic constants were estimated with high accuracy for cores with high coring angles by the single strip load method. The strip load and Brazilian method accurately determined the five elastic constants for all ranges of coring angles. Validation using Asan gneiss showed that both the approaches of the suggested method can determine the five elastic constants using a single-orientation core. Most of the experimental results were within the range of variations often observed in rock mechanics experiments. The method combining uniaxial compression and Brazilian tests was additionally proposed even though it required an empirical relation of the second shear modulus for horizontally and vertically layered cores. Further, the experimental results were discussed in terms of heterogeneity, nonlinear stress–strain relationship, and Saint–Venant empirical relation. The existing method using a single uniaxial compression test involving the Saint–Venant empirical relation was also tested, showing limited reliability for low coring angles. The suggested methods using a single-orientation core will contribute to a convenient determination of elastic constants of transversely isotropic rocks.