A methodology to determine the elastic properties of anisotropic rocks from a single uniaxial compression test

Abstract

This paper introduces a new methodology to measure the elastic constants of transversely isotropic rocks from a single uniaxial compression test. We first give the mathematical proof that a uniaxial compression test provides only four independent strain equations. As a result, the exact determination of all five independent elastic constants from only one test is not possible. An approximate determination of the Young's moduli and the Poisson's ratios is however practical and efficient when adding the Saint–Venant relation as the fifth equation. Explicit formulae are then developed to calculate both secant and tangent definitions of the five elastic constants from a minimum of four strain measurements. The results of this new methodology applied on three granitic samples demonstrate a significant stress-induced nonlinear behavior, where the tangent moduli increase by a factor of three to four when the rock is loaded up to 20 MPa. The static elastic constants obtained from the uniaxial compression test are also found to be significantly smaller than the dynamic ones obtained from the ultrasonic measurements. Keywords: Transversely isotropic rock, Elastic constants, Young's modulus, Poisson's ratio, Seismic anisotropy, Uniaxial compression, Granite