Cylindrical shaped plugs can be tested using a Hoek-Cell like apparatus that allows for efficient and inexpensive measurements of a rock’s static elastic properties. However, when it comes to Transverse Isotropic material, this approach has a natural limitation due to the isotropic radial stresses; particular attention to the boundary conditions and the proper design of pressurization steps is warranted. Typical attempts to constrain the complete set of compliances ( S), using multiple plugs of different orientations, are impeded by the heterogeneity and pressure-dependent elasticities inherent to sedimentary rocks. Through stepwise pressure increases, we can constrain four normal compliances S 11, S 12, S 13, S 33 , describing two Young’s moduli and three Poison’s ratios using a single horizontal plug drilled parallel to the rock’s isotropic plane, contrary to the common assumption that at both horizontal and vertical plugs are needed. The measurement of the shear modulus S 44 needs to be obtained using a plug that is drilled oblique to the isotropic plane; replicating the in-situ stress environment is not possible using this approach. Lastly, the specimen’s anisotropic plane’s geometry is elliptical under isotropic radial stress; this causes a discrepancy between the strain gauge’s contraction and the actual strain. We propose an iterative inversion approach to account for this issue and calculate the exact strains useful for inferring S ij from measurements reported by strain gauges. The example included in this writing shows that without correction, inferred values of S ij may suffer errors of 20%.
Parabolas in the isotropic plane
