Mechanical properties of rocks with marked weak planes such as foliation, schistosity or bedding, are not isotropic. The deformability of these rocks is transversely anisotropic (TI), and, therefore, different axial strains are observed according to the load direction, being equal in directions within the weakness plane. Their elastic behavior is theoretically defined by five independent constants. In this study, a relatively large number of strain data sets collected from compressive tests on slate are used to estimate these constants. Two main approaches are followed. The first consists in solving the corresponding compliance matrix equation by means of the least square best fit multi-regression approach in groups of samples, which are then averaged. The second is based on minimizing the error in the stress invariant by means of a non-linear gradient algorithm. Results are analyzed aiming to learn how to manage strain variability in the process of TI elastic parameter estimate.
Determining the elastic constants is important to understand and model the behavior of rocks and rock masses. A number of common metamorphic and sedimentary rocks such as shales, schists, slates or gneisses present marked foliation, so they are transversely isotropic materials, whose behavior is controlled by the orientation of these weakness planes. In these materials, the elastic behavior changes according to the direction in which a load is applied in relation to the transverse anisotropy plane. This behavior can be theoretically defined by five independent elastic parameters, namely two Young's moduli (E and E’), two Poisson's ratio (ν and ν’) and a shear modulus (G).
Analytical methods based on Lekhnistskii's (1963) elasticity analyses can be used to obtain these parameters, as those proposed by Barla (1974) or Amadei (1982). To determine these elastic constants, several authors proposed theoretical approaches (Barla 1974, Amadei 1996, Chen et al 1998). The number of different oriented cores (typically two or three) should be adapted to the number of available equations to obtain the five elastic constants. If more strain data are available, the least square approach was recommended by Amadei (1996) to calculate the elastic constants that the best fitted test results.
