Deformational Response of Rocks to Uniaxial, Biaxial, and Triaxial Loading or Unloading Regimes

In material sciences, it is a well-known fact that linear or linearized theory based on Hooke's law does not offer a satisfactory description of solids in special regimes, which include e.g. too high strains under large uniaxial stresses. Therefore, in general, the response to biaxial or triaxial loading cannot be obtained as superposition of uniaxial load responses. Striking paper book example of material demonstrating such behavior is rubber subjected to uniaxial or isotropic compression. Despite this fact, linear mechanical moduli, being secant or differential, determined through standard rock-mechanics tests, mostly from the uniaxial compression, are still widely used for description of deformational behavior of rocks. Without doubt, an appropriate interpretation of these effective quasi-elastic or stiffness moduli can give useful information about mechanical properties of the rocks, especially in comparative sense. However, for more reliable constitutive modeling of any solid materials, paricularly rocks, an experimental investigation of deformational responses to uniaxial, biaxial and triaxial loading or unloading regimes is very useful. This contribution presents the results of an experimental case study on homogeneous sandstone exposed to isotropic triaxial, and equi-biaxial or uniaxial loading regimes. The measured deformational response of this rock is compared with behavior of elastic solid materials. Finally, benefit of the experimental testing for constitutive modeling based on phenomenological description is briefly discussed.