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.
Investigation of mechanical behavior of rocks under applied external stress fields constitutes necessary base for understanding many natural geophysical processes in the Earth's crust, or for solutions of engineering problems connected with a wide spectrum of human activities. For these tasks, simple or very sophisticated numerical models can be adopted. However, for a satisfactory prediction of mechanical evolutions, these models need experimental data in the form of basic mechanical parameters. Rocks usually represent the complicated aggregates of mineral grains of variable size, chemical compositions, or magnitude of binding forces. Such microscopically heterogeneous materials, when subjected to increasing external stress, from the start of loading, undergo reversible elastic deformation, as well as permanent deformation originating preferably from microfractures.
Standard material engineering can successfully adopt generalized Hook's law, describing elastic and mostly linear response through constant elastic moduli, for majority of construction materials at sufficiently low strains. However, in rock mechanics, the mechanical moduli determined from laboratory experiments play the role of linearized effective coefficients rather than constant intrinsic material parameters. For ideal material described through linear relations between strain and stress, a deformational response to general loading conditions can be determined through superposition of uniaxial loads. Therefore, the simplest uniaxial compression/extension laboratory test may be often sufficient to estimate the deformational response in other loading regimes including general triaxial stress state. This consideration is widely used also in geomechanical modeling, i.e. Young moduli and Poisson ratios determined from uniaxial tests on rocks as secant or linearized coefficient are accepted as inputs. However, such attempt is not fully satisfied, and laboratory investigation of the deformational behavior of rocks under alternative triaxial loading regimes is necessary.