Three-dimensional numerical modeling of hydrostatic tests of porous rocks in a triaxial cell

• Hydrostatic test of sandstone is modeled closely to the experimental conditions.
• Stresses and strains in the models are different from the nominal/average values.
• They strongly depend on the friction between the sample and the steel platens.

It is known that there is stress concentration at specimen ends during experimental rock tests. This causes a deviation of the measured nominal (average) stresses and strains from the actual ones, but it is not completely clear how strong it could be. We investigate this issue by numerical modeling of the hydrostatic tests using a reasonably simple constitutive model that reproduces the principal features of the behavior of porous rocks at high confining pressure, PcPc. The model setup includes the stiff (steel) platens and the cylindrical model rock specimen separated from the platens by the frictional interfaces with friction angle ϕint. The whole model is subjected to the quasi-statically increasing normal stress PcPc. During this process, the hydrostats PcPc(ε) are computed in the same way as in the real tests (ε is the average volume strain). The numerical hydrostats are very similar to the real ones and are practically insensitive to ϕint. On the contrary the stresses and strains within the specimen, are extremely sensitive to ϕint. They are very heterogeneous and are characterized by a strong (proportional to ϕint) along-axis gradient, which evolves with deformation. A strong deviation of the stress state at the specimen ends from the isotropic state results in inelastic deformation there at early loading stages. It follows that the nominal stresses and strains measured in the experimental tests can be very different from the actual ones, but they can be used to calibrate constitutive models via numerical simulations.