An experimentally constrained constitutive model for geomaterials with simple friction-dilatancy relation in brittle to ductile domains

Complexity of the mechanical behavior of geomaterials makes it very difficult to formulate constitutive models (both at micro- and macro-scales) valid for different loading conditions and deformation regimes. To make progress in understanding this complexity, we take advantage of the large set of data for the synthetic rock analog GRAM1, a granular, frictional, dilatant, and cohesive material formed of bonded rigid particles. We use also data from literature for two real rocks. All data are from conventional triaxial tests conducted for a wide range of confining pressures covering the material behavior from brittle fracturing to ductile flow. The data processing allowed to define both the yield function and the inelastic volume strain as functions of the mean stress σm and the accumulated inelastic strain γ¯p. The internal friction coefficient and dilatancy factor calculated from these functions were shown to be different but evolving very similarly with σm and γ¯p for all the three materials. This allowed to relate the yield and plastic potential functions and thereby to complete the constitutive formulation within the framework of the classical elastoplasticity theory. The obtained results are also used to elucidate the relation between the yield surface and failure envelope as well as the meaning of the internal friction coefficient derived from the failure envelope which is routinely used in geomechanical applications and which is very different from the internal friction coefficient derived from the yield function.