Towards a general state-variable constitutive relation to describe granular deformation

Triaxial-compression experiments were performed on cylindrical quartz sand-packs to explore the universality of state-variable constitutive relations used to describe granular deformation. Samples were subjected to relaxation-creep experiments similar to slide–hold–slide tests from friction studies. For relaxation-creep tests, a constant rate of axial shortening was interrupted by time intervals for which the applied shortening rate was set to zero. During holds, loadforce decayed exponentially with time and the total stress-relaxation scales with the logarithm of hold time, consistent with friction tests. On reloading after holds, stress monotonically increases to the pre-hold steady-state levels without displaying the restrengthening of static friction often observed from shear tests on granular layers. We find that the existing rate- and state-variable friction laws can model the transient strength behavior during relaxation creep and subsequent reloading by using simple assumptions about the deformation of cylindrical sand-packs in triaxial compression. By analogy with the rate- and state-friction constitutive relations, we propose a generalized state-variable expression for granular deformation in simple and pure shear. Although additional experiments under a variety of load boundary geometries and load paths will be needed, such a general constitutive relation may ultimately describe granular deformation under a broad range of conditions (e.g., for large variations in loading rate, shear stress, normal stress, mean stress) and may be applicable to a variety of research problems that involve deformation within granular media.