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Unified creeping model identifying the critical state of granular materials

The mechanical properties of granular materials at a low shear rate are frequently viewed as rate-independent, and a rate-independent constitutive relation is used to describe the mechanical behaviors of the granular material. However, time-dependent behaviors (or creeping behaviors) become significant in the long run. In this paper, we conduct triaxial experiments to observe the creep of granular materials under both dynamic and static loading conditions. Three typical creeping behaviors, aging, transitional, and fluidic, have been observed. To describe the time-dependent behaviors, an internal state variable characterizing the fluidity of the granular system is introduced to propose a rate-dependent constitutive relation which we call in this paper, a state evolution model. A characteristic strain is also introduced into the model to account for the influences of historic strain on the current state. The experiments are analyzed using the proposed model and it has been found that our model can well discern the observed three creeping behaviors. A criterion to identify the stability of a granular system is also given out based on the proposed model. Two key factors dominating the stability of the granular system are recognized – shear wave velocity and critical velocity. Our laboratory experiments in combination with the proposed criterion offer a physical explanation of the intrinsic triggering mechanism of system evolution from a stable to fluidic state: decrease in wave velocity or/and critical velocity.