A rate-dependent breakage model based on the kinetics of crack growth at the grain scale

Experimental evidence indicates that granular soils under high confining stress accumulate deformation over time, with processes such as creep, relaxation and strain-rate sensitivity being controlled by the growth of internal flaws and the delayed fracture of individual particles. In this paper, a connection between the theory of subcritical crack propagation and the continuum modelling of crushable soils is established by exploiting an analogy between the processes that promote energy release upon the fracture of single particles and those that are responsible for delayed comminution in soil samples. Models describing the kinetics of crack propagation have been reinterpreted from a thermodynamic standpoint, showing that the energy loss during crack growth includes higher-order terms which augment the dissipation by surface area creation. This result has inspired the introduction of similar higher-order terms in the dissipation function of a continuum breakage model, thus hypothesising that the rate dependence of collective crushing can be seen as the macroscopic outcome of the growth of cracks in individual grains. This choice leads to a rate-dependent continuum model characterised by a breakage growth rate controlled by the same coefficient that governs the kinetics of crack growth in the grain-forming minerals (the so-called stress corrosion index). It is shown that the model exhibits good agreement with the creep and relaxation response measured for a range of soils tested under oedometric and triaxial conditions. These results corroborate the hypotheses about the link between subcritical crack growth and the energetics of delayed comminution and set a vision to model delayed fracture processes occurring in fluid-infiltrated reactive environments.