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The interplay between grain crushing and segregation controls the dynamics of dense granular flows that underpin many natural hazards. We address this issue for the first time by developing a simple lattice model with three interacting rules—for grain crushing, mixing, and segregation. In earthquake faults, particles are trapped, they crush and mix, but do not segregate. In this case the model produces power law distributions, consistent with previous models. When segregation by kinetic sieving is added to the model, we predict depth‐dependent lognormal distributions as previously observed, but not explained, in pyroclastic flows, debris flows, rock avalanches, and dry snow avalanches. Fractal gradings in fault gouges are controlled by mixing and crushingLognormal gradings in avalanches are controlled by crushing and segregationA multiscale model has been proposed for grading evolution in natural hazards

Conventional plasticity models follow rich mathematical formulations. However, they typically lack a physical basis, so their predictive quality is strongly correlated with the number of fitting parameters used. More recent hydrodynamic principles inject physical clarity by separating scales using distinct thermal and granular temperatures. However, existing hydrodynamic models also require many parameters to reproduce a wide variety of experimental observations. This paper combines the advantages of these two approaches to construct a new physics-based hydrodynamic-plasticity model formulation, which is comprehensively predictive. An illustrative model is developed that relies on only five parameters, all of which have been previously defined and calibrated. Four parameters are easily determined from common geotechnical experiments and address diverse rate-independent phenomena, including pressure and density dependent elasticity, pressure- and density-dependent dilation behaviours, critical state relationships under continuous shearing, liquefying cyclic hystereses, and initial stress-ratio dependent extensional shear response. The one remaining parameter enables the recovery of the rate-dependent rheology of friction and density during steady flow, as well as material response during transient loading. A key feature that further distinguishes the current formulation from previous hydrodynamic ones is that here granular temperature is being related to the measurable kinetic pressure. [ABSTRACT FROM AUTHOR]

Comminution is the process of grainsize reduction due to grain crushing, which is common in both natural and industrial problems that involve brittle granular media. Grain crushing is a stochastic process, where the strength of individual grains is determined both by their own size and mineralogy, and the local arrangement of their neighbouring particles, here termed grainsize fabric. The relationship between these effects was described previously using a stochastic lattice model of comminution, whose most general form further includes segregation and mixing. While the stochastic segregation and mixing dynamics have simple analogous differential equations for describing the equivalent continuum behaviour, until now the stochastic comminution dynamics has lacked a smooth representation. Here we resolve this gap by developing a homogeneous continuum model that is based on the same stochastic physics. We show that the new model yields the same results as the stochastic lattice model in the limit of indefinitely large lattices. Given a time varying stress state, the model describes the time-evolution of the grainsize distribution by representing the state of the system in terms of a two-dimensional joint distribution over grainsize and local-average grainsize. The model has a scalable numerical implementation with a simple deterministic rule for time-evolution. [ABSTRACT FROM AUTHOR]