ON REYNOLDS' DILATANCY AND SHEAR BAND EVOLUTION: A NEW PERSPECTIVE

Abstract

Dense granular media exhibit rich phenomenology when subject to imposed stresses and strains. This is a result of the many degrees of freedom present in an assembly of grains and the nonlinear interactions between the grains. Their complex behavior include the self-organization of load-bearing columnar structures known as force chains across a wide range of spatial scales. Behavior akin to phase transitions from a strong solid-like to a weak liquid-like response can also be observed with shear bands, i.e. regions where force chains collectively buckle, being the signature microstructure in this transition from the stable to the failure regime. An inherent aspect of shear bands and dense granular failure is the phenomenon of dilatancy, i.e. expansion in volume, when the material is subjected to a combined compression and shear. To understand the origins of dilatancy, it is useful to consider the granular material as a mixture of two components: grains and the interstitial material filling the voids or pores between the grains. The grains within a dense granular material respond to applied loads by rearranging to create local zones which contract and dilate. Extant studies of this mechanical response are typically focused on the solid skeleton, in particular, the topology of the network representing the physical contacts between grains. Here, we propose an alternative perspective which is to consider network representations of the evolving anisotropic pore space. We demonstrate how to construct pore space networks that express the local size of voids about a grain through network edge weights. We investigate sectors of the loading history when a percolating giant component of the pore space network exists. By defining two weight functions for edge properties, we: (i) discover via a recurrence plot-based analysis a temporal time scale for jamming–unjamming (contractant-dilatant) dynamics in shear bands; and show that (ii) the formation of a persistent shear band in response to the deformation places grains in a configuration predisposed to the efficient transport of interstitial material as evidenced by the location of percolating shortest path routes through the most dilatant sites. A proper understanding of the micromechanics of pore evolution with respect to shear bands and dilatancy is key to a range of applications such as modeling ground water flow, dewatering systems, carbon capture and sequestration.