Percolating contacts network and force chains during interface shear in granular media

Abstract

The concept of force chains transmitting stress through granular materials is well established; however identification of individual force chains and the associated quantitative analysis is non-trivial. This paper proposes two algorithms to (1) find the network of percolating contacts that control the response of loaded granular media, and (2) decompose this network into the individual force chains that comprise it. The new framework is demonstrated considering data from discrete element method simulations of a ribbed interface moving against a granular sample. The subset of contacts in the material that transfers load across the sample, namely the percolating contact network (\(G_{perc}\)), is found using the maximum flow algorithm. The resulting network is fully-connected and its maximum flow value corresponds to the force percolating the system in the direction normal to the ribbed wall. \(G_{perc}\) re-orientates in response to the ribbed interface movement and transmits 85–\(95\%\) of the stress, with only 40–\(65\%\) of the contacts in the sample. Then, \(G_{perc}\) is split into individual force chains using a novel implementation of the widest path problem. Results show that denser materials with increased force-chain centrality promote a higher density of force chains, which results in a higher macro-scale strength during interface shearing. The contribution of force chains in the network is revealed to be highly centralized, composed by a small set of strong and long-lived force chains, plus a large set of weak and short-lived force chains.