Abstract
Strong force chains form when any granular material is subjected to load. A prior study used Delaunay triangulations to investigate the role of interparticle friction coefficient, μ, in stabilising the strong force chains [1]. In this follow-on paper, the effects of μ and the intermediate stress ratio, b , are compared. Numerical samples were sheared triaxially until critical state was attained. The contact networks and Delaunay triangulations of the particle centroids were both obtained at the end of each simulation. As μ is increased, the numbers of contacts in the contact networks decrease consistently. The numbers of edges, faces or tetrahedra in the Delaunay triangulations all increase with increasing μ up to 0.25 and become approximately constant thereafter. Changing b has no significant effect. The percentage of faces in the triangulation comprising three contacts shows a linearly-decreasing trend with increasing angle of shearing resistance. This is because only orthogonal loads are applied. Triangular structures require larger lateral supporting forces to maintain their stability than columnar structures when subjected to an axial load; hence, σ 3 ′ is expected to be larger relative to σ 1 ′ when triangular motifs are more prevalent. An increased proportion of triangular structures therefore leads to a lower ϕ cv ′.
Highlights
The stress distribution is highly heterogeneous within any granular material subjected to load
A range of complementary investigation tools including DEM simulation [2], photoelasticity experiments [3] and analytical modelling [4,5] indicate that the dominant failure mechanism in a granular material is buckling failure of the strong force chains
The number of contacts decreases with increasing μ; Fig. 3a shows that the number of edges in the Delaunay triangulations increases with μ up to μ = 0.25 and remains approximately constant thereafter
Summary
The stress distribution is highly heterogeneous within any granular material subjected to load. Delaunay triangulations are again used, on this occasion to compare the effects of μ and the intermediate stress ratio, b, on force chain stability. Starting from the stable, isotropic sample described above, each of these ‘varying b’ triaxial shearing simulations was run by initially increasing μ from 0.0 to 0.25, and using a stress-control algorithm to either impose plane strain conditions or else The ‘varying μ’ data set [6] consisted of six drained shearing simulations at constant μ values of 0.0, 0.1, 0.25, 0.5, 0.75 or 1.0.
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