Granular matter and the marginal rigidity state

Model experiments are reported on the build-up of granular piles in two dimensions. These show that, as the initial density of falling grains is increased, the resulting pile has decreasing final density and its coordination number approaches the low value predicted for the theoretical marginal rigidity state. This provides the first direct experimental evidence for this state of granular matter. We trace the decrease in the coordination number to the dynamics within an advancing yield front between the consolidated pile and the falling grains. We show that the front’s size diverges as the marginal rigidity state is approached, suggesting a critical phenomenon. (Some figures in this article are in colour only in the electronic version) Recent theoretical works [1–5] have suggested that a distinctive, marginal rigidity state exists for rigid cohesionless grains. This state is characterized by low connectivity and exhibits stress transmission governed by its geometry alone. It has yet to be established whether this applies to real granular matter, such as sand or grain, but it is a candidate to underpin recent success in modelling macroscopic stress transmission [6, 7]. Here we present the first direct experimental evidence, from idealized granular systems in two dimensions as shown in figure 1, that the marginal solid state of matter does indeed exist. Our experiments also reveal a diverging lengthscale, suggesting that the state is a true critical phenomenon. The key idea behind this state is that rigid grains falling to form a pile will rearrange and consolidate, until their mean coordination number z reaches a critical value zc at which the net force and torque on each grain can first be balanced by the intergranular forces. At this marginal rigidity state the forces, and hence the transmission of stress, are exactly determined by balance alone, without reference to any internal constitutive behaviour of the individual grains. This state separates fluid from conventional solid: so long as z < zc, mechanical balance cannot in general be obtained and the system is fluid. By contrast, when z > zc the system can be mechanically balanced, but additional information is needed to determine the intergranular forces. The extra information usually comes from constitutive stress–strain relations and consistency of the strain field, leading to stress transmission typical of traditional solids. 0953-8984/05/242481+07$30.00 © 2005 IOP Publishing Ltd Printed in the UK S2481 S2482 R Blumenfeld et al