Emergence of Structure in Columns of Grains and Elastic Loops

TL;DR

This paper explores how structures made of rocks and elastic loops emerge and stabilize, revealing the roles of friction and elasticity in determining the critical spacing for stability.

Contribution

It introduces a model linking grain friction and loop elasticity to the critical spacing needed for stable granular structures.

Findings

Higher friction increases stable contact angles and critical spacing.

Greater bending rigidity of loops improves pressure containment.

Derived a linear relation for frictional critical spacing.

Abstract

It is possible to build free-standing, load-bearing structures using only rocks and loops of elastic material. We investigate how these structures emerge, and find that the necessary maximum loop spacing (the critical spacing) is a function of the frictional properties of the grains and the elasticity of the confining material. We derive a model to understand both of these relationships, which depends on a simplification of the behavior of the grains at the edge of a structure. We find that higher friction leads to larger stable grain-grain and grain-loop contact angles resulting in a simple function for the frictional critical spacing, which depends linearly on friction to first order. On the other hand, a higher bending rigidity enables the loops to better contain the hydrostatic pressure of the grains, which we understand using a hydroelastic scale. These findings will illuminate the stabilization of dirt by plant roots, and potentially enable the construction of simple adhesion-less structures using only granular material and fiber.