Experimental Observation of the Onset of Percolation in Freshwater Granular Ice

Abstract

AbstractThe inferred narrow range of crack densities of crustal rocks at depths >1 km has been interpreted to imply that crack networks at depth are in a state of criticality with densities restricted to values near the percolation threshold. Their state is critical in the sense that at crack densities above this threshold, both the permeability and compliance increase significantly, allowing pore fluids to disperse and stresses to relax, limiting further crack growth. This analysis assumes that the crack density percolation threshold is similar to that of crack networks composed of randomly located cracks, yet network structure due to crack growth processes is known to impact the percolation threshold. Using ice as a model material for rock, we show experimentally that near the brittle‐to‐ductile transition, the crack density at the percolation threshold depends on the strain rate. At higher strain rates, the strain at percolation is scale invariant, and the crack density percolation threshold is similar to that of random crack networks. At lower strain rates, the strain at percolation increases with sample size, and percolation occurs at crack densities significantly below that at which percolation occurs in random crack networks. Near the brittle‐to‐ductile transition in the deeper crust, crack growth and coalescence may depend on strain rate, changing the nature of crack network criticality.