Earlier today I posted a bit of an update on this topic here: percolation part 1, 13 March, and promised more detail. Here I will present a bit of the supporting results of simulations.
I started with notional 1 m x 1 m specimens of each “soil type,” then increased the size of individual soil grains uniformly by set factors ranging from 1 (base case) to 2, making note of the size of typical and largest clusters, and associated “density” or void ratio. I also looked at a larger specimen, 2 m x 4 m, for the broadly graded material, to examine expected scale effects.
Looking at the “broadly graded” soil, here is the base condition:
I’ve emphasized 21 of the largest individual clusters, including the largest one in black. At this stage, the soil matrix is comprised of non-connected individual clusters. One can deduce that shear stresses applied at the specimen boundaries could not be transmitted through the model, since there is no contact between particles, and the void spaces (whether filled with a pore fluid, or consisting of a gas or vacuum) cannot transmit shear forces.
Next look at the model at a density near where the largest individual interconnected cluster has grown to the full size of the model:
At this point we have the model space spanned by a fractal structure of interconnected soil particles. The largest cluster is emphasized in black.
Finally we can look at a case where density has exceeded the critical value by some substantial amount. I’ll get to this a little later today, but here are the grain size curves for the broadly graded soil in the base case, at particle diameter 1.5 times the base case, and 2 times: