A geometric basis for critical states in soil, more…

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 generated three different simulated soils, made of randomly distributed circular “soil particles.” The initial grain size distributions for my three artificial soils are here:

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:


About petequinn

I'm a Canadian geotechnical engineer specializing in the study of landslides. I started this page to discuss some mathematical topics that interest me, initially this involved mostly prime numbers, but more recently I've diverted focus back to a number of topics of interest in geotechnique, geographic information systems and risk. I completed undergraduate training in engineering physics at Royal Military College (Kingston, Ontario), did a masters degree in civil (geotechnical) engineering at University of British Columbia (Vancouver), and doctorate in geological engineering at Queen's University (Kingston). I was a military engineer for several years at the beginning of my career, and did design and construction work across Canada and abroad. I've worked a few years for the federal government managing large environmental clean up projects in Canada's arctic, and I've worked across Canada, on both coasts and in the middle, as a consulting geotechnical engineer. My work has taken me everywhere in Canada's north, to most major Canadian cities and many small Canadian towns, and to Alaska, Chile, Bermuda, the Caribbean, Germany, Norway, Sweden, Bosnia, and Croatia. My main "hobby" is competitive distance running, which I may write about in future.
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