A geometric basis for critical states in soil mechanics

This will be a very brief post just to clarify my purpose for discussing percolation phenomena and fractals. This is not about the search for a better cup if coffee or generating psychedelic computer images, this is serious stuff for people who work with dirt. 🙂

What I’m getting at us the idea that a percolation phenomenon may be operating in the soil media, which is a complex 3D network of interconnected solid soil particles separated by some pore fluid (often water and/or air, but sometimes involving other fluids.

In soil mechanics we see dramatic behaviour (collapse, bifurcation, liquefaction, etc) when the soil is brought to a critical state through loading via any number of different stress paths or strain paths. The critical state is a critical density (more commonly described in terms of voids ratio) that appears to be more or less unique for a given stress state, largely independent of stress path or strain path.

I believe that the percolation phenomenon can be used to explain the existence of a critical state for a variable grain size/shape granular matrix (soil).

I think the explanation will require consideration of the change in several things as the geometry of interconnected particle clusters changes near the critical density:
– distribution of stresses across particle clusters
– stiffness at contacts within and between particle clusters
– flow characteristics of the pore fluid as it is redistributed through the complex matrix geometry during deformation, and
– pore pressure acting on and between individual soil grains and clusters

This last point may be the most important, and could suggest the basis for some significant adjustments to Terzaghi’s principle of effective stress. In any event, the scale independence of the soil particle clusters at the critical density would be consistent with other phenomena associated with brittle failure mechanisms in soil.

More to follow in due course…


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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