Fractals and Geotechnique, Continued

A few more words to continue yesterday’s line of thought.

Soil and rock are comprised of discontinuous media.  In simple terms, these can be subdivided into a “skeleton” of relatively stiff and strong blocks or particles interconnected by direct point to point contact and separated by void spaces.  The void spaces, or pore spaces, are filled with a pore fluid, which may be comprised of air and/or water and/or some other gas/fluid.

We like to distinguish between “saturated” and “unsaturated” soils, whereby the pore spaces are either completely filled with pore fluid (mos often assumed to be water) or not.

In saturated soils, we will assume that the soil (or rock) particles are individually very stiff and strong, but the soil matrix (i.e. interconnected aggregation of particles) may be considered as relatively compressible, in comparison with the pore fluid, which has substantial volumetric stiffness (assuming we are dealing with water).  We also assume that the pore fluid has no ability to resist shear distortion, whereas the soil matrix will have, by comparison, considerable shear strength and stiffness.

When we describe the state of stress in a soil element, we invoke the principle of effective stress.  Soil behaviour is believed (and has been experimentally demonstrated) to be governed by the stress in the soil matrix.  If we know the total stress within an element of the soil-pore fluid mixture, then we can calculate the effective stress, or stress in the soil matrix, by subtracting the stresses acting on the pore fluid.

If we accept that the description of stress can be simplified into two independent components – shear stress and volumetric stress – and we apply the basic assumptions previously mentioned (notably that water has volumetric stiffness but no shear stiffness), then for a given soil element:

Effective Stress (S’) = Effective Shear Stress (T’) + Effective Volumetric Stress (V’)

S’ = Total Shear Stress (T) + Total Volumetric Stress (V) – Fluid Shear Stress (nil) – Fluid Volumetric Stress (U) = T + V – U

more to follow…

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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