More on geotechnique and fractals…

This looks like it will take some time to come out between bouts of actual work.  :-)

The main point in yesterday’s post is that we like to try to simplify soil and rock behaviour to that of some uniform unit element, and we then apply basic mechanics, making assumptions of uniform stress and strain.

These assumptions imply that we believe the material properties can be adequately represented by some uniform values (perhaps “mean” values – more on that later).  And the experimental evidence in soil mechanics, particularly, suggests that these assumptions are often adequate, particularly when we limit our focus to some relatively narrow scale in time and/or space.

However, there are numerous physical phenomena in soil and rock mechanics, and in groundwater flow, where the behaviour differs depending on the scale of observation.  When this is the case, it is suggestive of the possibility that some fractal aspect of the material may be at work.

Since our basic physical formulations rely directly on Euclidian descriptions of the problem geometry, and a qualitative examination of the materials at hand hints at fractal geometric properties, one is left to wonder if a better (i.e. more consistently correct across a range of scales, in time or space) solution might be derived by re-working the geometric characteristics using fractal geometry.

The following is a brief list of some of the physical phenomena in geotechnique that suggest fractal behaviour a work, and thus might benefit from a fractal analysis:

  • distribution of landslides in space and time; also, clustering of landslides in space and time
  • grain size distribution of selected geological units, such as block-in-matrix rocks and other forms of debris flow/deposition
  • spatial variability of soils properties for consideration in probabilistic finite element analysis, slope stability analysis or settlement analysis
  • fracture of brittle (more precisely quasi-brittle) geological materials (includes physical behaviour as well as geometric patterns of fracture)
  • variation in strength-deformation properties with changes in rate of loading or rate of deformation
  • variability in ductility/brittleness across ranges of scale (in time and space)
  • groundwater flow
  • advance and retreat of glaciers
  • principle of effective stress

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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