I’ve been reading a little about fractal geometry lately, following up on an interest that developed a couple of years ago but remained unexplored until I found a little time while on vacation in Greece. Like the prime number work, this is a little bit of a hobby project, one again benefiting greatly from ideas and input from my son John.
As a geotechnical engineer, I rely on a daily basis on the sciences of soil mechanics and rock mechanics, both relatively young disciplines, when compared with other branches of applied science and engineering.
The thing that first attracted me to geotechnique, while starting never completed masters studies in structural engineering, was its complexity and uncertainty. The physical properties of soil, rock and groundwater are highly variable and disordered, requiring considerable engineering judgement to select appropriate numbers for design. By contrast, most “standard” engineering materials, like concrete, steel, and even timber, have well defined engineering properties.
We typically deal with the material variability in geotechnical problems by selecting appropriate (large) factors of safety, thus providing some reasonable certainty that the actual strength or stiffness exceeds our reasonable estimate, and thus minimizing the possibility of failure. Traditionally, we use a working stress design approach, using a factor of safety to separate the assumed strength from the anticipate loads.
In recent years, there has been a move toward a limit states design approach, whereby instead of simply applying a judgement-based safety factor to account for uncertainty, we would rather attempt to define the uncertainty with some precision and account for it explicitly.
In my view, we are a LONG way from being able to apply limit states design on a consistent basis, primarily because we don’t tend to try to quantify material uncertainty in a rigourous and consistent basis, but also, importantly, because of the variability in the nature of variability. Every site is different, with different types of material, some of which have unique or particular aspects not commonly encountered.
The physics of soil and rock mechanics are based on a “normal” Euclidean description of problem geometry. I expect that much of the uncertainty embedded in geotechnical problems could be better characterized through re-evaluating the geometric aspects of the physics via fractal geometry.
More to follow…