Fractal Representation of Soil Cohesion

Abstract

Evaluation of soil cohesion is usually based on measurements made on laboratory-scale samples. Some previous studies point out a decreasing trend in cohesion as the test specimen size increases. Although this trend is, in general, attributed qualitatively to fractures and macropores associated with larger samples, no rational basis has been put forth thus far to upscale cohesion. In this study, the soil medium is idealized as a self-similar fractal system, which contains successive groups of pores that can be scaled in size with respect to each other. A simple relationship between cohesion and sample size is developed using fractal principles. The relationship is demonstrated using experimental data. The fractal dimension of the soil medium, which enters in this relationship, is of both theoretical and practical importance. It draws out the analogy between scale-dependency of cohesion and porosity and enables one to make judgments on the characteristic specimen size required in the assessment of soil cohesion.