Estimation of cracked soil's representative elementary volume based on fractal dimension

Natural soil may be cracked due to wetting-drying cycles, shearing or other effects. Most cracks tend to be connected and form a network. A crack network on a natural soil surface is a random and disordered system. It is hard to describe the distribution characteristics of cracks by the traditional statistical method. Generally, the crack network has fractal dimension. The theory of fractal dimension can be used to describe the distribution characteristics of cracks. Crack images are taken by a digital camera on a soil surface and converted to gray images. A method for determining fractal dimension by photograph is established based on the fractal theory. Then, the fractal dimension of soil cracks can be obtained. According to the physical meaning of representative elementary volume (REV), a method for estimating the cracked soil's REV based on the fractal dimension is presented; and some examples are analyzed. The results show that the fractal dimensions are increased with the increasing of crack density, crack aperture and the development of secondary crack. The REV is related to the homogeneity of crack density and crack aperture. It is easy and credible to estimate the cracked soil's REV by the method mentioned above.