Tortuosity of crack networks in swelling clay soils

Tortuosity of the crack network in a swelling clay soil determines the actual mean length of flow through the cracks and is an important factor influencing the hydraulic properties of the soil. In the literature there are works related only to tortuosity of the pore system of a nonswelling-soil matrix. The approach to estimate tortuosity proposed here is based on an established model of crack network geometry in swelling clay soils. Dependency of the tortuosity on the connectedness of a statistically isotropic crack network is derived from the fact that connected cracks outline fragments (peds) and are their boundaries. The second parameter that characterizes the crack network, the mean spacing between cracks, does not influence the tortuosity. The estimated two- and three-dimensional tortuosities vary from 1.5 to 2.2 and from 1.4 to 3.25, respectively, when connectedness decreases from unity to zero (for instance, with increasing soil depth). A proposed method for processing a two-dimensional image of crack networks enabled us to estimate experimental two- and three-dimensional tortuosities and connectedness of an assumedly isotropic crack network. This direct estimation from two-dimensional images is practical for sufficiently large values of connectedness. Data of seventeen different two-dimensional images (available in the literature) were used to show the applicability of the proposed dependencies of tortuosity on crack connectedness in the range 0.5 to 1.