Networks originating from the multiple cracking of different scales in rocks and swelling soils

Abstract

The objective of this work is not a fracture prediction or prevention. We are interested in modeling the crack network geometry in rocks and swelling soils and in the application of the model to rock volume fragmentation or preferential flow in swelling soils. Natural and explosion-induced rock fragmentation is important in geophysics and mining. Preferential flow in swelling soils is important in agricultural and environmental engineering. The presentation gives a brief review of the authors' work in this area. A concentration criterion of crack connection and effective independency of cracks in the case of multiple cracking are a basis for the modeling of a crack network. This basis enables one to introduce a condition of fragment formation at crack connection and a number of relevant concepts (an average cracking – an average crack number of x dimension in volume; crack connection probability of x dimension; fragment formation probability; average and maximum fragment dimensions; crack connectedness – a ratio connected to the total number of cracks; and crack network tortuosity), as well as to suggest quantitative relations between the concepts. In the frame of an application, the average fragment dimension and crack connectedness (or the maximum fragment dimension and fragment formation probability) can depend on the spatial coordinates and parameters specific for the application. The simplest application relates to the block-dimension distribution of a rock mass for statistically homogeneous conditions. The second application relates to the granulometric composition of a blasted rock mass in quarries. In this case the specific parameters are the preliminary rock disturbance (including natural cracking), charge construction, blasting scheme and others. The third application relates to the shrinkage crack network geometry in swelling clay soils, the spatial coordinate being the soil depth. The specific parameters are an upper layer thickness (of a few tens of centimeters) of intensive cracking and the maximum crack depth (its boundary being the depth of the water table level). Crack width, depth, spacing, volume, and tortuosity of the crack network are estimated by using the shrinkage curve of the soil and a water content profile. The fourth application relates to the hydraulic properties of capillary crack networks in swelling soils as compared to those of the soil matrix. For all the applications considered, comparison between the model prediction and available data shows good agreement.