Analysis of aperture evolution in a rock joint using a complex network approach

A complex network approach to characterize a rough fracture is developed. Some metric spaces (similarity measurements) between apertures profiles are set up, and a general evolutionary network in two directions (parallel and perpendicular to the shear direction) is constructed. Evaluation of the network shows the connectivity degree (distribution of edges) of network, after a transition step, falls into a stable state that coincides with a Gaussian distribution. Based on this event, and real observations of the complex network changes, an algorithm is proposed in which evolution of a network is accomplished using preferential and random attachments of edges, while the number of nodes is fixed. Evolution of clustering coefficients and number of edges display similar patterns observed in shear stress, hydraulic conductivity and dilation changes, which can be engaged to estimate shear strength distribution of asperities. Distinguishing the contact profiles and their changes, despite the former case, disclosed growing networks, which can shed light on the details of changes within intra-topology of profiles.