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

Abstract

Abstract:In this study, we develop a complex network approach on a rough fracture, where 6 evolution of elementary aperture during translational shear is characterized. In this manner, based on 7 the Euclidean measure, we make evolutionary networks in two directions (in parallel and 8 perpendicular to the shear direction) and on the measured apertures' profiles. Evaluation of the 9 emerged networks shows the connectivity degree (distribution) of networks, after a transition step; fall 10 in to the stable states which are coincided with the Gaussian distribution. Based on this event, we 11 present a model in which evolving (decaying) of networks are accomplished using a preferential 12 detachment (based on certain probability) of edges. Also, evolving of cluster coefficients and number 13 of edges displays similar patterns as well as are appeared in shear stress and dilation changes, 14 respectively. 15

Topological complexity of frictional interfaces: friction networks

“…With respect to single fracture behaviour, the opening spaces (i.e. aperture patches) were mapped onto networks based on a Euclidean metric (Ghaffari et al, 2009(Ghaffari et al, , 2010. The results showed the clustering coefficient of obtained networks roughly to scale with the mechanical or hydraulic properties of the shear fracture.…”

Complex aperture networks

“…(1)) and building a complex network (Fig.1a) on the X-profiles, gradual changes of the adjacency matrix form of the appeared networks are obtained. The results demonstrate that, after a phase transition step, the patterns of similarities are restricted to the adjacency of each profile [37]. Except for the boundary profiles, the influence distance on each side of a profile changes from 2 to 20 pixels (0.…”

“…This step of the analysis is based on the granularity of the collected information [17]. Choosing a constant value for  is associated with the current accuracy of the data accumulation in which, after the maximum threshold, the system (the aperture evolution) loses its dominant order [37,39]. .…”

“…In our earlier studies, we captured the structural complexity of rough surfaces and scaling with the properly constructed networks [17,37]. In addition, we used a network approach on aperture profiles which was constructed by employing two measure criteria: "Euclidean, correlation and Chebishev".…”

Three-dimensional laser imaging for rock mass characterization

“…Joint orientation can be measured using Principal Component Analysis (PCA) [7,18,25,26]. A variety of methods have been proposed to measure surface roughness [18,[27][28][29][30][31][32].…”