Analysis of Aperture Evolution in a Rock Joint Using a Complex Network Approach

TL;DR

This paper introduces a complex network approach to analyze aperture evolution in rock joints during shear, revealing stable states and network dynamics that correlate with mechanical and hydraulic properties.

Contribution

It presents a novel complex network model for aperture evolution, linking network topology changes to physical properties and introducing the concept of growing networks in this context.

Findings

Network connectivity stabilizes in Gaussian distribution after transition.

Evolving network patterns correlate with shear stress and hydraulic conductivity.

The model suggests surface destruction follows a combination of random and preferential processes.

Abstract

In this study, we develop a complex network approach on a rough fracture, where evolution of elementary aperture during translational shear is characterized. In this manner, based on some hidden metric spaces (similarity measurements) between apertures profiles, we make evolutionary network in two directions (in parallel and perpendicular to the shear direction) and on the measured apertures profiles. Evaluation of the emerged network shows the connectivity degree (distribution) of network, after a transition step; fall in to the stable states which are coincided with the Gaussian distribution. Based on this event and real observations of the complex network changes, a simple model has been proposed in which evolving (decaying) of network is accomplished using a preferential detachment of edges. This suggests that destroying of surfaces is accomplished in a manner that is followed as a combination of random and preferential selection of each element. Also, evolving of cluster coefficients and number of edges displays similar patterns as well as are appeared in shear stress, hydraulic conductivity and dilation changes, which can be engaged to estimate shear strength distribution of asperities. Distinguishing of the contact profiles (or their equivalent : percolating clusters) and their changes, despite the former case, disclosed new side of a network, namely growing networks, which shed light the details of changes within intra-topology of profiles. Keywords: Complex Network, Aperture Evolution, Rock Joint