Analysis of Aperture Evolution in a Rock Joint Using a Complex Network Approach
📝 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
💡 Analysis
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
📄 Content
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Analysis of Aperture Evolution in a Rock Joint Using a 1 Complex Network Approach1 2 Hamed .O.Ghaffari & Mostafa.Sharifzadeh 3 Department of Mining & Metallurgical Engineering, Amirkabir University of Technology, Tehran, Iran 4
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Abstract: In this study, we develop a complex network approach on a rough fracture, where
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evolution of elementary aperture during translational shear is characterized. In this manner, based on
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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
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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,
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respectively.
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Keywords: Complex Network, Aperture Evolution, Rock Joint
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- Introduction
17 Understanding of rock joint behaviors, either in single or swarm form, under the several 18 natural or artificial forces has allocated numerous researches during the evolution of rock 19 mechanics field. Scientists have shed light on the several approaches to capture interacted 20 rock joint(s) manners as well as analytical solutions to hybrid numerical methods and the 21 methods based upon indirect investigations such as fractal , statistical or natural based 22 computing methods [1]-[3]. Rock joint performance as a result of collective behavior of the 23 constructed elements (say fraction/pixel in each surface), interacting with each other, 24 determines nonlinear picture of a changeable system. Obviously, one cannot predict the rich 25 behavior of the whole by merely extrapolating from the treatment of its units [23].
26 1 .The paper has been submitted to International Journal of Rock Mechanics &Mining Sciences 2
This is a prevalent gesture of complex systems. The success in describing of interwoven 1 systems using physical tools as a major reductionism is associated with the simplifications of 2 the interactions between the elements so that complexity reduction is a rescue pathway to 3 regulation of approximated analyses of collective particles having swing states, complicated 4 structures, and diversity of relations among elements. Dissection of phenomena under 5 investigation into a list of interacting unites- which are building blocks (granules) of system- 6 connected by pair-wise connections, can be revealed in complex networks, which provide a 7 mathematical framework to analysis of wide range of complex systems. Picturing, modeling 8 and evaluation in a simple and intuitive way are some of the discriminated features of 9 complex networks [4],[5].Complex networks have been developed in the several fields of 10 science and engineering for example social, information, technological, biological and 11 earthquake networks are the main distinguished networks [6]-[9]. 12 On the other hand, to catch on Hydro-mechanical and mechanical behavior of a rock 13 joint, domination on to the surface morphology evolution as well as aperture is irrefutable. In 14 this way, characterization of aperture of a rock fracture has been realized by using several 15 techniques such assigning of probability distributions (random field theory) [1], [2] and – 16 [11], [12] correlation length [14], fractals [13] and spatial correlation (semi-variorums) [3]. In 17 this study, we provide a complex network approach on the aperture evolution during 18 transitional shear accounting in two separated directions of shear while the disclosed 19 networks involve the inherent difficulties such dynamical concepts of components, changing 20 the wiring diagrams and meta- complications. Also, upon the consequences we present an 21 algorithm, offering a general view of transitions of an elementary aperture distribution, which 22 its main core is associated by preferential detaching of similar granules. In addition to these 23 procedures, the mechanical properties and hydraulic conductivity of the being joint are 24 compared with the networks properties. 25 The first part of this article covers the employed method, some preliminary aspects of 26 networks measurements, and the proposed algorithm on the real results accompanying an 27 analytical solution for the algorithm. The next section includes the results obtained from the 28 experimental tests on a rock joint and the arranged complex networks. In discussion part, we 29 inv
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