The shear strength and stick-slip behavior of a rough rock joint are analyzed using the complex network approach. We develop a network approach on correlation patterns of void spaces of an evolvable rough fracture (crack type II). Correlation among networks properties with the hydro -mechanical attributes (obtained from experimental tests) of fracture before and after slip is the direct result of the revealed non-contacts networks. Joint distribution of locally and globally filtered correlation gives a close relation to the contact zones attachment-detachment sequences through the evolution of shear strength of the rock joint. Especially spread of node's degree rate to spread of clustering coefficient rate yielded possible stick and slip sequences during the displacements. Our method can be developed to investigate the complexity of stick-slip behavior of faults as well as energy /stress localization on crumpled shells/sheets in which ridge networks are controlling the energy distribution.
Deep Dive into Small World Property of a Rock Joint(Complexity of Frictional Interfaces: A Complex Network Perspective).
The shear strength and stick-slip behavior of a rough rock joint are analyzed using the complex network approach. We develop a network approach on correlation patterns of void spaces of an evolvable rough fracture (crack type II). Correlation among networks properties with the hydro -mechanical attributes (obtained from experimental tests) of fracture before and after slip is the direct result of the revealed non-contacts networks. Joint distribution of locally and globally filtered correlation gives a close relation to the contact zones attachment-detachment sequences through the evolution of shear strength of the rock joint. Especially spread of node’s degree rate to spread of clustering coefficient rate yielded possible stick and slip sequences during the displacements. Our method can be developed to investigate the complexity of stick-slip behavior of faults as well as energy /stress localization on crumpled shells/sheets in which ridge networks are controlling the energy distribut
During the last decade, complex networks have been used increasingly in different fields of science and technology [1][2][3]. Initial applications of complex networks in geosciences were mostly related to earthquakes [4][5][6]. Characterization of spatial and temporal structural complexity of such recursive events has been the main objective of the related research [7][8][9][10][11][12][13].
Understanding of spatio-temporal topological complexity of events based on field measurements can disclose some other facets of these intra/extra woven events.
Studies pertaining to the topological complexity and its application in some geoscience fields reveals that acquisition and gathering of direct information (especially in temporal scale) is difficult and in many cases are (were) impossible (at least with current technologies). In addition to complex earthquake networks, recently the analysis of climate networks, volcanic networks, river networks and highway networks, as the large scale measurements, have been taken into account [9][10][11][12][13]. In small scales, topological complexity has been evaluated in relation to geoscience fields such as the gradation of soil particles, fracture networks, aperture of fractures, and granular materials [14][15][16][17][18][19][20]. The initial step refers to organizational step which tries to find out possible dominant well-known structures within the system. Next step in the most of the mentioned works is to provide a suitable and simple method to yield a similar structure. Such algorithm may support the evolution of structure in spatial or/and temporal cases [21].
May be the most important structural complexity in geological fields is related to fracture networks. Fracture networks with dilatancy [22], joint networks in excavation damaged zones, cracking in pavements (or other natural/man-made structures) and fault networks in large scale have been recognized [23][24][25]. In the analysis of these networks, the characterization of fractures in a proper space such as friction-displacement space is an essential step. Furthermore, with taking the direct relationship between void spaces and contact areas in to account, one may interest in considering the induced topological complexity of the opening elements (nonfrictional contacts) into the fracture behavior. Using linear elastic fracture mechanics, we know aperture or aspect ratio is generally the index to available energy in growth of rupture. Crack like behavior of rupture in frictional interfaces also support the role of contact areas and equivalently apertures. In addition, the variations of fluid flow features (such as permeability and tortuosity) directly are controlled with aperture spaces. In order to characterize the main attributes of the fractured systems, e.g. mechanical and hydraulic properties, several methods have been suggested in the literature [26][27][28][29][30]. Recently, the authors have proposed the implementation of a complex network analysis for the evolution of micro-scale apertures in a rough rock fracture [18][19]. Based on a Euclidean measure, the results confirmed the dependency of hydro-mechanical properties to the attributes of characterized aperture networks.
The present study is also related to the complex aperture networks. However, the current study presents the analysis of frictional forces during shearing based on the correlation of apertures in a rock joint. The analysis is associated with set up a network on an attribute (such as aperture distribution) in an area. The aforementioned method has also been employed in the analysis of the coupled partial differential equations which was related to two-phase flow [31].
With respect to avalanche-like behavior of collective motion of the ensemble discrete contacts (in the vicinity of a phase transition step), we try to characterize the collective behavior of aperture strings using networks. In this paper we will answer the following three questions: 1) Is there any (hidden) complex structure in the experimentally observed apertures? 2) What is the effect of specific structural complexity of apertures on mechanical response of a fracture? 3) How do apertures regulate with each other to show well-known slip-friction curve? In other words, can we relate the topological complexity of apertures to the evolution path of the fracture?
The organization of the paper is as follows: Section 2 includes a brief description of networks and their characterization. In addition, the construction procedure of aperture networks is explained. Section 3 covers a summary of the experimental procedure. The last section presents the evaluation of the pre-and post-peak (stick-slip) behavior of a rock joint which is followed by the analysis of the constructed network.
In this section we describe a general method of setting up a network on a fracture surface while the surface property is a superposition of very narrow profiles (ribbons) of one attribute of the
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