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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.

In this study, over different scenarios we will simulate a week coupling of hydromechanical loads in a long term CO2 injection with a hypothetical reservoir while the effect of pore water pressure and then multi-phase flow procedure has been ignored. In the first basic case the homogenous case has been considered when the theory of poroelasticity was employed. Second case covers the effects of directional heterogeneity, constructed by random faults, on the flow paths of gas and other attributes of the system. Also, in the latter case the impact of stress state as an active loads (body loads) has been regarded. Thanks to multiple directional heterogeneity, which induces only one heterogenic parameter (intrinsic permeability), distinguishable flow paths can be recognized. In another process, the failure ability of system regard to Mohr-Columb criterion is measured as well as options that, presumably, the system has continuum faults (zero cohesion). The results over different cases shows absedince of ground surface (heave), more probable propagation of failure area and the role of directional heterogeneity to change the evolution path of system.

In this study, we investigate the complexity of two-phase flow (air/water) in a heterogeneous soil sample by using complex network theory, where the supposed porous media is non-deformable media, under the time-dependent gas pressure. Based on the different similarity measurements (i.e., correlation, Euclidean metrics) over the emerged patterns from the evolution of saturation of non-wetting phase of a multi-heterogeneous soil sample, the emerged complex networks are recognized. Understanding of the properties of complex networks (such degree distribution, mean path length, clustering coefficient) can be supposed as a way to analysis of variation of saturation profiles structures (as the solution of finite element method on the coupled PDEs) where complexity is coming from the changeable connection and links between assumed nodes. Also, the path of evolution of the supposed system will be illustrated on the state space of networks either in correlation and Euclidean measurements. The results of analysis showed in a closed system the designed complex networks approach to small world network where the mean path length and clustering coefficient are low and high, respectively. As another result, the evolution of macro -states of system (such mean velocity of air or pressure) can be scaled with characteristics of structure complexity of saturation. In other part, we tried to find a phase transition criterion based on the variation of non-wetting phase velocity profiles over a network which had been constructed over correlation distance.

In this study, we investigate the appeared complexity of two-phase flow (air/water) in a heterogeneous soil where the supposed porous media is non-deformable media which is under the timedependent gas pressure. After obtaining of governing equations and considering the capillary pressuresaturation and permeability functions, the evolution of the model unknown parameters were obtained. In this way, using COMSOL (FEMLAB) and fluid flow/script Module, the role of heterogeneity in intrinsic permeability was analysed. Also, the evolution of relative permeability of wetting and non-wetting fluid, capillary pressure and other parameters were elicited. In the last part, a complex network approach to analysis of emerged patterns will be employed., Comment: This paper has been withdrawn by the author. A report /version 2- Due to copy right the manuscript is not available

In this study, we investigate the appeared complexity of two-phase flow (air-water) in a heterogeneous soil where the supposed porous media is non-deformable media which is under the time-dependent gas pressure. After obtaining of governing equations and considering the capillary pressure-saturation and permeability functions, the evolution of the models unknown parameters were obtained. In this way, using COMSOL (FEMLAB) and fluid flow-script Module, the role of heterogeneity in intrinsic permeability was analysed. Also, the evolution of relative permeability of wetting and non-wetting fluid, capillary pressure and other parameters were elicited., Comment: This paper has been withdrawn by the author due to repetition of some parts in other publications