  Complexity of fluid flow in a rough fracture is induced by the complex
configurations of opening areas between the fracture planes. In this study, we
model fluid flow in an evolvable real rock joint structure, which under certain
normal load is sheared. In an experimental study, information regarding about
apertures of the rock joint during consecutive 20 mm displacements and fluid
flow (permeability) in different pressure heads have been recorded by a scanner
laser. Our aim in this study is to simulate the fluid flow in the mentioned
complex geometries using the lattice Boltzmann method (LBM), while the
characteristics of the aperture field will be compared with the modeled fluid
flow permeability To characterize the aperture, we use a new concept in the
graph theory, namely: complex networks and motif analysis of the corresponding
networks. In this approach, the similar aperture profile along the fluid flow
direction is mapped in to a network space. The modeled permeability using the
LBM shows good correlation with the experimental measured values. Furthermore,
the two main characters of the obtained networks, i.e., characteristic length
and number of edges show the same evolutionary trend with the modeled
permeability values. Analysis of motifs through the obtained networks showed
the most transient sub-graphs are much more frequent in residual stages. This
coincides with nearly stable fluid flow and high permeability values.
