Vol.:(0123456789) 1 3 Rock Mechanics and Rock Engineering https://doi.org/10.1007/s00603-019-01864-y ORIGINAL PAPER Modelling of Flow–Shear Coupling Process in Rough Rock Fractures Using Three‑Dimensional Finite Volume Approach Ebrahim Karimzade 1  · Masoud Cheraghi Seifabad 1  · Mostafa Sharifzadeh 2  · Alireza Baghbanan 1 Received: 26 June 2018 / Accepted: 20 May 2019 © Springer-Verlag GmbH Austria, part of Springer Nature 2019 Abstract A computational code has been developed based on fnite-volume method (FVM) to investigate fuid fow-through rough- walled rock fractures during shear processes, considering evolutions of aperture and contact area with shear displacement. In the code, the full 3-D Navier–Stokes equation is solved in a cell-centered collocated variable arrangement and the pres- sure–velocity coupling is performed using the SIMPLE algorithm. A series of coupled shear-fow tests under constant normal stress of 3 MPa with diferent shear displacements of 1–10 mm were conducted and their results were compared with numerical simulations results. The comparison shows good agreement between the simulated and measured results. Aperture distribution during shear was evaluated by superimposing the upper and lower fracture surfaces according to the initial aperture and dilation at diferent shear displacements. The results show that contact area evolution dominates the variations of fow rate as well as fow pattern in a rough fracture. In addition, there is a linear relationship between aperture coefcient of variation and contact area ratio during shear. The simulation results also demonstrate the deviation of veloc- ity profles from the ideal parabolic form in some regions due to the formation of eddy fows. This behavior may have been caused by the inertial efects, which can be characterized by the Navier–Stokes equation, while some simplifed equations such as Reynolds equation or Stokes equation cannot capture these efects. Keywords Rough-walled rock fracture · 3-D Navier–Stokes · Contact area evolution · Finite-volume method · SIMPLE algorithm List of symbols ρ Fluid density  Fluid viscosity  The angle between e f and n f  Kinematic viscosity  p Pressure under-relaxation factor  V Momentum under-relaxation factor  x i Unit vector in Cartesian coordinates x Vector of unknown variables  ip Weighing function ip Integration point ip(f ) Number of integration points along face f NE(P) Elements surrounding the element P Nf(P) Faces surrounding the element P S Surface of a fnite volume S f Surface vector of face f S f Magnitude of S f n f Unit vector normal to the face f e f Vector linking the elements straddling the face f u Flow velocity vector u f Velocity vector at face f u i,P Cartesian component of the velocity vector at ele- ment P u i,N Cartesian component of the velocity vector at ele- ment N u i,f Cartesian component of the velocity vector at face f u ∗ f Rhie–Chow interpolated fow velocity at face f u ∗ i,f Cartesian component of u ∗ f u ∗ i,P Cartesian component of Rhie–Chow interpolated fow velocity at element P u  i,P Cartesian component of the velocity correction at element P p Pressure * Masoud Cheraghi Seifabad cheraghi@cc.iut.ac.ir 1 Department of Mining Engineering, Isfahan University of Technology, Isfahan, Iran 2 Department of Mining and Metallurgy Engineering, Western Australian School of Mines, Curtin University, Bentley, Australia