Geomechanics Numerical Code for Modelling Contact in Fractures and other Discontinuities using Virtual Element Method

The purpose of this paper is to present a numerical code for rock mechanics modelling of discontinuities such as fractures, joints and faults. We implement this in an open-source Matlab Reservoir Simulation Toolbox designated for rapid prototyping of geomechanics, reservoir modelling and simulation problems. Appropriate and explicit modelling of such discontinuities become a central element of the scientific discussions. In particular, we contemplate processes when fractures open, close and slip due to stress changes in the subsurface. Existing numerical codes use either long-syntax programming languages where details of implementation are not explicitly shown or commercial simulators that often lack the flexibility for implementing new ideas. We use the recently developed Virtual Element Method (VEM) and solve contact problems that allow fractures to dynamically interact with the surrounding rock mass and each other, transferring contacting stress across faces due to closure and friction. This method has advantages over standard Finite Elements or Finite Volumes in solving the contact problem because it handles complex, not necessarily convex grid geometries and hanging nodes. For the contact problems, we implement contact detection, normal and tangential contact interaction algorithms. We provide numerical examples and match to analytical solutions in order to validate employed algorithms.