Seminar given by Prof. Bernhard Schrefler, Uni. of Padova, Italy

The pressure and stress evolution in fracturing saturated porous media is investigated on meso-mechanics and macro-mechanics level. Crack propagation under external loading (peel test and biaxial loading), assigned pressure and assigned flux (fracking) is considered. For meso-mechanics investigations a lattice model is used which has been introduced in a Biot-type formulation. The avalanche behaviour of the cracking events is evidenced.

At macro mechanics level both standard Finite Elements with remeshing and appropriate crack-tip advancement algorithm, and XFEM are used. A cohesive fracture model is adopted together with a discrete crack approach and without predetermined fracture path. The Rankine criterion is used for fracture nucleation and advancement. In the standard FE approach the fracture follows in a 2D setting directly the direction normal to the maximum principal stress while in the 3D case the fracture follows the face of the element around the fracture tip closest to the normal direction of the maximum principal stress at the tip. This procedure requires continuous updating of the mesh around the crack tip to take into account the evolving geometry. The updated mesh is obtained by means of an efficient mesh generator based on Delaunay tessellation [1, 2, 3]. Comparison is made with the XFEM method. The governing equations for all approaches are written in the framework of porous media mechanics and are solved numerically in a fully coupled manner. Numerical examples include well injection (constant inflow) in a geological setting, hydraulic fracture in 2D and 3D concrete dams (increasing pressure) and a peeling test for a fully saturated porous medium; stepwise tip advancement and pressure oscillations are shown. A comparison with results found in literature and with the solutions obtained with the XFEM method evidences the shortcomings of methods like PUFEM, XFEM and Phase Field methods when used in their traditional way for the simulation of the coupled phenomena going on at the crack tip