3-d Modeling of Coupled Subsurface Flow-stress by Mixed Finite Elements

The accurate simulation of coupling between flow and stress in saturated porous media is a major issue in a broad variety of fields, ranging from reservoir engineering to biomechanics. Despite the intensive research carried out in recent years, the numerical solution to the partial differential equations governing the behaviour of real fluid saturated heterogeneous porous media still represents a demanding task. In the present communication an original fully coupled 3-D Mixed Finite Element (MFE) model is developed with the aim at reducing the numerical oscillations of the pore pressure predicted with the aid of traditional FEs. Using a mixed approach for the flow equation enforces an element-wise conservative velocity field with a similar order of approximation for both pore pressure and stress. This helps stabilize the numerical solution and obtain a more accurate calculation of the fluxes. The MFE model is validated against Terzaghi’s analytical solution and successfully tested in two large size realistic and computationally challenging applications, i.e. the consolidation of a river embankment and the Noordbergum effect due to groundwater withdrawal from a shallow confined aquifer.