A new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems Original Research Article

In order to accurately model the behaviour of geostructures it is usually not possible to neglect the interaction between the soil skeleton and the pore fluid. Classical finite element models taking into account this interaction are formulated in terms of the displacement and pore pressure fields and are based on the assumption that the fluid acceleration relative to the soil skeleton is negligible. This type of mixed problems is similar to others found in solid and fluid mechanics and might give rise to numerical instabilities unless certain requirements are met. There are two classical approaches to this problem. The first is usually known as the Zienkiewicz–Taylor patch test for mixed formulations. As a consequence of this test the interpolation degree of the displacement field is required to be higher than the corresponding one of the pressure field. Mathematically speaking this is a necessary condition for stability. The second approach, mathematically more involved, is usually known as the Babŭska–Brezzi inf–sup condition and constitutes a sufficient condition for stability. However it is possible to obtain stable formulations circumventing the interpolation degree requirement through the so-called stabilization techniques. These techniques were initially applied in the context of fluid mechanics and later extended to solid mechanics. This article presents a new formulation in which stabilization is achieved through an approach based on the Simo–Rifai enhanced strain element.