Stabilized low-order finite elements for failure and localization problems in undrained soils and foundations Original Research Article

Geomaterials in general, and soils in particular, are highly nonlinear materials presenting a very strong coupling between solid skeleton and intersticial water. In the limit of zero compressibility of water and soil grains and zero permeability (which correspond to the classical ‘undrained’ assumption of Soil Mechanics), the functions used to interpolate displacements and pressures must fulfill either the Babuska-Brezzi conditions or the much simpler patch test proposed by Zienkiewicz and Taylor. These requirements exclude the use of elements with equal order interpolation for pressures and displacements, for which spurious oscillations may appear. The simplest elements with continuous pressures which can be used in 2D are the quadratic triangle and quadrilateral with linear and bilinear pressures, respectively. The purpose of this paper is to present a stabilization technique allowing the use of both linear triangles for displacements and pressures (T3P3) and bilinear quadrilaterals (Q4P4). The proposed element will be applied to obtain limit loads and failure surfaces in simple boundary value problems for which analytical solutions exist.