A fractional step algorithm allowing equal order of interpolation for coupled analysis of saturated soil problems

The accurate prediction of the behaviour of geostructures is based on the strong coupling between the pore fluid and the solid skeleton. If the relative acceleration of the fluid phase relative to the skeleton is neglected, the equations describing the problem can be written in terms of skeleton displacements (or velocities) and pore pressures.

This mixed problem is similar to others found in solid and fluid dynamics. In the limit case of zero permeability and incompressibility of the fluid phase, the restrictions on the shape functions used to approximate displacements and pressures imposed by Babuska–Brezzi conditions or the Zienkiewicz–Taylor patch test hold.

As a consequence, it is not possible to use directly elements with the same order of interpolation for the field variables.

This paper proposes a generalization of the fractional-step method introduced by Chorin for fluid dynamics problems, which allows to circumvent BB restrictions in the incompressibility limit, thus making it possible to use elements with the same order of interpolation. Copyright © 2000 John Wiley & Sons, Ltd.