ABSTRACT
To simulate the response of saturated geomaterials requires a numerical approach such as the finite element method that employs a generalized Biot formulation. Under isothermal conditions, the primary dependent variables are displacements (u) and pore pressure (p), which are suitably coupled. The stability of such “u-p” elements requires that the displacement approximation be one order higher than the pressure approximation. Typical elements employ quadratic and linear approximation for u and p, respectively. Since, according to Darcy’s law, the velocity of flow is proportional to the gradient of the pore pressure, the approximate velocity is thus constant over an element. In slow “consolidation-type” problems the accurate computation of such velocities is not crucial, as they are generally very small. The need to accurately simulate the effects associated with rising sea levels, rapidly rising flood waters, etc., however, now requires that accurate approximate velocities be computed. Consequently, robust and computationally efficient higher-order u-p elements need to be used in simulating such problems. The development of such elements that are is not a straightforward undertaking. This paper explains this difficulty and, as a measure to overcome it, describes some non-conforming elements that have been recently developed.
