Plane Strain versus Axisymmetric Modeling of Convex Levees

Abstract

The Natomas basin is a 21,450-ha area north of downtown Sacramento, California. The developed area relies on levees for flood protection along its perimeter. The western boundary is a 29.9-km-long levee that protects the area from flooding by the Sacramento River. Since its construction over a century ago, this levee has experienced a myriad of performance issues. From 2008 to 2011, a team of engineers completed design and construction of remedial measures with the objective of ending the historic performance issues. Along one stretch, the Sacramento River and levee make a sharp bend at a constant levee radius of approximately 515 m. During the design processes, the levee was analyzed using a two-dimensional plane strain model despite this relatively sharp convex bend. This paper presents a review of the plane strain and axisymmetric formulations in which it is shown that the radial (horizontal) scale of the axisymmetric formulation is not arbitrary and requires additional planning by the modeler. A comparison of the results (seepage gradients and computed factor of safety for stability) from numerical modeling of levees using plane strain and axisymmetric formulations through the use of a case history is then presented. The computed gradients for the convex axisymmetric case are higher than those computed using a plane strain formulation. For the cross sections used in this study, the increase is greater than previously reported. Moreover, the increase is not systematic and is unique to each cross section.