A parametric study of twenty earthen levee cross sections from southeastern Louisiana using the LMVD Method of Planes and other limit equilibrium procedures

The LMVD Method of Planes has been used for many years by the New Orleans District of the U.S. Army Corps of Engineers to analyze the stability of flood control structures in the New Orleans hurricane protections system. The Method of Planes assumes a three-part, noncircular slip surface and generally does not satisfy any form of static equilibrium. In computing a factor of safety, the Method of Planes considers a balance of horizontal “resisting” and “driving” forces in computing a factor of safety. To better understand how the results of slope stability analyses with the Method of Planes compare with results from more rigorous procedures capable of analyzing slip surfaces with different shapes, a parametric study was performed by analyzing twenty earthen levee cross sections believed to represent the various levee configurations in southeastern Louisiana. Analyses were performed with a force equilibrium procedure that assumed a horizontal inclination for the interslice forces and Spencer’s (1967) procedure, and the results were compared with the solutions from the Method of Planes. The force equilibrium procedure with horizontal side forces was selected because the procedure is believed to yield results that are similar to results from the Method of Planes, and Spencer’s procedure was utilized because it is the only procedure considered in this study to completely satisfy static equilibrium. The analyses performed with the force equilibrium and Spencer’s procedures included analyses for the critical slip surfaces from the Method of Planes as well as analyses for critical circular and noncircular slip surfaces. It was shown with the results of the analyses that the shape of the assumed slip surface has a great effect on the differences in the factors of safety from Spencer’s procedure and the Method of Planes.