Interior point optimization and limit analysis: an application

The well-known problem of the height limit of a Tresca or von Mises vertical slope of height h, subjected to the action of gravity stems naturally from Limit Analysis theory under the plane strain condition. Although the exact solution to this problem remains unknown, this paper aims to give new precise bounds using both the static and kinematic approaches and an Interior Point optimizer code. The constituent material is a homogeneous isotropic soil of weight per unit volume gamma. It obeys the Tresca or von Mises criterion characterized by C cohesion. We show that the loading parameter to be optimized, gammah/C, is found to be between 3.767 and 3.782, and finally, using a recent result of Lyamin and Sloan (Int. J. Numer. Meth. Engng. 2002; 55:573), between 3.772 and 3.782. The proposed methods, combined with an Interior Point optimization code, prove that linearizing the problem remains efficient, and both rigorous and global: this point is the main objective of the present paper. Copyright (C) 2003 John Wiley Sons, Ltd.