Lower Bound Axisymmetric Limit Analysis Using Drucker–Prager Yield Cone and Simulation with Mohr–Coulomb Pyramid

Abstract

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker–Prager (D–P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D–P yield cone with the Mohr–Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors Nc, Nqand Nγhave been computed, as a function of ϕ, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.