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, Nq and Nγ have 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.

Undrained lower bound solutions for end bearing capacity of shallow circular piles in non‐homogeneous and anisotropic clays

“…Unlike the LP technique, the uses of these convex cones in SOCP and SDP allow a classical yield criterion to be expressed in its native form without the linearization of yield function in the LP technique, thereby providing a powerful and accurate SOCP and SDP optimization method for stability analyses. The LB FELA under axisymmetric condition using the nonlinear optimization technique was also implemented for various failure criteria including Mohr‐Coulomb, Hoek–Brown, von Mises, and Drucker‐Prager . Unlike SOCP and SDP, the nonlinear optimization technique requires a yield surface to be smoothened at its sharp corners or vertices so that the gradient and Hessian matrix of the inequality constraints associated with the yield surface are uniquely defined.…”

“…The LB FELA under axisymmetric condition using the nonlinear optimization technique was also implemented for various failure criteria including Mohr-Coulomb, 63 Hoek-Brown, 64 von Mises, 65 and Drucker-Prager. 66 Unlike SOCP and SDP, the nonlinear optimization technique requires a yield surface to be smoothened at its sharp corners or vertices so that the gradient and Hessian matrix of the inequality constraints associated with the yield surface are uniquely defined. Those existing researches on the axisymmetric LB FELA are summarized in Table 1.…”