Ultimate bearing capacity of elliptical tip by upper bound analysis

For the anchor pile with elliptical tip and T-bar, the bearing capacity and factor are obtained based on the upper-bound limit analysis of plasticity considering the influences of the aspect ratio of the elliptical tip (ξ≥1) and the friction coefficient. The velocity fields and hodographs of the elliptical tip of the anchor pile and T-bar are introduced. The total energy dissipation is figured by summing up each part of the internal energy dissipation and the energy dissipation on the velocity discontinuous surface. The bearing factor is equal to the ratio of the total energy dissipation over the velocity and diameter of the elliptical tip and soil strength. It is found that for ξ=1, there is a good consistency between the upper bound solutions and the previous results. Therefore, the upper bound models for the elliptical tip are rational. The influences of friction force become more significant with the increasing ξ for the penetration resistance coefficient. The upper and lower-bound solutions maintain consistency. The upper bound solutions of the bearing capacity are generally larger than the lower ones as the decreasing friction factor.