Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis

Abstract

Bearing capacity factors, Nc, Nq, and Nγ, for a conical footing are determined by using the lower and upper bound axisymmetric formulation of the limit analysis in combination with finite elements and optimization. These factors are obtained in a bound form for a wide range of the values of cone apex angle (β) and [Formula: see text] with δ = 0, 0.5[Formula: see text], and [Formula: see text]. The bearing capacity factors for a perfectly rough (δ = [Formula: see text]) conical footing generally increase with a decrease in β. On the contrary, for δ = 0°, the factors Nc and Nq reduce gradually with a decrease in β. For δ = 0°, the factor Nγ for [Formula: see text] ≥ 35° becomes a minimum for β ≈ 90°. For δ = 0°, Nγ for [Formula: see text] ≤ 30°, as in the case of δ = [Formula: see text], generally reduces with an increase in β. The failure and nodal velocity patterns are also examined. The results compare well with different numerical solutions and centrifuge tests’ data available from the literature.