The uplift capacity of helical anchors is generally taken as the control condition for design in different applications, including transmission tower foundations and offshore structures. However, it is difficult to identify the failure surface for a deep helical anchor, which may result in an incorrect assessment of uplift capability. This research proposes a new unified method to estimate the uplift capacity of deep single-helix and multi-helix anchors based on the investigation of failure mechanisms. The deep failure mode was identified by FEM analysis using a modified Mohr–Coulomb model considering the strain softening of sand, along with the coupled Eulerian–Lagrangian technique. Thereby, a simplified rupture surface is proposed, and the equations estimating the uplift capacity are presented by the limit equilibrium method. Two important factors—the lateral earth pressure coefficient and the average internal friction angle included in the equations—are discussed and determined. The comparisons with centrifugal tests verify the reasonability of the proposed method.

In elastoplastic analyses, a yield function needs convexities and C1 continuities, to meet the requirement of return mapping algorithms. However, many classic criteria in geotechnical engineering have shortages: either numerical issues (nonconvexity and gradient discontinuities) or insufficient physical properties (lack of tensile strength and compressive cap). To overcome these deficiencies, a smoothed classic (SC) yield function is proposed after combining the generalized classic yield function, a robust smoothing technique, and investigations on physical meanings. It can reflect general soil properties, including basic shear strength, tensile strength, compressive cap, and the impact of intermediate principal stress. The yield function is convex and C2 continuous; therefore, it avoids many numerical issues in describing general strength behavior. In addition, it can provide a close approximation to the Mohr–Coulomb criterion to avoid discontinuous gradients. Formulas for the gradient, the Hessian, and the calibration procedure are provided.