Semiempirical Estimation Formula of Uplift Capacity of Two-Plate Helical Anchors in Sand

To estimate the uplift capacity of two-plate helical anchors in sand, a series of laboratory model tests were conducted with particle image velocimetry (PIV) to investigate the soil deformation around the anchors under varying relative densities, embedment ratios (H/D), and spacing ratios (S/D). The test observations reveal a critical embedment ratio (H/D)crit. When H/D ≤ (H/D)crit, the failure mechanism of the soil above the top plate manifests as a general shear failure extending to the ground. When H/D > (H/D)crit, the failure mode gradually transitions from global general shear to local shear failure. The anchor spacing exerts a prominent control on surrounding soil deformation, as shear failure zones induced by two anchor plates partially overlap at small spacings. A critical spacing ratio (S/D)crit is also identified: for S/D ≤ (S/D)crit, cylindrical shear failure develops within the inter-plate soil mass, whereas independent bearing failure occurs for S/D > (S/D)crit. Combining the effects of sand relative density, embedment ratio, and spacing ratio, four distinct failure modes for two-plate anchors are proposed. Based on limit equilibrium theory and measured soil deformation fields, a single-plate uplift capacity is derived that incorporates the sand dilation angle, internal friction angle, and embedment ratio. Integrating this single-plate solution with the four categorized failure mechanisms of two-plate anchors, unified semiempirical prediction formulas are established for uplift capacity under diverse geometric and soil conditions. Comparative analyses against conventional design approaches demonstrate that the proposed formulas are mechanically compatible with both the cylindrical shear method and the independent plate bearing method, delivering a unified calculation framework applicable across all embedment and spacing scenarios.