Three-dimensional upper-bound limit analysis of ultimate pullout capacity of anchor plates using variation method

The uplift bearing capacity of anchor plates has been the focus of geotechnical engineering research. In this study, based on the upper-bound limit analysis theory and considering the nonlinear characteristics of geomaterials, the three-dimensional uplift behavior of a shallow horizontal anchor plate was analyzed. Based on the variational principle, virtual power principle, and equilibrium equation, the ultimate pullout forces of rectangular and circular anchor plates were derived, and the dimensionless breakout factor and failure mechanism of the overlying soil were obtained. The ultimate pullout forces were in good agreement with the existing research results, and the principal stresses along the rupture surface agreed well with that obtained by numerical analysis, which could demonstrate the effectiveness and accuracy of the proposed method. Moreover, the effects of the nonlinear coefficient, anchor size and aspect, embedment ratio, and surface overload on the breakout factor were investigated. Meanwhile, the shape modification factors of rectangular and circular anchor plates were obtained. The findings of this study can provide a useful reference for anchor plate design.