Upper-Bound Limit Analysis of Ultimate Pullout Capacity of Expanded Anchor Cable

Expanded anchor cables have been widely used in the rapid development of underground engineering. However, there are still some deficiencies in the computation of the ultimate bearing capacity of expanded anchor cables. Based on the upper-bound theorem of limit analysis, the upper-bound solution of the ultimate bearing capacity of an expanded anchor cable was derived. For this calculation, the instability mechanism of the soil at the front surface of the anchorage segment of the expanded anchor cable was assumed to satisfy the logarithmic spiral failure model, its 3D velocity discontinuity surface was generated using the spatial discretization technique, and the optimal solution was determined through the particle swarm optimization (PSO) algorithm. The breakage mechanism of the anchorage side surface was assumed to appear at the interface between the anchorage body and the soil, and its velocity field satisfied the requirements of the associated flow rule. The accuracy of the proposed analytical solution was well-verified through a comparison with three-dimensional numerical simulations, and its superiority was also well-demonstrated in comparison to the existing theoretical calculation method. Subsequently, the influence of the key parameters of the anchor cable on the ultimate lateral resistance, end resistance, and total pullout capacity was discussed. The results showed that: the anchorage segment diameter, anchorage segment length, and buried depth of the expanded anchor cable had a great influence on the ultimate lateral resistance, ultimate end resistance, and total ultimate pullout capacity; however, the anchorage segment length had little influence on the ultimate end resistance, and the inclination angle of the anchor cable had relatively little influence on the resistance.