Limit analysis approach for accessing stability of three-dimensional (3-D) slopes reinforced with piles

An upper bound solution for tunnel face stability analysis considering the free span

“…Unlike nail reinforcements that work by axial force only, and that can fail by tension or by pull-out from the soil (Michalowski, 2005), forepole umbrellas typically resist forces perpendicular to its axis, and they therefore work by shear and by bending -i.e., like a beam-. A similar problem can be found in slope stability analyses considering anti-slide piles (e.g., Rao et al, 2017); however, in that case, the vertical piles receive horizontal forces that depend on displacements (e.g., Winkler model), whereas in the tunnel face stability problem the support element is horizontal and receives the weight of the ground over it. Pinyol and Alonso (2011), for undrained soils, stated that the micropiles forming the umbrella are characterized by a limiting (yielding) bending moment, and that the soil reacts against the micropile with a force per meter of micropile given by c d 9 u (Broms, 1964), where c u is the undrained strength of the soil and d the diameter of the micropile.…”

Working mechanism and method for theoretical calculation of arch–chord coupled anti‐sliding structure

“…Based on the upper bound analysis method, Nian et al 7 analyzed the influence of the optimal location of the anti‐slide piles, soil heterogeneity, and anisotropy on slope stability; he deduced an expression for the upper bound of the safety factor of a three‐dimensional slope, reinforced by anti‐slide piles. Gao et al 8 and Rao et al 9 optimized the design parameters of pile locations and pile spacing based on a three‐dimensional failure mechanism of a sliding body. Zhang et al 10 considered transferring a larger sliding force in the middle of the sliding body to the sides with a smaller sliding force through the anti‐sliding piles arranged in the arch, and analyzed the mechanical characteristics of the pile with an arch‐coupled beam on the pile top.…”