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Prestressed anchor cables are commonly utilized to reinforce slopes in earthquake-prone zones. The existing upper bound limit analyses of seismic slopes reinforced with prestressed anchor cables have the following limitations: (1) neglecting variable seismic excitations; (2) ignoring the three-dimensional spatial layout of cables because of using the plane-strain analysis. In this study, the time-space effects of seismic waves are analytically described by sin-cos functions incorporating wave amplification or soil damping. Based on the upper bound of plastic theory and a three-dimensional discretized failure mechanism, internal energy dissipation rate and work rates contributed by gravitational forces, variable seismic excitations, and prestressed anchor cables are computed. An energy-based function of dynamic factors of safety (DFS) is established, followed by a global optimization to identify the critical harmonic pattern of DFS. The accuracy is checked by numerical simulations where the seismic stability of an engineering slope adjacent to Yu-Huai railway is evaluated. Comparisons also show that the conventional simplified method not only cannot reflect the spatial layout of cables but also overestimate the mechanical contribution of cables. Finally, the dominant effects of the layout of cables, soil properties as well as physical parameters of seismic waves on the DFS and the critical failure mechanism are discussed. A method to evaluate the stability of seismic cable-reinforced slopes A kinematical admissible 3D failure mechanism of cable-reinforced slopes is generated Critical harmonic pattern of safety factors is explicitly obtained. Effect of cable layout, dynamic parameters and soil properties are discussed. [ABSTRACT FROM AUTHOR]

In the existing upper bound limit analyses (UBLA) of rotational slopes reinforced with prestressed anchor cables, the mobilized axial forces of all cables are assumed to be equal to the ultimate pullout force. However, such an assumption overestimates the mechanical contribution of prestressed anchor cables, resulting in excessively high safety factors. In this technical note, we aim to tackle this issue by proposing a pseudo-plastic design concept, in which soil masses and prestressed cables are treated as plastic and elastic-plastic, respectively, when slopes collapse. A pseudo-plastic failure model of prestressed anchor cables is proposed, where the variation of tension forces and movement of anchor heads are accounted for. Several interesting conclusions are drawn as follows: (1) Contrary to the conventional plastic failure mode of cables, upper bound solutions obtained by the proposed model are much closer to the exact solutions. (2) Variation of factors of safety (FSs) against the accumulated rotational displacement can be explained by the force-displacement curve obtained in the pullout test of prestressed anchor cables. (3) The sliding slope reinforced with cables may turn out to be stable after a slight rotational movement, which can be utilized in the economical design. [ABSTRACT FROM AUTHOR]