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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 1527659, 10 pages
Research Article

Displacement of Pile-Reinforced Slopes with a Weak Layer Subjected to Seismic Loads

1School of Civil Engineering, Tianjin University, Tianjin 300072, China
2Key Laboratory of Coast Civil Structure Safety, Tianjin University, Ministry of Education, Tianjin 300072, China
3State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China

Received 30 May 2016; Accepted 14 August 2016

Academic Editor: Giovanni Garcea

Copyright © 2016 Haizuo Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The presence of a weak layer in a slope requires special attention because it has a negative impact on slope stability. However, limited insight into the seismic stability of slopes with a weak layer exists. In this study, the seismic stability of a pile-reinforced slope with a weak thin layer is investigated. Based on the limit analysis theory, a translational failure mechanism for an earth slope is developed. The rotational rigid blocks in the previous rotational-translational failure mechanism are replaced by continuous deformation regions, which consist of a sequence of rigid triangles. The predicted static factor of safety and collapse mechanism in two typical examples of slopes with a weak layer compare well with the results obtained from the available literature and by using the Discontinuity Layout Optimization (DLO) technique. The lateral forces provided by the stabilizing piles are evaluated using the theory of plastic deformation. An analytical solution for estimating the critical yield acceleration coefficient for the pile-reinforced slopes is derived. Based on the proposed translational failure mechanism and the corresponding critical yield acceleration coefficient, Newmark’s analytical procedure is employed to evaluate the cumulative displacement. Considering different real earthquake acceleration records as input motion, the effect of stabilizing piles and varying the spacing of piles on the cumulative displacement of slopes with a weak layer is investigated.