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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 1985458, 11 pages
Research Article

Upper-Bound Multi-Rigid-Block Solutions for Seismic Performance of Slopes with a Weak Thin Layer

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

Correspondence should be addressed to Haizuo Zhou

Received 17 July 2017; Accepted 22 October 2017; Published 26 November 2017

Academic Editor: Giovanni Garcea

Copyright © 2017 Gang Zheng 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 has an adverse influence on the seismic performance of slopes. The upper-bound solution serves as a rigorous method in the stability analysis of geotechnical problems. In this study, a multi-rigid-block solution based on the category of the upper-bound theorem of limit analysis is presented to examine the seismic performance of nonhomogeneous slopes with a weak thin layer. Comparison of the static factors of safety is conducted with various solutions (i.e., limit analysis with a different failure mechanism, limit equilibrium solution, and numerical method), and the results exhibit reasonable consistency. An analytical solution in estimating the critical yield acceleration coefficient is derived, and the influence of slope angle, slope height, and soil strength on the critical yield acceleration coefficient and failure mechanism is analyzed. Subsequently, Newmark’s analytical procedure is employed to evaluate cumulative displacement with various real earthquake acceleration records as input motion. Results show that the strength and geometric parameters have a remarkable influence on the critical yield acceleration coefficient, and the cumulative displacement increases with the increasing slope angle.