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Shock and Vibration
Volume 2016 (2016), Article ID 4158785, 10 pages
Research Article

Study on the Seismic Active Earth Pressure by Variational Limit Equilibrium Method

1College of Civil Engineering, Chongqing University, Chongqing 400045, China
2Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Ministry of Education, Chongqing 400045, China

Received 8 January 2016; Revised 19 April 2016; Accepted 8 May 2016

Academic Editor: Sergio De Rosa

Copyright © 2016 Jiangong Chen 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.


In the framework of limit equilibrium theory, the isoperimetric model of functional extremum regarding the seismic active earth pressure is deduced according to the variational method. On this basis, Lagrange multipliers are introduced to convert the problem of seismic active earth pressure into the problem on the functional extremum of two undetermined function arguments. Based on the necessary conditions required for the existence of functional extremum, the function of the slip surface and the normal stress distribution on the slip surface is obtained, and the functional extremum problem is further converted into a function optimization problem with two undetermined Lagrange multipliers. The calculated results show that the slip surface is a plane and the seismic active earth pressure is minimal when the action point is at the lower limit position. As the action point moves upward, the slip surface becomes a logarithmic spiral and the corresponding value of seismic active earth pressure increases in a nonlinear manner. And the seismic active earth pressure is maximal at the upper limit position. The interval estimation constructed by the minimum and maximum values of seismic active earth pressure can provide a reference for the aseismic design of gravity retaining walls.