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

Jiangong Chen,Richeng Hu,Zejun Yang,Haiquan Zhang

doi:10.1155/2016/4158785

Abstract

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.

Highlights

The magnitude and distribution of active earth pressure on the retaining wall under the seismic loading are the theoretical premises of the aseismic design for the retaining wall and play a vital role in evaluating the stability of the retaining wall in the seismic area
The variational limit equilibrium method is used to study the seismic active earth pressure on the gravity retaining wall under general conditions
The seismic active earth pressure is studied in the paper based on the variational limit equilibrium method, and the following conclusions are obtained

Summary

Introduction

The magnitude and distribution of active earth pressure on the retaining wall under the seismic loading are the theoretical premises of the aseismic design for the retaining wall and play a vital role in evaluating the stability of the retaining wall in the seismic area. Only the cases where the retaining wall is vertical and the backfill surface is horizontal without surcharge are considered in the calculation models, while the influences of wall-movement modes of the retaining wall on the magnitude and the action point position of seismic active earth pressure fail to be taken into account. The magnitude and the action point position of seismic active earth pressure depend on the coordinated deformation of soil-wall contact surface and vary with the change of wall-movement modes of the retaining wall [26]. The variational limit equilibrium method is used to study the seismic active earth pressure on the gravity retaining wall under general conditions (the retaining wall is inclined and coarse; the backfill is cohesive soil; the backfill surface is a curved surface with nonuniform surcharge). The interval of the seismic active earth pressure under different wall-movement modes can be effectively estimated by the proposed approach

Variational Analysis of Seismic Active Earth Pressure

Variational Limit Equilibrium Model of Seismic Active

Variational Solution of Seismic Active Earth Pressure

Calculated Result and Parameter Analysis

Conclusion