Study on the action of the active earth pressure by variational limit equilibrium method

Within the framework of limiting equilibrium approach, the problem of active earth pressure on rigid retaining wall is formulated in terms of the calculus of variations by means of Lagrange multipliers. It is transcribed as the functional of extreme‐value problem by two undetermined function arguments, and is further transformed into determining the minimax solution of restrained functions incorporating the geometrical relations of the problem. The function of (fmincon) in the optimization toolbox of MATLAB 6.1 can be used to find the minimax solution. Computation results show there exist two kinds of modes of failure sliding along plane surface and rotating around log‐spiral cylinder surface when the soil behind the walls reaches the critical active state. The magnitude of active earth pressure in the case of translational mode is less than that in the case of rotational mode. The location of action point of earth pressure in the case of translational mode is at or below \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}$\frac{1}{3}$\end{document} height of the wall, and in the case of rotational mode, is above \documentclass{article}\footskip=0pc\pagestyle{empty}\begin{document}$\frac{1}{3}$\end{document} height of the wall. Preliminary study indicates a pair of numbers by two theoretical modes can be regarded as an interval estimation of active pressure. Copyright © 2009 John Wiley & Sons, Ltd.