Abstract
A simple method is proposed for calculating the active and passive earth pressure coefficients in the general case of an inclined wall and a sloping backfill. The approach used is based on rotational log-spiral failure mechanisms in the framework of the upper-bound theorem of limit analysis. It is shown that the energy balance equation of a rotational log-spiral mechanism is equivalent to the moment equilibrium equation about the centre of the log-spiral. Numerical optimisation of the active and passive earth pressure coefficients is performed automatically by a spreadsheet optimisation tool. The implementation of the proposed method is illustrated using an example. The predictions by the present method are compared with those given by other authors.
Highlights
The problem of active and passive earth pressures acting against rigid retaining structures has been extensively studied in the literature since Coulomb.[1]
This variational limit equilibrium method may be extended to the active earth pressure problem, and the same conclusions remain valid in this case: (a) A log-spiral failure surface may be obtained from a variational maximisation procedure
The aim of this paper is to show that the upper-bound method in limit analysis for a rotational log-spiral failure mechanism gives rapid and good predictions for both active and passive earth pressures
Summary
The problem of active and passive earth pressures acting against rigid retaining structures has been extensively studied in the literature since Coulomb.[1]. A variational analysis has been applied to the passive earth pressure problem by Soubra et al.[2] Their approach is based on a limit equilibrium method, and the solution provides a log-spiral failure surface. It should be emphasised that their method, employed in this paper, can be categorised as an upper-bound in the framework of limit analysis where a rotational rigid body movement is considered. This variational limit equilibrium method may be extended to the active earth pressure problem, and the same conclusions remain valid in this case:
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