Limit analysis of cantilever retaining walls with spaced piles

A modified method is proposed for designing cantilever retaining walls with spaced piles. The approach used is based on a new translational three-dimensional failure mechanism within the framework of the upper-bound theorem of limit analysis. Numerical optimisation of the mechanism is performed by a minimisation procedure for the critical three-dimensional passive earth pressure coefficient. Internationally accepted analytical methods for designing these types of retaining structure assume a simplified rectilinear earth pressure distribution, not only for non-spaced piles but also for spaced piles, where the earth pressure distribution is multiplied by the pile spacing. The results of the proposed method indicate that the pile-to-pile spacing, depending on the input soil parameters, strongly influences the shape of the three-dimensional failure mechanism and the passive pressure along the embedment depth to the point of moment equilibrium. Distribution of the passive earth pressure is no longer rectilinear, but the earth mass contributing to the soil–pile interaction on the dredged side of the embedment depth is reduced, which leads to longer piles and higher inner forces in the retaining structure.