A closed form solution for a three dimensional passive earth pressure coefficient

Summary

Estimation of passive pressure under both static and seismic conditions is very important for the design of diaphragm walls, anchors, foundations etc. It has been shown in technical literature that in case of limited width of the “plate” on which earth pressure acts, the influence of the third dimension can be significant, due to side effects so that the three-dimensional passive earth pressure coefficient is greater than the two-dimensional one. Unfortunately, no closed form solution for the evaluation of this coefficient is available till now, but only results listed in tables or shown in plots versus B/H ratios, being B and H the plate width and height, respectively.

In this work, an extension of the classical Mononobe-Okabe-Kapila method is presented and a closed form solution for the evaluation of three-dimensional passive earth pressure coefficient is obtained and applied. Similarly to numerical approaches in literature, the pro- posed solution takes into account the friction angle of the soil and that of the soil-plate interface while, as a novelty, it allows to take into account the slope angle of the backfill, and seismic actions through a pseudo-static approach. The model is validated in static conditions, by comparisons with solutions obtained by other authors through different approaches.