The upper bound method of plasticity limit analysis is used to estimate the ultimate capacity of laterally loaded long piles. Based on a generic limiting force (or the ultimate soil resistance per unit length) profile, both freehead and fixed-head piles are considered. The current solutions can be reduced to available solutions for some special cases. Design charts may be constructed to estimate the lateral capacity of piles in terms of plastic moment and the parameters describing the limiting force profile.
Qin, H. Y., Oh, E. Y. N., Guo, W. D. & Dai, P. F. (2013). Upper bound limit analysis of lateral pile capacity. International Conference on State of the Art Pile Foundation and Pile Cast Histories (PILE 2013)