Abstract: Laterally loaded monopiles are commonly used for the offshore wind turbines, which means huge moment is applied to the monopiles. Lagrange multipliers are constructed to describe the balance of the moment and the lateral force. The functional extreme problem of the deflection curve is then transformed into nonlinear equations. Based on the matrix operations of Matlab, Newton’s method is applied to solve the equations. This new method is available for any nonlinear or segmented p-y curves. The algorithm can be efficiently used to obtain the deformation of piles at varied load and design parameters. Data of testing piles is examined, which shows good reliability of the numerical results. Numerical examples show that when the loading height is approximately the same as the pile length, almost all the deformations are induced by the moment, thus the checking of lateral bearing capacity becomes meaningless. Finally, the design of a monopile foundation under an offshore wind turbine is studied. Deformations of the piles with different lengths and diameters are calculated. The results of calculations reveal an effective length of the pile. The diameter of the pile is determined by the limit of lateral displacement. Pile with significantly smaller diameter will meet the limit of rotation angle.

Key words: Lagrange multiplier, monopile foundation, laterally loaded pile, p-y curve