基于拉格朗日乘数法的大弯矩水平受荷桩研究

Research on the laterally loaded piles under huge moment based on Lagrange multipliers method

水平受荷单桩常用于海上风机基础,该条件下单桩受到巨大的倾覆力矩。通过引入力和弯矩平衡的拉格朗日乘子,将桩身挠曲线泛函极值问题转化为非线性方程组。方程组求解采用牛顿法,以Matlab矩阵运算实现。所提方法适用于任意非线性或分段形式的p-y(水平抗力-水平位移)曲线,计算迅速,可模拟荷载和桩身参数的变化。与试桩资料的对比表明,所提方法计算准确。算例研究表明,加载高度与桩长相仿时,绝大部分桩基变形是由桩顶弯矩导致,水平承载力校核失去意义。通过计算不同设计参数下的桩基变形曲线,研究了海上风机单桩基础的设计问题。研究表明,单桩基础存在明显的有效桩长。设计桩径是由水平位移限值决定的,更小的桩径就能满足规范中的转角限值。

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.