自由液面效应对跨海桥梁桩基波浪力的影响

Free surface effect on wave forces of the pile foundation for sea-crossing bridge

目前应用Morison方程估算小尺度柱体波浪合力(矩)时大多仅沿静水深积分,而忽略波浪自由液面影响。为探讨波浪自由液面对小尺度柱体波浪合力(矩)的影响,基于Morison方程、修正的线性Airy波浪理论和非线性Stokes2波浪理论,推导考虑自由液面影响下柱体波浪合力(矩)的计算公式。运用该计算公式,分析不同波况下,波浪自由液面对柱体波浪合力(矩)峰值的影响,同时对比修正的线性Airy波和非线性stokes2波的数值计算结果。研究结果表明:与线性波相比,由于stokes2波浪理论造出的波形波峰尖而陡,波谷宽而缓,其波浪合力(矩)峰值较大且相位提前。随着波高H的增加,水深与波长相对比值d/L减小,波浪自由液面对小尺度柱体波浪力的影响越来越大。当d/L大于某一临界值时,波浪自由液面及波浪非线性对柱体波浪合力(矩)影响很小。特别地,当d/L=0.1,H=Hb时,考虑了波浪自由液面影响后,波浪非线性修正系数CFd+η,CMd+η达到最大,CFd+η≈7.4,CMd+η≈10.2,表明对于浅水大波高情况,此时务必要同时考虑波浪非线性及自由液面的影响。

In current engineering application,total wave forces(moments)on piles are mostly obtained by integrating the Morison equation along static water depth but ignore the free surface effect.To study free surface effect on wave forces acting on small piles,total wave forces(moments)formulas were deduced based on Morison equations,modified Airy linear wave and stokes 2 wave theory.Applying the derived formulas,numerical results of maximum total wave forces(moments)under various wave conditions were analyzed.Meanwhile,the numerical results were compared between modified linear Airy and stokes 2 wave theory.It is found that,compared with linear wave theory,as the waveform created by stokes 2 wave theory performs higher and steeper peak,wider and flatter trough,maximum wave forces based on stokes 2 happens bigger at earlier phase.As wave height H increases,and relevant ratio of water depth and wave length d/L decreases,free surface effect on the wave forces(moments)becomes stronger.When d/L is bigger than a critical value,free surface effect and nonlinear wave effect get very weak on total wave forces(moments)acting on small piles.Especially,when d/L=0.1,wave height H equals the limited breaking wave height Hb,after considering free surface effect,nonlinear wave correction factor of CFd+η,CMd+ηreach the maximum values,CFd+η≈7.4,CMd+η≈10.2,it means for shallow water depth and big wave height conditions,nonlinear wave effect and free surface effect should be considered.