承台-群桩结构波浪力理论分析

Theoretical Analysis of Wave Force on Cap-pile Group Structure

目前桥梁基础的波浪力计算大多采用数值模拟的方式进行研究,但数值模拟存在计算成本高、耗时长等缺点。因此基于线性势流理论首次推导了承台-群桩结构的波浪绕射作用计算公式,求解得到了承台波浪力的半解析解。首先将承台-群桩结构简化为上层穿出水面、下层嵌入水底的双层多柱体结构,其中上层单柱体代表承台,下层多柱体代表群桩。然后将计算域划分为承台外侧和下侧2个子域,子域间的交界面函数通过傅里叶级数处理,通过匹配特征函数展开法对每一个子域的速度势函数进行求解,最终得到承台表面波浪力。在进行解的收敛性分析和与边界元软件进行大量的对比验证后,分析了桩半径和承台高度对承台表面波浪力的影响。研究发现:在小波数范围内,承台表面的量纲一的波浪力会随着群桩的存在而增大,并随着桩半径的增加而进一步增大;同时承台高度的增加会首先对波浪力的增加有促进作用,但在承台高度达到某一临界值后,承台量纲一的波浪力将会减小。首次基于势流理论推导的双层多柱体波浪作用的理论公式,为承台-群桩结构表面波浪力的求解提出了一种新的半解析方法,相较于数值模拟,其能在保证结果准确性的同时,也能使得计算更加方便快捷、成本低廉,为之后波浪作用理论的进一步完善提供有力支撑。

Currently, wave forces on bridge foundations are mainly analyzed through numerical simulations. However, the numerical simulation method has disadvantages of high calculation costs and extended time consumption. In this study, the calculation formula of the wave diffraction effect of cap-pile group structures was derived using the linear potential flow theory, and a semianalytical solution of the wave force of the cap was obtained. First, the cap-pile group structure was simplified as a double-layer multicolumn structure, and the calculation domain was then divided into two regions. Next, the interface function between the regions was processed using the Fourier series. Finally, the diffraction problem was solved using the matched eigenfunction expansion method. After the convergence analysis and comparison using the boundary element method software, the effect of the pile radius and cap height on the wave force of the cap was analyzed. The results show that the dimensionless wave force on the cap increases with the existence of the pile group and further increases with increasing pile radius. An increase in the cap height first increases the wave force, but after reaching the critical value, the dimensionless wave force of the cap decreases. In this study, the theoretical formula of the double-layer multicolumn wave action was derived using the potential flow theory for the first time, and a new semianalytical method was developed to determine the wave force of the cap-pile group structure. Compared to the numerical simulation method, the proposed method ensures accuracy and improves calculation convenience and costs, providing a reference for further improvement of the theory.