深水桥梁动水压力分析方法研究
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摘要
随着交通事业的快速发展,国内建设了大量的深水桥梁。这些深水桥梁多处于西部山区,这些地区是我国地震高发区。深水桥墩在水中振动时,桥墩的水下部分将受到动水压力作用。动水压力不仅会影响深水桥梁的动力特性,对动力响应也有较大的影响。地震作用下动水压力对桥梁结构的影响不可忽视。目前国内外对深水桥梁动水压力的研究,以及墩-水耦合作用的研究相对较少。国外规范对动水压力的计算结果不尽相同,国内相关规范仅能对跨径小于150米的简单截面类型深水桥梁的动水压力进行简化计算,不能满足当前大跨度深水桥墩动水压力计算的需要。目前广泛使用的动水压力计算方法都存在一些缺陷,对深水桥梁动水压力计算方法展开深入研究势在必行。
本文主要针对辐射波浪法、Morison方程和流体单元法存在的不足展开研究,分别对上述三种方法进行简化、扩展、改进,并提出了两种新的计算方法。主要内容如下：
1.简要介绍了线性辐射波浪理论,以及基于辐射波浪法的圆形空心桥墩内、外域水动水压力表达式,基于辐射波浪法的矩形空心墩内域水动水压力表达式,并建立了相应的墩-水耦合计算模型。简要介绍了Morison方程,并建立了基于Morison方程的墩-水耦合计算模型。简要介绍了流体单元法原理,并建立了墩-水耦合有限元模型。对上述三种方法的计算效率、精度及适用范围进行了对比分析。
2.对流体单元法中流体域边界条件进行了简化,对流体域取值范围、流体域网格划分精度进行了研究,得到了常用深水桥墩理想流体域范围及合理的网格划分精度,并建立了改进的流体单元法墩-水耦合有限元模型。
3.传统Morison方程只能计算小尺寸墩柱外域水动水压力,文中推导了能够同时计算小尺寸圆形空心墩、矩形空心墩内外域水动水压力的扩展Morison方程,验证了扩展Morison方程的合理性。并将扩展Morison方程与流体单元法、辐射波浪法计算结果进行了对比,以判定扩展Morison方程的正确性和计算精度。
4.基于辐射波浪法的圆形空心墩内、外域水动水压力表达式,以及矩形空心墩内域水动水压力表达式极其复杂,难于计算。通过参数分析、数值拟合等方式,对基于辐射波浪法的动水压力表达式进行了简化,得到了相应的简化表达式。算例表明简化表达式有很高的计算精度。
5.直接使用辐射波浪理论推导矩形墩外域水动水压力,将会遇到棘手的数学问题。文中提出了一种新的计算矩形墩外域水动水压力的方法——基于辐射波浪法与流体单元法的混合法。该方法使用流体单元法获得正方形桥墩相对于圆形桥墩的形状系数,并与基于辐射波浪法的圆形桥墩外域水动水压力表达式相乘,得到正方形桥墩外域水动水压力表达式。再使用流体单元法求解矩形桥墩长宽比系数,并与正方形桥墩外域水动水压力表达式相乘,得到矩形桥墩外域水动水压力表达式。文中将混合法与流体单元法、Morison方程的计算结果进行了对比,结果表明该方法具有较高的精度与计算效率。
6.圆端形桥墩、椭圆形桥墩也是工程中常见的桥墩类型。为了解决圆端形桥墩、椭圆形桥墩以及任意截面形状桥墩外域水动水压力计算,文中提出了另一种新的计算方法：基于频率降低率的附加质量比法。在动水压力对桥墩刚度无影响、动水附加质量沿着水深均匀分布的假设条件下,推导了桥墩在水中一阶频率降低率与附加质量之间的关系。利用流体单元法计算出各种截面类型桥墩的一阶频率降低率,从而得到附加质量比,进一步得到动水附加质量。使用该方法,文中提出了基于附加质量比法的圆形桥墩、正方形桥墩、矩形桥墩、圆端形桥墩、椭圆形桥墩外域水动水附加质量表达式。文中建立了基于附加质量比法的墩-水耦合计算模型,对每一种类型桥墩的动水附加质量表达式,使用流体单元法、辐射波浪法与混合法中的一种或两种进行对比,以验证附加质量比法的计算精度。
7.为了检验文中提出的两种新方法：混合法、附加质量比法在实际深水桥梁工程中应用时的正确性与精度,分别使用上述两种方法与流体单元法,对岷江庙子坪大桥连续刚构主桥进行了动力特性与地震响应对比分析。结果表明：流体单元法建模繁杂,单元、节点数量庞大,计算效率低,计算结果偏于保守；混合法与附加质量比法建模方便快捷,单元、节点数量小,计算效率很高,并有较高的计算精度。计算结果还表明：动水压力对连该桥的动力特性影响很小,而对该桥的地震影响很大,应该引起足够的重视。
With the development of transportation, many deep-water bridges have been built in our country. Most of these bridges locate in western mountainous area, where are zones of high earthquake probability. The submerged part of pier suffers hydrodynamic pressure when deep-water piers shake in water. Not only dynamic characteristic but also dynamic response of deep-water bridges would be affected by hydrodynamic pressure. So the hydrodynamic pressure caused by earthquakes can not be ignored. While fully research on hydrodynamic pressure and pier-water coupled vibration under earthquakes haven't been done, and codes about hydrodynamic pressure calculation both at home and abroad are imperfect. For example the calculation results of foreign codes are obviously different with each other, and codes in our country are only valid for those piers with span shorter than150m, and those with simple cross sections. So it is urgent to study the problem intensively.
The radiation wave method, Morison equation method and fluid element method are three hydrodynamic pressure calculation methods which are widely used nowadays. The hydrodynamic pressure expressions based on the radiation wave method are too complicated to apply in practice. Morison equation method is available for out-water hydrodynamic pressures, but unavailable for in-water ones. The fluid method can only be employed to calculate single pier because of poor calculation efficiency. The study manly focuses attention on how to modify these defects. Also two news methods have been proposed for the first time. The main achievements are described as follows:
1. Linear radiation theory is introduced, out-water and in-water hydrodynamic pressure expressions of circular hollow piers, and in-water hydrodynamic pressure expressions of rectangular hollow piers based on linear radiation theory have been deduced briefly. Then numerical calculation model of the pier-water interaction have been built respectively. The theory of Morison equation has been described and related numerical calculation model of pier-water interaction has been built also. The fluid element method theory has been presented and its FE model has been built too. At last comparison has been made between three methods to distinguish the calculation precision, calculation efficiency and application cope between them.
2. For fluid element method, fluid domain boundary has been simplified, and fluid domain scope and fluid domain mesh size have been studied. Then modified FE model has been built, appropriate fluid domain scope for commonly used deep-water piers and proper mesh size have been proposed.
3. Traditional Morison equation is efficient in out-water hydrodynamic pressure calculation for solid small piers. The expand Morison equation which considers both in-water and out-water hydrodynamic pressures are deduced for circular and rectangular hollow piers. Based on which, numerical calculation model of pier-water interaction is founded. And comparison has been made between fluid element method, radiation wave method and the expand Morison equation method in order to check validation and precision of the expand Morison equation.
4. The in-water and out-water hydrodynamic pressure expressions of circular hollow piers based on the radiation wave theory are too complicated to apply in practice. The in-water hydrodynamic pressure expressions of rectangular hollow piers are as complicated as the circular's. Simplifications have been done by parameter analysis and curve fitting, base on which the simple expressions have been advised respectively. Test results show that the simple expressions are as exact as the old ones, and are more efficient.
5. The math problems would become more difficult if the radiation wave method is used again to deduce out-water hydrodynamic pressure expressions of rectangular piers. Then a new method named hybrid method, which based on the fluid element method and the radiation wave method is proposed. The out-water hydrodynamic pressure expressiones of square piers are deduced by the way of multiplying the shape function of square piers, which has been worked out using the fluid element method, by the simplified out-water hydrodynamic pressure expression of circular piers. Then resulting expression is again multiplied by the LAB function (a function related to rectangle's length to width ratio) of rectangular pier which also has been worked out using the fluid method. The result is out-water hydrodynamic pressure expression for rectangular piers. At last the comparison between the hybrid method, the fluid element method and Morison equation method reveals that the hybrid method performs well in calculating precision and calculating efficiency.
6. Round-ended piers, elliptical piers and other shape piers are commonly used in practice, hydrodynamic pressure of them should not been ignored. A new method called added-mass ratio method is found especially for them. Base on the assumptions of structure stiffness would not been affected by hydrodynamic pressure and added-mass distributes along the height of submerge piers uniformly, the connection between piers natural frequency decrease and added-mass ratio can be achieved. Natural frequency decrease of all kinds of piers can be worked out easily by the fluid element method, so added-mass ratio is available for all kinds of piers. Added-mass ratio is defined as added-mass of unit height of pier to unit height mass of piers. Accordingly added-mass expressions of circular piers, square piers, rectangular piers, round-ended piers and elliptical piers have been advised. Also numerical calculation models of pier-water interaction are built, and the fluid element method and the radiation wave method or hybrid method are used to valid the new method, results show the added-mass ratio method has better precision and is efficiency.
7. In order to test these two new methods created in paper, a real deep-water continuous rigid frame bridge, well known as Min Jiang Miao Ziping bridge, which was destroyed seriously under5.12WenChuan Earthquake, is modeled with three methods, two new ones and the fluid element method. Calculation results show the fluid element method is complicated in modeling, number of generated cells and nodes is huge, the calculation efficiency is low, and precision is poorer than the two others. The hybrid method and added-mass ratio method have almost the same results. They are convenient in modeling, number of cells and nodes is small, their calculation efficiency is high and precision is better. Results also reveal that hydrodynamic pressure has little effect on dynamic characteristics of continuous rigid frame bridge, but has great impact on seismic response.
本文主要针对辐射波浪法、Morison方程和流体单元法存在的不足展开研究,分别对上述三种方法进行简化、扩展、改进,并提出了两种新的计算方法。主要内容如下：
1.简要介绍了线性辐射波浪理论,以及基于辐射波浪法的圆形空心桥墩内、外域水动水压力表达式,基于辐射波浪法的矩形空心墩内域水动水压力表达式,并建立了相应的墩-水耦合计算模型。简要介绍了Morison方程,并建立了基于Morison方程的墩-水耦合计算模型。简要介绍了流体单元法原理,并建立了墩-水耦合有限元模型。对上述三种方法的计算效率、精度及适用范围进行了对比分析。
2.对流体单元法中流体域边界条件进行了简化,对流体域取值范围、流体域网格划分精度进行了研究,得到了常用深水桥墩理想流体域范围及合理的网格划分精度,并建立了改进的流体单元法墩-水耦合有限元模型。
3.传统Morison方程只能计算小尺寸墩柱外域水动水压力,文中推导了能够同时计算小尺寸圆形空心墩、矩形空心墩内外域水动水压力的扩展Morison方程,验证了扩展Morison方程的合理性。并将扩展Morison方程与流体单元法、辐射波浪法计算结果进行了对比,以判定扩展Morison方程的正确性和计算精度。
4.基于辐射波浪法的圆形空心墩内、外域水动水压力表达式,以及矩形空心墩内域水动水压力表达式极其复杂,难于计算。通过参数分析、数值拟合等方式,对基于辐射波浪法的动水压力表达式进行了简化,得到了相应的简化表达式。算例表明简化表达式有很高的计算精度。
5.直接使用辐射波浪理论推导矩形墩外域水动水压力,将会遇到棘手的数学问题。文中提出了一种新的计算矩形墩外域水动水压力的方法——基于辐射波浪法与流体单元法的混合法。该方法使用流体单元法获得正方形桥墩相对于圆形桥墩的形状系数,并与基于辐射波浪法的圆形桥墩外域水动水压力表达式相乘,得到正方形桥墩外域水动水压力表达式。再使用流体单元法求解矩形桥墩长宽比系数,并与正方形桥墩外域水动水压力表达式相乘,得到矩形桥墩外域水动水压力表达式。文中将混合法与流体单元法、Morison方程的计算结果进行了对比,结果表明该方法具有较高的精度与计算效率。
6.圆端形桥墩、椭圆形桥墩也是工程中常见的桥墩类型。为了解决圆端形桥墩、椭圆形桥墩以及任意截面形状桥墩外域水动水压力计算,文中提出了另一种新的计算方法：基于频率降低率的附加质量比法。在动水压力对桥墩刚度无影响、动水附加质量沿着水深均匀分布的假设条件下,推导了桥墩在水中一阶频率降低率与附加质量之间的关系。利用流体单元法计算出各种截面类型桥墩的一阶频率降低率,从而得到附加质量比,进一步得到动水附加质量。使用该方法,文中提出了基于附加质量比法的圆形桥墩、正方形桥墩、矩形桥墩、圆端形桥墩、椭圆形桥墩外域水动水附加质量表达式。文中建立了基于附加质量比法的墩-水耦合计算模型,对每一种类型桥墩的动水附加质量表达式,使用流体单元法、辐射波浪法与混合法中的一种或两种进行对比,以验证附加质量比法的计算精度。
7.为了检验文中提出的两种新方法：混合法、附加质量比法在实际深水桥梁工程中应用时的正确性与精度,分别使用上述两种方法与流体单元法,对岷江庙子坪大桥连续刚构主桥进行了动力特性与地震响应对比分析。结果表明：流体单元法建模繁杂,单元、节点数量庞大,计算效率低,计算结果偏于保守；混合法与附加质量比法建模方便快捷,单元、节点数量小,计算效率很高,并有较高的计算精度。计算结果还表明：动水压力对连该桥的动力特性影响很小,而对该桥的地震影响很大,应该引起足够的重视。
With the development of transportation, many deep-water bridges have been built in our country. Most of these bridges locate in western mountainous area, where are zones of high earthquake probability. The submerged part of pier suffers hydrodynamic pressure when deep-water piers shake in water. Not only dynamic characteristic but also dynamic response of deep-water bridges would be affected by hydrodynamic pressure. So the hydrodynamic pressure caused by earthquakes can not be ignored. While fully research on hydrodynamic pressure and pier-water coupled vibration under earthquakes haven't been done, and codes about hydrodynamic pressure calculation both at home and abroad are imperfect. For example the calculation results of foreign codes are obviously different with each other, and codes in our country are only valid for those piers with span shorter than150m, and those with simple cross sections. So it is urgent to study the problem intensively.
The radiation wave method, Morison equation method and fluid element method are three hydrodynamic pressure calculation methods which are widely used nowadays. The hydrodynamic pressure expressions based on the radiation wave method are too complicated to apply in practice. Morison equation method is available for out-water hydrodynamic pressures, but unavailable for in-water ones. The fluid method can only be employed to calculate single pier because of poor calculation efficiency. The study manly focuses attention on how to modify these defects. Also two news methods have been proposed for the first time. The main achievements are described as follows:
1. Linear radiation theory is introduced, out-water and in-water hydrodynamic pressure expressions of circular hollow piers, and in-water hydrodynamic pressure expressions of rectangular hollow piers based on linear radiation theory have been deduced briefly. Then numerical calculation model of the pier-water interaction have been built respectively. The theory of Morison equation has been described and related numerical calculation model of pier-water interaction has been built also. The fluid element method theory has been presented and its FE model has been built too. At last comparison has been made between three methods to distinguish the calculation precision, calculation efficiency and application cope between them.
2. For fluid element method, fluid domain boundary has been simplified, and fluid domain scope and fluid domain mesh size have been studied. Then modified FE model has been built, appropriate fluid domain scope for commonly used deep-water piers and proper mesh size have been proposed.
3. Traditional Morison equation is efficient in out-water hydrodynamic pressure calculation for solid small piers. The expand Morison equation which considers both in-water and out-water hydrodynamic pressures are deduced for circular and rectangular hollow piers. Based on which, numerical calculation model of pier-water interaction is founded. And comparison has been made between fluid element method, radiation wave method and the expand Morison equation method in order to check validation and precision of the expand Morison equation.
4. The in-water and out-water hydrodynamic pressure expressions of circular hollow piers based on the radiation wave theory are too complicated to apply in practice. The in-water hydrodynamic pressure expressions of rectangular hollow piers are as complicated as the circular's. Simplifications have been done by parameter analysis and curve fitting, base on which the simple expressions have been advised respectively. Test results show that the simple expressions are as exact as the old ones, and are more efficient.
5. The math problems would become more difficult if the radiation wave method is used again to deduce out-water hydrodynamic pressure expressions of rectangular piers. Then a new method named hybrid method, which based on the fluid element method and the radiation wave method is proposed. The out-water hydrodynamic pressure expressiones of square piers are deduced by the way of multiplying the shape function of square piers, which has been worked out using the fluid element method, by the simplified out-water hydrodynamic pressure expression of circular piers. Then resulting expression is again multiplied by the LAB function (a function related to rectangle's length to width ratio) of rectangular pier which also has been worked out using the fluid method. The result is out-water hydrodynamic pressure expression for rectangular piers. At last the comparison between the hybrid method, the fluid element method and Morison equation method reveals that the hybrid method performs well in calculating precision and calculating efficiency.
6. Round-ended piers, elliptical piers and other shape piers are commonly used in practice, hydrodynamic pressure of them should not been ignored. A new method called added-mass ratio method is found especially for them. Base on the assumptions of structure stiffness would not been affected by hydrodynamic pressure and added-mass distributes along the height of submerge piers uniformly, the connection between piers natural frequency decrease and added-mass ratio can be achieved. Natural frequency decrease of all kinds of piers can be worked out easily by the fluid element method, so added-mass ratio is available for all kinds of piers. Added-mass ratio is defined as added-mass of unit height of pier to unit height mass of piers. Accordingly added-mass expressions of circular piers, square piers, rectangular piers, round-ended piers and elliptical piers have been advised. Also numerical calculation models of pier-water interaction are built, and the fluid element method and the radiation wave method or hybrid method are used to valid the new method, results show the added-mass ratio method has better precision and is efficiency.
7. In order to test these two new methods created in paper, a real deep-water continuous rigid frame bridge, well known as Min Jiang Miao Ziping bridge, which was destroyed seriously under5.12WenChuan Earthquake, is modeled with three methods, two new ones and the fluid element method. Calculation results show the fluid element method is complicated in modeling, number of generated cells and nodes is huge, the calculation efficiency is low, and precision is poorer than the two others. The hybrid method and added-mass ratio method have almost the same results. They are convenient in modeling, number of cells and nodes is small, their calculation efficiency is high and precision is better. Results also reveal that hydrodynamic pressure has little effect on dynamic characteristics of continuous rigid frame bridge, but has great impact on seismic response.
引文
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