Study On Hydrodynamic Analysis Methods Of Deep-water Bridges

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.