Study On The Calculation Method Of Wave-current Force In The Process Of Cofferdam Sinking

With the increasing number of sea-crossing bridges,large-diameter cofferdams are often used in the construction of bridge foundations under complex ocean conditions,such as steel suspension box cofferdams used in Pingtan Strait Railway Bridge,caisson construction of main channel bridge of HuTong Yangtze River Bridge,etc.In the marine environment,coffer-dam construction often undergoes the process of floating and sinking.In this process,coffer-dam will be subjected to the action of current,periodic action of wave,and wave-current force under the combined action of current and wave,the safety and stability of cofferdam during floating and sinking process are directly determined by the accurate prediction of cofferdam force in the early stage.Therefore,the main purpose of this paper is to obtain the calculation method of cofferdam force under the action of pure wave,pure current and wave-current in the process of cofferdam sinking.In this paper,based on the Morison equation and linear wave-current theory,the formulas for calculating the flow force,wave force and wave-current force of the cofferdam are obtained.Since the hydrodynamic coefficients C_D?C_M in the theoretical formulas are empirical param-eters,the variation law of the hydrodynamic coefficients of the cofferdam under pure current,pure wave and wave-current conditions is studied in this paper.Then,the spectrum analysis of liquid level and cofferdam force under pure flow conditions of AR=1/3²,U₀=0.2⁰.5m/s is carried out,and the law of variation of average height of liquid level and fluctuation amplitude of liquid level with slenderness ratio AR and velocity U₀ is obtained,as well as the law of variation of mean value and fluctuation amplitude of cofferdam force with slenderness ratio AR and velocity U₀ is obtained.Then,the dimensionless processing of the force data is carried out to obtain the variation rule of resistance coefficient C_D with Reynolds number Re and slenderness ratio AR:1.The drag coefficient decreases significantly compared with that of an infinite cylinder.In the case of a smaller slenderness ratio of AR=1/3,2/3the drag coefficient is 0.5<<0.8,and the drag coefficient remains in a relatively stable range and does not change greatly with the change of Reynolds number.When AR<1,the drag coefficient decreases obviously with the increase of Reynolds number.2.The drag coefficient C_D increases with the increase of slenderness ratio.In Re=4.6×10⁴,9.2×10⁴,11.5×10⁴,the drag coefficient of AR=1/3 is larger than that of AR=2/3.When Re=6.9×10⁴,9.2×10⁴,11.5×10⁴,the C_D value of AR=1 increases suddenly.The C_D value of AR=1 is larger than that of AR=4/3,which is close to that of AR=5/3.For wave surface and cofferdam force under pure wave condition,this paper analyses the variation of wave surface with slenderness ratio and horizontal wave force and vertical wave force with slenderness ratio under the same wave condition.Then the horizontal wave force data are processed in dimensionless way,and the variation laws of drag coefficient C_D and inertia force coefficient C_M with Reynolds number Re,KC and slenderness ratio AR are obtained:1.The ratio between wave height H and structure scale D is H/D?1,so the viscous effect of wave is weak.The maximum proportion of velocity force in wave force is 18.92%,and the minimum is only 3.32%.The resistance coefficient C_D is less than 0.7,and the minimum time is only 0.1,so the viscous effect of cofferdam in this paper can be ignored.2.The variation range of inertia force coefficient C_M of cofferdam is 1.4²,which is smaller than that of infinite cylinder.The variation law of inertia force coefficient with Reynolds num-ber is as follows:within the range of 3×10⁴?Re?4×10⁴,the inertia force coefficient changes little with Reynolds number;when?=4.5×10⁴,the relationship between inertia force coeffi-cient and KC number is as follows:C_M increases with the increase of KC number;the varia-tion rule of inertia force coefficient with slenderness ratio of cofferdam follows:C_M increases with the increase of AR,and when AR=2,the inertial force coefficient of cofferdam is close to the inertial force coefficient of through-length cylinder.Finally,the horizontal force of cofferdam under wave and current conditions is analyzed,and the law of horizontal force varying with wave height and wave period under different current velocities is obtained,as well as the law of horizontal force varying with current ve-locity under different wave height and wave period.By dimensionless treatment of horizontal force,the variation laws of drag coefficient C_D and inertia force coefficient C_M with Reyn-olds number Re,KC number and slenderness ratio AR are obtained.1.The resistance coefficient C_D of the cofferdam under the combined action of wave and current is smaller than that of the infinite cylinder.The rules of Cofferdam resistance coeffi-cient C_D varies with Reynolds number Re will change under different KC numbers.When KC?4.8,C_D basically does not change with Re.When KC?6.4,C_D increases with Re.The range of C_D is 0.45?C_D?1.03;The rules of Cofferdam resistance coefficient C_D varies with KC numbers will change under different Reynolds number Re.When Re?1×10⁵,C_D decreases with the increase of KC number.When Re is greater than 1.2,C_D fluctuates near a constant with the increase of KC number,and the range of C_D varies from 0.45 to 1.17.The change rule of C_D value with slenderness ratio AR is as follows:when the KC number and Reynolds number are small,C_D increases with AR and approaches the C_D value of the infi-nite cylinder.When the KC number and Reynolds number increase to a certain extent,C_D increases with AR and approaches the C_D value of the infinite cylinder,but increases sud-denly when AR=1,which is similar to the change rule of C_D value with AR in the pure flow condition.2.Inertial force coefficient cm of cofferdam under combined action of wave and current is smaller than that of infinite cylinder.The relationship between inertia force coefficient cm and Reynolds number Re is as follows:when the number of KC is small,the inertia force coeffi-cient C_M is basically unchanged with the increase of Reynolds number Re under large AR,while the inertia force coefficient C_M decreases with the increase of Reynolds number Re under small AR,and with the increase of KC number,the inertia force coefficient C_M of dif-ferent AR decreases with the increase of Reynolds number Re.The relationship between inertia force coefficient C_M and KC is as follows:When C_M increases with the increase of KC num-ber,the C_M value of T=1s decreases significantly compared with the C_M value of other wave periods,and C_M increases with the increase of KC number when Re increases gradually.The relationship between inertial force coefficient C_M and AR is as follows:C_M increases with the increase of AR,but with the increase of KC and Reynolds number,the relationship between cm and AR gradually fluctuates near a constant value.In addition,for the wave and current conditions corresponding to T=1s,the relationship between cm and AR will change at different flow velocities.