CN111460563A - Method for calculating wave current borne by box-type upper structure of sea-crossing bridge - Google Patents
Method for calculating wave current borne by box-type upper structure of sea-crossing bridge Download PDFInfo
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Abstract
The invention discloses a method for calculating wave flow force borne by a box-type superstructure of a sea-crossing bridge, which is based on numerical analysis results of the influence of flow velocity, wave characteristics, immersion coefficients and box beam geometric shapes on the wave flow force borne by the box beam superstructure, and converts the influence of the immersion coefficients, the thickness of a dimensionless bridge deck, the length of the dimensionless bridge deck and the flow velocity into quantitative values consisting of functions and fitting coefficients by combining least square algorithm and regression analysis. The estimation method for calculating the wave flow force borne by the box-type superstructure of the sea-crossing bridge, which is established by the invention, can simply, conveniently and accurately calculate the maximum wave flow force borne by the box-type superstructure of the sea-crossing bridge under different flow velocities, wave characteristics, immersion coefficients and box beam geometric shapes, and breaks through the problem that the wave flow force borne by the box beam structure under the combined action of waves and flows cannot be estimated by the conventional method.
Description
Technical Field
The invention relates to the technical field of cross-sea bridge stress calculation, in particular to a method for calculating wave current borne by a box-type superstructure of a cross-sea bridge.
Background
In recent years, natural disasters such as the katrina hurricane (2005), the avan hurricane (2004) in the united states and the typhoon sandei (2006) in the eastern part of china have caused serious damage to infrastructure and coastal structures. These extreme disasters cause significant damage to coastal bridges in shallow water environments near the coast. Coastal bridges are only designed to resist the usual wave forces where the water surface is often much lower than the beam height, but these extreme disasters often result in the water level rising significantly, causing billows to act directly on the beams which are usually placed under their own weight on a quay or connected by weak links. In such extreme cases, wave forces on the coastal bridge may exceed the load bearing capacity of the bridge and cause the bridge to crash and collapse. Therefore, it is a significant topic to determine a method for accurately predicting the wave force acting on a coastal bridge under extreme conditions. Most previous studies only considered the effect of waves, while in natural marine environments waves and currents usually occur simultaneously, but until recently the mechanism of wave-current interaction has not been studied. Currently, the research on the wave force on the box girder bridge is very limited, and there is no accurate formula for predicting the extreme wave force. Furthermore, there is a significant difference between wave flow interaction and individual waves. Therefore, wave flow interaction simulation in the study of box girder wave flow force can provide guidance for design and construction along the sea bridge girder.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for calculating tsunami load borne by a cross-sea bridge, and solves the defects in the prior art.
In order to realize the purpose, the technical scheme adopted by the invention is as follows:
a method for calculating wave current borne by a box-type superstructure of a sea-crossing bridge comprises the following specific steps:
the formula for calculating the maximum wave force in the horizontal and vertical directions can be written as:
FH＝G(aHH*2+bHH*+cH)λCHλWHλLHλUH(1)
FV＝G(aVH*2+bVH*+cV)λCVλWVλLVλUV(2)
wherein H*Is a dimensionless wave height (H)*H/L), H is the wave height, L is the calculated wavelength from Stokes fifth order theory without the influence of flow, G is the gravity of the box beamC,λW,λLAnd λURespectively, the influence coefficients of the immersion coefficient, the thickness of the dimensionless bridge floor, the length of the dimensionless bridge floor and the current speed on the maximum wave force.
The influence of the above factors is converted into a quantitative value (lambda) consisting of a function and fitting coefficients according to the numerical result and a regression methodC,λW,λLAnd λU). These quantified coefficients can be used to estimate wave flow forces under a variety of wave, ocean current and box beam conditions, whichThe quantization modes are as follows:
λCH＝(dHU0+eH)(1-Cs)+1 (3)
λWH＝fHW*+gH(5)
λWV＝fVW*+gV(6)
λLH＝hHL*+iH(7)
λLV＝hVL*+iV(8)
λUH＝jH(1/H*)+kH(9)
λUV＝jV(1/H*)2+kV(1/H*)+lV(10)
wherein a is()To l()Obtained according to a least squares fit, with subscripts H and V indicating the horizontal and vertical directions, respectively. All coefficients are shown in tables 2, 3 and 4, and are calculated numerically. The numerical simulation and quantification equation shows that the influence coefficient lambdaW，λLAnd λURespectively, as a function of the thickness of the dimensionless deck, the length of the dimensionless deck and the height of the dimensionless waves. While the submergence coefficient lambdaCThe influence coefficient of (c) is determined from the current flow rate and the depth of flooding.
TABLE 2 coefficients determined by curve fitting
TABLE 3 influence coefficient of dimensionless thickness and length of sheet
TABLE 4 influence coefficient of flow Rate
At this time, the procedure for estimating the maximum lateral and vertical wave forces in equations (1) to (10) and tables 2, 3 and 4 is as follows:
1. from the observed values of the wave conditions, H can be calculated*The value is obtained.
2. The values calculated in step 1 are combined with the box beam geometry, submergence conditions and current velocity and coefficient equations, while the coefficients in equations (1) to (10) are determined using tables 2 to 4. Then λ can be obtainedC,λW,λLAnd λUThe value of (c).
3. Using the values obtained from step 2, the maximum wave force under given conditions can be calculated using equations (1) and (2).
Compared with the prior art, the invention has the advantages that:
the maximum wave flow force on the box-type upper structure of the sea-crossing bridge under the condition of different flow velocities, wave characteristics, immersion coefficients and box beam geometry can be simply, conveniently and accurately calculated, and the problem that the wave flow force on the box beam structure under the combined action of waves and flows cannot be calculated by the conventional method is solved.
Drawings
FIG. 1 is a schematic view of the basic dimensions of a box girder used in the method of the present invention;
FIG. 2 is a schematic diagram of a numerical water tank used to verify the wave flow interaction established by the method of the present invention in an embodiment of the present invention;
FIG. 3 is a comparison graph of the maximum wave force result calculated by the method of the present invention and the numerical simulation calculation result; FIG. 3a is a comparison graph of lateral force results; FIG. 3b is a graph comparing vertical force results;
FIG. 4 is a schematic diagram of the calculation of parameters in the formula proposed by McPherson.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings by way of examples.
A method for calculating wave current borne by a box-type superstructure of a sea-crossing bridge comprises the following specific steps:
the formula for calculating the maximum wave force in the horizontal and vertical directions can be written as:
FH＝G(aHH*2+bHH*+cH)λCHλWHλLHλUH(1)
FV＝G(aVH*2+bVH*+cV)λCVλWVλLVλUV(2)
wherein H*Is a dimensionless wave height (H)*H/L), H is the wave height, L is the calculated wavelength from stokes' fifth order theory under no influence of flow, G is the gravity of the box beam, equal to 654.42kN/m, which is a constant calculated from the dimensions of the box beam shown in table 1 and fig. 1.
TABLE 1 model parameters
The maximum wave force is given by the wave force multiplied by the influence coefficient. In the equation, λC,λW,λLAnd λURespectively, the influence coefficients of the immersion coefficient, the thickness of the dimensionless bridge floor, the length of the dimensionless bridge floor and the current speed on the maximum wave force. The influence of the above factors is converted into a quantitative value (lambda) consisting of a function and fitting coefficients according to the numerical result and a regression methodC,λW,λLAnd λU). Thus, these quantized coefficients (obtained from a least squares algorithm) can be used to estimate wave flow forces under a variety of wave, ocean current and box beam conditions, and they are quantized as follows:
λCH＝(dHU0+eH)(1-Cs)+1 (3)
λWH＝fHW*+gH(5)
λWV＝fVW*+gV(6)
λLH＝hHL*+iH(7)
λLV＝hVL*+iV(8)
λUH＝jH(1/H*)+kH(9)
λUV＝jV(1/H*)2+kV(1/H*)+lV(10)
wherein a is()To l()Obtained according to a least squares fit, with subscripts H and V indicating the horizontal and vertical directions, respectively. Table 2, table 3 and table 4 list all coefficients used herein, which are numerically calculated. The numerical simulation and quantification equation shows that the influence coefficient lambdaW，λLAnd λURespectively, as a function of the thickness of the dimensionless deck, the length of the dimensionless deck and the height of the dimensionless waves. While the submergence coefficient lambdaCThe influence coefficient of (c) is determined from the current flow rate and the depth of flooding.
TABLE 2 coefficients determined by curve fitting
TABLE 3 influence coefficient of dimensionless thickness and length of sheet
TABLE 4 influence coefficient of flow Rate
At this time, the procedure for estimating the maximum lateral and vertical wave forces in equations (1) to (10) and tables 2, 3 and 4 is as follows:
1. from the observed values of the wave conditions, H can be calculated*The value is obtained.
2. The values calculated in step 1 are combined with the box beam geometry, submergence conditions and current velocity and coefficient equations, while using the above table to determine the coefficients in equations (1) to (10). Then λ can be obtainedC,λW,λLAnd λUThe value of (c).
3. Using the values obtained from step 2, the maximum wave force under given conditions can be calculated using equations (1) and (2).
Example 1
In order to verify the accuracy of the proposed method for calculating the wave flow force borne by the box-type superstructure of the sea-crossing bridge, the numerical simulation (shown in fig. 2) results are compared with the calculation results of the formulas 1 to 10, and the comparison results are shown in fig. 3 and table 5;
TABLE 5 comparison of the results of numerical simulation on the box girder superstructure with the results of calculation of the method proposed by the invention
The scatter plot and statistics shown in fig. 3 indicate that the proposed calculation method is accurate in calculating the maximum horizontal and vertical wave forces, and a comparison of the calculated values and numerical results is given in table 5, where a set of numerical simulations different from the conditions shown in the figure are used to validate the proposed equations. In comparison with the numerical results, Table 5 shows that the calculated values obtained with this method have an error of less than 8%. The result shows that the maximum wave force borne by the box-type upper structure of the sea-crossing bridge can be effectively calculated by the calculation method.
Example 2
To further verify the superiority of the proposed method, the proposed calculation method was compared with existing calculation methods for estimating the wave forces experienced by the superstructure of a T-beam.
McPherson (2008) proposed a new method based on the existing methodology and used the results of large-scale 3D wave experiments conducted at the university of texas a & M to calculate horizontal and vertical forces on a typical bridge section. Due to its simple form and good accuracy, the method proposed by McPherson can be used to estimate the wave forces on a typical bridge section in the united states.
The maximum wave force of the box beam was calculated using the formula proposed by McPherson. In this case, H is 6m, T is 8s, d is 20m, and U is0＝0m/s,C s0. Further, the box girder dimensions shown in table 1 and fig. 1 were used. The horizontal and vertical force equations are listed below:
FV＝Fhydrostatic+Fbirdge+Fair(11)
Fhydrostatic＝γzA-Fw(12)
Fw＝0.5γzA (13)
Fbirdge＝γVolbridge(14)
FH＝FH-front+FH-back(15)
FH-front＝0.5(nmax+hSWL-hgirder)HbridgeLbridgeγ (16)
when ηmax＜hdeck
FH-front＝0.5[(nmax+hSWL-hgirder)+(nmax+hSWL-hdeck)]HbridgeLbridgeγ (17)
When ηmax＞hdeck
FH-back＝0 (18)
When h is generatedSWL＜hgirder
FH-back＝0.5(hSWL-hgirder)2Lbridgeγ (19)
When h is generatedSWL＞hgirder
Fair＝(N-1)0.5γhAair(20)
Wherein Fhydrostetic,Fbridge,FwAnd FairRespectively representing the hydrostatic force, the buoyancy of the bridge, the bridge hydrodynamic force caused by wave climbing and the force caused by air capture; n is the number of girders; a. theairIs the cross-sectional area of air trapped between the bridges (this force is not taken into account in the calculations due to the geometry of the unsealed box beams); gamma is the unit weight of saline water, equal to 64lb/ft3；VolbridgeL is the volume of the bridge immersed in waterbridge1m is the length of the deck slab; h isSWL＝d＝20m；A＝WLbridge＝15m2Is the vertical projection area of the bridge deck span; n ismax＝1.3H/2＝3.9m；ηmax＝nmax+hSWL＝23.9m；Hgirder＝h1＝2.7m；hgirder＝hSWL＝20m；hdeck＝hSWL+h1-h2＝22.1m；z＝nmax–HgirderFig. 4 gives details of these parameters at 1.2m operating condition ηmax＝23.9m>hdeck＝22.1m and hSWL＝hgirderThe calculation when 20m is as follows:
FV＝Fhydrostatic+Fbridge+0＝0.5γzA+γVolbridge＝0.5*64lb/ft3*3.94ft*(49.24ft*3.28ft)+64lb/ft3*[(49.24ft*3.28ft*1.97ft)+(2.298ft*6.89ft+6.89ft*22.98)]＝51872.24lbs＝25.93tons＝254kN
FH＝FH-front+0＝0.5[(nmax+hSWL-hgirder)+(nmax+hSWL-hdeck)]γHbridgeLbridge＝0.5*[(78.46ft-65.66ft)+(78.46ft-72.55ft)]*64lb/ft3*8.86ft*3.28ft＝17399.28lbs＝8.70tons＝85kN
table 6 shows that the results calculated using the empirical equation proposed by McPherson are different from the numerical results under the same conditions.
TABLE 6 comparison of the wave forces to which the box girder superstructure is subjected, calculated by different methods
The empirical formula of McPherson gave a large maximum horizontal force value with an error of 64%, and a small maximum vertical force value with an error of 51.7%, compared to the maximum wave force obtained in the numerical results of table 5. These differences may be caused by the geometrical differences between typical T-beams and box beams. The empirical equation proposed by McPherson calculates the horizontal wave force on a T-beam from the cross-sectional area of the beam. However, box beams have a leading void, which may result in a substantial reduction in horizontal wave forces. In addition, the wave force on the bottom of the deck and the side portions of the bridge is not considered when calculating the maximum vertical force using empirical equations. Therefore, the maximum vertical force estimated by the empirical formula is much lower than that obtained by numerical simulation. However, the calculation method provided by the invention can effectively calculate the numerical result, and the error is only 3%. The superiority of the calculation method provided by the invention in calculating the wave flow force borne by the box-type superstructure of the sea-crossing bridge is effectively verified.
It will be appreciated by those of ordinary skill in the art that the examples described herein are intended to assist the reader in understanding the manner in which the invention is practiced, and it is to be understood that the scope of the invention is not limited to such specifically recited statements and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (1)
1. A method for calculating wave current borne by a box-type superstructure of a sea-crossing bridge is characterized by comprising the following specific steps:
the formula for calculating the maximum wave force in the horizontal and vertical directions can be written as:
FH＝G(aHH*2+bHH*+cH)λCHλWHλLHλUH(1)
FV＝G(aVH*2+bVH*+cV)λCVλWVλLVλUV(2)
wherein H*Is a dimensionless wave height (H)*H/L), H is the wave height, L is the calculated wavelength from stokes theory fifth order under no influence of flow, G is the gravity of the box beam, the maximum wave force is given by the wave force multiplied by the influence factor, in the equation λC,λW,λLAnd λURespectively referring to an immersion coefficient, a thickness of a dimensionless bridge deck, a length of the dimensionless bridge deck and an influence coefficient of the current speed on the maximum wave force;
the influence of the above factors is converted into a quantitative value (lambda) consisting of a function and fitting coefficients according to the numerical result and a regression methodC,λW,λLAnd λU) (ii) a These quantified coefficients can be used to estimate wave flow forces under various wave, ocean current and box beam conditions, and they are quantified as follows:
λCH＝(dHU0+eH)(1-Cs)+1 (3)
λWH＝fHW*+gH(5)
λWV＝fVW*+gV(6)
λLH＝hHL*+iH(7)
λLV＝hVL*+iV(8)
λUH＝jH(1/H*)+kH(9)
λUV＝jV(1/H*)2+kV(1/H*)+lV(10)
wherein a is()To l()Obtained according to a least squares fit, subscripts H and V representing the horizontal and vertical directions, respectively; table 2, table 3 and table 4 list all coefficients, which are numerically calculated; the numerical simulation and quantification equation shows that the influence coefficient lambdaW，λLAnd λUAre functions relating to the thickness of the dimensionless deck, the length of the dimensionless deck and the height of the dimensionless wave, respectively; while the submergence coefficient lambdaCThe influence coefficient of (a) is determined by the current flow rate and the depth of flooding;
TABLE 2 coefficients determined by curve fitting
TABLE 3 influence coefficient of dimensionless thickness and length of sheet
TABLE 4 influence coefficient of flow Rate
At this time, the procedure for estimating the maximum lateral and vertical wave forces in equations (1) to (10) and tables 2, 3 and 4 is as follows:
1. from the observed values of the wave conditions, H can be calculated*A value;
2. combining the values calculated in step 1 with the box beam geometry, submergence conditions and current velocity and coefficient equations, while determining the coefficients in equations (1) to (10) using tables 2 to 4; then λ can be obtainedC,λW,λLAnd λUA value of (d);
3. using the values obtained from step 2, the maximum wave force under given conditions can be calculated using equations (1) and (2).
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