CN107644144A - One kind floods coastal waters bridge superstructure wave force evaluation method - Google Patents
One kind floods coastal waters bridge superstructure wave force evaluation method Download PDFInfo
- Publication number
- CN107644144A CN107644144A CN201710992692.6A CN201710992692A CN107644144A CN 107644144 A CN107644144 A CN 107644144A CN 201710992692 A CN201710992692 A CN 201710992692A CN 107644144 A CN107644144 A CN 107644144A
- Authority
- CN
- China
- Prior art keywords
- wave
- equation
- sub
- potential
- omega
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Landscapes
- Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
Abstract
The present invention proposes a kind of evaluation method for flooding coastal waters bridge superstructure wave force, based on potential barrier Wave Theory, establish the theoretical meter model of bridge superstructure wave action under floodage, the governing equation of the model is Laplace's equation, meet that Free Surface, seabed can not pass through the boundary condition that impermeable and object plane normal velocity is zero simultaneously, it can solve to obtain velocity field by solving governing equation using the continuity of velocity potential and horizontal velocity, can both solve to obtain wave force using Bernoulli equation.The computational methods for the wave force established using the present invention, can accurately calculate the highest wave active force that coastal waters bridge structure is subject under floodage, the method degree of accuracy than before significantly improves.
Description
Technical Field
The invention relates to wave force calculation of a beam plate structure object in an offshore bridge engineering structure, in particular to an accurate estimation method of wave force of an upper structure submerging an offshore bridge.
Background
In recent decades, the economic development of coastal areas has placed increasing demands on rapid traffic networks, and bridges spanning gulf straits have been built as an important part of the national infrastructure. However, offshore bridge structures are located in complex marine environments and are vulnerable to typhoon waves and tsunami waves. The safety of these engineering structures becomes a key factor for guaranteeing the effectiveness of the traffic network in the human coastal region. Under complex marine environmental conditions, offshore bridge superstructures are subjected to direct wave forces and therefore must be designed to take into account the worst possible conditions at sea, which would otherwise result in serious catastrophic failure.
Since the destruction of a large number of offshore bridges in the gulf of mexico by hurricanes Ivan and Katrina in the united states, wave forces on bridge superstructures have been studied by a number of expert scholars worldwide. Based on the test result of the scale model, the U.S. highway administration (AASHTO) issued Guide specifications for bridge flexible to total stores in 2008, and the specifications provide a wave acting force estimation method for 6 kinds of bridge rib-form bridges recommended for AASHTO by using a numerical fitting method based on experimental data. Douglass et al propose a simplified calculation method of wave force of offshore bridges for engineering practice, which takes equivalent hydrostatic pressure as a reference load and considers that the wave load acting on the upper structure of the bridge is in a linear relationship with the reference load. Relatively speaking, the method has the advantages of clear physical meaning, concise formula and easy application. Both of the above methods have been shown to overestimate wave forces in submerged conditions (Jin and Meng,2011 guo et al 2015).
Disclosure of Invention
In view of the above disadvantages, the present invention aims to provide an accurate estimation method for the wave force of the upper structure of the submerged offshore bridge, which can repeatedly and stably generate a plurality of focused waves in a short time, so that the actual wave trough test can be used as the input wave, and the test efficiency can be improved.
In order to achieve the purpose, the technical scheme of the invention is as follows: an accurate estimation method for wave force of a submerged offshore bridge superstructure comprises the following specific steps:
for the periodic fluctuation problem, in which the time factors are separated, the flow field potential function is written as:
Φ(x,z,t)＝φ(x,z)e -iωt (1) In the formula, x and z are space coordinates, t is time, and omega is incident wave angular frequency (rad/s); wherein the complex velocity potential φ (x, z) still satisfies the Laplace control equation:
the boundary conditions satisfied by the flow field velocity potential function phi (x, z) are:
free interface
For x is less than or equal to B 1 ，x≥B J-1 ,z＝0 (3)
Wherein:
g is gravitational acceleration of 9.8m/s 2 。
Subsea conditions
For z = -d (4)
Surface of structure
Bottom surface (5)
Side (6)
The whole wave-structure action domain is divided into J sub-domains by utilizing the extension lines of the main girder ribs and the boundary of the bridge deck, and a speed potential function phi in each sub-domain j (x, z) in addition to the above-mentioned boundary conditions, should also be satisfied at the interface between adjacent subfieldsContinuity conditions of velocity potential continuity and horizontal velocity continuity:
φ j ＝φ j+1 (j＝1,2,…,J-1) (7)
the Laplace control equation is solved by adopting a separation variable method to obtain a general solution of the equation, the upper and lower boundary conditions are respectively applied to each sub-domain, and the expression of a speed potential function in each sub-domain is as follows:
in the sub-domain omega 1 The method comprises the following steps:
in the sub-domain omega J The method comprises the following steps:
in the sub-domain omega j (j =2,4, …):
in the sub-domain omega j (j =3,5, …):
wherein, the first and the second end of the pipe are connected with each other,
a-incident wave amplitude (m);
A 1n ，A J0 ，A Jn ，A jn ，B jn -determining a coefficient, wherein the coefficient is A 10 The term of (1) is the reflected wave velocity potential;
k 1n corresponding to the feature function Z 1n (z) ofThe characteristic value, wherein the first term is incident potential, the second term is reflection potential, and the series term is a non-propagation mode which is rapidly attenuated along with negative x-direction;
the first term of the formula (10) is transmission potential, and the series term is a non-propagation mode which rapidly attenuates along with the positive direction of x;
sub-field omega 1 And the subdomain Ω J The characteristic function of (a) is expressed as follows:
corresponding characteristic value k in the formula 1n The following equation is solved:
subdomain Ω j The characteristic functions for (j =2,4, …) are as follows:
corresponding characteristic value k jn Comprises the following steps:
k jn ＝nπ/(d-h 1 ),(n＝0,1,2,…) (16)
wherein A is jn And B jn For undetermined coefficients, the sub-field Ω j The characteristic functions corresponding to (j =3,5, …) are as follows
Corresponding characteristic value k jn Comprises the following steps:
k jn ＝nπ/(d-h),(n＝0,1,2,…) (18)
in addition, the characteristic functions of each sub-domain obtained according to the characteristics of the sum-Liouville eigenvalue problem vertically satisfy the orthogonal relation in the corresponding domain, and for omega 1 And Ω J Sub-region has：
To omega j (j =2,4, …) watershed:
for omega j (j =3,5, …) watershed:
each adjacent subdomain in the whole flow field needs to meet the continuity condition, and velocity potential expressions of each two adjacent subdomains are substituted into equations (7) and (8) according to the continuity condition, namely a linear equation set related to undetermined coefficients in a velocity potential function is obtained, and omega for the subdomains 1 And Ω 2 Substituting the velocity potential functions (9) and (11) into the velocity potential continuity condition equation (7) holds the following equation:
application subdomain Ω 2 The feature function orthogonality property is multiplied by a sub-domain omega on both sides of the equal sign of the upper formula 2 And at water depths (-d, -h) of (1) 1 ) Integration over the range yields the following system of linear equations:
in the formula:
similarly, substituting velocity potential functions (9) and (11) into the horizontal velocity continuity condition equation (8) holds the following equation:
application subdomain Ω 1 Orthogonality of characteristic function, which is multiplied by sub-field omega on both sides of equal sign of upper formula 1 And integrating the characteristic function in the water depth (-d, 0) range to obtain the following equation system:
[q m ] (N+1)×1 +{A 1m } (N+1)×1 ＝[G mn ] (N+1)×(N+1) {A 2n } (N+1)×1 +[H mn ] (N+1)×(N+1) {B 2n } (N+1)×1 (29)
in the formula:
q m ＝[1；0；0；…0] (30)
for adjacent sub-fields omega 2 And Ω 3 Substituting the speed potential functions (11) and (12) into the speed potential continuity condition equation (7), thenThen multiplying the two sides of the equation equal sign by a sub-domain omega respectively 3 And integrating the characteristic function in the water depth range (-d, -h), and applying the orthogonal characteristic of the characteristic function to obtain the following equation:
in the formula:
substituting the velocity potential functions (11) and (12) into the horizontal velocity continuity equation (8), and multiplying the equation equal sign by the sub-region omega 2 And in the depth range (-d, -h) 1 ) Internal integration, applying the orthogonal property of the characteristic function, the following equation is obtained:
in the formula:
similarly, for other adjacent subdomains, corresponding velocity potential functions are respectively substituted into a velocity potential and horizontal velocity continuity equation on the interface of the two subdomains, orthogonality of the corresponding subdomain characteristic functions is applied, a linear equation set related to undetermined coefficients in the velocity potential functions is obtained, and the linear equation set obtained by all the continuity equations is connected, namely undetermined coefficients in the velocity potential are solved;
in which the sub-region omega 1 And the subdomain Ω J The coefficients before the corresponding reflection term and transmission term in the velocity potential function of (1) are the reflection coefficient and transmission coefficient of the wave-structure action:
C r ＝A 10 ；C t ＝A J0 (43)
and satisfies the following conditions:
C r 2 +C t 2 ＝1 (44)
so as to ensure the energy conservation of the whole wave field;
integrating the pressure along the structure surface using a linear Bernoulli equation to obtain the force of the waves on the submerged bridge superstructure, wherein
The vertical acting force is as follows:
the horizontal acting force is as follows:
wherein:
n-unit normal vector of structure surface;
p-wave pressure field (Pa);
rho-density of wave water body (kg/m) 3 )；
And obtaining the wave action force generated by the incident wave action with the wave amplitude A and the circular frequency omega on the bridge superstructure in the submerged state by the formula (45-46).
The invention also has the following technical characteristics: according to the concrete bridge structure form, appropriate structure geometric parameters can be selected, and therefore the method is applied to deducing the wave action force.
The method for accurately estimating the maximum wave action force on the upper structure of the bridge in the submerged state is deduced based on the potential flow theory, and the effectiveness and the accuracy of the estimation method are verified through a specific wave water tank test. By applying the wave force estimation method provided by the invention, the wave acting force can be calculated when the offshore bridge structure is designed and selected, the design scheme is reasonably optimized, and the design wave load can be conveniently determined. The method for calculating the wave acting force established by the invention can accurately calculate the maximum wave acting force applied to the offshore bridge structure in the submerged state, and compared with the existing foreign method, the accuracy is obviously improved.
Drawings
FIG. 1 is a schematic diagram of a simplified theoretical model of wave force developed during derivation according to the method of the present invention;
FIG. 2 is a graph comparing the wave action force results calculated by the method of the present invention with the test results;
FIG. 3 is a cross-sectional view of a typical bridge construction with a Bulb-T72 type beam rib.
Fig. 4 is a cross-sectional view of a beam rib structure.
Detailed Description
The invention provides an estimation method for wave force of an upper structure of a submerged offshore bridge, which is characterized in that a theoretical meter model of the wave action of the upper structure of the bridge in a submerged state is established based on a potential flow wave theory, a control equation of the model is a Laplace equation, boundary conditions that a free surface and a seabed cannot penetrate and normal speed of an object plane is zero are met, a speed field can be obtained by solving the control equation and utilizing continuity of a speed potential and a horizontal speed, and wave acting force can be obtained by solving a Bernoulli equation. The calculation result is compared with the hydrodynamic model test data, and the effectiveness and the accuracy of the wave action force theoretical calculation method provided by the invention are verified. The following patents are further illustrative of the present invention:
example 1
A method for estimating wave force of a superstructure of a submerged offshore bridge comprises the following steps: based on ideal fluid, for a periodic fluctuation problem in which the time factor is separated, the flow field potential function can be written as:
Φ(x,z,t)＝φ(x,z)e -iωt (47) In the formula, x and z are space coordinates, t is time, and omega is incident wave angular frequency (rad/s); wherein the complex velocity potential φ (x, z) still satisfies the Laplace control equation:
the boundary conditions satisfied by the flow field velocity potential function phi (x, z) are as follows:
(1) Free interface
For x is less than or equal to B 1 ，x≥B J-1 ,z＝0 (49)
Wherein:
g-is the acceleration of gravity (9.8 m/s) 2 )。
(2) Subsea conditions
For z = -d (50)
(3) Surface of structure
Bottom surface (51)
Side (52)
As shown in FIG. 1, the whole wave-structure action domain can be divided into J sub-domains by using the extension lines of the main girder ribs and the boundary of the bridge deck, and a velocity potential function phi in each sub-domain j (x, z) in addition to satisfying the above boundary conditions, continuity conditions of velocity potential continuity and horizontal velocity continuity should be satisfied at the interfaces of adjacent subfields:
φ j ＝φ j+1 (j＝1,2,…,J-1) (53)
the Laplace control equation can be solved by applying a separation variable method to obtain a general solution of the equation, and upper and lower boundary conditions are respectively applied to each sub-domain shown in fig. 1, that is, an expression of a velocity potential function in each sub-domain can be written:
in the sub-domain omega 1 The following steps:
in the sub-domain omega J The method comprises the following steps:
in the sub-domain omega j (j =2,4, …):
in the sub-domain omega j (j =3,5, …):
wherein the content of the first and second substances,
a-incident wave amplitude (m);
A 1n ，A J0 ，A Jn ，A jn ，B jn -determining a coefficient, wherein the coefficient is A 10 The term of (a) is the reflected wave velocity potential;
k 1n corresponding to the feature function Z 1n (z) wherein the first term is the incident potential, the second term is the reflection potential, and the order terms are non-propagating modes that decay rapidly with the negative x-direction.
The first term of equation (56) is the transmission potential and the series terms are the non-propagating modes that decay rapidly with the x-direction.
Sub-field omega 1 And the subdomain Ω J The characteristic function of (a) is expressed as follows:
corresponding characteristic value k in the formula 1n The following equation is used to solve.
Sub-field omega j The characteristic functions corresponding to (j =2,4, …) are as follows
Corresponding characteristic value k jn Comprises the following steps:
k jn ＝nπ/(d-h 1 ),(n＝0,1,2,…) (62)
wherein A is jn And B jn For undetermined coefficients, the sub-field Ω j The characteristic functions corresponding to (j =3,5, …) are as follows
Corresponding characteristic value k jn Comprises the following steps:
k jn ＝nπ/(d-h),(n＝0,1,2,…) (64)
in addition, according to the characteristics of the sum-Liouville eigenvalue problem, the characteristic functions of all the sub-domains vertically meet the orthogonal relation in the corresponding domains, and the omega is subjected to the orthogonal relation 1 And Ω J The subdomains have:
for omega j (j =2,4, …) watershed:
for omega j (j =3,5, …) watershed:
each adjacent subfield in the whole flow field needs to satisfy continuity conditions, and velocity potential expressions of each two adjacent subfields are substituted into equations (53) and (54) according to the continuity conditions, so that a series of linear equations related to undetermined coefficients in a velocity potential function can be obtained. For sub-field Ω 1 And Ω 2 Will function of velocity potentialThe numbers (55) and (57) are substituted into the velocity potential continuity condition equation (53), and the following holds:
application subdomain Ω 2 The feature function orthogonality property is multiplied by a sub-domain omega on both sides of the equal sign of the upper formula 2 And at water depths (-d, -h) of characteristic equation (61) 1 ) Integration over the range yields the following system of linear equations:
in the formula:
similarly, substituting velocity potential functions (55) and (57) into the horizontal velocity continuity condition equation (54) holds the following equation:
application subdomain Ω 1 Orthogonality of characteristic function, which is multiplied by sub-field omega on both sides of equal sign of upper formula 1 Is characterized byThe function is integrated in the water depth (-d, 0) range, and the following equation system can be obtained:
[q m ] (N+1)×1 +{A 1m } (N+1)×1 ＝[G mn ] (N+1)×(N+1) {A 2n } (N+1)×1 +[H mn ] (N+1)×(N+1) {B 2n } (N+1)×1 (75)
in the formula:
q m ＝[1；0；0；…0] (76)
for adjacent sub-fields omega 2 And Ω 3 Substituting the speed potential functions (57) and (58) into the speed potential continuity condition equation (53), and multiplying the two sides of the equation equal sign by the sub-field omega respectively 3 And integrating in the water depth range (-d, -h), and applying the orthogonal characteristic of the characteristic function, the following equation can be obtained:
in the formula:
the velocity potential functions (57) and (58) are substituted into the horizontal velocity continuity equation (54) and then multiplied by the sub-field Ω on either side of the equation equal sign 2 And in the depth range (-d, -h) 1 ) Internal integration, applying the feature function orthogonality property, can obtain the following equation:
in the formula:
similarly, for other adjacent subdomains, corresponding velocity potential functions are respectively substituted into the velocity potential and horizontal velocity continuity equations on the interface of the two subdomains, and a series of linear equation sets related to undetermined coefficients in the velocity potential functions can be obtained by applying the orthogonality of the corresponding subdomain characteristic functions. And (4) simultaneously establishing a linear equation set obtained by all the continuity equations, so that undetermined coefficients in the velocity potential can be solved.
In which the sub-region omega 1 And the subdomain Ω J Corresponding reflection term and transmission in the velocity potential function of (1)The coefficients before the term are the reflection coefficient and transmission coefficient of the wave-structure action:
C r ＝A 10 ；C t ＝A J0 (89)
and satisfies the following conditions:
C r 2 +C t 2 ＝1 (90)
so as to ensure the energy conservation of the whole wave field.
The force of the waves acting on the submerged bridge superstructure is obtained by integrating the pressure along the structure surface using the linear Bernoulli equation, wherein
The vertical acting force is:
the horizontal acting force is as follows:
wherein:
n-unit normal vector of structure surface;
p-wave pressure field (Pa);
rho-density of wave water body (kg/m) 3 )。
Example 2
The wave action force generated by the incident wave action with the wave amplitude of A and the circular frequency of omega on the bridge superstructure in the submerged state can be obtained through settlement by the formula (45-46) in the example 1.
To further verify the wave action force calculation method proposed by the present invention, example 2 compares the wave action force calculated by the formulas (45-46) with the test results, for example, as shown in fig. 2.
It can be seen that: when the wave number kb is less than 1, the vertical wave force calculated by the potential flow theoretical model is sharply reduced along with the increase of the kb; when the wave number kb is larger than 1, the vertical wave force shows a slower descending trend along with the increase of the wave number kb; (2) When the wave number kb is less than 1, the horizontal wave force calculated by the potential flow theoretical model increases rapidly along with the increase of kb; when the wave number kb is larger than 1, the horizontal wave force is basically kept unchanged along with the increase of kb and shows a slight descending trend. It can be seen that the theoretical model based on the potential flow theory better estimates the wave force acting on the bridge superstructure model. Considering that the potential flow theory simplifies the free liquid level into a linear interface and meets the wave energy conservation, but in the actual experimental process, the wave attenuation, the wave crushing when acting with the structure, the energy dissipation phenomena such as the friction between the wave water body and the wall surface of the water tank and the bottom of the tank and the like exist, and the deck wave can offset a part of vertical wave force, so that the wave force measured in the model test is smaller than the calculation result of the potential flow theoretical model. The method for calculating the wave force of the superstructure of the bridge in the submerged state based on the potential flow theory can provide a basic load estimation method for the wave-proof design of the offshore bridge.
Example 3
In order to further simplify the calculation process, a simple calculation method for wave action can be established for a specific bridge structure. The bridge structure geometry is shown in fig. 3-4.
And fitting a simple calculation formula corresponding to the bridge type based on the calculation result of the potential flow theoretical model.
Horizontal wave force:
F H ＝ρghAC H (k 0 b) (1-93)
vertical wave force
F V ＝F B +ρgBAC V (k 0 b) (1-94)
Wherein:
C V ，C H -for the coefficients of the wave number, the calculation formula is as follows:
in the formula:
k 0 the wave number can be solved by a dispersion equation according to the water depth and the wave period;
b is half of the total span of the bridge superstructure;
c h1 ～c h6 and c v1 ～c v6 The values are 0.08, -0.03,2.25,0.09, -0.88,1.14 and-0.09,0.60, -1.01,0.81, -0.78,0.79, respectively.
Claims (1)
1. A method for estimating wave force of a superstructure of a submerged offshore bridge, the method comprising: for the periodic fluctuation problem, in which the time factors are separated, the flow field potential function is written as:
Φ(x,z,t)＝φ(x,z)e -iωt (1)
in the formula, x and z are space coordinates, t is time, and omega is incident wave angular frequency (rad/s); wherein the complex velocity potential φ (x, z) still satisfies the Laplace control equation:
the boundary conditions satisfied by the flow field velocity potential function phi (x, z) are as follows:
free interface
For x is less than or equal to B 1 ，x≥B J-1 ,z＝0 (3)
Wherein:
g is the acceleration of gravity, and is 9.8m/s 2 ；
Subsea conditions
For z = -d (4)
Surface of structure
Bottom surface (5)
Side (6)
The whole wave-structure action domain is divided into J subdomains by using the extension lines of the main beam ribs and the boundary of the bridge deck, and a speed potential function phi in each subdomain j (x, z) in addition to satisfying the above boundary conditions, continuity conditions of velocity potential continuity and horizontal velocity continuity should be satisfied at the interfaces of adjacent subfields:
φ j ＝φ j+1 (j＝1,2,…,J-1) (7)
the Laplace control equation is solved by adopting a separation variable method to obtain a general solution of the equation, the upper and lower boundary conditions are respectively applied to each sub-domain, and the expression of a speed potential function in each sub-domain is as follows:
in the sub-domain omega 1 The method comprises the following steps:
in sub-field Ω J The method comprises the following steps:
in the sub-domain omega j (j =2,4, …):
in the sub-domain omega j (j =3,5, …):
wherein the content of the first and second substances,
a-incident wave amplitude (m);
A 1n ，A J0 ，A Jn ，A jn ，B jn -determining a coefficient, wherein the coefficient is A 10 The term of (1) is the reflected wave velocity potential;
k 1n corresponding to the characteristic function Z 1n (z) a first term of the formula is incident potential, a second term of the formula is reflection potential, and a series term of the formula is a non-propagation mode which is rapidly attenuated along with negative direction x;
the first term of the formula (10) is transmission potential, and the series term is a non-propagation mode which rapidly attenuates along with the positive direction of x;
sub-field omega 1 And sub-field Ω J The characteristic function of (a) is expressed as follows:
corresponding characteristic value k in the formula 1n The following equation is solved:
subdomain Ω j The characteristic functions for (j =2,4, …) are as follows:
corresponding characteristic value k jn Comprises the following steps:
k jn ＝nπ/(d-h 1 ),(n＝0,1,2,…) (16)
wherein A is jn And B jn For undetermined coefficients, sub-field Ω j The characteristic functions corresponding to (j =3,5, …) are as follows
Corresponding characteristic value k jn Comprises the following steps:
k jn ＝nπ/(d-h),(n＝0,1,2,…) (18)
in addition, the characteristic functions of each sub-domain obtained according to the characteristics of the sum-Liouville eigenvalue problem vertically satisfy the orthogonal relation in the corresponding domain, and are opposite to omega 1 And Ω J The subdomains have:
for omega j (j =2,4, …) watershed:
for omega j (j =3,5, …) watershed:
each adjacent subdomain in the whole flow field needs to satisfy continuity conditions, and velocity potential expressions of each two adjacent subdomains are substituted into equations (7) and (8) according to the continuity conditions, so that a linear equation set related to undetermined coefficients in a velocity potential function is obtained, and for subdomain omega 1 And Ω 2 Substituting the velocity potential functions (9) and (11) into the velocity potential continuity condition equation (7) holds the following equation:
application subdomain Ω 2 The feature function orthogonality property is multiplied by a sub-domain omega on both sides of the equal sign of the upper formula 2 And at water depths (-d, -h) of (1) and (15) 1 ) Integration over the range yields the following system of linear equations:
in the formula:
similarly, substituting velocity potential functions (9) and (11) into the horizontal velocity continuity condition equation (8) holds the following equation:
application subdomain Ω 1 Orthogonality of characteristic function, which is multiplied by sub-field omega on both sides of equal sign of upper formula 1 And integrating the characteristic function in the water depth (-d, 0) range to obtain the following equation system:
[q m ] (N+1)×1 +{A 1m } (N+1)×1 ＝[G mn ] (N+1)×(N+1) {A 2n } (N+1)×1 +[H mn ] (N+1)×(N+1) {B 2n } (N+1)×1 (29)
in the formula:
q m ＝[1；0；0；…0] (30)
for adjacent sub-fields omega 2 And Ω 3 Substituting the speed potential functions (11) and (12) into a speed potential continuity condition equation (7), and multiplying the two sides of an equation equal sign by a sub-domain omega respectively 3 And integrating the characteristic function in the water depth range (-d, -h), and applying the orthogonal characteristic of the characteristic function to obtain the following equation:
in the formula:
the velocity potential functions (11) and (12) are substituted into the horizontal velocity continuity equation (8) and thenMultiplying the equation equal sign by the sub-region omega respectively 2 And in the depth range (-d, -h) 1 ) Internal integration, applying the feature function orthogonality property, the following equation is obtained:
in the formula:
similarly, for other adjacent subdomains, corresponding velocity potential functions are respectively substituted into the velocity potential and horizontal velocity continuity equations on the interface of the two subdomains, and the orthogonality of the corresponding subdomain characteristic functions is applied to obtain a linear equation set related to undetermined coefficients in the velocity potential functions, and all the linear equation sets obtained by the continuity equations are combined, namely the undetermined coefficients in the velocity potential are solved;
in which the sub-region omega 1 And the subdomain Ω J The coefficients before the corresponding reflection term and transmission term in the velocity potential function of (1) are the reflection coefficient and transmission coefficient of the wave-structure action:
C r ＝A 10 ；C t ＝A J0 (43)
and satisfies the following conditions:
C r 2 +C t 2 ＝1 (44)
so as to ensure the energy conservation of the whole wave field;
integrating the pressure along the structure surface using a linear Bernoulli equation to obtain the force of the waves acting on the submerged bridge superstructure, wherein
The vertical acting force is:
the horizontal acting force is as follows:
wherein:
n-unit normal vector of structure surface;
p-wave pressure field (Pa);
rho-density of wave water body (kg/m) 3 )；
And obtaining the wave action force generated by the incident wave action with the wave amplitude A and the circular frequency omega on the bridge superstructure in the submerged state by the formula (45-46).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710992692.6A CN107644144A (en) | 2017-10-23 | 2017-10-23 | One kind floods coastal waters bridge superstructure wave force evaluation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710992692.6A CN107644144A (en) | 2017-10-23 | 2017-10-23 | One kind floods coastal waters bridge superstructure wave force evaluation method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN107644144A true CN107644144A (en) | 2018-01-30 |
Family
ID=61122555
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710992692.6A Pending CN107644144A (en) | 2017-10-23 | 2017-10-23 | One kind floods coastal waters bridge superstructure wave force evaluation method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107644144A (en) |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109373982A (en) * | 2018-10-31 | 2019-02-22 | 重庆交通大学 | A kind of calculation method of coastal waters phytal zone sea bed wave pressure |
| CN109726418A (en) * | 2018-07-17 | 2019-05-07 | 中国科学院力学研究所 | Descriptive model of the wave force amplitude of cylindrical-array in non-trapping region fluctuation spacing |
| CN110083796A (en) * | 2019-05-15 | 2019-08-02 | 中国海洋大学 | A kind of aperture breakwater implementing hydrodynamic analysis method |
| CN110929318A (en) * | 2019-10-25 | 2020-03-27 | 哈尔滨工业大学 | Extreme wave force calculation method for structural design of flat breakwater |
| CN111460563A (en) * | 2020-04-09 | 2020-07-28 | 重庆交通大学 | Method for calculating wave current borne by box-type upper structure of sea-crossing bridge |
| CN111695267A (en) * | 2020-06-16 | 2020-09-22 | 中国海洋大学 | Porous structure hydrokinetic analysis method |
| CN112639772A (en) * | 2020-03-04 | 2021-04-09 | 交通运输部天津水运工程科学研究所 | Wave force stress calculation method and system for underwater submergence |
-
2017
- 2017-10-23 CN CN201710992692.6A patent/CN107644144A/en active Pending
Non-Patent Citations (1)
| Title |
|---|
| ANXINGUO等: "Analytical solution of hurricane wave forces acting on submerged bridge decks", 《OCEAN ENGINEERING》 * |
Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109726418A (en) * | 2018-07-17 | 2019-05-07 | 中国科学院力学研究所 | Descriptive model of the wave force amplitude of cylindrical-array in non-trapping region fluctuation spacing |
| CN109726418B (en) * | 2018-07-17 | 2020-09-01 | 中国科学院力学研究所 | Description model of wave force amplitude of cylindrical array in fluctuation space of non-capture area |
| CN109373982A (en) * | 2018-10-31 | 2019-02-22 | 重庆交通大学 | A kind of calculation method of coastal waters phytal zone sea bed wave pressure |
| CN110083796A (en) * | 2019-05-15 | 2019-08-02 | 中国海洋大学 | A kind of aperture breakwater implementing hydrodynamic analysis method |
| CN110083796B (en) * | 2019-05-15 | 2020-09-29 | 中国海洋大学 | Hydrodynamic analysis method for open-hole breakwater |
| CN110929318A (en) * | 2019-10-25 | 2020-03-27 | 哈尔滨工业大学 | Extreme wave force calculation method for structural design of flat breakwater |
| CN110929318B (en) * | 2019-10-25 | 2022-03-29 | 哈尔滨工业大学 | Extreme wave force calculation method for structural design of flat breakwater |
| CN112639772A (en) * | 2020-03-04 | 2021-04-09 | 交通运输部天津水运工程科学研究所 | Wave force stress calculation method and system for underwater submergence |
| WO2021174440A1 (en) * | 2020-03-04 | 2021-09-10 | 交通运输部天津水运工程科学研究所 | Method and system for calculating wave force received by underwater submerged object |
| CN111460563A (en) * | 2020-04-09 | 2020-07-28 | 重庆交通大学 | Method for calculating wave current borne by box-type upper structure of sea-crossing bridge |
| CN111695267A (en) * | 2020-06-16 | 2020-09-22 | 中国海洋大学 | Porous structure hydrokinetic analysis method |
| CN111695267B (en) * | 2020-06-16 | 2024-03-01 | 中国海洋大学 | Hydrodynamic analysis method for porous structure |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN107644144A (en) | One kind floods coastal waters bridge superstructure wave force evaluation method | |
| Shafiei et al. | Experimental investigation of tsunami bore impact force and pressure on a square prism | |
| Cassidy et al. | Non-linear analysis of jack-up structures subjected to random waves | |
| Falconer | Water quality simulation study of a natural harbor | |
| Suh et al. | Hydrodynamic characteristics of pile-supported vertical wall breakwaters | |
| Qin et al. | Three-dimensional modeling of tsunami forces on coastal communities | |
| Isaacson | Wave runup around large circular cylinder | |
| Qi et al. | Local scour around a monopile foundation for offshore wind turbines and scour effects on structural responses | |
| Tomiczek et al. | Modified Goda equations to predict pressure distribution and horizontal forces for design of elevated coastal structures | |
| Liu et al. | Wave diffraction by vertical cylinder with multiple concentric perforated walls | |
| Kumar et al. | Wave scattering by flexible porous vertical membrane barrier in a two-layer fluid | |
| Negro Valdecantos et al. | Comparative study of breakwater crown wall–calculation methods | |
| Lin et al. | Waves propagating over a two-layer porous barrier on a seabed | |
| Yeh et al. | Moving boundary numerical surge model | |
| CN115961589B (en) | High pile baffle open breakwater and wharf and hydrodynamic characteristic analysis method thereof | |
| Singh et al. | The combined refraction–diffraction effect on water wave scattering by a vertical flexible–porous structure | |
| Magdalena et al. | Analytical and numerical studies for the reduction of wave run-up height by a submerged breakwater | |
| Liu et al. | SPH simulation of hydrodynamic responses for two novel types of silt curtain under combined wave-current conditions | |
| Van Thiel de Vries et al. | Modeling inner surf hydrodynamics during storm surges | |
| Jiang et al. | Propagation of Solitary Wave over Impermeable Submerged Double Breakwaters | |
| Qi et al. | Mud mass transport due to waves based on an empirical rheology model featured by hysteresis loop | |
| Kim et al. | Unsteady Flow Characteristics at Gate of Overtopping-type Submerged Breakwater | |
| Widyaningtias et al. | Depth of closure determination in the vicinity of coastal structure | |
| Murali et al. | Wave-induced pressures and forces on deck slabs near the free surface | |
| CN110929318B (en) | Extreme wave force calculation method for structural design of flat breakwater |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20180130 |