Hydrodynamic analysis method of baffle-rock-fill breakwater and baffle-rock-fill breakwater

Abstract

The present invention relates to a hydrodynamic analysis method for a baffle-rockfill breakwater, comprising the following steps: developing a new structural type of a baffle-rockfill breakwater, that is, dumping rockfill on the back-wave side of the baffle, and fixing the two sides of the rockfill structure with fence plates; for the new baffle-rockfill breakwater structure, establishing a hydrodynamic analysis mathematical model of the baffle-rockfill breakwater based on potential flow theory, porous medium theory, and separation of variables method; using a matching characteristic function method, establishing a linear equation group based on the boundary conditions of fluid motion; and determining the undetermined coefficients in the velocity potential by solving the equation group. The baffle-rockfill breakwater proposed in the present invention is an environmentally friendly structure with the advantages of low transmission, small wave force, and prevention of scouring of the bottom of the dike. The theoretical analytical hydrodynamic analysis method of the baffle-rockfill breakwater provided by the present invention has an efficient calculation speed and can provide a scientific basis for the engineering design and optimization of the baffle-rockfill breakwater.

Description

Technical Field

[0001] The invention belongs to the technical field of hydrodynamic analysis, and in particular relates to a hydrodynamic analysis method of a baffle-rockfill breakwater and a baffle-rockfill breakwater. Background Art

[0002] The open structure allows the exchange of hydrodynamics before and after the dike, which meets the requirements of my country for environmental protection in breakwater construction in recent years.

[0003] As a kind of open structure, the sheet pile baffle breakwater has the characteristics of simple structure, short construction period and low cost, and is widely used in marine engineering fields such as embankment protection. However, this structure also has certain disadvantages, such as severe scouring of the bottom of the embankment caused by excessive bottom flow velocity and severe transmission at low water level. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] In order to solve the above problems in the prior art, the present invention provides a hydrodynamic analysis method of a baffle-rockfill breakwater and a baffle-rockfill breakwater.

[0006] (II) Technical solution

[0007] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0008] A hydrodynamic analysis method for a baffle-rockfill breakwater comprises the following steps: for a new baffle-rockfill breakwater structure, a hydrodynamic analysis mathematical model of the baffle-rockfill breakwater is established based on potential flow theory, porous media theory and separation variable method;

[0009] Using the matching characteristic function method, a system of linear equations is established based on the boundary conditions of fluid motion;

[0010] By solving the equations, the unknown coefficients in the velocity potential are determined, and the reflection coefficient, transmission coefficient and energy dissipation coefficient of the baffle-rockfill breakwater are calculated.

[0011] Theoretical analysis is used in combination with multiple Galerkin approximations to simulate the pressure loss on both sides of the vertical baffle and establish a boundary value problem.

[0012] Preferably, the baffle-rockfill breakwater model in the method comprises:

[0013] The water depth of the baffle-rockfill breakwater is h, and the depth of its baffle into the water is a;

[0014] The porous rockfill structure has a width of 2b, a height of c, and a distance B from the baffle;

[0015] A two-dimensional plane coordinate system is established with the intersection of the vertical extension line of the porous rockfill center and the still water surface as the origin, where the positive direction of the x-axis is horizontal to the right and the positive direction of the z-axis is vertically upward;

[0016] The model is divided into 5 sub-areas;

[0017] Sub-area 1 is the water area on the wave-facing side of the baffle;

[0018] Sub-area 2 is the area between the baffle and the rockfill;

[0019] Sub-area 3 is the water area directly above the rock pile;

[0020] Sub-area 4 is the inner area of ​​the rockfill;

[0021] Sub-area 5 is the water area on the back side of the rock pile.

[0022] Preferably, the method further comprises: based on the separation of variables method, the velocity potential series expression of each sub-region satisfying the control equation, the free water surface boundary condition, the bottom boundary condition and the boundary condition of the upper surface of the submerged dike is:

[0023]

[0024] in, R m , A m , B m , T m , C m and D m is the coefficient to be determined;

[0025] φ j (x,z),j=1,2,3,4,5 are the expressions of velocity potential series representing sub-region j respectively.

[0026] Preferably, the method further comprises:

[0027] Z m (z), U m (z), V m (z) is the vertical characteristic function, and its expression is:

[0028]

[0029] Where ε is the rockfill porosity, s is the inertia coefficient, f is the linear resistance coefficient, and the wave number k is 0 , k m Satisfies the dispersion relation:

[0030] ω 2 =gk 0 tanh(k 0 h)=-gk m tan(km h),m=1,2,3,... (11)

[0031] Where g represents the acceleration due to gravity;

[0032] λ m is the root of the following complex dispersion equation:

[0033] ω 2 -gλ m tanhλ m h=P m (ω 2 tanλ m h-gλ m ),m=1,2,3,... (12)

[0034] Its value needs to be solved by the perturbation method.

[0035] Preferably, the method further comprises:

[0036] When solving the velocity potential function of each sub-region by matching characteristic function method, the velocity continuity and velocity potential continuity conditions between sub-regions are required, as shown in the following formula:

[0037] φ 1 (x,z)=φ 2 (x,z),-h≤z≤-a,x=-Bb (13)

[0038]

[0039] φ 2 (x,z)=φ 3 (x,z),-d≤z≤0,x=-b (15)

[0040]

[0041] φ 5 (x,z)=φ 3 (x,z),-d≤z≤0,x=b (17)

[0042]

[0043] Preferably, the method further comprises:

[0044] Based on the matching characteristic function expansion method, the series q in the velocity potential series expression is truncated to Q, and the series m and n are truncated to M; Q and M are both positive integers, and the following linear equations can be obtained:

[0045] [α qm ] Q×M {R m}M = {β q} Q (19)

[0046]

[0047] [ξ nm M×M {A m} M + [ζ nm M×M {B m} M - [δ nm M×M {C m} M + [η nm M×M {D m} M = 0 (22)

[0048]

[0049] [θ nm M×M {C m} M + [ρ nm M×M {D m} M - [σ nm M×M {T m} M = 0 (24)

[0050] - [μ nm M×M {C m} M + [v nm M×M {D m} M - [I] M×M {T m} M = 0 (25);

[0051] where I is the unit diagonal matrix, α qm , β q , χ nq , ξ nm , ζ nm , δ nm , η nm , μ nm , v nm , θ nm , ρ​​​​​​​​​nm , σ nm , X nm , Y nm , W nm , L nm , γ n are matrix coefficients.

[0052] Preferably, the method further comprises:

[0053] The reflection coefficient Kr is defined as the ratio of the reflected wave height to the incident wave height, and the transmission coefficient Kt is defined as the ratio of the transmitted wave height to the incident wave height. The reflection coefficient and transmission coefficient of the baffle-rockfill breakwater are:

[0054] Kr=|R 0 | (26)

[0055] Kt=|T 0 | (27).

[0056] Preferably, the method further comprises:

[0057] The velocity potential of each sub-region is governed by the Laplace equation and must also satisfy the following boundary conditions:

[0058] Free water surface boundary conditions:

[0059]

[0060] Bottom boundary conditions:

[0061]

[0062] Far field conditions:

[0063]

[0064] where φ 0 is the incident wave velocity potential, which is expressed as

[0065] Submerged dike surface boundary conditions:

[0066] φ 3 (x,z)=(s+if)φ 4 (x,z),z=-d,-b≤x≤b (32)

[0067]

[0068] In the formula, G represents the porosity influence coefficient, and its value depends on the opening ratio, shape and thickness of the fence board;

[0069] Boundary conditions at the baffle:

[0070]

[0071] Where E q is the unknown coefficient, p q is the Galerkin basis function, and its expression is as follows:

[0072]

[0073] Where N 2q (z) is the second kind 2q order Chebyshev polynomial:

[0074]

[0075] The technical solution also provides a baffle-rockfill breakwater, comprising: a baffle and a porous rockfill structure;

[0076] Both sides of the porous rockfill structure are fixed by fence plates;

[0077] The baffle is arranged in the water area in front of the wave-facing surface of the porous rockfill structure.

[0078] (III) Beneficial effects

[0079] The beneficial effects of the present invention are as follows: a hydrodynamic analysis method of a baffle-rockfill breakwater and a baffle-rockfill breakwater provided by the present invention have the following beneficial effects:

[0080] In view of some problems existing in the sheet pile baffle structure itself, the present invention further designs a sheet pile-porous rockfill structure and develops a corresponding hydrodynamic analysis method. The analysis method adopts theoretical analysis, and combines multiple Galerkin approximations to simulate the pressure loss on both sides of the vertical baffle to establish a boundary value problem, so that the square root singularity of the fluid velocity at the lower end point of the baffle can be correctly simulated, and the algorithm convergence speed and calculation speed are improved. The analysis has high calculation efficiency and can provide a scientific basis and guidance for the actual engineering application and optimization design of the sheet pile-porous rockfill structure.

[0081] The sheet pile-porous rockfill structure provided by the present application has the following advantages:

[0082] 1. The sheet pile-porous rockfill structure can significantly reduce the transmission wave height at low water level and under long wave action;

[0083] 2. Under the same wave-breaking action, the wave force on the optimized structural baffle is smaller, which improves the safety of the structure;

[0084] 3. The porous rockfill has the function of stabilizing the foundation, has a good protective effect, and can prevent the scouring of the bottom bed;

[0085] 4. Porous rockfill can prevent the bottom water flow from carrying silt into the rear harbor or water area;

[0086] 5. The optimized structure is still a permeable structure, which can realize water exchange and is an environmentally friendly structure;

[0087] 6. The structure is easy to obtain materials, simple to construct, fast to construct, and has good economic advantages. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 A hydrodynamic analysis method for a baffle-rock breakwater and a schematic diagram of wave action on the baffle-rock breakwater in the baffle-rock breakwater provided by the present invention. DETAILED DESCRIPTION

[0089] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation modes in conjunction with the accompanying drawings.

[0090] like Figure 1 As shown: This embodiment discloses a hydrodynamic analysis method of a baffle-rockfill breakwater, comprising the following steps: developing a new structural type of baffle-rockfill breakwater, that is, dumping rockfill on the back-wave side of the baffle, and fixing both sides of the rockfill structure with fence boards;

[0091] For the new baffle-rockfill breakwater structure, a hydrodynamic analysis mathematical model of the baffle-rockfill breakwater is established based on potential flow theory, porous media theory and separation variable method.

[0092] Using the matching characteristic function method, a system of linear equations is established based on the boundary conditions of fluid motion;

[0093] By solving the equations, the unknown coefficients in the velocity potential are determined, and the reflection coefficient, transmission coefficient and energy dissipation coefficient of the baffle-rockfill breakwater are calculated.

[0094] It should be noted that the method in this embodiment adopts theoretical analysis and combines multiple Galerkin approximations to simulate the pressure loss on both sides of the vertical baffle to establish a boundary value problem.

[0095] The baffle-rockfill breakwater model in the method described in this embodiment includes: the water depth of the sea area where the baffle-rockfill breakwater is located is h, and the depth of its baffle entering the water is a; the porous rockfill structure has a width of 2b and a height of c, and a spacing between the porous rockfill structure and the baffle is B; a two-dimensional plane coordinate system is established with the intersection of the vertical extension line of the center of the porous rockfill and the still water surface as the origin, wherein the positive direction of the x-axis is horizontally to the right, and the positive direction of the z-axis is vertically upward; the model is divided into 5 sub-areas; sub-area 1 is the water area on the wave-facing side of the baffle; sub-area 2 is the area between the baffle and the rockfill; sub-area 3 is the water area directly above the rockfill; sub-area 4 is the internal area of ​​the rockfill; and sub-area 5 is the water area on the wave-back side of the rockfill.

[0096] The porous rockfill structure in the figure is simplified as a uniform, continuous medium in the model, and its effect on fluid movement can be summarized as the influence of three parameters: rockfill porosity ε, inertia coefficient s and linear resistance coefficient f.

[0097] The method described in this embodiment also includes: based on the separation of variables method, the velocity potential series expression of each sub-region that satisfies the control equation, the free water surface boundary condition, the bottom boundary condition and the boundary condition on the surface of the submerged dike is:

[0098]

[0099] in, R m , A m , B m , T m , C m and D m is the coefficient to be determined;

[0100] φ j (x,z),j=1,2,3,4,5 are the expressions of velocity potential series representing sub-region j respectively.

[0101] Z m (z), U m (z), V m (z) is the vertical characteristic function, and its expression is:

[0102]

[0103] Where ε is the rockfill porosity, s is the inertia coefficient, f is the linear resistance coefficient, and the wave number k is 0 , k m Satisfies the dispersion relation:

[0104] ω 2 =gk 0 tanh(k 0 h)=-gk m tan(k m h),m=1,2,3,... (11)

[0105] Where g represents the acceleration due to gravity;

[0106] λ m is the root of the following complex dispersion equation:

[0107] ω 2 -gλ m tanhλ m h=P m (ω 2 tanλ m h-gλ m),m=1,2,3,... (12)

[0108] Its value needs to be solved by the perturbation method.

[0109] When solving the velocity potential function of each sub-region by matching characteristic function method, the velocity continuity and velocity potential continuity conditions between sub-regions are required, as shown in the following formula:

[0110] φ 1 (x,z)=φ 2 (x,z),-h≤z≤-a,x=-Bb (13)

[0111]

[0112] φ 2 (x,z)=φ 3 (x,z),-d≤z≤0,x=-b (15)

[0113]

[0114] φ 5 (x,z)=φ 3 (x,z),-d≤z≤0,x=b (17)

[0115]

[0116] Based on the matching characteristic function expansion method, the series q in the velocity potential series expression is truncated to Q, and the series m and n are truncated to M; Q and M are both positive integers, and the following linear equations can be obtained:

[0117] [α qm ] Q×M {R m} M ={β q} Q (19)

[0118]

[0119] [ξ nm ] M×M {A m} M +[ζ nm ] M×M {B m} M -[δ nm ] M×M {C m} M +[η nm ] M×M {D m}M =0 (22)

[0120]

[0121] [θ nm ] M×M {C m} M +[ρ nm ] M×M {D m} M -[σ nm ] M×M {T m} M =0 (24)

[0122] -[μ nm ] M×M {C m} M +[v nm 0 M×M {D m} M -[I] M×M {T m} M =0 (25).

[0123] Where I is the unit diagonal matrix, and the expressions of other coefficient matrices are shown in Table 1.

[0124] Table 1 Coefficient matrix expressions in the linear equations (19)–(25)

[0125]

[0126]

[0127] Among them J 2q+1 (k m a) I 2q+1 (k 0 a) are the first kind Bessel function and the first kind imaginary Bessel function respectively. Solving the linear equations simultaneously can obtain the values ​​of the unknown coefficients.

[0128] The reflection coefficient Kr is defined as the ratio of the reflected wave height to the incident wave height, and the transmission coefficient Kt is defined as the ratio of the transmitted wave height to the incident wave height. The reflection coefficient and transmission coefficient of the baffle-rockfill breakwater are:

[0129] Kr=|R 0 | (26)

[0130] Kt=|T 0 | (27).

[0131] The velocity potential of each sub-region is governed by the Laplace equation and must also satisfy the following boundary conditions:

[0132] Free water surface boundary conditions:

[0133]

[0134] Bottom boundary conditions:

[0135]

[0136] Far field conditions:

[0137]

[0138] where φ 0 is the incident wave velocity potential, which is expressed as

[0139] Submerged dike surface boundary conditions:

[0140] φ 3 (x,z)=(s+if)φ 4 (x,z),z=-d,-b≤x≤b (32)

[0141]

[0142] In the formula, G represents the porosity influence coefficient, and its value depends on the opening ratio, shape and thickness of the fence board;

[0143] Boundary conditions at the baffle:

[0144]

[0145] Where E q is the unknown coefficient, p q is the Galerkin basis function, and its expression is as follows:

[0146]

[0147] Where N 2q (z) is the second kind 2q order Chebyshev polynomial:

[0148]

[0149] The above control equations and boundary conditions constitute the complete boundary value problem of the wave acting on the baffle-rock breakwater model.

[0150] The complex dispersion equation wave number λ required in this embodiment is m , and the solution is as follows.

[0151] After rearranging the complex dispersion equation (12), we can obtain:

[0152]

[0153] To get the wave number λ m The value of can be solved by equation (43). The specific steps are as follows:

[0154] The complex dispersion equation is transformed into a function F of x and φ, and its expression is shown in (44), where x = λ m h,

[0155]

[0156] Select the initial value Φ 0 =1, we can get x 0 =k m h

[0157] After Taylor expansion of the function, the relationship between Δx and ΔΦ is as follows, where n is the number of perturbation steps;

[0158]

[0159] By gradually approximating the functional relationship between φ and x, we can get The corresponding initial value in It is the initial value in the wave number convergence domain. The root λ of the complex dispersion equation can be directly calculated by iteration m .

[0160] This embodiment also provides a baffle-rockfill breakwater, including: a baffle and a porous rockfill structure;

[0161] Both sides of the porous rockfill structure are fixed by fence plates;

[0162] The baffle is arranged in the water area in front of the wave-facing surface of the porous rockfill structure.

[0163] The technical principles of the present invention are described above in conjunction with specific embodiments. These descriptions are only for explaining the principles of the present invention and cannot be interpreted in any way as limiting the scope of protection of the present invention. Based on the explanations here, those skilled in the art can associate other specific implementations of the present invention without creative work, and these methods will fall within the scope of protection of the present invention.

Claims

1. A hydrodynamic analysis method for a baffle-rockfill breakwater, characterized in that: The steps include: Develop a new structure type of baffle-rockfill breakwater, that is, dump rockfill on the back side of the baffle, and use fence boards to fix the two sides of the rockfill structure; For the new baffle-rockfill breakwater structure, a hydrodynamic analysis mathematical model of the baffle-rockfill breakwater is established based on potential flow theory, porous media theory and separation variable method. Using the matching characteristic function method, a system of linear equations is established based on the boundary conditions of fluid motion; By solving the equations, the unknown coefficients in the velocity potential are determined, and the reflection coefficient, transmission coefficient and energy dissipation coefficient of the baffle-rockfill breakwater are calculated. Theoretical analysis is used to establish a boundary value problem for simulating the pressure loss on both sides of the vertical baffle in combination with multiple Galerkin approximations. The baffle-rockfill breakwater model in the method includes: The water depth of the baffle-rockfill breakwater is h, and the depth of its baffle into the water is a; The porous rockfill structure has a width of 2b, a height of c, and a distance B from the baffle; A two-dimensional plane coordinate system is established with the intersection of the vertical extension line of the porous rockfill center and the still water surface as the origin, where the positive direction of the x-axis is horizontal to the right and the positive direction of the z-axis is vertically upward; The model is divided into 5 sub-areas; Sub-area 1 is the water area on the wave-facing side of the baffle; Sub-area 2 is the area between the baffle and the rockfill; Sub-area 3 is the water area directly above the rock pile; Sub-area 4 is the inner area of ​​the rockfill; Sub-area 5 is the water area on the back side of the rock pile; The method further comprises: Based on the separation of variables method, the velocity potential series expression of each sub-area that satisfies the control equation, free water surface boundary conditions, bottom boundary conditions and submerged dike upper surface boundary conditions is: in, R m , A m , B m , T m , C m and D m is the coefficient to be determined; φ j (x,z),j=1,2,3,4,5 respectively represent the velocity potential series expressions of sub-region j; The method further comprises: Z m (z), U m (z), V m (z) is the vertical characteristic function, and its expression is: Where ε is the rockfill porosity, s is the inertia coefficient, and f is the linear resistance coefficient; the wave numbers k0 and k m Satisfies the dispersion relation: ω 2 =gk0tanh(k0h)=-gk m tank m h),m=1,2,3,... (11) Where g represents the acceleration due to gravity; λ m is the root of the following complex dispersion equation: oh 2 -gλ m tanhλ m h=P m (oh 2 tanλ m h-gλ m ),m=1,2,3,... (12) Its value needs to be solved by the perturbation method; The method further comprises: When solving the velocity potential function of each sub-region by matching characteristic function method, the velocity continuity and velocity potential continuity conditions between sub-regions are required, as shown in the following formula: φ1(x,z)=φ2(x,z),-h≤z≤-a,x=-Bb (13) φ2(x,z)φ3(x,z),-d≤z≤0,x=-b (15) φ5(x,z)=φ3(x,z),-d≤z≤0,x=b (17) The method further comprises: Based on the matching characteristic function expansion method, the series q in the velocity potential series expression is truncated to Q, and the series m and n are truncated to M; Q and M are both positive integers, and the following linear equations can be obtained: [α qm ] Q×M {R m} M ＝{β q} Q (19) [x] nm ] M×M {A m } M +[g nm ] M×M {B m } M -[d nm ] M×M {C m } M +[the nm ] M×M {D m } M =0 (22) [i nm ] M×M {C m } M +[p nm ] M×M {D m } M -[s nm ] M×M {T m } M =0 (24) -[μ nm ] M×M {C m { M +[v nm ] M×M {D m } M -[I] M×M {T m } M =0 (25); Where I is a unit diagonal matrix, α qm , β q , χ nq , ξ nm , nm , δ nm , η nm , μ nm 、v nm ,θ nm , nm , σ nm , X nm , Y nm , W nm , L nm , γ n is the matrix coefficient; The method further comprises: The reflection coefficient Kr is defined as the ratio of the reflected wave height to the incident wave height, and the transmission coefficient Kt is defined as the ratio of the transmitted wave height to the incident wave height. The reflection coefficient and transmission coefficient of the baffle-rockfill breakwater are: Kr=|R0| (26) Kt=|T0| (27); The method further comprises: The velocity potential of each sub-region is governed by the Laplace equation, and the following boundary conditions must also be met: Free water surface boundary conditions: Bottom boundary conditions: Far field conditions: Where φ0 is the incident wave velocity potential, which is expressed as Submerged dike surface boundary conditions: φ3(x,z)=(s+if)φ4(x,z),z=-d,-b≤x≤b (32) In the formula, G represents the porosity influence coefficient, and its value depends on the opening ratio, shape and thickness of the fence board; Boundary conditions at the baffle: Where E q is the unknown coefficient, p q is the Galerkin basis function, and its expression is as follows: Where N 2q (z) is the second kind 2q order Chebyshev polynomial:

2. A baffle-rockfill breakwater for executing the hydrodynamic analysis method of the baffle-rockfill breakwater according to claim 1, characterized in that: include: baffles and porous rockfill structures; Both sides of the porous rockfill structure are fixed by fence plates; The baffle is arranged in the water area in front of the wave-facing surface of the porous rockfill structure.

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