Wave overtopping prediction method for mangrove-seawall hybrid protection system

Abstract

This invention relates to a wave overpass prediction method for mangrove-seawall hybrid protection systems. Different attenuation parameter expressions are established for root-stem-canopy mangroves and root-stem mangroves, respectively. The predicted seawall toe wave height is then substituted into a recalibrated TAW overpass formula to obtain the average overpass discharge. This invention can rapidly predict the average overpass discharge of a mangrove-seawall hybrid protection system given known incident wave conditions, mangrove geometry, and seawall geometry. It is applicable to engineering design, scheme comparison, and ecological seawall safety assessment.

Description

Technical Field

[0001] This invention relates to a wave overtopping prediction method for a mangrove-seawall hybrid protection system, belonging to the fields of coastal engineering, ecological disaster reduction and overtopping prediction technology. Background Technology

[0002] In recent decades, climate change has had an increasingly significant impact on natural systems and human society, leading to continuous sea-level rise and frequent extreme coastal hydrological events. This has resulted in a significant increase in the risk of disasters in coastal areas, placing higher demands on the safety level, protective effectiveness, and long-term adaptability of coastal protection engineering. Traditional coastal flood control systems, with rigid engineering facilities such as seawalls as their core, can reduce the risk of coastal disasters to some extent, but under the long-term trend of accelerating sea-level rise, they suffer from drawbacks such as high maintenance costs, significant ecological damage, and poor environmental compatibility.

[0003] Against this backdrop, nature-based solutions have received sustained attention. Their eco-friendly and sustainable advantages have made them a hot topic in coastal protection research. Mangroves, in particular, are widely used in coastal ecological protection systems due to their excellent wave attenuation and shoreline stabilization functions. However, in highly exposed or spatially confined coastal areas, relying solely on natural measures often fails to achieve the required protection levels. Composite solutions combining traditional engineering structures with natural measures can provide the necessary risk reduction capabilities while preserving the ecological and social benefits of the natural system. Existing research indicates that the wave attenuation capacity of mangroves is closely related to vegetation geometry, water depth, wave conditions, and canopy submersion status. For mangroves with canopies, the canopy layer has a significant wave dissipation effect when the water level is close to the geometric center of the canopy; for mangroves without canopies, the attenuation parameters are not only related to vegetation volume parameters but are also significantly controlled by relative water depth. On the other hand, seawall overtopping prediction usually uses empirical formulas with seawall toe wave parameters as input, such as the TAW formula. In engineering practice and academic research, mangrove wave dissipation and seawall overtopping are generally studied separately, and a method that can directly predict the overtopping amount of the mangrove-seawall hybrid system from the incident wave conditions has not been established.

[0004] The most widely used technique for calculating wave dissipation in mangroves currently uses the Dalrymple vegetation wave dissipation equation as its core. This requires pre-determining the overall drag coefficient and then combining it with a layered model to characterize the vertical structure of the mangrove forest. The method involves establishing a power function relationship, substituting the values ​​into the wave height transmission formula to calculate the wave height at the dike toe, and finally using the TAW formula to solve for the overtopping amount. However, this method requires first fitting the attenuation coefficient and then inferring the drag coefficient. Existing formulas relating drag coefficients to hydrodynamic parameters are complex, highly dependent on experiments, require calibration of numerous parameters, and yield significantly different results from different formulas. This approach suffers from poor versatility, cumbersome engineering applications, and high calibration costs, failing to meet the engineering design, safety assessment, and widespread application needs of mangrove-seawall composite protection systems.

[0005] Therefore, it is necessary to propose a method applicable to different mangrove configurations that can explicitly predict the wave height at the toe of the seawall and further predict the average overtopping flow of the seawall, so as to make up for the shortcomings of existing technologies in quantitative calculation and engineering applicability, and meet the needs of engineering design and safety assessment. Summary of the Invention

[0006] This invention provides a wave overtopping prediction method for a mangrove-seawall hybrid protection system, applicable to different mangrove configurations, capable of explicitly predicting the wave height at the seawall toe and further predicting the average overtopping discharge of the seawall.

[0007] The technical solution adopted by this invention to solve its technical problem is: A wave overrun prediction method for a mangrove-seawall hybrid protection system includes the following steps: Step S1: Obtain the incident wave parameters, mangrove structure parameters, submerged vegetation height, and seawall geometric parameters of the area to be predicted. Step S2: Calculate the flooding volume fraction based on the parameters obtained in step S1; Step S3: Based on the inundation volume fraction obtained in step S2, and combined with the incident wave parameters and mangrove structure parameters obtained in step S1, construct the hydraulic inundation volume fraction. Step S4: Based on the hydraulic inundation volume fraction, calculate the wave height attenuation parameter according to the mangrove type in the area to be predicted. If the type is root-stem-canopy mangrove, construct a power law relationship to calculate the wave height attenuation parameter. If the type is root-stem mangrove, construct a correction relationship that introduces the vertical velocity shape factor to calculate the wave height attenuation parameter. Step S5: Based on the wave height attenuation parameters obtained in step S4, and combined with the wave direction length of the mangrove forest in the area to be predicted, calculate the effective wave height at the toe of the seawall in the area to be predicted. Step S6: Based on the effective wave height obtained in step S5, calculate the dimensionless average overflight discharge. Step S7: Calculate the average overrun flow to complete the wave overrun prediction for the area to be predicted; Furthermore, in step S1, the incident wave parameters include the effective wave height of the incident spectrum, the average period of the spectrum, the effective wavelength of the incident spectrum, and the wave number; wherein, the effective wavelength and wave number of the incident spectrum are calculated based on the average period of the spectrum and the local water depth; the mangrove structural parameters include the mangrove length along the wave direction, plant density, root diameter, stem diameter, root height, stem height, crown height, crown width, and crown projected area; the seawall geometric parameters include the seawall superelevation and the seawall slope; Furthermore, in step S2, the formula for calculating the submerged volume fraction is:

[0008] In the formula, For the submerged volume fraction, This represents the total number of mangrove model plants. For the submerged volume, The volume of water submerged in the area where the mangroves are located; , For mangrove plant density, This indicates the number of roots corresponding to a single tree. , Root density, The diameter of the root. The height of the submerged vegetation at the root zone. The diameter of the stem. The height of the submerged vegetation at the stem level. This represents the total canopy volume of a single mangrove model. The height of the submerged vegetation in the canopy. Tree crown height, The length of the mangrove forest along the wave direction. This refers to the horizontal width of the mangrove belt. This refers to the local water depth.

[0009] Furthermore, in step S3, the formula for calculating the volume fraction of hydraulic submersion is:

[0010] In the formula, The volume fraction of water submersion. For the submerged volume fraction, The effective wave height of the incident spectrum, The effective wavelength of the incident spectrum, The length of the mangrove forest along the wave direction. The height of the submerged vegetation at the stem level. This refers to the local water depth. Furthermore, in step S4, if the type is a root-stem-canopy mangrove, then its wave height attenuation parameter... The calculation formula is:

[0011] In the formula,

[0012] The wave height attenuation parameter for root-stem-canopy mangroves. This represents the empirical coefficient for root-stem-canopy type mangroves. The power-law exponent; If the type is a root-stem mangrove, then its wave height attenuation parameter The calculation formula is:

[0013] In the formula, The wave height attenuation parameter for root-stem mangroves, and For root-stem type mangroves, the empirical coefficient is... The vertical velocity shape factor, , For local water depth, Wave number; Furthermore, in step S5, the effective wave height is determined through the wave height transmission relationship, and the determination formula is as follows:

[0014] In the formula, Taking the length of the mangrove along the wave direction, the effective wave height is obtained as follows:

[0015] In the formula, The effective wave height at the toe of the seawall in the area to be predicted; Furthermore, in step S6, the formula for calculating the dimensionless average overwater discharge is:

[0016] In the formula, The dimensionless average wave discharge. The effective wave height at the toe of the seawall in the area to be predicted. This refers to the vertical height of the seawall crest relative to the still water level. The roughness factor affecting the seawall slope is... The wave oblique incidence influence factor is taken as follows: when the seawall slope is a smooth, impermeable slope and the wave is incident in the normal direction, take... , .

[0017] Furthermore, in step S7, based on the dimensionless average wave flow obtained in step S6, the average wave flow is further obtained. ; Output the effective wave height, dimensionless average overtopping discharge, and average overtopping discharge at the toe of the seawall in the area to be predicted.

[0018] By employing the above technical solutions, the present invention has the following beneficial effects compared to the prior art: 1. The wave overpass prediction method for the mangrove-seawall hybrid protection system provided by this invention couples the mangrove wave dissipation calculation and the seawall wave overpass calculation into a unified process, which can directly predict the average overpass flow from the incident wave conditions, mangrove parameters and seawall parameters, and is suitable for engineering applications. 2. The wave overtopping prediction method for the mangrove-seawall hybrid protection system provided by this invention is free from dependence on the drag coefficient, does not require calibration of multiple sets of hydrodynamic parameters, and directly calculates the attenuation with the submerged volume fraction as the core physical quantity. It is less affected by fluctuations in test conditions and formula selection. At the same time, the parameters are easy to obtain, reducing the workload of model tests and field monitoring. Within the applicable range of parameters, this method has good potential for engineering promotion. 3. The wave overtopping prediction method for the mangrove-seawall hybrid protection system provided by this invention distinguishes between two types of mangroves: root-stem-canopy type and root-stem type, and establishes different attenuation parameter expressions for each. This overcomes the problem that a single unified relationship cannot simultaneously adapt to both types of configurations. At the same time, it can accurately reflect the contribution of different layers to wave dissipation when the water level changes. The wave height at the seawall toe and the overtopping amount are closer to the measured values, enabling efficient matching between ecological engineering and seawall protection, and providing support for safety assessment. Attached Figure Description

[0019] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Figure 1 This is a flowchart of the wave overtopping prediction method for the mangrove-seawall hybrid protection system provided by the present invention; Figure 2 This is a schematic diagram of the layout of the mangrove-seawall hybrid protection system provided by the present invention; Figure 3 This is a comparison chart of the prediction results of wave height attenuation parameters for different types of mangroves in the preferred embodiment of the present invention, where 3a is a root-stem-canopy type mangrove and 3b is a root-stem type mangrove. Figure 4 This is a comparison chart of the predicted overflight volume and the measured overflight volume according to the preferred embodiment of the present invention. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to the accompanying drawings. The specific dimensions used in this embodiment are merely illustrative and do not limit the scope of protection of the present invention.

[0022] As described in the background section, existing research on the protection of mangrove-seawall combinations mainly focuses on engineering structural aspects such as breakwater layout, submerged breakwater coupling construction, and ecological shoreline morphology design. There is a lack of research on core methods for quantitatively reconstructing wave conditions at the toe of mangrove-seawall hybrid protection systems and accurately predicting seawall overtopping.

[0023] like Figure 2 The diagram shown is a schematic representation of the mangrove-seawall hybrid protection system provided in this application. Based on this system, wave overtopping prediction is performed. The entire prediction method is as follows: Figure 1 As shown, it includes the following steps: Step S1: Obtain the incident wave parameters, mangrove structure parameters, submerged vegetation height, and seawall geometry parameters of the area to be predicted; the incident wave parameters include the significant wave height of the incident spectrum. Spectral average period Effective wavelength of incident spectrum And wavenumber; here, the effective wavelength of the incident spectrum. The wave number is calculated based on the average period of the spectrum and the local water depth.

[0024] Mangrove structural parameters include the mangrove length along the wave direction. Plant density, root diameter , stem diameter Root height, stem height, crown height Tree crown width and canopy projected area; seawall geometric parameters including seawall crest superelevation. And the slope of the seawall.

[0025] Step S2: Calculate the flooding volume fraction based on the parameters obtained in step S1; the formula for calculating the flooding volume fraction is: , In the formula, For the submerged volume fraction, This represents the total number of mangrove model plants. For the submerged volume, The volume of water submerged in the area where the mangroves are located; , For mangrove plant density, This indicates the number of roots corresponding to a single tree. , Root density, The diameter of the root. The height of the submerged vegetation at the root zone. The diameter of the stem. The height of the submerged vegetation at the stem level. This represents the total canopy volume of a single mangrove model. The height of the submerged vegetation in the canopy. Tree crown height, The length of the mangrove forest along the wave direction. This refers to the horizontal width of the mangrove belt. This refers to the local water depth.

[0026] Step S3: Based on the inundation volume fraction obtained in Step S2, and combined with the incident wave parameters and mangrove structure parameters obtained in Step S1, construct the hydraulic inundation volume fraction; the formula for calculating the hydraulic inundation volume fraction is:

[0027] In the formula, The volume fraction of water submersion. For the submerged volume fraction, The effective wave height of the incident spectrum, The effective wavelength of the incident spectrum, The length of the mangrove forest along the wave direction. The height of the submerged vegetation at the stem level. This refers to the local water depth.

[0028] Steps S1 to S3 represent the first innovation of this application. They avoid the prior art strategy of first fitting the attenuation coefficient and then inferring the drag coefficient. Instead of calibrating multiple sets of dynamic parameters, the inundation volume fraction can be directly calculated based on the parameters readily available in step S1, reducing on-site calibration costs. The inundation volume fraction also reflects the actual proportion of water space occupied by vegetation, making it closer to actual working conditions than the drag coefficient. Continuing to use the inundation volume fraction as the core physical quantity for attenuation calculation simplifies engineering applications. Most importantly, it solves the problem in existing technologies where wave dissipation by mangroves and wave overburden at seawalls are typically considered separately, making it difficult to reflect the coupling effect between mangroves and seawalls.

[0029] Step S4 involves calculating wave height attenuation parameters based on the hydraulic inundation volume fraction and the mangrove type in the area to be predicted. This is the second innovation of this application: precisely matching the structural differences of mangroves allows for a quantitative comparison of the wave dissipation effects of different mangrove configurations, improving calculation accuracy. Simultaneously, it adapts to diverse mangrove types, covering different tree species structures, overcoming the problem that a single, uniform relationship cannot simultaneously adapt to two different configurations.

[0030] If the type is root-stem-canopy mangrove, construct a power-law relationship to calculate the wave height attenuation parameter; if the type is root-stem mangrove, construct a modified relationship that introduces the vertical velocity shape factor to calculate the wave height attenuation parameter. Specifically, if the mangrove forest type is root-stem-canopy type, then its wave height attenuation parameter The calculation formula is:

[0031] In the formula, The wave height attenuation parameter for root-stem-canopy mangroves. This represents the empirical coefficient for root-stem-canopy type mangroves. The power-law exponent; In root-stem-canopy type mangroves, the method used is based on The power-law relationship can accurately reflect the nonlinear resistance characteristics of roots, trunks, and canopies under wave reciprocating flow. It can perform independent calculations for different vegetation layers and better describe the enhanced dissipation and gradual saturation characteristics of the canopy as it transitions from partial to near-complete submersion.

[0032] If the type is a root-stem mangrove, then its wave height attenuation parameter The calculation formula is:

[0033] In the formula, The wave height attenuation parameter for root-stem mangroves, and For root-stem type mangroves, the empirical coefficient is... The vertical velocity shape factor, , For local water depth, For wave number.

[0034] In rhizomatous mangrove forests, a vertical velocity shape factor was introduced. The revised relationship calculation explicitly incorporates the influence of relative water depth into the attenuation parameter expression, improving the prediction accuracy across different water depth conditions. At the same time, the revision involves fewer parameters, thus adapting to different water depths and inundation conditions, and significantly improving the reliability and engineering applicability of seawall overtopping prediction.

[0035] Step S5: Based on the wave height attenuation parameters obtained in Step S4, and combined with the wave direction length of the mangrove forest in the area to be predicted, calculate the effective wave height at the toe of the seawall in the area to be predicted; the effective wave height is determined through the wave height transmission relationship, and the formula is as follows:

[0036] In the formula, Taking the length of the mangrove along the wave direction, the effective wave height is obtained as follows:

[0037] In the formula, The effective wave height is at the toe of the seawall in the area to be predicted.

[0038] Step S6: Based on the effective wave height obtained in step S5, calculate the dimensionless average overflight discharge; the calculation formula is:

[0039] In the formula, The dimensionless average wave discharge. The effective wave height at the toe of the seawall in the area to be predicted. This refers to the vertical height of the seawall crest relative to the still water level. The roughness factor affecting the seawall slope is... The wave oblique incidence influence factor is taken as follows: when the seawall slope is a smooth, impermeable slope and the wave is incident in the normal direction, take... , .

[0040] Step S7: Based on the dimensionless average wave flow obtained in step S6, continue to obtain the average wave flow. Output the effective wave height, dimensionless average overtopping flow, and average overtopping flow at the toe of the seawall in the area to be predicted, and complete the wave overtopping prediction for the area to be predicted.

[0041] Next, to verify the feasibility of the above solution, this application provides relevant embodiments. In step S4, The first step is to obtain basic parameters. The significant wave height of the incident spectrum was obtained for mangrove forests at three different spacing distances: 1m, 3m, and 5m. Spectral average period Initial water depth at the point of incidence Vertical height of the seawall crest relative to the still water level Mangrove length along wave direction The data includes parameters such as root diameter, stem diameter, root height, stem height, crown height, crown width, plant density, and submersion height of mangroves. Based on the presence or absence of a crown, mangroves are classified into root-stem-canopy type or root-stem type.

[0042] The second step is to determine the inundation volume fraction based on the inundation geometry of each component of the mangrove forest. .

[0043] The third step is to combine the effective wave height of the incident spectrum. Effective wavelength of incident spectrum Mangrove length along wave direction and relative submersion height Calculate the volume fraction of hydraulic submersion. .

[0044] The fourth step is to calculate the wave height attenuation parameters. .

[0045] Root-stem-canopy type mangroves adopt: ; Root-stem type mangroves adopt: .

[0046] Figure 3 In the figure, 3a is a schematic diagram comparing the fitting of wave height attenuation parameters when the mangrove is of the root-stem-canopy type, and 3b is a schematic diagram comparing the fitting of wave height attenuation parameters when the mangrove is of the root-stem type. In the figure, the vertical axis represents the measured wave height attenuation parameter, and the horizontal axis represents the predicted wave height attenuation parameter. It can be seen that the predicted values ​​and measured values ​​under the two types of mangrove conditions are generally close, indicating that the wave height attenuation parameter calculation method constructed in this application can better reflect the wave attenuation characteristics under different mangrove structure conditions.

[0047] Continue to step five and reconstruct the wave height at the embankment toe.

[0048] Step 6, Substituting the recalibrated TAW overpass formula, the dimensionless average overpass flow rate is obtained.

[0049] Step 7: Output the prediction results. Dimensionless average wave flow and average overflow .

[0050] like Figure 4 As shown, the dimensionless average overflight flow calculated in the embodiments is compared with the experimentally measured dimensionless average overflight flow. The data from each group are generally distributed around the 1:1 concordance line, indicating that the calculated results of the wave overflight prediction method for the mangrove-seawall hybrid protection system provided in this application have good consistency with the measured results. The overall evaluation index is NSE = 0.882, indicating that the wave overflight prediction method for the mangrove-seawall hybrid protection system provided in this application can effectively characterize the trend of overflight volume changes.

[0051] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0052] The meaning of "and / or" as used in this application includes situations where each exists alone or both exist simultaneously.

[0053] The term "connection" as used in this application can mean a direct connection between components or an indirect connection between components through other components.

[0054] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A wave overpass prediction method for a mangrove-seawall hybrid protection system, characterized in that: Includes the following steps: Step S1: Obtain the incident wave parameters, mangrove structure parameters, submerged vegetation height, and seawall geometric parameters of the area to be predicted. Step S2: Calculate the flooding volume fraction based on the parameters obtained in step S1; Step S3: Based on the inundation volume fraction obtained in step S2, and combined with the incident wave parameters and mangrove structure parameters obtained in step S1, construct the hydraulic inundation volume fraction. Step S4: Based on the hydraulic inundation volume fraction, calculate the wave height attenuation parameter according to the mangrove type in the area to be predicted. If the type is root-stem-canopy mangrove, construct a power law relationship to calculate the wave height attenuation parameter. If the type is root-stem mangrove, construct a correction relationship that introduces the vertical velocity shape factor to calculate the wave height attenuation parameter. Step S5: Based on the wave height attenuation parameters obtained in step S4, and combined with the wave direction length of the mangrove forest in the area to be predicted, calculate the effective wave height at the toe of the seawall in the area to be predicted. Step S6: Based on the effective wave height obtained in step S5, calculate the dimensionless average overflight discharge. Step S7: Calculate the average overtopping flow to complete the wave overtopping prediction for the area to be predicted.

2. The wave overtopping prediction method for the mangrove-seawall hybrid protection system according to claim 1, characterized in that: In step S1, the incident wave parameters include the effective wave height of the incident spectrum, the average period of the spectrum, the effective wavelength of the incident spectrum, and the wave number; wherein, the effective wavelength and wave number of the incident spectrum are calculated based on the average period of the spectrum and the local water depth; the mangrove structural parameters include the mangrove length along the wave direction, plant density, root diameter, stem diameter, root height, stem height, crown height, crown width, and crown projected area; the seawall geometric parameters include the seawall superelevation and the seawall slope.

3. The wave overtopping prediction method for the mangrove-seawall hybrid protection system according to claim 1, characterized in that: In step S2, the formula for calculating the submerged volume fraction is: ， In the formula, For the submerged volume fraction, This represents the total number of mangrove model plants. For the submerged volume, The volume of water submerged in the area where the mangroves are located; , For mangrove plant density, This indicates the number of roots corresponding to a single tree. , Root density, The diameter of the root. The height of the submerged vegetation at the root zone. The diameter of the stem. The height of the submerged vegetation at the stem level. This represents the total canopy volume of a single mangrove model. The height of the submerged vegetation in the canopy. Tree crown height, The length of the mangrove forest along the wave direction. This refers to the horizontal width of the mangrove belt. This refers to the local water depth.

4. The wave overtopping prediction method for the mangrove-seawall hybrid protection system according to claim 3, characterized in that: In step S3, the formula for calculating the volume fraction of hydraulic submersion is: ， In the formula, The volume fraction of water submersion. For the submerged volume fraction, The effective wave height of the incident spectrum, The effective wavelength of the incident spectrum, The length of the mangrove forest along the wave direction. The height of the submerged vegetation at the stem level. This refers to the local water depth.

5. The wave overtopping prediction method for the mangrove-seawall hybrid protection system according to claim 1, characterized in that: In step S4, if the type is root-stem-canopy mangrove, then its wave height attenuation parameter The calculation formula is: ， In the formula, The wave height attenuation parameter for root-stem-canopy mangroves. This represents the empirical coefficient for root-stem-canopy type mangroves. The power-law exponent; If the type is a root-stem mangrove, then its wave height attenuation parameter The calculation formula is: ， In the formula, The wave height attenuation parameter for root-stem mangroves, and For root-stem type mangroves, the empirical coefficient is... The vertical velocity shape factor, , For local water depth, For wave number.

6. The wave overtopping prediction method for the mangrove-seawall hybrid protection system according to claim 1, characterized in that: In step S5, the significant wave height is determined through the wave height transmission relationship, and the determination formula is as follows: ， In the formula, Taking the length of the mangrove along the wave direction, the effective wave height is obtained as follows: ， In the formula, The effective wave height is at the toe of the seawall in the area to be predicted.

7. The wave overtopping prediction method for the mangrove-seawall hybrid protection system according to claim 1, characterized in that: In step S6, the formula for calculating the dimensionless average overwater discharge is: ， In the formula, The dimensionless average wave discharge. The effective wave height at the toe of the seawall in the area to be predicted. This refers to the vertical height of the seawall crest relative to the still water level. The roughness factor affecting the seawall slope is... The wave oblique incidence influence factor is taken as follows: when the seawall slope is a smooth, impermeable slope and the wave is incident in the normal direction, take... , .

8. The wave overtopping prediction method for the mangrove-seawall hybrid protection system according to claim 7, characterized in that: In step S7, based on the dimensionless average wave flow obtained in step S6, the average wave flow is further obtained. ; Output the effective wave height, dimensionless average overtopping discharge, and average overtopping discharge at the toe of the seawall in the area to be predicted.

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