Simulation methods for levee breach and flood evolution

Abstract

The present invention belongs to the technical field of water conservancy engineering, and specifically discloses a method for simulating levee breach and flood evolution, including: step 1, using rectangular grids to divide the breach area of ​​the levee, and using unstructured grids to divide the river channel on one side of the levee and the protection area on the other side of the levee respectively; step 2, obtaining flood information in the unstructured grid, and interpolating the flood information into the rectangular grid; step 3, using a water-soil coupling dynamic model to determine the breach information of the breach area, and interpolating the breach information into the unstructured grid, repeating steps 2 and 3 until the preset conditions are met. The present invention uses a water-soil coupling dynamic model to describe the levee breach process, without the need to manually give parameters such as the breach rate and final breach size of the existing model, thereby realizing a fully automatic simulation of the levee breach process. The present invention adopts a structured-unstructured dual grid technology, taking into account the accuracy and efficiency of the levee breach process and the breach flood evolution calculation.

Description

Technical Field

[0001] The invention discloses a dike breach and flood evolution simulation method, belonging to the technical field of water conservancy engineering. Background Art

[0002] Levees are a crucial component of flood control systems, and the areas protected by them are called protected areas. In areas with long coastlines and complex geological conditions, substandard levee construction or substandard levee quality can lead to levee failure. Levee failure poses a significant threat to the lives and property of residents within protected areas. Therefore, simulations of levee failure and flood progression are essential.

[0003] Due to the irregular boundary conditions of the evolution range of natural dam breach floods, the use of rectangular grids in the simulation process is not very adaptable to complex boundary conditions. Therefore, unstructured grids are often used to enhance adaptability to complex boundary conditions. When using unstructured grids to calculate the collapse of breach terrain, the algorithm becomes complex due to the multi-directional terrain reconstruction and gradient calculation involved. At the same time, in order to better simulate the breach flow, the existing technology generally uses smaller-sized unstructured grids in the breach area and larger-sized unstructured grids in other areas. Since the calculation time step is the minimum time step of all grids, and the time step of the smallest-sized unstructured grid is often the smallest, that is, the time step in the calculation area is determined by the smallest unstructured grid size unit, which greatly limits the calculation efficiency. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for simulating dike breach and flood evolution to solve the technical problems of complex algorithms and low computational efficiency in the prior art of simulating dike breach and flood evolution using unstructured grids.

[0005] The present invention provides a method for simulating dike breach and flood evolution, comprising:

[0006] Step 1: using a rectangular grid to divide the breach area of ​​the levee, and using an unstructured grid to divide the river channel on one side of the levee and the protection area on the other side of the levee respectively;

[0007] Step 2: Obtain flood information in the unstructured grid and interpolate the flood information into the rectangular grid;

[0008] Step 3: Determine the breach information of the breach area using the water-soil coupled dynamic model, and interpolate the breach information into the unstructured grid. Repeat steps 2 and 3 until the preset conditions are met, and complete the levee breach and flood evolution simulation.

[0009] Preferably, the water-soil coupled dynamic model is a two-dimensional hydrodynamic model including a riverbed deformation equation; the riverbed deformation equation is determined according to the uplift flux and the sedimentation flux.

[0010] Preferably, the upward flux is determined based on the difference coefficient between the near-bottom sediment concentration and the vertical sediment concentration, the still water settling velocity of a single particle of sediment, and the saturated sediment transport rate of the local water flow bed load.

[0011] Preferably, the upward flux is determined according to the clay scouring rate and the sediment porosity.

[0012] Preferably, the sedimentation flux is determined based on the depth-averaged volumetric sediment concentration of the sediment, the coefficient of difference between the near-bottom sediment concentration and the vertical sediment concentration, and the still water sedimentation velocity of a single sediment particle.

[0013] Preferably, the length of the long side of the rectangular grid is shorter than the length of the shortest side of the unstructured grid.

[0014] Preferably, the unstructured grid is a triangular grid.

[0015] Preferably, the flood information includes water depth and flow velocity.

[0016] Preferably, the breach information includes water depth, flow velocity and terrain elevation.

[0017] Preferably, obtaining the flood information in the unstructured grid specifically comprises: obtaining the flood information in the unstructured grid using a two-dimensional hydrodynamic model.

[0018] Compared with the existing technology, the levee breach and flood evolution simulation method of the present invention has the following beneficial effects:

[0019] This method uses a coupled water-soil dynamic model to describe the levee breach process, eliminating the need for manual input of existing model parameters such as breach rate and final breach size. This allows for fully automated simulation of the levee breach process. The method also employs a dual structured-unstructured grid technique, ensuring both accuracy and efficiency in calculating both the levee breach process and the resulting flood. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Flowchart of a method for simulating dike breach and flood evolution according to an embodiment of the present invention.

[0021] Figure 2 Schematic diagram of constructing a levee failure model based on a dual grid according to an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In the following description, specific details such as particular system structures and techniques are provided for purposes of illustration, not limitation, to facilitate a thorough understanding of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.

[0023] The embodiment of the present invention provides a method for simulating dike breach and flood evolution, such as Figure 1 and Figure 2 As shown, including:

[0024] Step 1: Use rectangular grids to divide the breach area of ​​the embankment, and use unstructured grids to divide the river channel on one side of the embankment and the protection area on the other side of the embankment, such as Figure 2 shown.

[0025] After segmentation, the embodiment of the present invention interpolates the corresponding terrain onto rectangular grid nodes and unstructured grid nodes respectively.

[0026] Step 2: Obtain flood information in the unstructured grid and interpolate the flood information into the rectangular grid.

[0027] For example, given the initial conditions, boundary conditions, roughness and other parameter values ​​of the unstructured grid, the calculation is started using the existing two-dimensional hydrodynamic model, with the calculation starting at time t = 0. The initial conditions include the initial water depth and flow velocity.

[0028] In the embodiment of the present invention, it is first necessary to determine whether the time t is less than the preset maximum time t max , that is, t<t max , if so, after calculating a time step ΔT, the water depth and flow velocity of each node in the unstructured grid at time t are obtained as flood information.

[0029] After obtaining flood information, the present invention interpolates the flood information into a rectangular grid. Specifically, the water depth and flow velocity of each node in the unstructured grid are interpolated into the rectangular grid of the dike breach area. The specific interpolation method can adopt linear interpolation or natural neighbor interpolation method.

[0030] Step 3: Use the water-soil coupled dynamic model to determine the breach information of the breach area and interpolate the breach information into the unstructured grid. Repeat steps 2 and 3 until the preset conditions are met, completing the levee breach and flood evolution simulation.

[0031] After the interpolation in step 2 is completed, the embodiment of the present invention runs the water-soil coupled dynamic model and obtains the breach information of the breach area at time t+ΔT. The breach information that can be obtained includes parameters such as breach topography, breach flow process, breach flow velocity, water depth, water level, and breach topography elevation.

[0032] For example, the present invention interpolates the water depth, flow velocity, and terrain elevation on the rectangular grid nodes of the breach area back into the unstructured grid, and then repeats steps 2 and 3 until t≥t max , the interpolation here preferably adopts the inverse distance weighted method.

[0033] The existing model used to determine breach information in the breach zone is a two-dimensional shallow water dynamics control equation. This model assumes that the breach develops uniformly and does not adequately consider the physical mechanisms, resulting in inaccurate breach information. To address this issue, the present invention utilizes a water-soil coupled dynamics model in the breach zone. This model takes into account the movement of the water-sand mixture, making the resulting breach information more accurate. The present invention's water-soil coupled dynamics model is specifically as follows:

[0034] The governing equations for two-dimensional shallow water dynamics, based on the fundamental conservation laws of fluid mechanics, include the mass conservation equation and the momentum conservation equation. To accommodate the complex flow conditions and irregular terrain found in natural river channels, this paper organizes the basic governing equations into a harmonious conservation form:

[0035]

[0036] Where U is the conserved variable, F and G are flux variables, and S is the source term vector.

[0037]

[0038] Where U is the conserved quantity vector; h is the water depth; u and v are the water flow velocities in the x and y directions, respectively; x and y are spatial coordinates; and c is the depth-averaged volumetric sediment content.

[0039]

[0040] Where F is the convective flux vector in the x direction; h is the water depth; u and v are the water velocities in the x and y directions, respectively; x and y are spatial coordinates; c is the depth-averaged volumetric sediment content of the sediment; and g is the acceleration of gravity, which is taken as 9.8 m / s. 2 .

[0041]

[0042] Where G is the convective flux vector in the y direction; h is the water depth; u and v are the water velocities in the x and y directions, respectively; x and y are spatial coordinates; c is the depth-averaged volumetric sediment content of the sediment; and g is the acceleration of gravity, which is taken as 9.8 m / s. 2 .

[0043]

[0044] Where S is the source vector; h is the water depth; u and v are the water velocities in the x and y directions, respectively; x and y are spatial coordinates; c is the depth-averaged volumetric sediment content of the sediment; and g is the acceleration of gravity, which is 9.8 m / s. 2 ; E is the upward flux; D is the total sedimentation flux; p0 is the sediment porosity; S bx and S by are the riverbed slopes in the x and y directions respectively; S fx =-τ bx / ρ and S fy =-τ by / ρ are the resistance in the x and y directions respectively; ρ w and ρ s are the densities of clean water and sediment, respectively, and are 1.0×10 3 kg / m 3 and 2.65×10 3 kg / m 3 ; ρ=ρ w (1-c)+ρ s c is the density of the water-sand mixture; ρ0 = ρ w p0+ρ s (1-p0) is the saturated wet density of bed sand.

[0045] The riverbed deformation equation in the embodiment of the present invention is as shown in formula (6):

[0046]

[0047] Where t is time; z is riverbed elevation; E is the upwelling flux; D is the total sedimentation flux; and p0 is the sediment porosity.

[0048] Some unknown quantities in the above control equations cannot be directly obtained by solving the equations and require additional relationship formulas to determine. The bed resistance is calculated using the Manning roughness formula:

[0049]

[0050] Where, τ bx is the bed resistance in the x direction; τ by is the bed resistance in the y direction; ρ is the density of the water-sand mixture; g is the acceleration due to gravity, which is 9.8 m / s 2; h is the water depth; n is the Manning roughness coefficient; q x is the flow rate in the x direction; q y is the flow rate in the y direction.

[0051] The exchange of sediment between the water flow near the riverbed and the riverbed includes two different mechanisms: sediment uplift caused by turbulence and sediment settling caused by gravity. The difference between the uplift flux and the settling flux reflects the non-equilibrium characteristics of sediment transport by water flow. The settling flux is calculated as:

[0052] D=αwc (9)

[0053] Where α is the difference coefficient between the near-bottom sediment concentration and the vertical sediment concentration; w is the still water settling velocity of a single sediment particle, calculated using Zhang Ruijin's formula; and c is the depth-averaged volumetric sediment concentration of the sediment.

[0054] For levee failure processes based on sandy materials, since the material is mainly non-cohesive sand, the sediment initiation and transport are simulated using the bedload sediment basic formula in river dynamics. Since the Mayer-Peter-Muller formula (1948) was derived using a wide range of data and has strong adaptability, this paper uses it to calculate the bedload saturation sediment transport rate. The upward flux calculation formula is:

[0055] E=αwc e (10)

[0056] Where α is the difference coefficient between the sediment concentration near the bottom and the vertical sediment concentration; w is the still water settling velocity of a single particle of sediment; c e is the local water bed load saturation sediment transport rate, specifically the water bed load saturation sediment transport rate near the bed surface, which is determined according to formula (11):

[0057]

[0058] Where q b is the saturated bed load transport rate; h is the water depth; u and v are the water flow velocities in the x and y directions respectively; x and y are the spatial coordinates.

[0059] The above q b Determine according to formula (12):

[0060]

[0061] Where θ is the Shields parameter, also known as relative drag force, τ b is τ bx and τ by The resultant force; ρ is the density of the water-sand mixture; ρ s is the density of sediment, taking 2.65×10 3kg / m 3 ; d is the particle diameter; s is the relative density.

[0062] For embankment materials mainly composed of clay, viscosity plays an important role in its destruction process. Therefore, it is more appropriate to use the soil erosion destruction formula to simulate the collapse process. The present invention uses the scour rate formula to calculate the scour rate, and then obtains the upward flux calculation expression.

[0063] E=ε(1-p0) (13)

[0064] Where ε is the soil scouring rate; p0 is the sediment porosity; ε is determined according to formula (14):

[0065] ε=k d (τ b -τ c ) (14)

[0066] Where k d is the soil scour rate coefficient; τ b is τ bx and τ by The resultant force; τ c Critical starting shear stress of soil.

[0067] By employing different upwelling flux calculation methods for different levee materials, the present invention achieves consistency in the equations and numerical algorithms used to simulate levee breaches. Furthermore, conventional scour rate formulas can only calculate the scour process during a breach, but cannot account for the sedimentation downstream of the breach during its formation. However, the present model can calculate the sedimentation downstream of the breach during its formation phase when DE > 0. This demonstrates that the flux method employed by the present invention overcomes these issues with conventional scour rate formulas.

[0068] To better simulate flood flow from a breach, existing techniques typically use smaller unstructured grids in the breach area and larger unstructured grids in other areas. However, since the computational time step is the minimum of all grid time steps, and the smallest unstructured grid often has the smallest time step, the time step within the computational area is determined by the smallest unstructured grid cell size, significantly limiting computational efficiency. The present invention utilizes a dual structured-unstructured grid technique, limiting the length of the long side of the rectangular grid to less than the shortest side of the unstructured grid. This allows the use of a small rectangular grid to calculate the breach development and flow process, while a large unstructured grid is used to calculate the flood evolution process in other areas. Calculating collapse with a rectangular grid only requires considering two directions, simplifying the computational steps. Furthermore, the small grid allows for detailed simulation of the breach process and flow field. Using a large unstructured grid for the entire computational area increases the time step and reduces the number of computational steps. For example, when calculating flood storage and detention areas, the small rectangular grid is meter-scale, and the large unstructured grid is approximately 100 meters. For indoor experiments, the small grid is centimeter-scale, and the large grid is no more than 0.5 meters. Furthermore, the present invention uses interpolation to transfer water depth, flow velocity and terrain information between the rectangular grid and the unstructured grid. This method takes into account both calculation accuracy and efficiency.

[0069] The unstructured grid in the embodiment of the present invention may be a polygonal grid, preferably a triangular grid.

[0070] This method uses a coupled water-soil dynamic model to describe the levee breach process, eliminating the need for manual input of existing model parameters such as breach rate and final breach size. This allows for fully automated simulation of the levee breach process. The method also employs a dual structured-unstructured grid technique, ensuring both accuracy and efficiency in calculating both the levee breach process and the resulting flood.

[0071] The above descriptions are merely several embodiments of the present invention and do not constitute any form of limitation to the present invention. Although the present invention is disclosed as above in terms of preferred embodiments, they are not intended to limit the present invention. Any technician familiar with the present profession who, without departing from the scope of the technical solution of the present invention, makes slight changes or modifications using the technical contents disclosed above are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for simulating levee breach and flood evolution, characterized in that: include: Step 1: using a rectangular grid of a structured grid to segment the breach area of ​​the embankment, and using an unstructured grid to segment the river channel on one side of the embankment and the protection area on the other side of the embankment respectively; Step 2: Obtain flood information in the unstructured grid and interpolate the flood information into the rectangular grid; Step 3: using a water-soil coupled dynamic model to determine the breach information of the breach area, and interpolating the breach information into the unstructured grid, repeating steps 2 and 3 until the preset conditions are met, thereby completing the levee breach and flood evolution simulation; The water-soil coupled dynamic model is a two-dimensional hydrodynamic model including a riverbed deformation equation; The riverbed deformation equation is determined based on the uplift flux and the subsidence flux; The sedimentation flux is determined based on the depth-averaged volumetric sediment concentration of the sediment, the coefficient of difference between the near-bottom sediment concentration and the vertical sediment concentration, and the still water sedimentation velocity of a single sediment particle; The length of the long side of the rectangular grid is shorter than the length of the shortest side of the unstructured grid.

2. The levee breach and flood evolution simulation method according to claim 1, characterized in that: The upward flux is determined based on the difference coefficient between the near-bottom sediment concentration and the vertical sediment concentration, the still water settling velocity of a single particle of sediment, and the saturated sediment transport rate of the local water flow bedload.

3. The levee breach and flood evolution simulation method according to claim 1, characterized in that: The upward flux is determined based on the clay scouring rate and the sediment porosity.

4. The levee breach and flood evolution simulation method according to claim 1, characterized in that: The unstructured grid is a triangular grid.

5. The levee breach and flood evolution simulation method according to claim 1, characterized in that: The flood information includes water depth and flow velocity.

6. The levee breach and flood evolution simulation method according to claim 1, characterized in that: The breach information includes water depth, flow velocity and terrain elevation.

7. The levee breach and flood evolution simulation method according to claim 1, characterized in that: Obtain flood information within the unstructured grid, specifically: A two-dimensional hydrodynamic model is used to obtain flood information within the unstructured grid.

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