A determination method for calculating the water-blocking area of vegetation based on the cantilever beam theory

Abstract

The present invention discloses a determination method for calculating the water blocking area of vegetation based on the cantilever beam theory, which relates to the technical field of water conservancy engineering and includes the following steps: Step 1, obtaining the water blocking area of a single plant of vegetation without the action of water flow; Step 2, deriving a calculation formula for the projected water blocking area of vegetation under the action of water flow based on the cantilever beam theory; Step 3, data verification. The determination method for calculating the water blocking area of vegetation based on the cantilever beam theory adopted by the present invention generalizes the vegetation as a cantilever beam, and calculates the water blocking area of vegetation with different stiffnesses and morphological changes based on the deflection differential equation of the cantilever beam. This method expands the universality of the calculation method for the water blocking area of vegetation and is applicable to various types of vegetation with different stiffnesses and morphologies; the water blocking area of vegetation obtained by this method replaces the water blocking area calculated by a simple method and is brought into the calculation model of the flow velocity distribution, which can improve the accuracy of the flow velocity distribution prediction model.

Description

Technical Field

[0001] The present invention relates to the technical field of water conservancy engineering, and in particular to a method for determining the water blocking area of vegetation based on the cantilever beam theory calculation. Background Art

[0002] At present, in the flume experiments of vegetation communities, most scholars use uniform and slender rigid cylindrical rods to generalize vegetation and construct vegetation communities. However, this kind of rigid rod has a single shape, with a single diameter d, which does not change vertically and will not deform under the action of water flow. Therefore, the water blocking area A of a single plant of vegetation constructed by such rods can be calculated by the diameter d of a single plant of vegetation and the depth h of the water flow submerging the vegetation, and A = dh.

[0003] However, compared with the generalized rigid rods, real vegetation has the following characteristics: First, the shape of real vegetation is diverse, non-uniform and complex, and the cross-sectional diameter changes with the height of the vegetation, which brings difficulties to the determination of the water blocking area of vegetation. Second, the stiffness of real vegetation is different, and it will bend under the action of water flow. The occurrence of bending leads to the water blocking area of the vegetation being the front projection area after bending. In recent years, in order to further explore the variation law of the water flow structure under the action of different types of vegetation, some scholars have gradually used simulation vegetation with different shapes and stiffnesses to replace the uniform and slender cylindrical rods. However, when using different simulation vegetation to carry out flume experiments, how to determine the water blocking area of vegetation with different shapes and stiffnesses is a key issue.

[0004] Since the degree and shape of bending of vegetation with different stiffnesses and shapes in water are important factors determining the water blocking area of vegetation. The degree of bending of vegetation in water changes with the drag force exerted by the water flow, and its cross-sectional diameter changes with the height. Therefore, the calculation method of the water blocking area of a single rigid and uniform slender cylindrical rod, A = dh, cannot meet the calculation of the water blocking area of a single plant of simulation vegetation. A new method needs to be established to determine the water blocking area of a single plant of simulation vegetation. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for determining the water blocking area of vegetation based on the cantilever beam theory, and through this method, the water blocking area of a single plant of simulation vegetation with higher accuracy can be obtained.

[0006] To achieve the above purpose, the present invention provides a method for determining the water blocking area of vegetation based on the cantilever beam theory, including the following steps:

[0007] Step 1: Obtain the water blocking area of a single plant of vegetation without the action of water flow;

[0008] Step 2: Derive the calculation formula for the projected water blocking area of vegetation under the action of water flow based on the cantilever beam theory;

[0009] Step 3: Data verification.

[0010] Preferably, the said Step 1 includes the following steps:

[0011] S1. Collect vegetation images, rotate a single simulated vegetation along its circumferential direction, and obtain single simulated vegetation images at several angles;

[0012] S2. Image preprocessing, perform binarization processing on the obtained single simulated vegetation images at several angles;

[0013] S3. Construct a simulated vegetation diameter-height model d(z);

[0014] S4. Obtain the water blocking area of a single simulated vegetation without the action of water flow conditions.

[0015] Preferably, the said Step 2 includes the following steps:

[0016] S1. Generalize the curved vegetation into a cantilever beam and establish a coordinate system;

[0017] S2. Calculate the internal water flow adjustment distance L of the vegetation community d ;

[0018] S3. Calculate the internal water flow velocity U of the vegetation community d Longitudinal distribution;

[0019] S4. Calculate the longitudinal distribution of the drag force F inside the vegetation community d Calculation;

[0020] S5. Calculate the water blocking area of the vegetation under the action of water flow based on the cantilever beam theory.

[0021] Preferably, the formula for calculating the water blocking area is

[0022]

[0023] In the formula, F d is the drag force inside the vegetation community, E is the elastic modulus of the vegetation, I is the moment of inertia of the cross-section, h v is the projected height of the vegetation after bending under the action of water flow, and z is the height from the bottom of the water tank.

[0024] Preferably, the formula for calculating the longitudinal distribution of the water flow velocity inside the vegetation community is

[0025]

[0026] In the formula, U d(f) is the water flow velocity in the fully developed area inside the vegetation community, U d(0) is the water flow velocity at the starting point (x = 0) of the vegetation community, and L d is the internal water flow adjustment distance of the vegetation community.

[0027] Preferably, the calculation formula for the water flow adjustment distance inside the vegetation community is

[0028]

[0029] In the formula, b is the width of the vegetation community, C d is the vegetation drag coefficient, and a is the water-blocking area of a single vegetation.

[0030] Preferably, the calculation formula for the longitudinal distribution of the drag force inside the vegetation community is

[0031]

[0032] In the formula: U d is the average flow velocity inside the vegetation community, and ρ is the density of water.

[0033] Therefore, the present invention adopts the above-mentioned determination method for calculating the water-blocking area of vegetation based on the cantilever beam theory. The vegetation is generalized as a cantilever beam, and based on the deflection differential equation of the cantilever beam, the water-blocking areas of vegetation with different stiffnesses and morphological changes are calculated. This method expands the universality of the calculation method for the water-blocking area of vegetation and is applicable to various types of vegetation with different stiffnesses and morphologies; the water-blocking area of vegetation obtained by this method replaces the water-blocking area calculated by a simple method and is substituted into the calculation model of the flow velocity distribution, which can improve the accuracy of the flow velocity distribution prediction model.

[0034] Next, through the drawings and embodiments, the technical solution of the present invention will be further described in detail. Description of the Drawings

[0035] Figure 1 is the vegetation image;

[0036] Figure 2 is the vegetation image and the binary image;

[0037] Figure 3 is the vegetation diameter-height change curve;

[0038] Figure 4 is the schematic diagram of the bending of the vegetation under the action of water flow. Detailed Embodiments

[0039] The technical solution of the present invention will be further described below through the drawings and embodiments.

[0040] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings as understood by those of ordinary skill in the field to which the present invention pertains. The "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. The terms such as "comprising" or "including" mean that the elements or objects appearing before this term cover the elements or objects listed after this term and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left" and "right" are only used to indicate relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0041] Embodiment

[0042] The present invention provides a determination method for calculating the water-blocking area of vegetation based on the cantilever beam theory, comprising the following steps:

[0043] Step 1: Obtain the water-blocking area of a single plant of vegetation without the action of water flow.

[0044] S1: Collect vegetation images, rotate a single plant of simulated vegetation along its circumferential direction, and obtain single-plant simulated vegetation images at several angles, as Figure 1-2 shown.

[0045] S2: Perform image preprocessing, and perform binary processing on the obtained single-plant simulated vegetation images at several angles.

[0046] S3: Construct a simulated vegetation diameter-height model d(z), intercept several cross-sections along the height direction of each single-plant simulated vegetation image, obtain the widths of each cross-section, convert the widths of each cross-section into the diameters of the corresponding cross-sections of the simulated vegetation, and then obtain the diameters of the corresponding cross-sections of the single-plant simulated vegetation images at different angles. As shown in Table 1, average and summarize the diameters of the corresponding cross-sections of the single-plant simulated vegetation images at different angles to obtain the simulated vegetation diameter-height model d(z), as Figure 3 shown. Table 1 Statistical table of the change of the diameter of a single plant of simulated vegetation with height at different angles (0°, 90°, 180°, 270°)

[0047]

[0048] S4: Obtain the water-blocking area of a single plant of simulated vegetation without the action of water flow conditions. Integrate the simulated vegetation diameter-height model d(z) along its height direction to obtain the water-blocking area a of a single plant of simulated vegetation without the action of water flow conditions:

[0049] In the formula, h represents the water depth from the bottom of the simulated vegetation to the designed position of the submerged simulated vegetation.

[0050] Step 2: Derive the calculation formula for the water-blocking area of the vegetation projection under the action of water flow based on the cantilever beam theory;

[0051] S1. Generalize the curved vegetation as a cantilever beam. According to the knowledge of material mechanics, the curved vegetation is generalized as a cantilever beam for research. Establish the Figure 4 shown coordinate system (x, z), where the vertical coordinate z represents the height from the bottom of the flume, and the initial height of the vegetation is L v , and the projected height of the vegetation after bending under the action of water flow is h v , that is, the height of the vegetation after bending.

[0052] Assume that the elastic modulus of the vegetation is constant for the same type of vegetation, and the vegetation is fixedly connected to the bottom of the riverbed. It can be known from material mechanics that the deflection differential equation of the beam is:

[0053]

[0054] In the formula: M is the bending moment, E is the elastic modulus of the vegetation, and I is the moment of inertia of the cross-section.

[0055] Take a micro-element ds on the curved vegetation for analysis, where θ is the bending angle, as Figure 1 shown, and we can get:

[0056]

[0057]

[0058] S2. Calculate the internal water flow adjustment distance L of the vegetation community d .

[0059]

[0060] In the formula, b is the width of the vegetation community.

[0061] S3. Calculate the internal flow velocity U of the vegetation community d Longitudinal distribution.

[0062] The longitudinal distribution of the flow velocity in the rigid vegetation community can be calculated by the following formula

[0063]

[0064] In the formula, U d(f) is the flow velocity in the fully developed area of the water flow in the vegetation community, U d(0) is the flow velocity at the starting point (x = 0) of the vegetation community, and L d is the internal water flow adjustment distance of the vegetation community.

[0065] In the fully developed region of the water flow, the average flow velocity and the flow velocity at the starting point of the vegetation community can be calculated by the following formulas respectively

[0066]

[0067]

[0068] where g is the acceleration due to gravity, H is the water depth, S is the water surface slope, and C f is the riverbed resistance coefficient, is the area occupied by vegetation per unit area. For rigid vegetation generalized as wooden sticks, the diameter of the vegetation remains unchanged vertically, and the water-blocking area a (= dh v ). For rigid vegetation with a real shape, the diameter of the vegetation varies vertically, and the water-blocking area is For flexible vegetation that undergoes bending and reconstruction deformation under the action of water flow, the orthographic projection area after bending is a f (= a r cosθ).

[0069] S4. Drag force F inside the vegetation community d Longitudinal distribution calculation.

[0070] Assume that the total load uniformly distributed vertically on each flexible vegetation in the water flow is the drag force F d . And the direction of the drag force is perpendicular to the z-axis, then the bending moment M can be expressed as:

[0071]

[0072] Substituting Equation (8) into Equation (3) gives

[0073]

[0074] For a steady open-channel vegetation flow, the water flow drag force is

[0075]

[0076] where ρ is the density of water, C d is the vegetation drag force coefficient, a (= dh v ) is the water-blocking area of a single vegetation, d is the diameter of the vegetation, and U d is the average flow velocity inside the vegetation community.

[0077] S5. Calculate the water-blocking area of vegetation under the action of water flow based on the cantilever beam theory.

[0078] From Equation (9), we can get

[0079]

[0080] Based on the measured data of various types of vegetation, the vertical variation relationship of diameter d(z) can be obtained. Therefore, the projected water-blocking area a of various types of vegetation reconstructed and deformed under the action of water flow f can be expressed as

[0081]

[0082] Step 3: Data verification.

[0083] According to the measured data in Table 1, Figure 2 . Figure 2 In [ ], the solid line is the measured value, the short line is the variance, and the dashed line is the fitting curve. It can be seen that the fitting condition is very good within the variance range, and R 2 = 0.9987m. The specific expression of d(z) in this implementation case is as follows:

[0084] d(z) = 657.87z 5 - 334.31z 4 + 52.443z 3 - 1.9395z 2 + 0.0658z + 0.0078

[0085] Integrating the simulated vegetation diameter-height model d(z) along its height direction gives the water-blocking area a of a single simulated vegetation without the action of water flow conditions:

[0086]

[0087] In this implementation case, the width b of the vegetation community is 0.33m, the density n of the vegetation community is 80 plants / m -1 , the length L of the vegetation community is 4.4m. Therefore, the total number of plants N in the vegetation community can be calculated as 117 plants, and the drag coefficient C d = 1. At this time, the equivalent diameter of a single plant needs to be calculated When the water depth h = 0.2m, d e = 0.0002m. The equivalent water-blocking area a of a single plant d = Na / h = 1.64m. Substituting a d and substituting other parameters into Equation (4), the water flow adjustment distance L d = 3.25 ± 1.25m.

[0088] According to Equation (5), to find U d it is necessary to first obtain the velocity U d(f) in the fully developed area of the water flow and the velocity U d(0) at x = 0 at the starting point of the vegetation community.

[0089] In this implementation case, the gravitational acceleration g = 9.8m / s 2, the water surface slope S = 0.1‰, the water depth h = 0.2m, and the bed coefficient C f = 0.005, and the vegetation coverage rate Substituting the above parameters into Equation (6), the velocity U in the fully developed flow region inside the vegetation community can be obtained d(f) = 0.03m / s.

[0090] In addition, the upstream flow velocity U0 = 0.17m / s in this implementation case. According to Equation (7), the velocity U at x = 0 at the starting point of the vegetation community can be calculated d(0) = 0.147m / s.

[0091] Finally, substituting the above parameters into Equation (5), the velocity U at any position inside the vegetation community can be obtained d .

[0092] The calculated velocity U d Longitudinal distribution. Substituting the density of water ρ = 1000kg / m 3 , the drag coefficient C d = 1, and the equivalent water-blocking area a d = Na / h = 1.64m into Equation (10), the longitudinal distribution of the drag force F inside the vegetation community can be obtained d Longitudinal distribution.

[0093] Table 2 Longitudinal distribution table of velocity and drag force inside the vegetation community

[0094]

[0095]

[0096] Currently, the longitudinal distribution of the velocity and drag force inside the vegetation community is known. According to Equations (8) and (11), the bending moment and the cosine value of the front projection of a single plant of vegetation at each height can be calculated respectively.

[0097] This implementation case takes the bending degree of a single plant of vegetation in the fully developed flow region (x > 3.3m) as an example. The elastic modulus of a single plant of vegetation is E = 3630MPa, and the moment of inertia I(z) = (πd(z)^4) / 64, where d(z) is the fitting curve of the vegetation diameter-height change obtained in S1. The specific calculation results are shown in Table 3 below.

[0098] Table 3 Calculation table of the water-blocking area of vegetation projection

[0099]

[0100]

[0101] Integrating the data in the last column of Table 3 along the water depth according to Equation (12) gives the projected water-blocking area a of the vegetation under the action of the water flow. f . In this implementation case, the water depth h is 0.2 m. Therefore, That is, the projected water-blocking area of the vegetation under the action of the water flow is obtained.

[0102] Therefore, the present invention adopts the above-described determination method for calculating the water-blocking area of vegetation based on the cantilever beam theory. The vegetation is generalized as a cantilever beam, and based on the deflection differential equation of the cantilever beam, the water-blocking areas of vegetation with different stiffnesses and morphological changes are calculated. This method expands the universality of the calculation method for the water-blocking area of vegetation and is applicable to various types of vegetation with different stiffnesses and morphologies. In most existing analytical prediction models for the velocity distribution in vegetated channels, the parameter of the water-blocking area of vegetation is included. When the simple calculation method of A = dh is used to obtain the water-blocking area of vegetation, it causes these analytical models to be unable to accurately predict the velocity distribution within the vegetation community. After adopting this method, replacing the water-blocking area calculated by the simple method with the water-blocking area of vegetation obtained by this method and substituting it into the calculation model of the velocity distribution can improve the accuracy of the velocity distribution prediction model.

[0103] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A determination method for calculating the water-blocking area of vegetation based on the cantilever beam theory, characterized in that Including the following steps: Step 1: Obtain the water-blocking area of a single vegetation without the action of water flow; Step 2: Derive the calculation formula for the projected water-blocking area of vegetation under the action of water flow based on the cantilever beam theory; Step 3: Data verification; Step 2 includes the following steps: S1: Generalize the curved vegetation as a cantilever beam and establish a coordinate system; S2. Calculate the internal water flow adjustment distance L of the vegetation community d ; S3. Calculate the flow velocity U inside the vegetation community d Longitudinal distribution; S4. Drag force F inside the vegetation community d Longitudinal distribution calculation; S5: Calculate the water-blocking area of vegetation under the action of water flow based on the cantilever beam theory; The calculation formula for the water-blocking area is where F d is the drag force inside the vegetation community, E is the elastic modulus of the vegetation, I is the moment of inertia of the cross-section, h v is the projected height after the vegetation bends under the action of the water flow, and z is the height from the bottom of the flume; The longitudinal adjustment distance of the water flow inside the vegetation community is where b is the width of the vegetation community, C d is the vegetation drag force coefficient, and a is the water-blocking area of a single piece of vegetation.

2. The determination method for calculating the vegetation water blocking area based on the cantilever beam theory according to claim 1, wherein: The said Step 1 includes the following steps: S1: Collect vegetation images, rotate the single simulated vegetation along its circumferential direction, and obtain single simulated vegetation images at several angles; S2: Image preprocessing, perform binary processing on the obtained single simulated vegetation images at several angles; S3: Construct the simulated vegetation diameter-height model d(z); S4: Obtain the water-blocking area of a single simulated vegetation without the action of water flow conditions.

3. The determination method for calculating the vegetation water-blocking area based on the cantilever beam theory according to claim 2, wherein: The calculation formula for the longitudinal distribution of the flow velocity inside the vegetation community is where U d(f) is the flow velocity in the fully developed region of the water flow within the vegetation community, and U d(0) is the flow velocity at x = 0 at the starting point of the vegetation community, and L d is the water flow adjustment distance within the vegetation community.

4. The determination method for calculating the vegetation water-blocking area based on the cantilever beam theory according to claim 3, characterized in that: The calculation formula for the longitudinal distribution of the drag force inside the vegetation community is where: U d is the average flow velocity within the vegetation community, and ρ is the density of water.

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