Method for predicting overtopping dam break peak flow of earth and rockfill dam

Abstract

The invention belongs to the technical field of hydraulics, and particularly relates to an earth and rockfill dam overtopping dam break peak flow prediction method, which comprises the following steps: collecting a water level-area-reservoir capacity curve, a dam crest elevation and a dam site section reservoir bottom elevation data of a prediction target reservoir; according to the dam crest elevation and the water level-reservoir capacity curve, the reservoir capacity is obtained through linear interpolation, and the maximum dam break height is obtained by subtracting the dam site section reservoir bottom elevation from the dam crest elevation; according to the water level-area curve, converting the water level into false height by taking the reservoir bottom elevation as a reference surface, and fitting the false height to obtain a power coefficient; acquiring a flow coefficient by adopting a linear fitting mode according to the database data of the broken dam case; and predicting the reservoir dam break peak flow according to the breach peak flow calculation formula. The dam break peak flow prediction index provided by the invention is clear in physical significance, has a remarkable linear correlation characteristic with the dam break peak flow, is easy to obtain, and can be used as a trend analysis index to test the rationality of a calculation result.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydraulics, and particularly relates to a method for predicting the peak discharge of an earth-rock dam during overtopping failure. Background Art

[0002] As of the end of 2020, there were 98,566 reservoir dams of various types in the country, including 93,694 small reservoirs, accounting for 95.06% of the total (18,229 small (1) type and 75,465 small (2) type, accounting for 18.49% and 76.56% of the total respectively). Classified by dam type, there are more than 90,000 earth-rock dams, accounting for 91.8%. From 1954 to 2021, a total of 3,558 reservoir dams failed in China, including 3,356 earth-rock dams (including concrete face rockfill dams), accounting for 94.32% of the total number of failed dams, exceeding the proportion of earth-rock dams in the total number of dams. Statistical results of the causes of reservoir dam failures show that more than 50% of the dam failure accidents are caused by flood overtopping.

[0003] Dam-break floods bring catastrophic consequences to human society, and there are painful lessons both at home and abroad. With the rapid development of China's economic society, the consequences of reservoir dam failures are far more disastrous than those in other countries. In order to prevent or mitigate the impact of dam-break floods, it is extremely crucial to quickly and accurately predict key dam-break parameters such as the peak discharge of dam-break. Due to limited reliable record information / databases and the complex relationships between different elements of the dam-break time, predicting the peak discharge of dam-break has always been challenging. Common methods include empirical formulas, model tests, computational fluid dynamics (CFD) simulations, etc., which usually result in a high degree of uncertainty in the predicted values of ±0.5 to ±1 order of magnitude.

[0004] The main disadvantages of model tests are time-consuming, laborious and costly; the CFD model requires accurate and reliable detailed information and conditional assumptions, and sufficient reliable calibration and verification information. Otherwise, the complexity of the model and the sensitivity of the parameters may quickly lead to unreliable simulation results. Empirical formulas are still widely used because of their simple structure and convenient parameter acquisition. Since the 1970s, scholars at home and abroad have proposed a series of statistical regression expressions for the peak discharge of the breach. The selected statistical indicators include the water depth above the bottom of the breach at the time of dam-break, dam height, reservoir storage capacity, reservoir storage capacity above the bottom of the breach at the time of dam-break, breach depth, storage capacity at the time of dam-break, water level at the time of dam-break, dam body length, average width of the dam body, etc.; some regression expressions also include parameters related to dam type (homogeneous dam, core wall dam, concrete face rockfill dam), failure mode (overtopping, seepage failure), erosion resistance of dam materials, etc.

[0005] There are mainly two problems with many previous statistical regression expressions for the peak discharge of breach: 1) The selected parameters are simple, but the dimensions of the expressions are inconsistent and lack clear physical meanings; 2) The dimensions of the expressions are consistent, but the selected parameters are difficult to obtain, such as the reservoir capacity or water level during dam break, the reservoir capacity or water depth above the bottom of the breach during dam break, etc. These parameters are difficult to obtain when predicting the peak discharge of dam break.

[0006] In view of this, the inventor expects to provide a method for predicting the peak discharge of overtopping dam break of earth-rock dams. Summary of the Invention

[0007] The purpose of the present invention is to overcome the above problems existing in the traditional technology, provide a method for predicting the peak discharge of overtopping dam break of earth-rock dams, design a prediction expression for the peak discharge of the breach, and the parameters of the expression have clear physical meanings and are easy to obtain.

[0008] To achieve the above technical objectives and reach the above technical effects, the present invention is realized through the following technical solutions:

[0009] The present invention provides a method for predicting the peak discharge of overtopping dam break of earth-rock dams, including the following steps:

[0010] S1. Collect data on the water level - area - capacity curve of the reservoir to be predicted, the elevation of the dam crest, and the elevation of the reservoir bottom at the dam site section;

[0011] S2. According to the elevation of the dam crest and the water level - capacity curve, obtain the reservoir capacity by linear interpolation, and subtract the elevation of the reservoir bottom at the dam site section from the elevation of the dam crest to obtain the maximum dam break height;

[0012] S3. According to the water level - area curve, convert the water level to a false height with the elevation of the reservoir bottom as the reference plane, and fit it with a power function to obtain the power coefficient;

[0013] S4. According to the data in the database of dam break cases, obtain the discharge coefficient by linear fitting;

[0014] S5. Predict the peak discharge of reservoir dam break according to the calculation formula for the peak discharge of the breach.

[0015] Further, the reservoir capacity corresponding to the elevation of the dam crest can determine the water volume that can cause dam break, denoted as the reservoir capacity W max ; the difference between the elevation of the dam crest and the elevation of the reservoir bottom at the dam site section can determine the head of the breach, denoted as the maximum dam break height H max ; the peak discharge of dam break is related to the reservoir capacity W max and the maximum dam break height H max , and W max / H max has the physical meaning of the average water surface area of the reservoir.

[0016] Furthermore, the breach discharge of the reservoir dam is generally calculated using the broad-crested weir formula, and the expression is as follows:

[0017]

[0018] In the formula, Q b is the breach discharge; m 0 is the discharge coefficient; g is the acceleration due to gravity; B is the net width of the breach; H is the head of the breach;

[0019] According to the broad-crested weir formula Therefore, it is defined that is the head parameter.

[0020] Furthermore, W max / H max has the physical meaning of the average water surface area of the reservoir, while has the meaning of the maximum net width of the breach. According to the broad-crested weir formula, Therefore, it is defined that is the net width parameter of the breach.

[0021] Furthermore, the relationship between the reservoir water level and area generally shows a power function relationship, and the expression is as follows:

[0022] H = aA m (2)

[0023] In the formula, H is the reservoir water level; A is the water surface area; a and m are coefficients that can be obtained by fitting the reservoir water level - area curve;

[0024] According to the water level - area relationship curve, the reservoir storage capacity W max corresponding to H max can be obtained by integration, and the expression is as follows:

[0025]

[0026] In the formula, h is the water depth;

[0027] Substituting Equation (2) into Equation (3) and integrating, we get:

[0028]

[0029] The breach discharge is closely related to the gravitational potential energy of the reservoir water storage. The expression for the gravitational potential energy of the reservoir water storage is as follows:

[0030]

[0031] In the formula, ρ is the density of water;

[0032] Substituting Equation (2) into Equation (5) and integrating, we get:

[0033]

[0034] Weighted head H w is defined as the ratio of the gravitational potential energy of the reservoir storage volume to its weight, and the expression is as follows:

[0035]

[0036] Define the reservoir shape parameter r as the weighted head H w and H max The ratio is a dimensionless parameter, and the expression is as follows:

[0037]

[0038] Furthermore, by integrating the head parameter and the breach net width parameter, a comprehensive influence function K of the peak breach discharge is proposed, and the expression is as follows:

[0039]

[0040] Furthermore, in addition, Q b,max is also related to factors such as the acceleration of gravity g, the density of water ρ, the viscosity of water η, and the surface tension σ. The expression of Q is derived through dimensional analysis b,max ;

[0041] The dimensional analysis based on the π theorem is as follows:

[0042] The peak breach discharge Q b,max can be written in the following general functional form:

[0043] Q b,max = r β f(K, ρ, g, η, σ) (10)

[0044] In the formula, β is a coefficient that can be obtained through data fitting.

[0045] Furthermore, there are 5 independent variables in formula (10). Selecting K, ρ, and g as the basic physical quantities, the dimensionless numbers are respectively:

[0046]

[0047] According to the π theorem, the dimensionless number relationship representing the peak breach discharge can be composed of π, π 4 、π 5 :

[0048]

[0049] In the formula, ν = η / ρ is the kinematic viscosity;

[0050] Let the discharge coefficient Then there is:

[0051]

[0052] The expression in formula (13) comprehensively considers the influence of water head and reservoir shape on the peak discharge of the breach, has harmonious dimensions, clear physical meaning, and the parameters are easy to obtain, and the discharge coefficient m is given. 0 The relational expression of influencing factors.

[0053] The beneficial effects of the present invention are as follows:

[0054] 1. The physical meaning of the predicted index of the dam-break peak discharge proposed by the present invention is clear, has a significant linear correlation characteristic with the dam-break peak discharge, the index is easy to obtain, and can be used as a trend analysis index to test the rationality of the calculation results. It should be noted that the discharge coefficient m of the present invention 0 is obtained by fitting with measured data. In subsequent work, m 0 can be obtained through experiments. The dimensional analysis result of the present invention clarifies its influencing factors and points out the direction for the experiments.

[0055] 2. Based on variables such as the reservoir capacity W max of the reservoir, the maximum dam-break height H max and the power coefficient of the water level - area curve, etc., the present invention first proposes the influencing parameters of the peak discharge of overtopping dam-break of earth-rock dams, which are respectively the water head parameter the net width parameter of the breach the reservoir shape parameter and proposes the comprehensive influence function of the peak discharge of the breach

[0056] 3. Based on the π theorem, the present invention deduces the expression of the peak discharge of the breach: This formula comprehensively considers the influence of water head and reservoir shape on the peak discharge of the breach, has harmonious dimensions, clear physical meaning, and the parameters are easy to obtain, and the discharge coefficient m is given. 0 The relational expression of influencing factors.

[0057] 4. The correlation between the predicted result of the peak discharge of the breach proposed by the present invention and the actual value is good, and the square of the correlation coefficient reaches 0.8296. The method of the present invention can accurately and quickly predict the peak discharge of overtopping dam-break of earth-rock dams, provide technical support for reservoir flood control and emergency rescue and the evacuation of downstream people, and has a very broad application and promotion prospect.

[0058] Of course, it is not necessary for any product implementing the present invention to achieve all the above advantages simultaneously. Brief Description of the Drawings

[0059] To more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0060] Figure 1 For Q b,max Schematic diagram of the correlation between the actual value and the predicted value. Specific embodiments

[0061] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0062] This embodiment provides a method for predicting the peak discharge of overtopping failure of an earth-rock dam, including the following steps:

[0063] S1. Collect data on the water level - area - storage capacity curve, crest elevation, and bottom elevation of the dam site section of the reservoir to be predicted;

[0064] S2. According to the crest elevation and the water level - storage capacity curve, obtain the reservoir storage capacity through linear interpolation, and subtract the bottom elevation of the dam site section from the crest elevation to obtain the maximum dam - break height;

[0065] S3. According to the water level - area curve, convert the water level to a false height with the bottom elevation as the reference plane, and fit it with a power function to obtain the power coefficient;

[0066] S4. According to the data in the database of dam - break cases, obtain the discharge coefficient by linear fitting;

[0067] S5. Predict the peak discharge of the reservoir dam - break according to the formula for calculating the peak discharge of the breach.

[0068] In this embodiment, the reservoir storage capacity corresponding to the crest elevation can determine the water volume that can cause dam - break, denoted as the reservoir storage capacity W max ; the difference between the crest elevation and the bottom elevation of the dam site section can determine the head of the breach, denoted as the maximum dam - break height H max ; the peak discharge of the dam - break is related to the reservoir storage capacity W max and the maximum dam - break height H max , and W max / H max has the physical meaning of the average water surface area of the reservoir.

[0069] (1) Head parameter

[0070] The breach discharge of a reservoir dam is generally calculated using the broad-crested weir formula, and the expression is as follows:

[0071]

[0072] In the formula, Q b is the breach discharge; m 0 is the discharge coefficient; g is the acceleration due to gravity; B is the net width of the breach; H is the head of the breach.

[0073] According to the broad-crested weir formula Therefore, it is defined that is the head parameter.

[0074] (2) Net width of breach parameter

[0075] W max / H max has the physical meaning of the average water surface area of the reservoir, while has the meaning of the maximum net width of the breach. According to the broad-crested weir formula, Therefore, it is defined that is the net width of breach parameter.

[0076] (3) Reservoir shape parameter

[0077] The relationship between reservoir water level and area generally shows a power function, and the expression is as follows:

[0078] H = aA m (2)

[0079] In the formula, H is the reservoir water level; A is the water surface area; a and m are coefficients that can be obtained by fitting the reservoir water level - area curve.

[0080] According to the water level - area relationship curve, the reservoir storage capacity W max corresponding to H max can be obtained by integration, and the expression is as follows:

[0081]

[0082] In the formula, h is the water depth.

[0083] Substituting Equation (2) into Equation (3) and integrating, we get:

[0084]

[0085] The breach discharge is closely related to the gravitational potential energy of the reservoir water storage. The expression of the gravitational potential energy of the reservoir water storage is as follows:

[0086]

[0087] In the formula, ρ is the density of water.

[0088] Substituting Equation (2) into Equation (5) and integrating gives:

[0089]

[0090] Weighted head H w is defined as the ratio of the gravitational potential energy of the reservoir storage volume to its weight, and the expression is as follows:

[0091]

[0092] Define the reservoir shape parameter r as the ratio of the weighted head H w to H max which is a dimensionless parameter, and the expression is as follows:

[0093]

[0094] (4) Comprehensive influence function of the peak discharge at the breach

[0095] By integrating the head parameter and the breach net width parameter, a comprehensive influence function K of the peak discharge at the breach is proposed, and the expression is as follows:

[0096]

[0097] In addition, Q b,max is also related to factors such as the gravitational acceleration g, the density ρ of water, the viscosity η of water, and the surface tension σ. The expression of Q is derived through dimensional analysis b,max .

[0098] The dimensional analysis based on the π theorem is as follows:

[0099] The peak discharge Q at the breach b,max can be written as the following general functional form:

[0100] Q b,max = r β f(K, ρ, g, η, σ) (10)

[0101] In the formula, β is a coefficient that can be obtained through data fitting.

[0102] There are 5 independent variables in the above formula. Selecting K, ρ, and g as the basic physical quantities, the dimensionless numbers are respectively:

[0103]

[0104] According to the π theorem, the dimensionless number relationship representing the peak discharge at the breach can be composed of π, π 4 , π 5 :

[0105]

[0106] where ν = η / ρ is the kinematic viscosity.

[0107] Let the discharge coefficient Then we have:

[0108]

[0109] The expression of Equation (13) comprehensively considers the influence of the water head and the reservoir shape on the peak discharge of the breach, with dimension harmony, clear physical meaning, easy-to-obtain parameters, and gives the influence factor relationship of the discharge coefficient m 0

[0110] The specific application of this embodiment is as follows: Using the data of the domestic and foreign earth-rock dam breach case databases (see Table 1), according to the reservoir capacity data corresponding to different water levels and Equation (4), the a and m values of the water level - area curves of each reservoir are obtained by using the non-linear fitting method, and then the reservoir shape parameter r of each reservoir is calculated according to Equation (8). Based on the actual Q b,max , W max , H max values, and the calculated reservoir shape parameter r of each reservoir, the discharge coefficient m 0 and the power coefficient β are obtained by using the non-linear fitting method according to Equation (13), and then the predicted value of Q b,max is calculated. The correlation relationship between the actual value and the predicted value of Q b,max is shown in Figure 1 .

[0111] Table 1 Homogeneous dam breach case database

[0112]

[0113]

[0114]

[0115] Case studies show that under the condition of overtopping dam breach, the correlation relationship between the predicted value and the actual value of the peak discharge Q b,max is relatively good, the square of the correlation coefficient reaches 0.8296, and the trend is significant.

[0116] The above analysis shows that the peak discharge prediction index proposed by the present invention has clear physical meaning, has a significant linear correlation characteristic with the peak discharge of the dam breach, the index is easy to obtain, and can predict the peak discharge of the overtopping earth-rock dam breach. It should be noted that the discharge coefficient m 0 of the present invention is obtained by fitting with measured data. In subsequent work, m 0 can be obtained through experiments. The dimensional analysis result of the present invention clarifies its influencing factors and points out the direction for the experiments.

[0117] ​Implementation conclusions

[0118] (1) Based on variables such as reservoir storage capacity W max , maximum dam-break height H max , power coefficient of water level - area curve, etc., the influencing parameters of the peak discharge of overtopping dam-break of earth-rock dams are proposed for the first time, which are head parameter net width parameter of breach reservoir shape parameter The comprehensive influence function of peak discharge of breach is proposed

[0119] (2) Based on the π theorem, the expression of peak discharge of breach is derived: This formula comprehensively considers the influence of head and reservoir shape on the peak discharge of breach, with harmonious dimensions, clear physical meaning, and easy-to-obtain parameters, and gives the relational expression of influencing factors of discharge coefficient m 0 .

[0120] (3) Case studies show that the predicted results of the peak discharge of breach proposed by the present invention have a good correlation with the actual values, and the square of the correlation coefficient reaches 0.8296. The method of the present invention can accurately and quickly predict the peak discharge of overtopping dam-break of earth-rock dams, providing technical support for reservoir flood control and emergency rescue and the evacuation of downstream people, and has a very broad application and promotion prospect.

[0121] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor limit the invention to the specific embodiments. Obviously, many modifications and changes can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principle and practical application of the present invention, so that those skilled in the relevant technical field can well understand and utilize the present invention. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A method for predicting the peak flow of earth-rock dam overtopping and dam-break, characterized in that: The steps include: S1. Collect the predicted target reservoir water level-area-capacity curve, dam top elevation, and dam site section reservoir bottom elevation data; S2. According to the dam crest elevation and the water level-storage capacity curve, the reservoir capacity is obtained by linear interpolation, and the maximum dam break height is obtained by subtracting the reservoir bottom elevation at the dam site section from the dam crest elevation; S3, according to the water level-area curve, the water level is converted into a false height with the reservoir bottom elevation as the reference surface, and a power function is used to fit it to obtain a power coefficient; S4. According to the data of the dam breach case database, the discharge coefficient is obtained by linear fitting method; S5. Predict the reservoir dam breach peak flow rate based on the breach peak flow rate calculation formula.

2. The method for predicting the peak flow of earth-rock dam overtopping and dam-break according to claim 1 is characterized in that: The reservoir capacity corresponding to the dam crest elevation can determine the amount of water that can break the dam, which is recorded as the reservoir capacity W max The difference between the dam crest elevation and the dam bottom elevation can determine the breach head, which is recorded as the maximum dam breach height H max ; Dam break peak flow and reservoir capacity W max and the maximum dam break height H max About W max / H max It has the physical meaning of the average water surface area of ​​the reservoir.

3. The method for predicting the peak flow of earth-rock dam overtopping and dam-break according to claim 2 is characterized in that: The reservoir dam breach flow is generally calculated using the wide crest weir formula, which is expressed as follows: In the formula, Q b is the breach flow; m0 is the flow coefficient; g is the gravity acceleration; B is the net width of the breach; H is the breach head; According to the broad crested weir formula So define is the water head parameter.

4. The method for predicting the peak flow of earth-rock dam overtopping and dam-break according to claim 3 is characterized in that: W max / H max It has the physical meaning of the average water surface area of ​​the reservoir, and It has the meaning of the maximum clear width of the breach. According to the formula of wide crested weir, So define It is the net width parameter of breach.

5. The method for predicting the peak flow rate of earth-rock dam overtopping and dam-break according to claim 4 is characterized in that: The relationship between reservoir water level and area is generally a power function, expressed as follows: H=aA m (2) In the formula, H is the reservoir water level; A is the water surface area; a and m are coefficients, which can be obtained by fitting the reservoir water level-area curve; According to the water level-area relationship curve, H can be obtained by integration. max The corresponding reservoir capacity W max , the expression is as follows: Where h is the water depth; Substituting formula (2) into formula (3), we can get: The breach flow is closely related to the gravitational potential energy of the reservoir water storage capacity. The gravitational potential energy expression of the reservoir water storage capacity is as follows: Where ρ is the density of water; Substituting formula (2) into formula (5), we can get: Weighted head H w It is defined as the ratio of the gravitational potential energy of the water storage in the reservoir to its weight, expressed as follows: Define the reservoir shape parameter r as the weighted hydraulic head H w With H max The ratio is a dimensionless parameter, expressed as follows:

6. The method for predicting the peak flow rate of earth-rock dam overtopping and dam-break according to claim 5 is characterized in that: The head parameter and the breach net width parameter are integrated to propose the comprehensive influence function K of the breach peak flow, which is expressed as follows:

7. The method for predicting the peak flow rate of overtopping and dam-break of earth-rock dam according to claim 6, characterized in that: Q b,max It is also related to factors such as gravitational acceleration g, water density ρ, water viscosity η and surface tension σ. Q can be deduced through dimensional analysis. b,max Expression of Based on the dimensional analysis of the π theorem, the peak flow rate Q b,max It can be written as the following general function: Q b,max =r β f(K,ρ,g,η,σ) (10) In the formula, β is the coefficient, which can be obtained by data fitting.

8. The method for predicting the peak flow rate of overtopping and dam-break of earth-rock dam according to claim 7, characterized in that: There are five independent variables in formula (10). K, ρ, and g are selected as basic physical quantities, and the numbers of dimension one are: According to the π theorem, π, π4, and π5 can be used to form a dimensionless numerical relationship to characterize the peak flow of the breach: Where, ν = η / ρ is the kinematic viscosity; Let flow coefficient So we have:

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