Method for predicting flood peak flow of earth-rock dam overtopping breach

Abstract

This invention discloses a method for predicting the peak flow of a breach in an earth-rock dam, comprising the following steps: Step 1: Collect basic data; Step 2: Determine the initial breach parameters and calculation time step; Step 3: Calculate the breach flow at the dam crest; Step 4: Calculate the normal water depth at the breach; Step 5: Calculate the water depth in the velocity-increased zone at the breach; Step 6: Calculate the average flow velocity at the breach; Step 7: Calculate the average shear force of the flow at the bottom and sides of the breach; Step 8: Calculate the erosion velocity at the bottom and sides of the breach; Step 9: Calculate the average shear force of the flow at the downstream toe of the dam; Step 10: Calculate the erosion velocity at the downstream toe of the dam; Step 11: Calculate the dam stability coefficient within the breach area; Step 12: Adjust the terrain and perform corresponding calculations; Step 13: Output the peak flow of the breach. This invention overcomes the shortcomings of previous methods, as the calculation results are not sensitive to the initial breach size, thus improving the accuracy of the calculation results.

Description

Technical Field

[0001] This invention relates to the field of water conservancy engineering, and more particularly to the field of flood control and disaster reduction technology. Background Technology

[0002] Humans construct various types of dams to transform and utilize nature, achieving significant economic and social benefits in areas such as flood control, power generation, navigation, water supply, and soil erosion control. To date, my country has built nearly 100,000 dams of various types (the International Commission on Large Dams defines a dam as one with a height exceeding 15 meters, or a reservoir capacity exceeding 3 million cubic meters and a height exceeding 5 meters). Earth-rock dams account for the vast majority of these, exceeding 90% of the total number of dams built nationwide.

[0003] In addition, in order to control soil erosion, my country has built a large number of silt-retention dams. According to statistics, there are currently 58,800 silt-retention dams in the Loess Plateau region. These dams are generally relatively small in size and have a small reservoir capacity, and most of them are homogeneous earth dam structures.

[0004] Due to unpredictable factors, if the dam collapses, it will cause incalculable losses to the lives and property of people downstream, and the dam will also cease to function.

[0005] Statistics show that from 1954 to 1990 alone, 3,242 dams collapsed in my country, of which earth-rock dams accounted for more than 90%, causing significant losses to the country and its people. For example, in 1975, the collapse of the Banqiao and Shimantan reservoirs caused severe flooding in 26 counties (cities), 425 townships, and 8,997 administrative villages, affecting 10.295 million people.

[0006] Furthermore, due to their low design and construction standards, silt-retention dams are prone to severe flooding caused by excessive rainfall, making them highly susceptible to collapse. This can lead to a chain reaction of dam failures, resulting in significant loss of life and property downstream. In 1988, torrential floods in Shanxi Province caused varying degrees of flooding in 98 counties, destroying over 4,000 silt-retention dams, affecting an area of ​​over 600,000 hectares, causing 295 deaths and direct economic losses of 780 million yuan. In 1993, a sudden torrential rainstorm centered on Yan'an City damaged 1,459 silt-retention dams and destroyed 239 highway bridges and culverts, affecting six surrounding counties (cities) and causing direct economic losses of 160 million yuan.

[0007] Calculating the peak discharge of an earth-rock dam breach is an indispensable task in the design of various downstream engineering projects and downstream flood control. It serves as the basis for assessing the impact of the breached water flow on the downstream area and the potential losses, as well as for formulating downstream protection plans. Furthermore, it is crucial for facilitating preventative measures and the development of emergency response plans. Therefore, more accurate calculation of the maximum discharge of an earth-rock dam breach is of paramount importance.

[0008] There are several existing models for predicting earth-rock dam failure, which can be mainly divided into three categories:

[0009] The first type is the parametric model. This type of model is derived by collecting and statistically summarizing data from dam break examples and using regression analysis to obtain some empirical expressions (formulas). Basically, it calculates the breach characteristics (breach width and depth, etc.), peak flow, and dam break duration by inputting parameters such as reservoir capacity, initial water level, and dam height.

[0010] The second category is numerical models. These models mainly use the Saint-Venant equation or shallow water equation to describe the characteristics of the breach flow. Combined with the sediment transport equation and the slope stability equation, they can ultimately determine the important parameters of earth-rock dam failure, such as the peak flow of the breach, the duration of the breach, and the morphological characteristics of the breach.

[0011] The third type is the mathematical model. This type of model generally assumes the initial breach shape (rectangular, trapezoidal, triangular, etc.), uses weir flow or gate outflow to calculate the breach outflow, and the breach develops in a certain way. Through calculation and simulation, the main parameters of earth-rock dam failure can be obtained.

[0012] Among the three models mentioned above, the parametric model is simple and quick, but its applicability is poor, and it may produce errors of magnitude when calculating the peak flow of a dam break.

[0013] Numerical models can accurately simulate the flow of water during dam breaks; however, their calculations require a large amount of measured data of the dam body and are time-consuming, making them less applicable in emergency situations.

[0014] Compared to the aforementioned parametric models, mathematical models offer higher computational accuracy and faster, more convenient computation speed compared to numerical models. Mathematical models simplify the simulation of dam-break water flow, thus saving considerable computation time. However, previous mathematical models have oversimplified the calculation of breach water flow, and the calculation of the breach bottom and lateral widening based on this may cause significant errors in calculating the peak flow of the dam-break flood. Summary of the Invention

[0015] The purpose of this invention is to provide a model for predicting the peak flow of an earth-rock dam in the event of a breach. This model improves the calculation method for the flow and erosion at the breach crest and considers the stability of the dam body within the breach area. Compared with previous models, this invention is closer to the actual physical process of a dam breach, overcoming the shortcomings of previous numerical models that require a large amount of measured data of the dam body and are time-consuming. At the same time, it improves the accuracy of the calculation results compared with previous mathematical model calculation methods. The calculation results are not sensitive to the initial breach size and have better applicability. This invention can provide important technical support for assessing the impact of earth-rock dam breaches on downstream areas and for developing emergency response plans.

[0016] To achieve the above objectives, the method for predicting the peak flow of an earth-rock dam overtopping breach according to the present invention is carried out according to the following steps:

[0017] Step 1: Collect the basic parameters of the earth-rock dam for which failure is to be calculated;

[0018] Step 2: Determine the initial breach parameters at the dam crest and the calculation time step;

[0019] Step 3: Calculate the breach flow at the dam crest;

[0020] Step 4: Calculate the normal water depth at the breach crest of the dam;

[0021] Step 5: Calculate the water depth in the area where the flow velocity increases at the dam crest breach;

[0022] Step 6: Calculate the average flow velocity of the water flow at the breach crest of the dam;

[0023] Step 7: Calculate the average shear force of the water flow at the bottom and on both sides of the breach at the top of the dam;

[0024] Step 8: Calculate the erosion rate at the bottom and sides of the breach in the dam crest;

[0025] Step 9: Calculate the average shear force of the water flow at the downstream toe of the dam;

[0026] Step 10: Calculate the erosion rate at the downstream toe of the dam;

[0027] Step 11: Calculate the dam stability coefficient within the breach area;

[0028] Step 12: Adjust the terrain and perform the corresponding calculations;

[0029] Step 13: Output the peak flow rate of the dam break

[0030] In step 1, the basic parameters of the earth-rock dam collected include the dam axis length L. d0 L d0 The unit is meters, and the initial dam crest width is B. d0 (Unit: meters), Height H from dam foundation to dam crest d0 (Unit: meters), Initial slope coefficient of upstream dam body (m) du(0) (dimensionless coefficient), initial slope coefficient of downstream dam body m dd(0) (dimensionless coefficient), median particle size d of dam material 50 (Unit: millimeters), initial reservoir capacity V0 (unit: cubic meters), initial water level h v(0) (Unit: meters) and reservoir capacity curve, as well as the upstream inflow process.

[0031] In step 2, the initial breach at the dam crest is defined as a rectangle based on existing mathematical models, with an initial breach width of B. t0 (Unit: meters), initial breach depth: h t0(Unit: meters); B t0 The length L of the dam axis is less than or equal to d0 h takes values ​​within the range of 1%. t0 less than or equal to H d0 Values ​​are taken within 1% of the meter. The calculation time step is Δt, in seconds.

[0032] In step 3, the water depth upstream of the dam breach at time t is H. (t) (Unit: meters). The depth of the breach at time t is h. (t) (Unit: meters), the width of the breach at time t is B. (t) (Unit: meters). Time t represents the time up to a certain moment in the calculation, t = nΔt, where n is an integer, n = 0, 1, 2, 3..., and Δt is the calculation time step Δt (unit: seconds). When n = 0, it is the initial state.

[0033] The flow rate Q at the breach at time t is... (t) Calculate using Formula 1:

[0034] Formula 1:

[0035] In the formula, Q (t) Let m be the flow rate at the dam crest breach at time t, in cubic meters per second; m is the flow coefficient, a dimensionless empirical coefficient obtained from the textbook "Hydraulics"; B (t) Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 for calculation; H (t) Let H be the water depth upstream of the dam breach at time t, in meters, and let H be the initial water depth. v(0) -h t0 When t > 0, use formula 33 for calculation; g is the acceleration due to gravity, in meters per second. 2 .

[0036] In step 4, the normal water depth h at time t is... z(t) (Unit: meters) Calculated using Formula 2:

[0037] Formula 2:

[0038] In the formula, h z(t) At time t, the normal water depth at the breach crest of the dam is expressed in meters. H is the velocity coefficient, which is a dimensionless empirical coefficient obtained from the textbook "Hydraulics"; (t) Let H be the water depth upstream of the dam breach at time t, in meters, and let H be the initial water depth. v(0) -h t0 When t > 0, use formula 33 for calculation.

[0039] In step 5, the water depth h in the area where the flow velocity of the breach at time t increases is... c(t) (Unit: meters) Calculated using Formula 3:

[0040] Formula 3:

[0041] Among them, h z(t) Let F be the normal water depth at time t, expressed in meters, calculated using formula 2; r(t) Let be the Froude number of the breach flow at time t, which is a dimensionless parameter and is calculated using Formula 4:

[0042] Formula 4:

[0043] In the formula: Q (t) B represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. (t) Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 to calculate; h (t) Let h be the depth of the breach at time t, in meters, with an initial value of h. t0 When t > 0, use formula 30 for calculation; g is the acceleration due to gravity, in meters per second. 2 .

[0044] In step 6, the length L of the breach at time t is... B(t) Calculate using Formula 5:

[0045] Formula 5:

[0046] In the formula, L B(t) Let be the length of the breach at time t, in a horizontal direction perpendicular to the dam axis, expressed in meters. The initial value is... B d0 h represents the initial dam crest width in meters. (t) Let h be the depth of the breach at time t, in meters, with an initial value of h. t0 When t > 0, use formula 30 for calculation; m du(t) Let m be the upstream slope coefficient of the dam body at time t, which is a dimensionless coefficient. The upstream slope remains constant during the dam failure process. du(t) Equal to the original slope coefficient m du(0) m dd(t) Let be the downstream slope of the dam at time t, and be a dimensionless coefficient. The initial value is the initial downstream slope coefficient m. dd(0) When t > 0, use formula 34 for calculation.

[0047] The average water depth h at time t of the dam crest breach is calculated using Formula 6. a(t) (Unit: meters)

[0048] Formula 6:

[0049] Where: h z(t) The normal water depth at the crest of the dam breach is in meters, calculated using formula 2; L B(t) Let h be the length of the breach at time t, in meters, calculated using formula 5; c(t) The water depth in the zone where the flow velocity increases at the dam crest breach is expressed in meters and is calculated using Formula 3.

[0050] The average flow velocity u at time t of the breach at the dam crest is calculated using Formula 7. a(t) (Unit: meters per second):

[0051] Formula 7:

[0052] In the formula, Q (t) B represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. (t) Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 to calculate; h a(t) The average water depth of the breach is expressed in meters and is calculated using Formula 6.

[0053] In step 7, the average shear force τ at the bottom of the breach at time t is... b(t) (Unit: Newtons / square meter) Calculated using Formula 8:

[0054] Formula 8:

[0055] In the formula, ρ is the density of water, in kilograms per cubic meter, obtained from the textbook "Hydraulics"; u a(t) Let C be the average flow velocity of the breached water at time t, expressed in meters per second, calculated using formula 7; f(t) The friction coefficient of the water flow at time t is a dimensionless coefficient, calculated using formula 9:

[0056] Formula 9:

[0057] In the formula: Re (t) Let t be the Reynolds number of the breached water flow at time t, which is a dimensionless number and is calculated using Formula 10.

[0058] Formula 10:

[0059] In the formula: u a(t) R represents the average flow velocity of the breached water at time t, expressed in meters per second, calculated using formula 7. (t) Let B be the hydraulic radius of the breach at time t, in meters, approximately equal to B. (t)B (t) Let t be the width of the breach at the dam crest, in meters; v be the kinematic viscosity of water, in meters. 2 / second, obtained from the textbook "Hydraulics".

[0060] The average shear force τ acting on the two sidewalls of the breach at time t w(t) Calculate using Formula 11:

[0061] Formula 11:

[0062] In the formula: C f(t) ρ is the coefficient of friction of the water flow at time t, calculated using formula 9; ρ is the density of water, in kilograms per cubic meter, obtained from the textbook "Hydraulics"; u a(t) Let t be the average flow velocity of the water at the breach at the dam crest, in meters per second, calculated using formula 7.

[0063] In step 8, the scour depth Δh at the bottom of the breach at time t within the time interval Δt is... (t) Calculate using formula 12:

[0064] Formula 12: Δh (t) =k d (τ b(t) -τ c ) δ Δt;

[0065] Where: Δh (t) τ is the scour depth at the bottom of the breach on the dam crest within time Δt, in meters; Δt is the calculation time step, in seconds; b(t) denoted as t, representing the average shear force of the water flow at the bottom of the breach at time t, expressed in N / m², calculated using formula 8; δ represents the scour index of the dam material, a dimensionless coefficient, taken as 1.0 for cohesive soil and 1.5 for non-cohesive soil. The material properties of the dam are determined by on-site sampling by staff, which is then sent to a geotechnical laboratory for particle size analysis; k d The erosion velocity coefficient of the dam material is expressed in meters per second and is calculated using formula 13.

[0066] Formula 13:

[0067] In formula 12, τ c The critical shear force for dam material activation is expressed in Newtons per square meter (N / m²) and is calculated using formula 14.

[0068] Formula 14:

[0069] In the formula: d 50 The median particle size of the dam material is expressed in millimeters.

[0070] The width of the collapse of the sidewalls on both sides of the dam crest breach within the time interval Δt at time t is ΔB. (t) Calculate using Formula 15:

[0071] Formula 15: ΔB (t) =βk d (τ w(t) -τ c ) δ Δt

[0072] In the formula: ΔB (t) τ is the width of the collapsed sidewalls on both sides of the dam crest breach within time Δt, in meters; Δt is the calculation time step, in seconds; β is an adjustment coefficient, a dimensionless coefficient, determined according to the collapse mode on both sides of the breach. This invention addresses the cantilever failure mode of the collapse mode on both sides of the breach, and β is set to 1.0; w(t) τ is the average shear force exerted by the water flow at time t on both sides of the breach at the dam crest, expressed in Newtons per square meter (N / m²), calculated using formula 11; c The critical shear force for dam material activation is expressed in Newtons per square meter and is calculated using Formula 14. δ is the scour index of dam material, a dimensionless coefficient. For cohesive soil, δ is taken as 1.0, and for non-cohesive soil, δ is taken as 1.5. The properties of dam material are determined by on-site sampling by staff and sent to the geotechnical laboratory for determination.

[0073] In step 9, the flow velocity v at the downstream toe of the dam at time t is... p(t) (Unit: meters per second) Calculated using Formula 16:

[0074] Formula 16:

[0075] In the formula: g is the acceleration due to gravity, with units of meters per second. 2 H d0 The height from the dam foundation to the dam crest, in meters, is obtained from the data collected in step 1; h (t) Let h be the depth of the breach at time t, in meters, with an initial value of h. t0 When t > 0, formula 30 is used for calculation; ξ2 is the friction loss coefficient along the flow path, which is a dimensionless coefficient obtained from the textbook "Hydraulics"; V c(t) Let t be the average flow velocity in the area where the flow velocity increases at the breach at the dam crest, expressed in meters per second, calculated using formula 17.

[0076] Formula 17:

[0077] In the formula: Q (t) Let h be the breach flow rate at time t, in cubic meters per second, calculated using formula 1; c(t) B represents the water depth in the zone where the flow velocity increases at time t, expressed in meters, calculated using formula 3. (t)Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 for calculation;

[0078] The average shear force τ at the downstream slope toe of the dam at time t is calculated using Formula 18. p(t (Unit: Newtons per square meter)

[0079] Formula 18:

[0080] In the formula: ρ is the density of water, in kilograms per cubic meter; V p(t) The downstream slope toe velocity of the water flow is expressed in meters per second and is calculated using formula 16; C fp(t) Let t be the friction coefficient of the downstream slope toe of the dam at time t. It is a dimensionless coefficient and is calculated using formula 19.

[0081] Formula 19:

[0082] In the formula: Re p(t) Let t be the Reynolds number of the downstream slope toe of the dam at time t, which is a dimensionless number and is calculated using formula 20.

[0083] Formula 20:

[0084] In the formula: V p(t) Let h be the flow velocity at the downstream toe of the dam at time t, in meters per second, calculated using formula 16; c(t) Let t be the water depth in the zone where the flow velocity increases at the dam crest breach, in meters, calculated using Formula 3; v is the kinematic viscosity of water, in meters. 2 / second, obtained from the textbook "Hydraulics".

[0085] In step 10, the erosion distance ΔH at the downstream toe of the dam body during the time interval Δt at time t is... p(t) (Unit: meters) Calculate using formula 21:

[0086] Formula 21: ΔH p(t) =k d (τ p(t) -τ c ) δ Δt;

[0087] In the formula: Δt is the calculation time step, in seconds; k d The erosion velocity coefficient of the dam material, in meters per second, is calculated using formula 13; τ p(t) τ is the average shear force of the water flow at the downstream toe of the dam at time t, expressed in N / m², calculated using formula 18; cThe critical shear force for dam material activation is expressed in Newtons per square meter and is calculated using Formula 14. δ is the scour index of dam material, a dimensionless coefficient. For cohesive soil, δ is taken as 1.0, and for non-cohesive soil, δ is taken as 1.5. The properties of dam material are determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory for determination.

[0088] In step 11, the dam stability coefficient S within the breach area at time t is... c(t) The dimensionless coefficient is calculated using formula 22:

[0089] Formula 22:

[0090] In the formula: when S c(t) When S ≥ 1.0, the dam body within the breach area is stable, and a sudden dam failure will not occur; when S c(t) When the value is less than 0, the dam body within the breach area will experience slippage and instability, leading to a sudden dam failure.

[0091] In Formula 22, F w(t) Let t be the water pressure exerted by the upstream water on the dam body within the breach area at time t, in Newtons, calculated using formula 23:

[0092] Formula 23: F w(t) =0.5γ w B (t) (H d0 -h (t) (H) d0 -h (t) +2H (t) );

[0093] In Formula 22, F sb(t) The shear force between the dam body and the dam foundation within the breach area at time t, expressed in Newtons, is calculated using formula 24.

[0094] Formula 24:

[0095] In Formula 22, F sw(t) The shear force between the dam body and the soil on both sides within the breach area at time t, expressed in Newtons, is calculated using formula 25.

[0096] Formula 25:

[0097] In Formula 22, F cb(t) The bond force between the dam body and the dam foundation within the breach area at time t, expressed in Newtons (N), is calculated using formula 26.

[0098] Formula 26: F cb(t) =CB d0 B (t) ;

[0099] In Formula 22, F cw(t) The bond force between the block and both sides of the dam body within the breach area at time t, expressed in Newtons (N), is calculated using formula 27.

[0100] Formula 27: F cw(t) =C(B d0 +L B(t) (H) d0 -h (t) )

[0101] In formulas 22 to 27,

[0102] γ w This is the specific gravity of water, measured in Newtons per cubic meter, with a value of 9.8 × 10⁻⁶. 3 Niu per cubic meter;

[0103] B (t) The width of the breach at time t is in meters.

[0104] H d0 The height from the dam foundation to the dam crest, as determined in step 1, is in meters.

[0105] h (t) The depth of the dam crest breach at time t, determined in step 2, is expressed in meters, with an initial value of h. t0 When t > 0, use formula 30 for calculation;

[0106] H (t) Let H be the water depth upstream of the dam breach at time t, in meters, and let H be the initial water depth. v(0) -h t0 When t > 0, use formula 33 for calculation;

[0107] γ is the wet unit weight of the dam material, expressed in Newtons per cubic meter. It is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory.

[0108] The internal friction angle of the dam material, in degrees, is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory.

[0109] L B(t) Let be the length of the breach at time t, in meters, with an initial value of . When t > 0, use formula 5 for calculation;

[0110] B d0 The initial dam crest width determined in step 1, in meters;

[0111] C represents the bond strength of the dam material, measured in Newtons per square meter (N / m²), which is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory.

[0112] K is a coefficient, a dimensionless coefficient, calculated using formula 28:

[0113] Formula 28:

[0114] In the formula: The internal friction angle of the dam material, in degrees, is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory.

[0115] In step 12, if S c(t) ≥1.0, adjust the terrain, and adjust each parameter as shown in Formulas 29 to 34. Repeat steps 3 to 11.

[0116] ①The width of the breach at the dam crest at time t+Δt is B (t+Δt) (Unit: meters) Calculated using formula 29;

[0117] Formula 29: B (t+Δt) =B (t) +ΔB (t) ;

[0118] In the formula: B (t) ΔB represents the width of the breach at time t, in meters. (t) Let t be the width of the collapse of the sidewalls on both sides of the breach at time t within time Δt, in meters, calculated using formula (15).

[0119] ②Depth h of the breach at time t+Δt (t+Δt) (Unit: meters), calculated using formula 30;

[0120] Formula 30: h (t+Δt) =h (t) +Δh (t) ;

[0121] Where: h (t) Δh represents the depth of the dam crest breach at time t, in meters. (t) Let t be the depth of the breach in the dam crest within the time interval Δt at time t, in meters, calculated using formula (12).

[0122] ③At time t+Δt, the water depth H upstream of the dam crest breach (t+Δt) (Unit: meters) is determined using the following method:

[0123] At time t, the water depth upstream of the dam breach is H. (t) The reservoir capacity is V. (t) (Unit: cubic meters), the change in reservoir capacity ΔV at time t+Δt. (t+Δt) (Unit: cubic meters) Calculate using formula 31;

[0124] Formula 31: ΔV (t+Δt) =(Q(t) -Q in(t) )Δt;

[0125] In the formula: Q (t) Q represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. in(t) Δt represents the inflow rate at time t, in cubic meters per second, determined based on the upstream inflow process; Δt is the calculation time step, in seconds.

[0126] Reservoir capacity V at time t+Δt (t+Δt) (Unit: cubic meters) Calculated using formula 32:

[0127] Formula 32: V (t+Δt) =V (t) -ΔV (t) ;

[0128] Calculate the reservoir capacity V at time t+Δt. (t+Δt) Then, based on the reservoir capacity curve collected in step one, the reservoir water level H at t+Δt can be obtained using linear interpolation. v(t+Δt) (Unit: meters), then the water depth H upstream of the dam breach at time t+Δt is... (t+Δt) Calculate using formula 33;

[0129] Formula 33: H (t+Δt) =H v(t+Δt) -h (t+Δt) ;

[0130] ④ Downstream slope of the dam at time t+Δt (m) dd(t+Δt) Calculate using formula 34;

[0131] Formula 34:

[0132] Where: m dd(t) Let H be the downstream slope of the dam at time t, and H be a dimensionless coefficient. d0 h represents the initial height from the dam foundation to the dam crest, in meters. (t+Δt) Let ΔH be the depth of the breach at time t+Δt, in meters, calculated using formula 30; p(t) The erosion distance at the downstream toe of the dam within time Δt is in meters and is calculated using formula 21.

[0133] If S c(t) If the value is less than 1.0, adjust the terrain and adjust the parameters as shown in Formulas 29 to 34. Then, substitute the adjusted parameters into Formula 1 to complete the calculation.

[0134] The above calculations are repeated until the water erosion capacity can no longer change the dam's topography or the reservoir is emptied; each completion of step 12 constitutes one cycle.

[0135] Step 13: Output the breach flow rate Q during each loop calculation. (t) The maximum value is the peak flow rate of the dam break.

[0136] The present invention has the following advantages:

[0137] Based on previous mathematical model calculation methods, this patent improves the calculation methods for water flow and erosion at the bottom of the breach, and takes into account the stability of the dam body within the breach area. It develops a new prediction model for the peak flow of the overtopping breach of an earth-rock dam. Through a new algorithm and iterative calculation, it overcomes the shortcomings of previous numerical models that require a large amount of measured data of the dam body and are time-consuming. At the same time, it improves the accuracy of the calculation results compared with previous mathematical model calculation methods. The calculation results are not sensitive to the initial breach size, avoiding large errors between the predicted peak flow of the dam breach and the actual value.

[0138] Specifically, this invention improves the calculation methods for calculating the water flow at the dam crest breach and the erosion at the bottom of the breach based on the previous mathematical model theory of earth-rock dam failure. It also considers the stability of the dam body within the breach area and develops a new prediction model algorithm for the peak flow of earth-rock dam overtopping failure. Compared with previous models, this patent is closer to the actual physical process of dam failure, has better applicability and higher accuracy, and can provide important technical support for assessing the impact of earth-rock dam failure on downstream areas and for developing emergency plans.

[0139] Using this invention, and based on the characteristics of the Banqiao Reservoir in China in 1975, the breach flow process curve of the Banqiao Reservoir was calculated. Comparing the calculated results with the measured results: the measured breach duration was approximately 5.5 hours, and the peak breach flow Q... p 78100m 3 / s, the calculated dam breach time is approximately 5.1 hours, and the calculated peak flood flow Q is... p 81863m 3 / s, the calculated peak flow rate of the dam break is 4.82% lower than the measured error, which is more accurate than the calculation results of similar models. Attached Figure Description

[0140] Figure 1 is a flowchart of the model calculation of the present invention;

[0141] Figure 2 This is the water level and storage capacity curve of Banqiao Reservoir;

[0142] Figure 3 This refers to the inflow process of Banqiao Reservoir;

[0143] Figure 4 Calculate the breach flow rate process for the model;

[0144] Figure 5 The process of calculating the breach flow rate for different scenarios. Detailed Implementation

[0145] As shown in Figure 1, the method for predicting the peak flow of an earth-rock dam overtopping breach according to the present invention is carried out according to the following steps:

[0146] Step 1: Collect the basic parameters of the earth-rock dam for which failure is to be calculated;

[0147] Step 2: Determine the initial breach parameters at the dam crest and the calculation time step;

[0148] Step 3: Calculate the breach flow at the dam crest;

[0149] Step 4: Calculate the normal water depth at the breach crest of the dam;

[0150] Step 5: Calculate the water depth in the area where the flow velocity increases at the dam crest breach;

[0151] Step 6: Calculate the average flow velocity of the water flow at the breach crest of the dam;

[0152] Step 7: Calculate the average shear force of the water flow at the bottom and on both sides of the breach at the top of the dam;

[0153] Step 8: Calculate the erosion rate at the bottom and sides of the breach in the dam crest;

[0154] Step 9: Calculate the average shear force of the water flow at the downstream toe of the dam;

[0155] Step 10: Calculate the erosion rate at the downstream toe of the dam;

[0156] Step 11: Calculate the dam stability coefficient within the breach area;

[0157] Step 12: Adjust the terrain and perform the corresponding calculations;

[0158] Step 13: Output the peak flow rate of the dam break.

[0159] In step 1, the basic parameters of the earth-rock dam collected include the dam axis length L. d0 (Unit: meters), Initial dam crest width B d0 (Unit: meters), Height H from dam foundation to dam crest d0 (Unit: meters), Initial slope coefficient of upstream dam body (m) du(0) (dimensionless coefficient), initial slope coefficient of downstream dam body m dd(0) (dimensionless coefficient), median particle size d of dam material 50 (Unit: millimeters), initial reservoir capacity V0 (unit: cubic meters), initial water level h v(0) (Unit: meters) and reservoir capacity curve, as well as the upstream inflow process.

[0160] In step 2, the initial breach at the dam crest is defined as a rectangle based on existing mathematical models, with an initial breach width of B. t0 (Unit: meters), initial breach depth: ht0 (Unit: meters); B t0 The length L of the dam axis is less than or equal to d0 h takes values ​​within 1% of the range (unit: meters). t0 less than or equal to H d0 Values ​​are taken within 1% of the meter. The calculation time step is Δt, in seconds.

[0161] In step 3, the water depth upstream of the dam breach at time t is H. (t) (Unit: meters). The depth of the breach at time t is h. (t) (Unit: meters), the width of the breach at time t is B. (t) (Unit: meters). Time t represents the time up to a certain moment in the calculation, t = nΔt, where n is an integer, n = 0, 1, 2, 3..., and Δt is the calculation time step Δt (unit: seconds). When n = 0, it is the initial state.

[0162] The flow rate Q at the breach at time t is... (t) Calculate using Formula 1:

[0163] Formula 1:

[0164] In the formula, Q (t) Let m be the flow rate at the dam crest breach at time t, in cubic meters per second; m is the flow coefficient, a dimensionless empirical coefficient obtained from the textbook "Hydraulics"; B (t) Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 for calculation; H (t) Let H be the water depth upstream of the dam breach at time t, in meters, and let H be the initial water depth. v(0) -h t0 When t > 0, use formula 33 for calculation; g is the acceleration due to gravity, in meters per second. 2 .

[0165] In step 4, the normal water depth h at time t is... z(t) (Unit: meters) Calculated using Formula 2:

[0166] Formula 2:

[0167] In the formula, h z(t) At time t, the normal water depth at the breach crest of the dam is expressed in meters. H is the velocity coefficient, which is a dimensionless empirical coefficient obtained from the textbook "Hydraulics"; (t) Let H be the water depth upstream of the dam breach at time t, in meters, and let H be the initial water depth. v(0) -h t0 When t > 0, use formula 33 for calculation.

[0168] In step 5, the water depth h in the area where the flow velocity of the breach at time t increases is... c(t) (Unit: meters) Calculated using Formula 3:

[0169] Formula 3:

[0170] Among them, h z(t) Let F be the normal water depth at time t, expressed in meters, calculated using formula 2; r(t) Let be the Froude number of the breach flow at time t, which is a dimensionless parameter and is calculated using Formula 4:

[0171] Formula 4:

[0172] In the formula: Q (t) B represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. (t) Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 to calculate; h (t) Let h be the depth of the breach at time t, in meters, with an initial value of h. t0 When t > 0, use formula 30 for calculation; g is the acceleration due to gravity, in meters per second. 2 .

[0173] In step 6, the length L of the breach at time t is... B(t) Calculate using Formula 5:

[0174] Formula 5:

[0175] In the formula, L B(t) Let be the length of the breach at time t, in a horizontal direction perpendicular to the dam axis, expressed in meters. The initial value is... B d0 h represents the initial dam crest width in meters. (t) Let h be the depth of the breach at time t, in meters, with an initial value of h. t0 When t > 0, use formula 30 for calculation; m du(t) Let m be the upstream slope coefficient of the dam body at time t, which is a dimensionless coefficient. The upstream slope remains constant during the dam failure process. du(t) Equal to the original slope coefficient m du(0) m dd(t) Let be the downstream slope of the dam at time t, and be a dimensionless coefficient. The initial value is the initial downstream slope coefficient m. dd(0) When t > 0, use formula 34 for calculation.

[0176] The average water depth h at time t of the dam crest breach is calculated using Formula 6. a(t) (Unit: meters)

[0177] Formula 6:

[0178] Where: h z(t) The normal water depth at the crest of the dam breach is in meters, calculated using formula 2; L B(t) Let h be the length of the breach at time t, in meters, calculated using formula 5; c(t) The water depth in the zone where the flow velocity increases at the dam crest breach is expressed in meters and is calculated using Formula 3.

[0179] The average flow velocity u at time t of the breach at the dam crest is calculated using Formula 7. a(t) (Unit: meters per second):

[0180] Formula 7:

[0181] In the formula, Q (t) B represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. (t) Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 to calculate; h a(t) The average water depth of the breach is expressed in meters and is calculated using Formula 6.

[0182] In step 7, the average shear force τ at the bottom of the breach at time t is... b(t) (Unit: Newtons / square meter) Calculated using Formula 8:

[0183] Formula 8:

[0184] In the formula, ρ is the density of water, in kilograms per cubic meter, obtained from the textbook "Hydraulics"; u a(t) Let C be the average flow velocity of the breached water at time t, expressed in meters per second, calculated using formula 7; f(t) The friction coefficient of the water flow at time t is a dimensionless coefficient, calculated using formula 9:

[0185] Formula 9:

[0186] In the formula: Re (t) Let t be the Reynolds number of the breached water flow at time t, which is a dimensionless number and is calculated using Formula 10.

[0187] Formula 10:

[0188] In the formula: u a(t) R represents the average flow velocity of the breached water at time t, expressed in meters per second, calculated using formula 7. (t) Let B be the hydraulic radius of the breach at time t, in meters, approximately equal to B.(t) B (t) Let t be the width of the breach at the dam crest, in meters; v be the kinematic viscosity of water, in meters. 2 / second, obtained from the textbook "Hydraulics".

[0189] The average shear force τ acting on the two sidewalls of the breach at time t w(t) Calculate using Formula 11:

[0190] Formula 11:

[0191] In the formula: C f(t) ρ is the coefficient of friction of the water flow at time t, calculated using formula 9; ρ is the density of water, in kilograms per cubic meter, obtained from the textbook "Hydraulics"; u a(t) Let t be the average flow velocity of the water at the breach at the dam crest, in meters per second, calculated using formula 7.

[0192] In step 8, the scour depth Δh at the bottom of the breach at time t within the time interval Δt is... (t) Calculate using formula 12:

[0193] Formula 12: Δh (t) =k d (τ b(t) -τ c ) δ Δt;

[0194] Where: Δh (t) τ is the scour depth at the bottom of the breach on the dam crest within time Δt, in meters; Δt is the calculation time step, in seconds; b(t) denoted as t, representing the average shear force of the water flow at the bottom of the breach at time t, expressed in N / m², calculated using formula 8; δ represents the scour index of the dam material, a dimensionless coefficient, taken as 1.0 for cohesive soil and 1.5 for non-cohesive soil. The material properties of the dam are determined by on-site sampling by staff, which is then sent to a geotechnical laboratory for particle size analysis; k d The erosion velocity coefficient of the dam material is expressed in meters per second and is calculated using formula 13.

[0195] Formula 13:

[0196] In formula 12, τ c The critical shear force for dam material activation is expressed in Newtons per square meter (N / m²) and is calculated using formula 14.

[0197] Formula 14:

[0198] In the formula: d 50 The median particle size of the dam material is expressed in millimeters.

[0199] The width of the collapse of the sidewalls on both sides of the dam crest breach within the time interval Δt at time t is ΔB. (t) Calculate using Formula 15:

[0200] Formula 15: ΔB (t) =βk d (τ w(t) -τ c ) δ Δt

[0201] In the formula: ΔB (t) τ is the width of the collapsed sidewalls on both sides of the dam crest breach within time Δt, in meters; Δt is the calculation time step, in seconds; β is an adjustment coefficient, a dimensionless coefficient, determined according to the collapse mode on both sides of the breach. This invention addresses the cantilever failure mode of the collapse mode on both sides of the breach, and β is set to 1.0; w(t) τ is the average shear force exerted by the water flow at time t on both sides of the breach at the dam crest, expressed in Newtons per square meter (N / m²), calculated using formula 11; c The critical shear force for dam material activation is expressed in Newtons per square meter and is calculated using Formula 14. δ is the scour index of dam material, a dimensionless coefficient. For cohesive soil, δ is taken as 1.0, and for non-cohesive soil, δ is taken as 1.5. The properties of dam material are determined by on-site sampling by staff and sent to the geotechnical laboratory for determination.

[0202] In step 9, the flow velocity v at the downstream toe of the dam at time t is... p(t) (Unit: meters per second) Calculated using Formula 16:

[0203] Formula 16:

[0204] In the formula: g is the acceleration due to gravity, with units of meters per second. 2 H d0 The height from the dam foundation to the dam crest, in meters, is obtained from the data collected in step 1; h (t) Let h be the depth of the breach at time t, in meters, with an initial value of h. t0 When t > 0, formula 30 is used for calculation; ξ2 is the friction loss coefficient along the flow path, which is a dimensionless coefficient obtained from the textbook "Hydraulics"; V c(t) Let t be the average flow velocity in the area where the flow velocity increases at the breach at the dam crest, expressed in meters per second, calculated using formula 17.

[0205] Formula 17:

[0206] In the formula: Q (t) Let h be the breach flow rate at time t, in cubic meters per second, calculated using formula 1; c(t) B represents the water depth in the zone where the flow velocity increases at time t, expressed in meters, calculated using formula 3.(t) Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 for calculation.

[0207] The average shear force τ at the downstream slope toe of the dam at time t is calculated using Formula 18. p(t) (Unit: Newtons per square meter)

[0208] Formula 18:

[0209] In the formula: ρ is the density of water, in kilograms per cubic meter; V p(t) The downstream slope toe velocity of the water flow is expressed in meters per second and is calculated using formula 16; C fp(t) Let t be the friction coefficient of the downstream slope toe of the dam at time t. It is a dimensionless coefficient and is calculated using formula 19.

[0210] Formula 19:

[0211] In the formula: Re p(t) Let t be the Reynolds number of the downstream slope toe of the dam at time t, which is a dimensionless number and is calculated using formula 20.

[0212] Formula 20:

[0213] In the formula: V p(t) Let h be the flow velocity at the downstream toe of the dam at time t, in meters per second, calculated using formula 16; c(t) Let t be the water depth in the zone where the flow velocity increases at the dam crest breach, in meters, calculated using Formula 3; v is the kinematic viscosity of water, in meters. 2 / second, obtained from the textbook "Hydraulics".

[0214] In step 10, the erosion distance ΔH at the downstream toe of the dam body during the time interval Δt at time t is... p(t) (Unit: meters) Calculate using formula 21:

[0215] Formula 21: ΔH p(t) =k d (τ p(t) -τ c ) δ Δt;

[0216] In the formula: Δt is the calculation time step, in seconds; k d The erosion velocity coefficient of the dam material, in meters per second, is calculated using formula 13; τ p(t) τ is the average shear force of the water flow at the downstream toe of the dam at time t, expressed in N / m², calculated using formula 18; cThe critical shear force for dam material activation is expressed in Newtons per square meter and is calculated using Formula 14. δ is the scour index of dam material, a dimensionless coefficient. For cohesive soil, δ is taken as 1.0, and for non-cohesive soil, δ is taken as 1.5. The properties of dam material are determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory for determination.

[0217] In step 11, the dam stability coefficient S within the breach area at time t is... c(t) The dimensionless coefficient is calculated using formula 22:

[0218] Formula 22:

[0219] In the formula: when S c(t) When S ≥ 1.0, the dam body within the breach area is stable, and a sudden dam failure will not occur; when S c(t) When the value is less than 0, the dam body within the breach area will experience slippage and instability, leading to a sudden dam failure.

[0220] In Formula 22, F w(t) Let t be the water pressure exerted by the upstream water on the dam body within the breach area at time t, in Newtons, calculated using formula 23:

[0221] Formula 23: F w(t) =0.5γ w B (t) (H d0 -h (t) (H) d0 -h (t) +2H (t) );

[0222] In Formula 22, F sb(t) The shear force between the dam body and the dam foundation within the breach area at time t, expressed in Newtons, is calculated using formula 24.

[0223] Formula 24:

[0224] In Formula 22, F sw(t) The shear force between the dam body and the soil on both sides within the breach area at time t, expressed in Newtons, is calculated using formula 25.

[0225] Formula 25:

[0226] In Formula 22, F cb(t) The bond force between the dam body and the dam foundation within the breach area at time t, expressed in Newtons (N), is calculated using formula 26.

[0227] Formula 26: F cb(t) =CB d0 B (t) ;

[0228] In Formula 22, F cw(t) The bond force between the block and both sides of the dam body within the breach area at time t, expressed in Newtons (N), is calculated using formula 27.

[0229] Formula 27: F cw(t) =C(B d0 +L B(t) (H) d0 -h (t) )

[0230] In formulas 22 to 27,

[0231] γ w This is the specific gravity of water, measured in Newtons per cubic meter, with a value of 9.8 × 10⁻⁶. 3 Niu per cubic meter;

[0232] B (t) The width of the breach at time t is in meters.

[0233] H d0 The height from the dam foundation to the dam crest, as determined in step 1, is in meters.

[0234] h (t) The depth of the dam crest breach at time t, determined in step 2, is expressed in meters, with an initial value of h. t0 When t > 0, use formula 30 for calculation;

[0235] H (t) Let H be the water depth upstream of the dam breach at time t, in meters, and let H be the initial water depth. v(0) -h t0 When t > 0, use formula 33 for calculation;

[0236] γ is the wet unit weight of the dam material, expressed in Newtons per cubic meter. It is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory.

[0237] The internal friction angle of the dam material, in degrees, is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory.

[0238] L B(t) Let be the length of the breach at time t, in meters, with an initial value of . When t > 0, use formula 5 for calculation;

[0239] B d0 The initial dam crest width determined in step 1, in meters;

[0240] C represents the bond strength of the dam material, measured in Newtons per square meter (N / m²), which is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory.

[0241] K is a coefficient, a dimensionless coefficient, calculated using formula 28:

[0242] Formula 28:

[0243] In the formula: The internal friction angle of the dam material, in degrees, is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory.

[0244] In step 12, if S c(t) ≥1.0, adjust the terrain, and adjust each parameter as shown in Formulas 29 to 34. Repeat steps 3 to 11.

[0245] ①The width of the breach at the dam crest at time t+Δt is B (t+Δt) (Unit: meters) Calculated using formula 29;

[0246] Formula 29: B (t+Δt) =B (t) +ΔB (t) ;

[0247] In the formula: B (t) ΔB represents the width of the breach at time t, in meters. (t) Let t be the width of the collapse of the sidewalls on both sides of the breach at time t within time Δt, in meters, calculated using formula (15).

[0248] ②Depth h of the breach at time t+Δt (t+Δt) (Unit: meters), calculated using formula 30;

[0249] Formula 30: h (t+Δt) =h (t) +Δh (t) ;

[0250] Where: h (t) Δh represents the depth of the dam crest breach at time t, in meters. (t) Let t be the depth of the breach in the dam crest within the time interval Δt at time t, in meters, calculated using formula (12).

[0251] ③At time t+Δt, the water depth H upstream of the dam crest breach (t+Δt) (Unit: meters) is determined using the following method:

[0252] At time t, the water depth upstream of the dam breach is H. (t) The reservoir capacity is V. (t) (Unit: cubic meters), the change in reservoir capacity ΔV at time t+Δt. (t+Δt) (Unit: cubic meters) Calculate using formula 31;

[0253] Formula 31: ΔV (t+Δt) =(Q(t) -Q in(t) )Δt;

[0254] In the formula: Q (t) Q represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. in(t) Δt represents the inflow rate at time t, in cubic meters per second, determined based on the upstream inflow process; Δt is the calculation time step, in seconds.

[0255] Reservoir capacity V at time t+Δt (t+Δt) (Unit: cubic meters) Calculated using formula 32:

[0256] Formula 32: V (t+Δt) =V (t) -ΔV (t) ;

[0257] Calculate the reservoir capacity V at time t+Δt. (t+Δt) Then, based on the reservoir capacity curve collected in step one, the reservoir water level H at t+Δt can be obtained using linear interpolation. v(t+Δt) (Unit: meters), then the water depth H upstream of the dam breach at time t+Δt is... (t+Δt) Calculate using formula 33;

[0258] Formula 33: H (t+Δt) =H v(t+Δt) -h (t+Δt) ;

[0259] ④ Downstream slope of the dam at time t+Δt (m) dd(t+Δt) Calculate using formula 34;

[0260] Formula 34:

[0261] Where: m dd(t) Let H be the downstream slope of the dam at time t, and H be a dimensionless coefficient. d0 h represents the initial height from the dam foundation to the dam crest, in meters. (t+Δt) Let ΔH be the depth of the breach at time t+Δt, in meters, calculated using formula 30; p(t) The erosion distance at the downstream toe of the dam within time Δt is in meters and is calculated using formula 21.

[0262] If S c(t) If the value is less than 1.0, adjust the terrain and adjust the parameters as shown in Formulas 29 to 34. Then, substitute the adjusted parameters into Formula 1 to complete the calculation.

[0263] The above calculations are repeated until the water erosion capacity can no longer change the dam's topography or the reservoir is emptied; each completion of step 12 constitutes one cycle.

[0264] Step 13: Output the breach flow rate Q during each loop calculation. (t) The maximum value is the peak flow rate of the dam break.

[0265] Example 1

[0266] As shown in Figure 1 to Figure 5 As shown, this embodiment uses Banqiao Reservoir as an example for calculation, and refers to Table 1.

[0267] Table 1 (Water Level and Storage Capacity of Banqiao Reservoir):

[0268] 0.25 0 19.46 3.329 0.85 0.001 19.61 3.397 4.7 0.047 20.74 3.926 14.36 1.493 21.16 4.124 14.48 1.529 21.37 4.23 16.86 2.298 22.26 4.714 18.56 2.953 22.82 5.029 18.59 2.966 22.84 5.04 18.72 3.021 24.15 5.842 18.94 3.112 24.3 5.945 19.28 3.251 24.5 6.01

[0269] Step 1: Collect basic data on Banqiao Reservoir, including dam morphology parameters such as dam length, width, and height, upstream and downstream slopes, dam material gradation, and upstream flow conditions. The dam height H of Banqiao Reservoir is... d0 It is 24.5 meters long, and the width of the dam crest is B. d0 It is 6.0 meters high, and the length of the dam crest is L. d0 The slope is 2020 meters, and the upstream and downstream slope coefficients are m. du0 m dd0 The values ​​are 0.33 and 0.40 respectively. The initial storage capacity V0 is 6.01 × 10⁻⁶. 8 The reservoir capacity is 1 cubic meter, with an initial water level of 24.5 m. See the attached water level-reservoir capacity curve. Figure 2 ;. Median particle size d of dam material 50 It has a thickness of 2.0 mm and a bulk density of γ of 1.90 × 10⁻⁶. 4 N / m³, cohesive strength C is 4.76 × 10⁻⁶. 3 Newtons per square meter, internal friction angle The angle is 37°; the water specific gravity is γ. w 9.8×10 3 Niu / cubic meter; the inflow process is shown in the attached figure. Figure 3 As shown.

[0270] Step 2: Determine the basic parameters of the initial breach at the top of the dam and the calculation time step Δt. The initial breach shape at the top of the Banqiao Reservoir is taken as rectangular, with a width B. t0 10 meters, depth h t0 The initial water level in the reservoir is 0.2 meters. The initial water level in the reservoir is level with the top of the dam. The calculation time step Δt is 30 seconds.

[0271] Step 3: Calculate the breach flow rate Q at time t according to formula (1). (t) ;

[0272] Formula 1:

[0273] In the formula, Q (t)Let be the flow rate at the dam crest breach at time t, in cubic meters per second; m is the flow coefficient, a dimensionless empirical coefficient, which, according to the textbook "Hydraulics," is 0.35; B (t) Let H be the width of the breach at time t, in meters. The initial value is 10 meters. When t > 0, formula 29 is used for calculation. (t) Let t be the water depth upstream of the dam breach at time t, in meters. The initial water depth is 0.2 meters. When t > 0, formula 33 is used for calculation. g is the acceleration due to gravity, which is 9.81 m / s². 2 .

[0274] In step 4, the normal water depth h at time t is... z(t) (Unit: meters) Calculated using Formula 2:

[0275] Formula 2:

[0276] In the formula, h z(t) At time t, the normal water depth at the breach crest of the dam is expressed in meters. H is the velocity coefficient, a dimensionless empirical coefficient, which, according to the textbook "Hydraulics," is 1.0; (t) Let t be the water depth upstream of the breach at the dam crest, in meters. The initial water depth is 0.2 meters. When t > 0, formula 33 is used for calculation.

[0277] In step 5, the water depth h in the area where the flow velocity of the breach at time t increases is... c(t) (Unit: meters) Calculated using Formula 3:

[0278] Formula 3:

[0279] Among them, h z(t) Let F be the normal water depth at time t, expressed in meters, calculated using formula 2; r(t) Let be the Froude number of the breach flow at time t, which is a dimensionless parameter and is calculated using Formula 4:

[0280] Formula 4:

[0281] In the formula: Q (t) B represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. (t) Let h be the width of the breach at time t, in meters. The initial value is 10 meters. When t > 0, formula 29 is used for calculation. (t) Let be the depth of the breach at time t, in meters. The initial value is 0.2 meters. When t > 0, formula 30 is used for calculation. g is the acceleration due to gravity, which is 9.81 m / s². 2 .

[0282] In step 6, the length L of the breach at time t is... B(t)Calculate using Formula 5:

[0283] Formula 5:

[0284] In the formula, L B(t) B is the length of the breach at time t, in a horizontal direction perpendicular to the dam axis, expressed in meters. d0 The initial dam crest width is 6 meters; h (t) Let be the depth of the breach at time t, in meters. The initial value is 0.2 meters. When t > 0, formula 30 is used for calculation. du(t) Let m be the upstream slope coefficient of the dam body at time t, which is a dimensionless coefficient. The upstream slope remains constant during the dam failure process. du(t) Equal to the original slope coefficient m du(0) , is 0.33; m dd(t) Let t be the downstream slope of the dam at time t, and t be a dimensionless coefficient. The initial value is the initial downstream slope coefficient of 0.40. When t > 0, formula 34 is used for calculation.

[0285] The average water depth h at time t of the dam crest breach is calculated using Formula 6. a(t) (Unit: meters)

[0286] Formula 6:

[0287] Where: h z(t) The normal water depth at the crest of the dam breach is in meters, calculated using formula 2; L B(t) Let h be the length of the breach at time t, in meters, calculated using formula 5; c(t) The water depth in the zone where the flow velocity increases at the dam crest breach is expressed in meters and is calculated using Formula 3.

[0288] The average flow velocity u at time t of the breach at the dam crest is calculated using Formula 7. a(t) (Unit: meters per second):

[0289] Formula 7:

[0290] In the formula, Q (t) B represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. (t) Let h be the width of the breach at time t, in meters. The initial value is 10 meters. When t > 0, formula 29 is used for calculation. a(t) The average water depth of the breach is expressed in meters and is calculated using Formula 6.

[0291] In step 7, the average shear force τ at the bottom of the breach at time t is... b(t) (Unit: Newtons / square meter) Calculated using Formula 8:

[0292] Formula 8:

[0293] In the formula, ρ is the density of water, which, according to the textbook "Hydraulics," is 1000 kg / m³; u a(t) Let C be the average flow velocity of the breached water at time t, expressed in meters per second, calculated using formula 7; f(t) The friction coefficient of the water flow at time t is a dimensionless coefficient, calculated using formula 9:

[0294] Formula 9:

[0295] In the formula: Re (t) Let t be the Reynolds number of the breached water flow at time t, which is a dimensionless number and is calculated using Formula 10.

[0296] Formula 10:

[0297] In the formula: u a(t) R represents the average flow velocity of the breached water at time t, expressed in meters per second, calculated using formula 7. (t) Let B be the hydraulic radius of the breach at time t, approximately equal to B. (t) B (t) Let t be the width of the breach at the dam crest, in meters; v be the kinematic viscosity of water, in meters. 2 / second, according to the textbook "Hydraulics", is 0.000001 meters. 2 / Second.

[0298] The average shear force τ acting on the two sidewalls of the breach at time t w(t) Calculate using Formula 11:

[0299] Formula 11:

[0300] In the formula: C f(t) ρ is the coefficient of friction of the water flow at time t, calculated using formula 9; ρ is the density of water, which, according to the textbook "Hydraulics," is 1000 kg / m³; u a(t) Let t be the average flow velocity of the water at the breach at the dam crest, in meters per second, calculated using formula 7.

[0301] In step 8, the scour depth Δh at the bottom of the dam crest breach during the time interval Δt (30 seconds) at time t is... (t) Calculate using formula 12:

[0302] Formula 12: Δh (t) =k d (τ b(t) -τ c ) δ Δt;

[0303] Where: Δh(t) τ is the scour depth at the bottom of the dam crest breach within time Δt, in meters; Δt is the calculation time step, which is 30 seconds; b(t) Let be the average shear force of the water flow at the bottom of the breach at time t, expressed in N / m², calculated using formula 8; δ is the scour index of the dam material, a dimensionless coefficient, taken as 1.0 for cohesive soil and 1.5 for non-cohesive soil; d is the median particle size of the dam material of Banqiao Reservoir. 50 It is 2.0 mm thick, a non-adhesive material, and δ = 1.5; k d The erosion velocity coefficient of the dam material is expressed in meters per second and is calculated using formula 13.

[0304] Formula 13:

[0305] In formula 12, τ c The critical shear force for dam material activation is expressed in Newtons per square meter (N / m²) and is calculated using formula 14.

[0306] Formula 14:

[0307] In the formula: d 50 The median particle size of the dam material is 2.0 mm.

[0308] The width ΔB of the sidewall collapse on both sides of the dam crest breach within the time interval Δt (30 seconds) at time t. (t) Calculate using Formula 15:

[0309] Formula 15: ΔB (t) =βk d (τ w(t) -τ c ) δ Δt

[0310] In the formula: ΔB (t) τ is the width of the collapsed sidewalls on both sides of the dam crest breach within time Δt, in meters; Δt is the calculation time step, which is 30 seconds; β is an adjustment coefficient, a dimensionless coefficient, determined according to the collapse mode on both sides of the breach. In this invention, the collapse mode on both sides of the breach is cantilever failure, and β is set to 1.0; w(t) τ is the average shear force exerted by the water flow at time t on both sides of the breach at the dam crest, expressed in Newtons per square meter (N / m²), calculated using formula 11; c The critical shear force for dam material activation, in N / m², is calculated using formula 14; δ is the scour index of the dam material, a dimensionless coefficient, taken as 1.0 for cohesive soil and 1.5 for non-cohesive soil; and d is the median particle size of the Banqiao Reservoir dam material. 50 It is 2.0 mm thick, is a non-adhesive material, and δ = 1.5.

[0311] In step 9, the flow velocity v at the downstream toe of the dam at time t is... p(t) (Unit: meters per second) Calculated using Formula 16:

[0312] Formula 16:

[0313] In the formula: g is the acceleration due to gravity, which is 9.81 m / s². 2 H d0 The height from the dam foundation to the dam crest, obtained from the data collected in step 1, is 24.5 meters; h (t) Let ξ be the depth of the breach at time t, in meters, initially 0.2 meters. When t > 0, it is calculated using formula 30; ξ2 is the friction loss coefficient, a dimensionless coefficient, which, according to the textbook "Hydraulics," is 0.2; V c(t) Let t be the average flow velocity in the area where the flow velocity increases at the breach at the dam crest, expressed in meters per second, calculated using formula 17.

[0314] Formula 17:

[0315] In the formula: Q (t) Let h be the breach flow rate at time t, in cubic meters per second, calculated using formula 1; c(t) B represents the water depth in the zone where the flow velocity increases at time t, expressed in meters, calculated using formula 3. (t) Let B be the width of the breach at time t, in meters, with an initial value of B. t0 When t > 0, use formula 29 for calculation.

[0316] The average shear force τ at the downstream slope toe of the dam at time t is calculated using Formula 18. p(t) (Unit: Newtons per square meter)

[0317] Formula 18:

[0318] In the formula: ρ is the density of water, which, according to the textbook "Hydraulics," is 1000 kg / m³; V p(t) The downstream slope toe velocity of the water flow is expressed in meters per second and is calculated using formula 16; C fp(t) Let t be the friction coefficient of the downstream slope toe of the dam at time t. It is a dimensionless coefficient and is calculated using formula 19.

[0319] Formula 19:

[0320] In the formula: Re p(t) Let t be the Reynolds number of the downstream slope toe of the dam at time t, which is a dimensionless number and is calculated using formula 20.

[0321] Formula 20:

[0322] In the formula: V p(t) Let h be the flow velocity at the downstream toe of the dam at time t, in meters per second, calculated using formula 16; c(t) Let t be the water depth in the zone where the flow velocity increases at the dam crest breach, in meters, calculated using Formula 3; v is the kinematic viscosity of water, in meters. 2 / second, according to the textbook "Hydraulics", is 0.000001 meters. 2 / Second.

[0323] In step 10, the erosion distance ΔH at the downstream toe of the dam body during the time interval Δt at time t is... p(t) (Unit: meters) Calculate using formula 21:

[0324] Formula 21: ΔH p(t) =k d (τ p(t) -τ c ) δ Δt;

[0325] In the formula: Δt is the calculation time step, in seconds; k d The erosion velocity coefficient of the dam material, in meters per second, is calculated using formula 13; τ p(t) τ is the average shear force of the water flow at the downstream toe of the dam at time t, expressed in N / m², calculated using formula 18; c The critical shear force for dam material activation is given by formula 14, expressed in Newtons per square meter. δ is the scour index of the dam material, a dimensionless coefficient, taken as 1.0 for cohesive soil and 1.5 for non-cohesive soil. d is the median particle size of the Banqiao Reservoir dam material. 50 It is 2.0 mm thick, is a non-adhesive material, and δ = 1.5.

[0326] In step 11, the dam stability coefficient S within the breach area at time t is... c(t) The dimensionless coefficient is calculated using formula 22:

[0327] Formula 22:

[0328] In the formula: when S c(t) When S ≥ 1.0, the dam body within the breach area is stable, and a sudden dam failure will not occur; when S c(t) When the value is less than 0, the dam body within the breach area will experience slippage and instability, leading to a sudden dam failure.

[0329] In Formula 22, F w(t) Let t be the water pressure exerted by the upstream water on the dam body within the breach area at time t, in Newtons, calculated using formula 23:

[0330] Formula 23: F w(t) =0.5γ w B(t) (H d0 -h (t) (H) d0 -h (t) +2H (t) );

[0331] In Formula 22, F sb(t) The shear force between the dam body and the dam foundation within the breach area at time t, expressed in Newtons, is calculated using formula 24.

[0332] Formula 24:

[0333] In Formula 22, F sw(t) The shear force between the dam body and the soil on both sides within the breach area at time t, expressed in Newtons, is calculated using formula 25.

[0334] Formula 25:

[0335] In Formula 22, F cb(t) The bond force between the dam body and the dam foundation within the breach area at time t, expressed in Newtons (N), is calculated using formula 26.

[0336] Formula 26: F cb(t) =CB d0 B (t) ;

[0337] In Formula 22, F cw(t) The bond force between the block and both sides of the dam body within the breach area at time t, expressed in Newtons (N), is calculated using formula 27.

[0338] Formula 27: F cw(t) =C(B d0 +L B(t) (H) d0 -h (t) )

[0339] In formulas 22 to 27,

[0340] γ w This is the specific gravity of water, measured in Newtons per cubic meter, with a value of 9.8 × 10⁻⁶. 3 Niu per cubic meter;

[0341] B (t) The width of the breach at time t is in meters.

[0342] H d0 The height from the dam foundation to the dam crest, as determined in step 1, is in meters.

[0343] h (t)The depth of the breach at time t, determined in step 2, is in meters. The initial value is 0.2 meters. When t > 0, formula 30 is used for calculation.

[0344] H (t) Let H be the water depth upstream of the dam breach at time t, in meters, and let H be the initial water depth. v(0) -h t0 When t > 0, use formula 33 for calculation;

[0345] γ is the wet unit weight of the dam material, which is 1.90 × 10⁻⁶. 4 Niu per cubic meter;

[0346] The internal friction angle of the dam material is 37°.

[0347] L B(t) Let be the length of the breach at time t, in meters, with an initial value of . When t > 0, use formula 5 for calculation;

[0348] B d0 The initial dam crest width determined in step 1 is 6.0 meters;

[0349] C represents the bond strength of the dam material, which is 4.76 × 10⁻⁶. 3 cows per square meter;

[0350] K is a coefficient, a dimensionless coefficient, calculated using formula 28:

[0351] Formula 28:

[0352] In the formula: The internal friction angle of the dam material is 37°.

[0353] In step 12, if S c(t) ≥1.0, adjust the terrain, and adjust each parameter as shown in Formulas 29 to 34. Repeat steps 3 to 11.

[0354] ①The width of the breach at the dam crest at time t+Δt is B (t+Δt) (Unit: meters) Calculated using formula 29;

[0355] Formula 29: B (t+Δt) =B (t) +ΔB (t) ;

[0356] In the formula: B (t) ΔB represents the width of the breach at time t, in meters, with an initial value of 10 meters. (t) Let t be the width of the collapse of the sidewalls on both sides of the breach at time t within time Δt, in meters, calculated using formula (15).

[0357] ②Depth h of the breach at time t+Δt (t+Δt) (Unit: meters), calculated using formula 30;

[0358] Formula 30: h (t+Δt) =h (t) +Δh (t) ;

[0359] Where: h (t) Let Δh be the depth of the breach at time t, in meters, with an initial value of 0.2 meters; (t) Let be the scour depth at the bottom of the breach at time t within the time interval Δt, in meters, calculated using formula (12).

[0360] ③At time t+Δt, the water depth H upstream of the dam crest breach (t+Δt) (Unit: meters) is determined using the following method:

[0361] At time t, the water depth upstream of the dam breach is H. (t) The reservoir capacity is V. (t) (Unit: cubic meters), the change in reservoir capacity ΔV at time t+Δt. (t+Δt) (Unit: cubic meters) Calculate using formula 31;

[0362] Formula 31: ΔV (t+Δt) =(Q (t) -Q in(t) )Δt;

[0363] In the formula: Q (t) Q represents the breach flow rate at time t, expressed in cubic meters per second, calculated using Formula 1. in(t) Δt represents the inflow rate at time t, in cubic meters per second, determined based on the upstream inflow process; Δt is the calculation time step, in seconds.

[0364] Reservoir capacity V at time t+Δt (t+Δt) (Unit: cubic meters) Calculated using formula 32:

[0365] Formula 32: V (t+Δt) =V (t) -ΔV (t) ;

[0366] Calculate the reservoir capacity V at time t+Δt. (t+Δt) Then, based on the reservoir capacity curve collected in step one, the reservoir water level H at t+Δt can be obtained using linear interpolation. v(t+Δt) (Unit: meters), then the water depth H upstream of the dam breach at time t+Δt is... (t+Δt) Calculate using formula 33;

[0367] Formula 33: H (t+Δt) =Hv(t+Δt) -h (t+Δt) ;

[0368] ④ Downstream slope of the dam at time t+Δt (m) dd(t+Δt) Calculate using formula 34;

[0369] Formula 34:

[0370] Where: m dd(t) Let H be the downstream slope of the dam at time t, and let H be a dimensionless coefficient with an initial value of 0.40. d0 The initial height from the dam foundation to the dam crest is 24.5 meters; h (t+Δt) Let ΔH be the depth of the breach at time t+Δt, in meters, calculated using formula 30; p(t) The erosion distance at the downstream toe of the dam within time Δt is in meters and is calculated using formula 21.

[0371] If S c(t) If the value is less than 1.0, adjust the terrain and adjust the parameters as shown in Formulas 29 to 34. Then, substitute the adjusted parameters into Formula 1 to complete the calculation.

[0372] The above calculations are repeated until the water erosion capacity can no longer change the dam's topography or the reservoir is emptied; each completion of step 12 constitutes one cycle.

[0373] Step 13: Output the breach flow rate Q during each loop calculation. (t) The maximum value is the peak flow rate of the dam break.

[0374] Based on the model calculations, the flow process curve of the breach at Banqiao Reservoir was obtained. Comparing the calculated results with the measured results: the measured breach duration was approximately 5.5 hours, and the peak flow rate Q was... p 78100m 3 / s, the calculated dam breach time is approximately 5.1 hours, and the calculated peak flood discharge Q is... p 81863m 3 The calculated peak flow rate of the dam break was 4.82% per second, which shows that the model calculation results are reliable and highly accurate.

[0375] To analyze the impact of the initial breach size on the breach flow rate process, calculations were performed on the following schemes (5 schemes in Table 2), where scheme 3 is the scheme actually used in this embodiment, and the other schemes are control schemes. The calculation results are as follows: Figure 4 As shown in Table 3, the calculation results are not sensitive to the initial ulcer size, indicating that the algorithm of the present invention is very effective.

[0376] Schemes 1-5 calculate the dam breach time as 4.78-5.13 hours, the peak flood time as 1.63-1.89 hours, and the peak flood flow as 79824 m³ / h. 3 / s~82496m 3 / s, the measured duration of the dam breach was approximately 5.5 hours, the peak flow occurred in 1.5 hours, and the peak flow rate Q p 78100m 3 / s, the calculated peak flow rate of each scheme deviated from the measured value by 2.21% to 5.04%. Overall, according to the principle of determining the initial breach size in this invention, the calculated peak flow rate of each scheme has little deviation. This indicates that the selection of the initial breach size has little impact on the calculated peak flow rate of the dam breach, which also shows that the calculation of this invention is stable and reliable, and has high practical value.

[0377] Table 2 Initial breach size under different calculation schemes

[0378]

[0379] Table 3 Comparison of Calculation Results for Different Schemes

[0380]

[0381] The above embodiments are only used to illustrate and not limit the technical solutions of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention without departing from the spirit and scope of the present invention. Any modifications or partial substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting the peak flow of an earth-rock dam during overtopping and breach, characterized in that... Follow these steps: Step 1: Collect the basic parameters of the earth-rock dam for which failure is to be calculated; Step 2: Determine the initial breach parameters at the dam crest and the calculation time step; Step 3: Calculate the breach flow at the dam crest; Step 4: Calculate the normal water depth at the breach crest of the dam; Step 5: Calculate the water depth in the area where the flow velocity increases at the dam crest breach; Step 6: Calculate the average flow velocity of the water flow at the breach crest of the dam; Step 7: Calculate the average shear force of the water flow at the bottom and on both sides of the breach at the top of the dam; Step 8: Calculate the erosion rate at the bottom and sides of the breach in the dam crest; Step 9: Calculate the average shear force of the water flow at the downstream toe of the dam; Step 10: Calculate the erosion rate at the downstream toe of the dam; Step 11: Calculate the dam stability coefficient within the breach area; Step 12: Adjust the terrain and perform the corresponding calculations; Step 13: Output the peak flow rate of the dam break; In step 2, the initial breach at the dam crest is set as a rectangle based on the existing mathematical model, with an initial breach width of B_t0 and an initial breach depth of h_t0. B_t0 is taken within 1% of the dam axis length L_d0, and h_t0 is taken within 1% of H_d0 meters. The calculation time step is Δt, in seconds. Both B_t0 and h_t0 are in meters; In step 5, the water depth h_c(t) in the area where the flow velocity of the breach increases at time t is calculated using formula 3: the unit of h_c(t) is meters; Formula 3: h_c(t)=[(F_r(t))² / (1+(F_r(t))²)]h_z(t); Where h_z(t) is the normal water depth at the breach crest of the dam at time t, in meters, calculated using formula 2; F_r(t) is the Froude number of the breach flow at time t, a dimensionless parameter, calculated using formula 4. Formula 4: \(F_r(t)=\frac{Q_{t}}{[B_{t}h_z(t)(gh_z(t)) 0.5 ; In the formula: Q_(t) is the flow rate of the breach at time t, in cubic meters per second, calculated using formula 1; B_(t) is the width of the breach at time t, in meters, with an initial value of B_t0, and calculated using formula 29 when t > 0; h_(t) is the depth of the breach at time t, in meters, with an initial value of h_t0, and calculated using formula 30 when t > 0; g is the acceleration due to gravity, in meters per second². In step 9, the flow velocity v_p(t) at time t downstream of the dam toe is calculated using formula 16: Equation 16: \(v_p(t)=\frac{[2g(H_{d0}-h_{(t)})+v_c(t)^2]}{(1+\xi_2)}\) 0.5 ; In the formula: v_p(t) is in meters per second, g is the acceleration due to gravity in meters per second²; H_d0 is the height from the dam foundation to the dam crest in meters, obtained from the data collected in step 1; h_(t) is the depth of the breach at the dam crest at time t in meters, initially valued at h_t0, and calculated using formula 30 when t > 0; ξ_2 is the head loss coefficient along the flow path, a dimensionless coefficient; v_c(t) is the average flow velocity in the area of ​​increased flow velocity at the breach at the dam crest at time t in meters per second, calculated using formula 17. Formula 17: v_c(t)=Q_(t) / [h_c(t)B_(t)]; In the formula: Q_(t) is the flow rate of the breach at time t, in cubic meters per second, calculated using formula 1; h_c(t) is the water depth in the zone of increased flow velocity at the dam crest at time t, in meters, calculated using formula 3; B_(t) is the width of the breach at time t, in meters, with an initial value of B_t0. When t > 0, it is calculated using formula 29. The average shear force τ_p(t) at the downstream toe of the dam at time t is calculated using Formula 18: Formula 18: τ_p(t)=C_fp(t)ρv_p(t)²; The unit of τ_p(t) is Newtons per square meter; In the formula: ρ is the density of water, in kilograms per cubic meter; v_p(t) is the flow velocity at the downstream toe of the dam, in meters per second, calculated using formula 16; C_fp(t) is the friction coefficient of the flow at the downstream toe of the dam at time t, a dimensionless coefficient, calculated using formula 19. Formula 19: C_fp(t) = 0.0237(Re_p(t))^(-0.25); In the formula: Re_p(t) is the Reynolds number of the downstream slope toe of the dam at time t, which is a dimensionless number and is calculated using formula 20; Formula 20: Re_p(t)=v_p(t)h_c(t) / ν; In the formula: v_p(t) is the flow velocity of the downstream slope toe of the dam at time t, in meters per second, calculated using formula 16; h_c(t) is the water depth in the area of ​​increased flow velocity at the breach crest of the dam at time t, in meters, calculated using formula 3; ν is the kinematic viscosity coefficient of water, in meters per second. In step 10, the erosion distance ΔH_p(t) at the downstream toe of the dam body within the time interval Δt at time t is calculated using formula 21: Form21:ΔH_p(t)=k_d(τ_p(t)-τ c )^δΔt. In the formula: ΔH_p(t) is in meters; Δt is the calculation time step in seconds; k_d is the erosion velocity coefficient of the dam material in meters per second, calculated using formula 13; τ_p(t) is the average shear force of the water flow at the downstream toe of the dam at time t, in Newtons per square meter, calculated using formula 18; τ c The critical shear force for dam material activation is expressed in Newtons per square meter and is calculated using Formula 14. δ is the scour index of dam material, a dimensionless coefficient. For cohesive soil, δ is taken as 1.0, and for non-cohesive soil, δ is taken as 1.

5. The properties of dam material are determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory for determination. In step 11, the dam stability coefficient S_c(t) within the breach area at time t is calculated using formula 22: Formula 22: S_c(t)=[F_sb(t)+F_sw(t)+F_cb(t)+F_cw(t)] / F_w(t); In the formula: S_c(t) is a dimensionless coefficient; when S_c(t)≥1.0, the dam body is stable within the breach area and the dam body will not suddenly collapse; when S_c(t)<0, the dam body slips and becomes unstable within the breach area and the dam body suddenly collapses. In Formula 22, F_w(t) is the water pressure exerted by the upstream water on the dam body within the breach area at time t, in Newtons, and is calculated using Formula 23: Formula 23: F_w(t)=0.5γ_wB_(t)(H_d0-h_(t))(H_d0-h_(t)+2H_(t)); In Formula 22, F_sb(t) is the shear force between the dam body and the dam foundation within the breach area at time t, in Newtons, and is calculated using Formula 24: Formula 24: F_sb(t)=0.5γB_(t)tanφ[(L_B(t)+B_d0)(H_d0-h_(t))]; In Formula 22, F_sw(t) is the shear force between the dam body and the soil on both sides within the breach area at time t, in Newtons (N), calculated using Formula 25: Formula 25: F_sw(t)=KγB_(t)tanφ[(L_B(t)+B_d0)(H_d0-h_(t))]; In Formula 22, F_cb(t) is the bond force between the dam body and the dam foundation within the breach area at time t, in Newtons, and is calculated using Formula 26: Formula 26: F_cb(t) = CB_d0B_(t); In Formula 22, F_cw(t) is the bond force between the block and both sides of the dam body within the breach area at time t, in Newtons (N), calculated according to Formula 27: Formula 27: F_cw(t)=C(B_d0+L_B(t))(H_d0-h_(t)); In formulas 22 to 27, γ_w is the water specific weight, in Newtons per cubic meter, with a value of 9.8 × 10³ Newtons per cubic meter; B_(t) represents the width of the breach at time t, in meters; H_d0 is the height from the dam foundation to the dam crest determined in step 1, in meters; h_(t) is the depth of the breach at time t determined in step 2, in meters. The initial value is h_t0. When t>0, formula 30 is used for calculation. H_(t) is the water depth upstream of the breach at time t, in meters. The initial water depth is H_v(0)-h_t0. When t>0, formula 33 is used for calculation. γ is the wet unit weight of the dam material, expressed in Newtons per cubic meter. It is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory. φ is the internal friction angle of the dam material, in degrees, which is determined by on-site sampling by the implementation personnel and sent to the geotechnical laboratory. L_B(t) is the length of the breach at time t, in meters. The initial value is B_d0+h_t0 / m_du(0)+h_t0 / m_dd(0). When t>0, Formula 5 is used for calculation. B_d0 is the initial dam crest width determined in step 1, in meters; C represents the bond strength of the dam material, measured in Newtons per square meter (N / m²), which is determined by on-site sampling by the implementation personnel and sent to a geotechnical laboratory. K is a coefficient, a dimensionless coefficient, calculated using formula 28: Formula 28: K=(1-sinφ) / (1+sinφ); In the formula: φ is the internal friction angle of the dam material, in degrees, which is determined by on-site sampling by the implementers and sent to the geotechnical laboratory.

2. The method for predicting the peak flow of an earth-rock dam overtopping breach according to claim 1, characterized in that: In step 1, the basic parameters of the earth-rock dam collected include the dam axis length L_d0, the initial dam crest width B_d0, the dam foundation to dam crest height H_d0, the initial upstream slope coefficient m_du(0), the initial downstream slope coefficient m_dd(0), the median particle size of the dam material d_50, the initial reservoir capacity V_0, the initial water level h_v(0) and the reservoir capacity curve, as well as the upstream inflow process; The units of L_d0, B_d0, H_d0 and h_v(0) are all meters; the units of m_du(0) and m_dd(0) are dimensionless coefficients; the unit of d_50 is millimeters; the unit of V_0 is cubic meters. In step 3, the water depth upstream of the breach at time t is H_(t); the breach depth at time t is h_(t); the breach width at time t is B_(t); time t represents the time up to a certain moment in the calculation, t=nΔt, n is an integer, n=0, 1, 2, 3..., Δt is the calculation time step Δt, when n=0, it is the initial state; The units for H_(t), h_(t), and B_(t) are all meters; the unit for Δt is seconds. The breach flow rate Q_(t) at time t is calculated using Formula 1: Formula 1: Q_(t)=mB_(t){(2g)} 0.5 H_(t)^(3 / 2); In the formula, Q_(t) is the flow rate at the breach at time t, in cubic meters per second; m is the flow coefficient, a dimensionless empirical coefficient; B_(t) is the width of the breach at time t, in meters, with an initial value of B_t0. When t > 0, it is calculated using formula 29; H_(t) is the water depth upstream of the breach at time t, in meters, with an initial water depth of H_v(0) - h_t0. When t > 0, it is calculated using formula 33; g is the acceleration due to gravity, in meters per second². In step 4, the normal water depth h_z(t) at time t is calculated using formula 2: the unit of h_z(t) is meters; Formula 2: h_z(t)=[2φ2² / (1+2φ2²)]H_(t); In the formula, h_z(t) is the normal water depth of the breach at time t, in meters; φ2 is the flow velocity coefficient, which is a dimensionless empirical coefficient; H_(t) is the water depth upstream of the breach at time t, in meters, and the initial water depth is H_v(0)-h_t0. When t>0, formula 33 is used for calculation. In step 6, the length of the breach at time t, L_B(t), is calculated using formula 5: Formula 5: L_B(t)=B_d0+h_(t) / m_du(t)+h_(t) / m_dd(t); In the formula, L_B(t) is the length of the breach at the top of the dam at time t, which is horizontal and perpendicular to the dam axis, in meters. The initial value is B_d0 + h_t0 / m_du(0) + h_t0 / m_dd(0); B_d0 is the initial width of the dam top; h_(t) is the depth of the breach at the top of the dam at time t, in meters. The initial value is h_t0. When t > 0, formula 30 is used for calculation; m_du(t) is the upstream slope coefficient of the dam body at time t, which is a dimensionless coefficient. The upstream slope remains unchanged during the dam breach, so m_du(t) is taken as equal to the original slope coefficient m_du(0); m_dd(t) is the downstream slope of the dam body at time t, which is a dimensionless coefficient. The initial value is the initial downstream slope coefficient m_dd(0). When t > 0, formula 34 is used for calculation. The average water depth h_a(t) at time t is calculated using Formula 6, in meters: Formula 6: h_a(t)=[h_z(t)(L_B(t)-3.5h_z(t))+3.5h_c(t)h_z(t)] / L_t0; In the formula: h_z(t) is the normal water depth at the top of the dam crest breach, in meters, calculated using formula 2; L_B(t) is the length of the dam crest breach at time t, in meters, calculated using formula 5; h_c(t) is the water depth in the zone where the flow velocity increases at the dam crest breach, in meters, calculated using formula 3. The average flow velocity u_a(t) at time t in the breach crest of the dam is calculated using Formula 7; the unit of u_a(t) is meters per second. Formula 7: u_a(t)=Q_(t) / [B_(t)h_a(t)]; In the formula, Q_(t) is the flow rate at the breach at time t, in cubic meters per second, calculated using formula 1; B_(t) is the width of the breach at time t, in meters, with an initial value of B_t0, and when t>0, calculated using formula 29; h_a(t) is the average water depth at the breach, in meters, calculated using formula 6. In step 7, the average shear force τ_b(t) of the water flow at the bottom of the breach at time t is calculated using formula 8: Formula 8: τ_b(t)=C_f(t)ρu_a(t)²; The unit of τ_b(t) is Newtons per square meter; In the formula, ρ is the water density, in kilograms per cubic meter; u_a(t) is the average flow velocity of the breached water at time t, in meters per second, calculated using formula 7; C_f(t) is the friction coefficient of the water flow at time t, a dimensionless coefficient, calculated using formula 9. Formula 9: C_f(t) = 0.0237Re(t)^(-0.25); In the formula: Re(t) is the Reynolds number of the breached water flow at time t, which is a dimensionless number and is calculated using formula 10; Formula 10: Re(t)=u_a(t)R_(t) / ν; In the formula: u_a(t) is the average flow velocity of the breach at time t, in meters per second, calculated using formula 7; R_(t) is the hydraulic radius of the breach at time t, in meters, approximately equal to B_(t); B_(t) is the width of the breach at time t, in meters; ν is the kinematic viscosity coefficient of water, in meters² / second. The average shear force τ_w(t) acting on the two sidewalls of the breach at time t is calculated using Formula 11: Formula 11: τ_w(t)=1.2C_f(t)ρu_a(t)²; In the formula: C_f(t) is the friction coefficient of the water flow at time t, calculated using formula 9; ρ is the density of water, in kilograms per cubic meter; u_a(t) is the average flow velocity of the water flow at the breach at time t, in meters per second, calculated using formula 7; In step 8, the scour depth Δh_(t) at the bottom of the breach at time t within the time interval Δt is calculated using formula 12: Formula 12: Δh_(t)=k_d(τ_b(t)-τ c )^δΔt; In the formula: Δh_(t) is the scour depth at the bottom of the breach at the dam crest within time Δt, in meters; Δt is the calculation time step, in seconds; τ_b(t) is the average shear force of the water flow at the bottom of the breach at time t, in Newtons per square meter, calculated using formula 8; δ is the scour index of the dam material, a dimensionless coefficient, δ is taken as 1.0 for cohesive soil and δ is taken as 1.5 for non-cohesive soil. The determination of the dam material properties is carried out by on-site sampling by staff and sent to the geotechnical laboratory for particle size analysis; k_d is the scour velocity coefficient of the dam material, in meters per second, calculated using formula 13; Formula 13: ; In Equation 13, τ c The critical shear force for the dam material at the start of operation is expressed in Newtons per square meter and is calculated using formula 14. Formula 14: In the formula: d 50 The median particle size of the dam material is expressed in millimeters. The width ΔB_(t) of the collapse of the sidewalls on both sides of the dam crest breach within the time interval Δt at time t is calculated using Formula 15: Formula 15: ΔB_(t)=βk_d(τ_w(t)-τ c )^δΔt; In the formula: ΔB_(t) is the width of the collapse of the sidewalls on both sides of the dam crest breach within time Δt, in meters; Δt is the calculation time step, in seconds; β is an adjustment coefficient, a dimensionless coefficient, determined according to the collapse mode on both sides of the breach. For the cantilever failure mode, β is set to 1.0; τ_w(t) is the average shear force exerted by the water flow at time t on the sidewalls of the dam crest breach, in Newtons per square meter, calculated using formula 11; τ c The critical shear force for dam material activation is expressed in Newtons per square meter and is calculated using Formula 14. δ is the scour index of dam material, a dimensionless coefficient. For cohesive soil, δ is taken as 1.0, and for non-cohesive soil, δ is taken as 1.

5. The properties of dam material are determined by on-site sampling by staff and sent to the geotechnical laboratory for determination. In step 12, if S_c(t)≥1.0, adjust the terrain and adjust each parameter as shown in formulas 29 to 34. Repeat steps 3 to 11. ①The width of the breach at time t+Δt, B_(t+Δt), is calculated using formula 29; Formula 29: B_(t+Δt)=B_(t)+ΔB_(t); In the formula: B_(t+Δt) is in meters; B_(t) is the width of the breach at time t, in meters; ΔB_(t) is the width of the collapse of the sidewalls on both sides of the breach at time t and time Δt, in meters, calculated using formula 15; ②The depth of the breach at the dam crest at time t+Δt is h_(t+Δt), where h_(t+Δt) is in meters and is calculated using formula 30; Formula 30: h_(t+Δt)=h_(t)+Δh_(t); In the formula: h_(t) is the depth of the breach at time t, in meters; Δh_(t) is the depth of the breach scour at time t within the time interval Δt, in meters, calculated using formula 12; ③The water depth H_(t+Δt) upstream of the dam breach at time t+Δt is determined using the following method: At time t, the water depth upstream of the breach at the dam crest is H_(t), and the reservoir capacity is V_(t), where V_(t) is in cubic meters. The change in reservoir capacity ΔV_(t+Δt) at time t+Δt is calculated using formula 31; Formula 31: ΔV_(t+Δt)=(Q_(t)-Q_in(t))Δt; The unit of ΔV_(t+Δt) is cubic meters; In the formula: Q_(t) is the breach flow rate at time t, in cubic meters per second, calculated using Formula 1; Q_in(t) is the inflow rate at time t, in cubic meters per second, determined based on the upstream inflow process; Δt is the calculation time step, in seconds. The reservoir capacity V_(t+Δt) at time t+Δt is calculated using formula 32: Formula 32: V_(t+Δt)=V_(t)-ΔV_(t); The unit of V_(t+Δt) is cubic meters; After calculating the reservoir capacity V_(t+Δt) at time t+Δt, the reservoir water level H_v(t+Δt) at time t+Δt can be obtained by linear interpolation based on the reservoir capacity curve collected in step one. Then, the water depth H_(t+Δt) upstream of the dam breach at time t+Δt is calculated using formula 33; the unit of H_(t+Δt) is meters. Formula 33: H_(t+Δt)=H_v(t+Δt)-h_(t+Δt); ④ The downstream slope m_dd(t+Δt) at time t+Δt is calculated using formula 34; Formula 34: m_dd(t+Δt)=[m_dd(t)(H_d0-h_(t+Δt))] / [H_d0-h_(t+Δt)-m_dd(t)ΔH_p(t)]; In the formula: m_dd(t) is the downstream slope of the dam at time t, which is a dimensionless coefficient; H_d0 is the height from the initial dam foundation to the dam crest, in meters; h_(t+Δt) is the breach depth at the dam crest at time t+Δt, in meters, calculated using formula 30; ΔH_p(t) is the erosion distance at the downstream toe of the dam within time Δt, in meters, calculated using formula 21. If S_c(t) < 1.0, adjust the terrain and adjust each parameter as shown in Formulas 29 to 34. Then substitute the adjusted parameters into Formula 1 to complete the calculation. The above calculations are repeated until the water erosion capacity can no longer change the dam topography or the reservoir is emptied. Each completion of step 12 completes one cycle; Step 13: Output the breach flow rate Q_(t) during each loop calculation, and take the maximum value as the peak flow rate of the dam breach.

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