A method for calculating the development of a dike breach

Abstract

This invention provides a method for calculating the development process of a dike breach, relating to the field of flood disaster prevention. The method considers the influence of water flow forces on the breach development rate, uses the breach unit width flow rate as the main parameter, and establishes a parametric expression between the breach flow elements and the development process, calculating the two main development processes: lateral widening and vertical downward shearing. This invention can calculate the entire breach development process; the calculation method provided by this invention requires few parameters, and the breach unit width flow rate—the main parameter for calculating the breach development process—can be directly obtained from the broad-crested weir flow rate formula, exhibiting high feasibility, good repeatability and scientific validity, and a simple calculation process; the breach unit width flow rate reflects the scouring effect of water flow on the breach sediment, and the calculation formula established based on the actual breach development mechanism is more consistent with the physical mechanism.

Description

Technical Field

[0001] This invention relates to the field of flood disaster prevention, specifically a method for calculating the development process of dike breaches. Background Technology

[0002] Dikes, as a crucial component of flood control engineering, are widely used worldwide and play a vital role in socio-economic development. However, in scenarios such as super-standard floods, dike breaches can cause severe harm to the lives and property of people in flood-affected areas. The dike breach process is a process of interaction between the dike materials and the breached water flow. Quantitative analysis of the breach development rate is of great significance for breach process simulation, downstream flood development prediction, and the formulation of emergency evacuation plans.

[0003] Existing techniques for calculating breach development processes mainly fall into two categories. One category is parametric models based on statistical data. These models use statistical methods to perform regression analysis on historical breach data, establishing empirical formulas for key geometric and physical parameters such as breach widening, breach incision, breach shape, and breach time. These formulas are relatively simple in structure and can quickly assess the breach development process. However, establishing these empirical formulas typically requires a large amount of measured data. Due to the inherent danger and complexity of breaches, the collected data is extremely limited, and the accuracy of the data is also poor. Therefore, empirical formulas have certain limitations. Furthermore, these models do not address the actual breach mechanism, resulting in low accuracy and unstable calculation results.

[0004] Another type is the mathematical model based on physical mechanisms, which mainly uses methods such as hydraulics and sediment dynamics. It uses differential equations to describe the development of breaches and the erosion process, and can simulate the actual breach process more realistically. However, this method is complex to solve and the calculations mostly contain some parameters that are not easy to measure on site. These factors limit the establishment and general applicability of the equations.

[0005] For example, when studying the development of levee breaches, soil mechanics methods are often used to express the soil erosion width (rate) using water flow shear stress, soil initiation shear stress, and erosion coefficient, and to establish a parametric expression for the breach development process with shear stress as the variable:

[0006] E = k d Δt(τ-τ c ) or V z =k d (τ-τ d )

[0007] Where E is the scouring width, k d Let τ be the erosion coefficient, Δt be time, and τ be the average shear stress of the water flow. d V is the initiation shear stress of the soil. zThe erosion rate is the rate at which soil is washed away. Soil will only be washed away by the water flow when the shear stress of the water flow is greater than the shear stress of the soil. The formula shows that the erosion rate is influenced not only by the force of the water flow but also by the erosion coefficient and the initial shear stress of the soil. Both the erosion coefficient and the critical shear stress are related to the properties of the soil itself. The erosion coefficient is the most important parameter determining the magnitude of soil erosion. Numerous empirical formulas exist for calculating the critical shear stress of different soil types, and the two are related. However, the solution for the shear stress of the water flow is greatly affected by the water depth. Because the elevation changes drastically at the breach, the bottom elevation of the breach is difficult to measure, making it impossible to accurately determine the water depth. At the initial stage of a breach, the water depth is very small, and the water-sand interface is even more difficult to distinguish, further complicating the determination of the water depth.

[0008] Besides drawing on methods from soil mechanics, some studies consider the effect of hydrodynamics on sediment erosion, establishing a relationship between the breach flow rate Q and the breach incision rate and widening rate, with the breach flow rate Q as the main variable. However, the breach process is an interaction between the levee material and the breach flow; the breach size affects the magnitude of the breach flow rate, which cannot accurately reflect the strength of the water flow's effect on sediment erosion. This leads to different forms and parameters in the expressions for the breach development rate and breach flow rate at different stages of breach development, and the relationship between the breach development rate and breach flow rate also varies under different inflow rates.

[0009] Previous studies have mainly focused on the breach mechanism, influencing factors, and breach process, but have not yet proposed a theoretical calculation model that can reasonably describe the development of the breach when the levee overflows. Moreover, the few relevant studies are all qualitative analyses and have not given the determinants of breach development or the quantitative relationship between them. Summary of the Invention

[0010] To address the aforementioned shortcomings of existing technologies, this invention provides a method for calculating the development process of a dike breach, proposing a method based on the unit width flow rate q of the breach. 单 As variables, calculation formulas were established for the transverse widening rate and vertical downward shear rate of the breach, which are applicable to the entire breach process and to test conditions with different inflow rates.

[0011] This is achieved using the following technical solution:

[0012] A method for calculating the development process of a dike breach, using the unit width discharge of the breach as the main parameter, establishes a parametric formula for the breach development process, including the following steps:

[0013] Step 1: Calculate the breach flow of the dike according to the formula (1) for the flow rate of a broad-crested weir:

[0014]

[0015] μ -- breach flow coefficient, dimensionless number;

[0016] Q -- Flood discharge from the breach in the dike, in cubic meters per second (m³) 3 / s;

[0017] B -- Width of the water surface at the breach, in meters;

[0018] h represents the depth of the breach, in meters (m).

[0019] Step 2: Based on the dike breach flow calculated in Step 1, the unit width flow of the breach is calculated using equation (2):

[0020]

[0021] q 单 --Flow rate per unit width of the breach, in cubic meters 2 / s;

[0022] Step 3: Based on the unit width flow rate of the breach calculated in Step 2, establish calculation formulas for the unit width flow rate of the breach, the transverse widening rate of the breach, and the vertical downward shear rate.

[0023] Step 4: Based on the lateral widening rate and vertical incision rate of the breach calculated in Step 3, calculate the lateral widening development process and the vertical incision development process of the breach, respectively.

[0024] Furthermore, step three specifically includes:

[0025] The transverse widening rate of the ulcer is calculated using equation (3a):

[0026]

[0027] The vertical downward shear rate of the ulcer is calculated using equation (3b):

[0028]

[0029] γ B --The rate of lateral widening of the breach, which physically represents the lateral expansion width of the breach per unit time, in m / s;

[0030] γ H --Vertical downward tangential velocity of the ulcer, in m / s;

[0031] a B b B a H b H --Erosion coefficient, a dimensionless parameter;

[0032] q 单c --The critical flow rate per unit width at the breach is related to the initiation shear stress and inherent properties of the soil, in meters (m). 2 / s.

[0033] Furthermore, step four specifically includes:

[0034] The lateral widening and development process of the breach is calculated using equation (4a):

[0035] B t+Δt =B t +γ B ·Δt(4a)

[0036] The vertical incision development process of the ulcer can be calculated using equation (4b):

[0037] H t+Δt =Z b0 -Z bt+Δt (4b)

[0038] B t+Δt --The transverse width of the breach at time t+Δt, in meters;

[0039] B t --Horizontal width of the breach at time t, in meters;

[0040] H t+Δt --Vertical depth of the breach at time t+Δt, in meters;

[0041] Z b0 --Elevation of the bottom of the breach at initial time 0, in meters;

[0042] Z bt+Δt --Elevation of the bottom of the breach at time t+Δt, in meters;

[0043] Δt -- Breach rupture time step, in seconds.

[0044] Elevation Z of the bottom of the breach at time t+Δt bt+Δt The calculation formula is as follows:

[0045]

[0046] Furthermore, at time t+Δt, the transverse width B of the breach t+Δt The calculation formula is as follows:

[0047]

[0048] Right now:

[0049]

[0050] Furthermore, the vertical depth of the ulcer at time t+Δt is H. t+Δt The calculation formula is as follows:

[0051]

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] (1) Compared with traditional empirical formulas, the present invention makes up for the shortcomings of the existing technology, such as the unclear nature of the breach development formula and the lack of physical meaning. The breach development process calculation method provided in the present invention has strong physical meaning.

[0054] (2) The unit width flow rate of the breach is essentially the same as the breach flow rate, but the unit width flow rate can more clearly illustrate the strength of the hydrodynamic effect on sediment scouring. It can avoid the influence of the breach size on the hydrodynamic effect of the breach in different stages. In form, it can describe the development process of the breach in the entire breach process, establish a unified quantitative expression for the whole process, calculate the entire process of the breach's lateral widening and vertical downward cutting development, and is applicable to test conditions with different inflow rates.

[0055] (3) The calculation method provided by the present invention requires few parameters, and the only measurement value involved in the calculation process is the water level value, which is easy to obtain. It has high feasibility, good repeatability and scientificity, and the calculation process is simple. Attached Figure Description

[0056] Figure 1 A schematic diagram showing the comparison between calculation and actual measurement of the change process of the transverse width of the breach;

[0057] Figure 2 A schematic diagram comparing the calculated and measured changes in the vertical depth of the ulcer.

[0058] Figure 3 This is a flowchart of one embodiment of the method for calculating the ulcer development process of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] Please see Figure 3 This invention provides a method for calculating the development process of a dike breach, comprising the following steps:

[0061] Step 1: Calculate the breach flow Q of the dike according to the formula (1) for the flow rate of a broad-crested weir:

[0062]

[0063] μ -- breach flow coefficient, dimensionless number;

[0064] Q -- Breach flow rate, unit m 3 / s;

[0065] B -- Width of the water surface at the breach, in meters;

[0066] h represents the depth of the breach, in meters (m).

[0067] Step 2: Calculate the unit width flow rate q of the breach using equation (2). 单 :

[0068]

[0069] q 单 --Flow rate per unit width of the breach, in cubic meters 2 / s;

[0070] h -- Breach depth, in meters (m). This occurs when the bottom elevation of the breach is higher than the downstream water level, i.e., Z. 蓄 ≤Z btn When h = ZZ btn When the bottom elevation of the breach is lower than the downstream water level, i.e., Z 蓄 >Z btn When h = ZZ 蓄 Z represents the breach water level. 蓄 This refers to the water level downstream of the breach.

[0071] Step 3: Calculate the transverse widening rate γ of the ulcer using equation (3a). B :

[0072]

[0073] The vertical downward shear rate γ of the ulcer is calculated using equation (3b). H :

[0074]

[0075] γ B --Lateral widening rate of the ulcer, in m / s;

[0076] γ H --Vertical downward tangential velocity of the ulcer, in m / s;

[0077] a B b B a H b H --Erosion coefficient, a dimensionless parameter;

[0078] q 单c --Critical flow rate per unit width of the breach, in meters 2 / s.

[0079] Step 4: Calculate the lateral widening and development process of the breach using equation (4a):

[0080]

[0081] The vertical incision development process of the ulcer can be calculated using equation (4b):

[0082]

[0083] B t+Δt --The transverse width of the breach at time t+Δt, in meters;

[0084] B t --Horizontal width of the breach at time t, in meters;

[0085] H t+Δt --Vertical depth of the breach at time t+Δt, in meters;

[0086] Z b0 --Elevation of the bottom of the breach at initial time 0, in meters;

[0087] Z bt+Δt --Elevation of the bottom of the breach at time t+Δt, in meters;

[0088] Δt -- Breach rupture time, in seconds.

[0089] Where: the transverse width of the breach at time t+Δt is B t+Δt The calculation formula is as follows:

[0090]

[0091] Right now:

[0092]

[0093] Vertical depth of the breach at time t+Δt: Vertical depth of the breach H t+Δt The calculation formula is as follows:

[0094]

[0095] The invention will now be further illustrated with a specific application example.

[0096] (1) Test conditions

[0097] The experimental system consisted of a river channel, scourable lateral dikes, a non-scourable floor, and a flood detention area. The main channel was 10m long and 1m wide. The scourable lateral dikes were parallel to the direction of the incoming flow, and the non-scourable floor measured 4.3m x 2.5m. During the experiment, water flowing through the dike breach could freely exit the floodplain without affecting the breach flow. In all experiments, the dikes were constructed using non-cohesive, homogeneous sandy material with a median particle size d. 50 The model uses uniform coarse sand with a thickness of 1 mm. The embankment is 3 m long, 0.3 m high, and 0.1 m wide at the top. The slope of the inner and outer embankments is 1:2, and the width of the bottom is 1.3 m. To ensure that the location of the overtopping breach is the same, a rectangular initial gap with a depth of 0.02 m and a width of 0.1 m is excavated at the top of the embankment 0.85 m from the upstream end.

[0098] (2) Calculation of breach flow

[0099] First, determine the initial transverse width of the breach as B0 = 0.1m, and the bottom elevation of the breach as Z. b0 =0.28m. Taking the moment when the initial breach of the dike just overflows as the initial time, i.e., t1 = 0s, as the water level Z rises before the breach, the unit width discharge of the breach increases, and the breach begins to expand. Calculate the breach discharge Q of the dike according to the broad-crested weir discharge formula (1):

[0100]

[0101] μ -- breach flow coefficient, dimensionless number;

[0102] (3) Calculation of flow rate per unit width of the breach

[0103] The unit width flow rate q of the breach can be calculated from equation (2). 单 :

[0104]

[0105] In t n At a certain moment, the breach unit flow rate exceeds the critical unit flow rate, and the breach begins to expand. At this point, the bottom elevation of the breach is higher than the downstream water level, i.e., Z. 蓄 ≤Z btn h = ZZ btn The unit width flow rate of the breach

[0106] (4) Calculation of the rate of ulcer development

[0107] The transverse widening rate of the ulcer is calculated using equation (3a):

[0108]

[0109] The vertical downward shear rate of the ulcer is calculated using equation (3b):

[0110]

[0111] (5) Calculation of the breach development process

[0112] t is calculated using equation (4a). n+1 The process of the breach widening horizontally:

[0113]

[0114] The vertical incision development process of the ulcer can be calculated using equation (4b):

[0115]

[0116] t n At any given moment, the transverse width and vertical depth of the breach have not changed, therefore B tn =B0=0.1, The critical scour flow rate per unit width was obtained from the experimental data as q. 单c =0.01m 2 / s,a B =0.00008, b B =67.813, a H =0.0004, b H = 86.53, substituting into equation (4a,b) yields:

[0117]

[0118]

[0119] t was calculated n+1 The size of the breach at time t is used as the initial breach size for the next calculation. The above steps are repeated to calculate t. n+2 By measuring the size of the ulcer at any given time and repeating this step, the development process of the ulcer can be obtained.

[0120] In this embodiment, the process of calculating the change in the transverse width of the ulcer is as follows: Figure 1 The process of vertical depth change of the ulcer is as follows: Figure 2 .from Figure 1 and Figure 2 It can be seen that the breach topography obtained using the breach development process calculation method provided by this invention matches the measured topographic data very well. Referring to the accuracy evaluation standard, the coefficient of determination (DC) is used to represent the degree of agreement between the calculated and measured processes, where 0 ≤ DC ≤ 1. The closer DC is to 1, the better the agreement between the calculated and measured processes. The calculation formula is as follows:

[0121]

[0122] In the formula: DC is the deterministic coefficient; x i y is the calculated value for the breach terrain. i These are measured values ​​for the breach terrain. The values ​​represent the average of the measured values. The coefficient of determination (DC) between the calculated and measured values ​​of the breach width is 0.986, and the coefficient of determination (DC) between the calculated and measured values ​​of the breach depth is 0.989. This indicates that the breach topographic development process calculated based on the comprehensive formula for breach development rate matches the actual breach development process to a good extent.

[0123] This invention provides a method for calculating the development process of a dike breach, relating to the field of flood disaster prevention. The method considers the influence of water flow forces on the breach development rate, uses the unit width flow rate of the breach as the main parameter, and establishes a parametric expression between the water flow elements of the breach and the development process to calculate the two main development processes: lateral widening and vertical downward shearing. The advantages of this method are: firstly, it can calculate the entire process of breach development and is applicable to different inflow rate test conditions; secondly, it requires few parameters, and the unit width flow rate of the breach, the main parameter for calculating the breach development process, can be directly obtained from the formula for the flow rate of a broad-crested weir, exhibiting high feasibility, good repeatability and scientific validity, and a simple calculation process; thirdly, the unit width flow rate of the breach reflects the scouring effect of water flow on the breach sediment, and the calculation formula established based on the actual development mechanism of breaches is more consistent with the physical mechanism. The method for calculating the development process of dike breaches provided by this invention clarifies the relationship between the development rate of breaches in non-cohesive dikes and hydraulic elements, and establishes a quantitative relationship expression, which is of great significance for predicting the process of dike breach and flood evolution.

[0124] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method of calculating the development of a breach in a dike, characterized in that: With breach single-width flow as the main parameter, the parameter formula of the breach development process is established, including the following steps: Step one: according to the wide crest weir flow formula (1), the dike breach flow is calculated: （1）； - breach flow coefficient, dimensionless number; Q - dike breach discharge, in m 3 / s; B--the water surface width at the breach, unit m; The breach water depth is the difference between the river water level and the breach bottom elevation when the water level outside the dike is lower than the breach bottom elevation, or the difference between the river water level and the water depth outside the dike. Step two: based on the dike breach flow calculated in step one, the single-width flow of the breach is calculated by formula (2): （2）； -- breach discharge per unit width, in m 2 / s; Step three: based on the single-width flow of the breach calculated in step two, the calculation formula of the single-width flow of the breach, the lateral expansion rate of the breach and the vertical incision rate of the breach is established, Step four: based on the lateral expansion rate and the vertical incision rate of the breach calculated in step three, the development process of the lateral expansion of the breach and the development process of the vertical incision of the breach are calculated respectively; Step three specifically includes: The lateral expansion rate of the breach is calculated by formula (3a): （3a）； The vertical incision rate of the breach is calculated by formula (3b): （3b）； --the rate of transverse expansion of the breach, which has a physical meaning of the transverse expansion width of the breach per unit time, in units of m / s; -- rate of vertical downward cutting of the breach, in m / s; a B , b B , a H , b H - erosion coefficient, dimensionless parameter; Critical value of single-width flow discharge of the breach, related to the incipient shear stress of the soil and its own properties, unit m 2 / s; Step four specifically includes: The development process of the lateral expansion of the breach is calculated by formula (4a): （4a）； The development process of the vertical incision of the breach is calculated by formula (4b): （4b）； -- Instantaneous breach lateral width, in m; - t time of the breach transverse width, in m; -- Instantaneous breach vertical depth, in meters; -- initial breach bottom elevation at time 0, in meters; -- Instantaneous breach bottom elevation, in meters; -- breach closure time step, in s, Time of breach bottom elevation The formula for calculating the time of breach bottom elevation is as follows: （5）。 2. The method of claim 1, wherein: the moment of time at which the breach occurs The formula for calculating the lateral width of the breach is as follows: （6a）； That is: （6b）。 3. The method of claim 1, wherein: Time Moment Depth of breach Depth of breach The calculation formula is as follows: （6c）。

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