Method for determining geometric and time characteristic parameters of breach of barrier dam based on overtopping collapse

Abstract

This invention discloses a method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure. The method includes collecting basic parameters and determining the reservoir capacity characteristic coefficient; determining the final breach morphology parameters; calculating the water depth in front of the dam corresponding to the peak flow rate based on the actual discharge volume at the end of the breach and its corresponding depth, the discharge volume at the peak flow rate, and the reservoir capacity characteristic coefficient; determining the breach bottom width at the peak flow rate by combining empirical coefficients with the final breach bottom width; calculating the vertical breach depth at the peak flow rate based on the sediment transport balance principle, the final breach bottom width, and the trapezoidal similarity principle; and solving for the duration of the rapid development stage of the breach based on the water balance equation and the peak flow calculation formula. This invention proposes a method for determining breach development parameters, including the duration of the rapid development stage reaching the peak flow rate, the breach morphology at the peak, and the total breach duration of this stage, enabling scientific prediction of the discharge flow process during a landslide dam overtopping failure.

Description

Technical Field

[0001] This invention belongs to the field of emergency response to landslide dam geological disasters, and specifically relates to a method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure. Background Technology

[0002] Landslide dams are typically formed by landslides or collapses triggered by natural events such as earthquakes or heavy rainfall, which block river channels. The resulting landslide-dammed lakes pose an extremely high risk of breaching. Unlike well-designed and compacted artificial earth-rock dams, landslide dams have loose structures, uneven materials, and are highly unstable. They are more prone to instability under the influence of reservoir water level fluctuations, posing a serious threat to downstream areas. Overtopping is the most common breaching mode. After water flows over the dam crest, erosion occurs, the breach gradually develops and expands, and eventually the dam collapses suddenly, resulting in a destructive flood.

[0003] Currently, methods for dam-break flood simulation mainly include statistical models, parametric models, simplified models based on physical processes, and refined models. While refined models can accurately simulate processes such as water flow, sediment, and dam deformation, they have high parameter requirements and are computationally complex, making them suitable primarily for cohesive earth dams but not commonly used for emergency response calculations of landslide dams. Statistical models fit historical dam-break case data and can quickly estimate breach parameters, but they often neglect the physical properties of the dam material and the dynamic processes of upstream flow, limiting their application to estimating peak flow values. Furthermore, the rapid estimation of the final breach morphology and duration in statistical models is largely based on data fitting, lacking a systematic consideration of material properties and hydraulic conditions, making it difficult to guarantee the reasonableness of the calculation results.

[0004] In contrast, parametric models and simplified models based on physical processes achieve a better balance between practicality and efficiency, exhibiting stronger engineering applicability. Parametric models simulate the breach process by pre-setting breach development patterns and key parameters, but their application heavily relies on expert experience; otherwise, scenario analysis of various breach morphologies and durations is required, increasing computational complexity. Simplified models based on physical processes, on the other hand, reasonably generalize based on the description of erosion and slope stability mechanisms, such as assuming uniform breach widening and constraining the final breach depth using statistical results, thus improving computational efficiency while maintaining certain physical meaning. However, the rationality of the assumptions used in these simplified models still needs improvement to make the calculation process more closely reflect actual working conditions. Furthermore, determining the breach discharge process requires measuring the vertical distribution characteristics of dam materials at various heights and performing multiple iterations of shear stress calculations, which is insufficient to meet the rapid response calculation requirements of breach management.

[0005] It is evident that existing landslide dam failure simulation and prediction methods still heavily rely on the accurate determination of key parameters such as breach morphology and development duration. However, current rapid estimations of these parameters are largely based on data fitting, lacking support from physical mechanisms. In particular, the definition of the breach development process duration is vague, and related research is scarce, directly impacting the practical effectiveness and emergency adaptability of existing models. Therefore, it is necessary to conduct in-depth research to propose more reasonable methods for determining breach parameters, providing theoretical support for existing breach flood process prediction models and improving the scientific rigor and timeliness of emergency responses. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention provides a method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure.

[0007] According to one aspect of the present invention, a method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on a roof-overflow failure is provided, comprising:

[0008] Collect basic parameters including dam body shape parameters, river width, upstream river topographic data, and reservoir capacity-water depth relationship curves to determine reservoir capacity characteristic coefficients;

[0009] Predict the final vertical failure degree of the dam and calculate the final vertical failure depth. Calculate the actual discharge volume at the time of failure and its corresponding upstream water depth, and the final breach morphology parameters of the dam. Determine the final vertical failure degree of the dam based on logistic regression formulas and engineering experience, calculate the final vertical failure depth, and calculate the actual discharge volume at the time of failure based on the final vertical failure depth, upstream river topographic data, and reservoir capacity-water depth relationship curve. Determine the corresponding upstream water depth, final breach top width, and final breach bottom width of the dam based on the actual discharge volume at the time of failure.

[0010] Based on the discharge volume at peak flow, the actual discharge volume at the end of the breach, the water depth in front of the dam corresponding to the actual discharge volume at the end of the breach, and the reservoir capacity characteristic coefficient, calculate the water depth in front of the dam corresponding to the discharge volume at peak flow.

[0011] The relationship between the breach bottom width at peak flow and the final breach bottom width is established by using empirical coefficients to determine the breach bottom width at peak flow.

[0012] Based on the principle of sediment transport balance and the final breach bottom width, the average volumetric sediment content, the sediment content at the peak flow time, and the projected area of ​​the breach at the peak flow time are derived. Then, based on the principle of trapezoidal similarity, the vertical breach depth at the peak flow time is calculated through the dam shape parameters.

[0013] Based on the water balance equation and peak flow calculation formula, combined with the breach projection area, sediment content, ratio of the water depth in front of the dam corresponding to the discharge volume at the peak flow time to the water depth in front of the dam corresponding to the actual discharge volume at the end of the breach, and the flow coefficient determined by engineering experience, the duration of the rapid development stage of the breach is calculated.

[0014] The shape parameters of the landslide dam include the height of the pass, the length of the top of the dam along the river channel, the length of the bottom of the dam along the river channel, and the upstream and downstream slope angles of the dam.

[0015] Furthermore, the methods for determining the storage capacity characteristic coefficient include:

[0016] The relationship between the reservoir capacity and water depth of the landslide dammed lake is fitted as a power function: W represents the reservoir capacity of the landslide dammed lake, and H represents the corresponding water depth (water depth in front of the dam).

[0017] The power function is subjected to a logarithmic transformation, and then linear regression analysis is performed on a logarithmic coordinate system. The intercept of the linear regression line is the reservoir capacity characteristic coefficient. The slope of the straight line is the reservoir capacity characteristic coefficient. .

[0018] Furthermore, the duration of the rapid development phase of the landslide dam failure is set. The peak flow rate is reached at 1 / 3 of the time. The discharge from the reservoir is 1 / 3 of the actual discharge at the end of the breach. This is used to calculate the water depth in front of the dam corresponding to the discharge at the peak flow rate. The expression is:

[0019] ;

[0020] in, The actual water discharge at the moment the breach ends corresponds to the water depth in front of the dam. This is the storage capacity characteristic coefficient.

[0021] Furthermore, the breach width is used to determine the peak flow time. The expression is as follows:

[0022] ;

[0023] in, The final breach width is given by r, which is an empirical coefficient. The rules for its value are as follows: ① When a common earth-rock mixed landslide dam partially collapses, the breach width after the flood peak accounts for about 1 / 5 to 1 / 6 of the final breach width laterally, so r = 4 / 5 to 5 / 6; ② For dams with almost complete soil collapse: r = 1. For this type of dam, the headward erosion time is longer. When the "steep slope" develops back to the upstream dam slope, the downstream water flow has a large potential energy, and the breach develops rapidly to near its final form. At the flood peak (when the breach flow reaches its peak), the breach width is approximately equal to the final breach width.

[0024] Furthermore, it is used to calculate the average volumetric sand content. Sand content at peak flow rate and the projected area of ​​the breach at peak flow time The expression is as follows:

[0025] When the final vertical failure rate of the dam body is greater than 1 / 2 of the dam height

[0026] ;

[0027] ;

[0028] ;

[0029] When the final vertical failure degree of the dam body is ≤1 / 2 of the dam height

[0030] ;

[0031] ;

[0032] ;

[0033] in, The actual discharge volume at the end of the breach, parameter The water depth in front of the dam corresponding to the discharge volume at peak flow. The actual discharge volume at the end of the breach corresponds to the water depth in front of the dam. The ratio of .

[0034] Furthermore, the specific steps for calculating the vertical inrush depth at the peak flow time using the trapezoidal similarity principle are as follows:

[0035] The length of the dam bottom along the river channel is calculated using the dam shape parameters; these parameters include the length of the dam top along the river channel, the dam height at the pass, and the upstream and downstream slope angles of the dam.

[0036] By combining the trapezoidal similarity formulas and substituting the calculated breach projection area at the peak flow time, the vertical breach depth at the peak flow time can be estimated.

[0037] Furthermore, the expression for calculating the vertical inrush depth at the peak flow moment is as follows:

[0038] ;

[0039] ;

[0040] Among them, the length of the top of the dam along the river channel Length of the dam base along the river channel The mountain pass is high. slope angle .

[0041] Furthermore, the rapid development phase used to calculate the failure rate lasted for... The expression is as follows:

[0042] ;

[0043] In the formula: This is the flow coefficient.

[0044] According to a second aspect of the present invention, an apparatus for determining the geometric and temporal characteristic parameters of a landslide dam breach based on a roof overtopping failure is provided, the apparatus being used to implement the steps of the above-described method.

[0045] According to a third aspect of the present invention, a method for predicting the outflow process of a landslide dam breach is provided, comprising predicting the outflow process of a landslide dam breach based on geometric and temporal characteristic parameters of the breach; wherein the geometric and temporal characteristic parameters of the landslide dam breach are obtained based on the above-described parameter determination method.

[0046] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0047] 1. This invention, starting from the physical mechanism, proposes a method for determining parameters characterizing breach development beyond the final breach morphology. This method mainly includes the duration of peak flow reached during the rapid development phase, the breach morphology at peak flow, and the total breach duration during this phase. This avoids several assumptions in model calculations regarding breach morphology (1 / 3 breach, 2 / 3 breach, complete breach, etc.), breach duration (1 hour, 2 hours, etc.), and the uniform variation of the breach throughout the entire time period. The results can be used together with the predicted final breach morphology as model input parameters to calculate the breach discharge flow process. Alternatively, the parameters characterizing breach development can be directly used to estimate the generalized breach discharge flow process during the rapid development phase of the breach.

[0048] 2. This invention only needs to determine some key parameters characterizing the development of the breach, such as the duration of reaching the peak flow in the rapid development stage, the breach morphology at the peak, and the total breach duration in this stage, to determine the breach discharge flow process. This effectively avoids the drawbacks of existing models that require multiple iterations of measuring the vertical characteristics of the dam material at various heights and calculating shear stress when determining the breach discharge flow process, thus meeting the needs of rapid response calculation for breach disposal.

[0049] 3. This invention makes the flow process prediction more consistent with the actual physical mechanism of overtopping failure, and the prediction results can be adapted to different application scenarios such as refined engineering assessment and disaster emergency decision-making, providing reliable technical support for disaster prevention and control and engineering assessment of landslide dam overtopping failure. Attached Figure Description

[0050] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0051] Figure 1 A flowchart illustrating the method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on a roof-over-breach failure, provided in an embodiment of the present invention.

[0052] Figure 2 The projected area of ​​the ulceration in an embodiment of the present invention. ;

[0053] Figure 3 This paper presents the lateral widening and temporal relationship of the erosion section / breach at each stage of the dam crest failure process under typical experimental conditions in an embodiment of the present invention. (a) represents condition I-1, (b) represents condition I-2, (c) represents condition I-3, (d) represents condition I-4, (e) represents condition I-7, and (f) represents condition I-10. 50 The median particle size;

[0054] Figure 4 To establish a small-scale physical model of the river channel (high-definition cameras were set up at the front of the dam, the top of the dam, and the downstream of the dam to capture the water storage and breaching process).

[0055] Figure 5 The terrain in the small-scale river channel solid model is scaled down based on the A landslide dam.

[0056] Figure 6 This is a particle size distribution curve of the test dam material;

[0057] Figure 7The diagram shows the cross-sectional shape of dams with different length-to-height ratios, where (a) represents working condition III-6, (b) represents working condition III-7, and (c) represents working condition III-8.

[0058] Figure 8 A comparison of the generalized outflow process of a flood failure based on the triangle principle during the rapid development phase with the actual outflow process of a flood failure.

[0059] Figure 9 To compare the outflow process during the rapid development stage of a dam-break unsteady flow model with the actual outflow process during a dam-break;

[0060] Figure 10 The results of the model calculation of the outflow process and the actual outflow process are compared, where (a) is condition 1-5 (the vertical direction of the dam body is greater than or equal to half-outflow); (b) is condition 1-8 (the vertical direction of the dam body is less than half-outflow). Detailed Implementation

[0061] The terms “comprising” and “having”, and any variations thereof, in the specification, claims, and accompanying drawings of this invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or apparatus that includes a series of steps or units, not necessarily limited to those explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0062] 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. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0063] The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure provided in this invention embodiment is as follows: Figure 1 As shown, it includes:

[0064] Collect basic parameters including dam body shape parameters, river width, upstream river topographic data, and reservoir capacity-water depth relationship curves to determine reservoir capacity characteristic coefficients;

[0065] The final vertical failure degree of the dam body is determined based on logistic regression formula and engineering experience. The final vertical failure depth is calculated. Based on the final vertical failure depth, upstream river topographic data and reservoir capacity-water depth relationship curve, the actual discharge volume at the end of the failure is calculated and the corresponding water depth in front of the dam, the final top width and bottom width of the dam breach are determined.

[0066] Based on the discharge volume at peak flow, the actual discharge volume at the end of the breach, the water depth in front of the dam corresponding to the actual discharge volume at the end of the breach, and the reservoir capacity characteristic coefficient, calculate the water depth in front of the dam corresponding to the discharge volume at peak flow.

[0067] The relationship between the breach bottom width at peak flow and the final breach bottom width is established by using empirical coefficients to determine the breach bottom width at peak flow.

[0068] Based on the principle of sediment transport balance and the final breach bottom width, the average volumetric sediment content, the sediment content at the peak flow time, and the projected area of ​​the breach at the peak flow time are derived. Then, based on the principle of trapezoidal similarity, the vertical breach depth at the peak flow time is calculated through the dam shape parameters.

[0069] Based on the water balance equation and peak flow calculation formula, combined with the breach projection area, sediment content, ratio of the water depth in front of the dam corresponding to the discharge volume at the peak flow time to the water depth in front of the dam corresponding to the actual discharge volume at the end of the breach, and the flow coefficient determined by engineering experience, the duration of the rapid development stage of the breach is calculated.

[0070] I. The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on a roof-over-breach failure according to embodiments of the present invention specifically includes the following steps:

[0071] Step S1: Determine the basic parameters and determine the storage capacity characteristic coefficient.

[0072] S1.1 Collect core basic parameters of the landslide dam, reservoir area, and river channel: river width (m), complete topographic data of the upstream river channel, reservoir capacity-water depth relationship curve, and dam shape parameters including dam height at the pass. Length of the dam crest along the river channel Length of the dam base along the river channel Downstream slope of the dam and upstream slope angle .

[0073] S1.2 Determine the reservoir capacity characteristic coefficients α and s: Fit the relationship between the reservoir capacity and water depth of the landslide dammed lake area into a power function form:

[0074]

[0075] Where W represents the reservoir capacity of the landslide dammed lake, and H represents the corresponding water depth;

[0076] S1.3 Perform a logarithmic transformation on the above power function and solve it using linear regression in a logarithmic coordinate system. and The storage capacity characteristic coefficient can be calculated on a logarithmic coordinate system, where... The intercept is... The slope represents the actual volume of water discharged at the end of the subsequent flood breach. (m³) and the actual discharge volume at the end of the breach corresponding to the water depth in front of the dam. (m) is calculated based on this relationship. Regardless of Is it equal to the height of the mountain pass dam? Under the same reservoir area's capacity-water depth relationship curve and The values ​​are the same.

[0077] Step S2: Predict the final vertical failure degree of the dam body and calculate the final vertical failure depth.

[0078] S2.1 uses a logistic regression formula combined with engineering experience to determine the final vertical failure degree of the dam body, which is divided into two categories: final vertical failure degree ≤ 1 / 2 dam height and final vertical failure degree > 1 / 2 dam height.

[0079] S2.2 Calculate the final vertical breach depth (m): For the high mountain pass dam The product of the final vertical collapse degree.

[0080] S2.3 Calculate the actual discharge volume at the end of the breach. (m³): Based on the determined final vertical breach depth The results were obtained by combining upstream river topographic data and reservoir capacity-water depth relationship curves. .

[0081] S2.4 Determine the water depth corresponding to the maximum actual discharge capacity upstream of the dam by combining upstream river topographic data and reservoir capacity-water depth relationship curves. (m), which is the actual water discharge at the moment the breach ends, corresponding to the water depth in front of the dam.

[0082] Step S3: Calculate the final breach morphology parameters of the dam body (top width) Bottom width )

[0083] In patent CN116561529B (authorization announcement date 2025.02.28), the inventors proposed a rapid prediction method for the final vertical failure degree of a dam by analyzing the relationship between lake parameters, dam parameters, and the final vertical failure degree (the ratio of the final vertical failure depth to the dam height at the pass). This method includes logistic regression formulas and empirical judgments for predicting the dam's vertical (final vertical failure degree) failure at 1 / 3 (dam height), 1 / 2, 2 / 3, or complete failure (equal to dam height), as well as application methods for dam structures with vertically binary and ternary superimposed structures.

[0084] Based on this, formulas for calculating the final breach top and bottom widths (determination coefficient R) were established for different degrees of final vertical failure of the dam body. 2 All are greater than 0.86, which can basically meet the needs of predicting the final transverse widening (top width and bottom width) of the breach in experiments and practical applications.

[0085] Scenario 1: When the final vertical failure is less than or equal to 1 / 2 of the dam height,

[0086] (R 2 =0.96) (1)

[0087] (R 2 =0.86) (2)

[0088] Scenario 2: When the final vertical failure degree is greater than 1 / 2 dam height,

[0089] (R 2 =0.98) (3)

[0090] (R 2 =0.97) (4)

[0091] In the formula: The final breach width is in meters (m). The final breach width is in meters (m). The actual discharge volume at the end of the breach, in m 3 The final vertical breach depth can be calculated based on the relationship curve between the upstream river topography and the reservoir capacity and water depth after the final vertical breach depth is determined. The width of the river channel; The final vertical breach depth is expressed in meters (m). Indicates the projected area of ​​the breach ( Figure 2 ).

[0092] Step S4: Calculation of breach morphology parameters at peak flow rate

[0093] The breach morphology parameters at the peak flow time are the core parameters characterizing the rapid development stage of the breach, including the water depth in front of the dam corresponding to the discharge volume at the peak flow time, the breach bottom width, and the vertical breach depth. This invention first verifies the rationality of the assumption of the peak flow occurrence time through theoretical derivation, and then calculates each morphology parameter in turn.

[0094] S4.1 Time assumptions for reaching peak dam failure flow

[0095] During the source erosion process, the erosion rate is low and the breach depth is limited; the downstream storage capacity during this stage is... The proportion in the middle is very small. During the process of scour and sedimentation balance and restoration to stability, the outflow is close to the upstream inflow, the water level in the upstream reservoir remains stable, and the outflow capacity is also extremely small during this stage. Therefore, the area enclosed by the outflow process and duration during the rapid development stage of the breach can be approximated as equal to... Based on the principle of water balance, the expression can be written as:

[0096] (5)

[0097] In the formula: For peak flow rate, m 3 / s; The duration of the source erosion process is ,but The duration of the rapid development phase during the collapse process is s.

[0098] Assuming in At that moment, the dam breach flow reached its peak, and the actual discharge from the reservoir at that moment was the same as the actual discharge at the end of the breach. One-third of it. Its rationality is verified from a theoretical derivation perspective.

[0099] Assume the actual discharge volume at the end of the landslide dam breach. The actual discharge volume at the end of the breach corresponds to the water depth in front of the dam. The relationship is:

[0100] (6)

[0101] In the formula: and The storage capacity characteristic coefficient can be calculated on a logarithmic coordinate system, where... The intercept is... The slope is denoted as .

[0102] Then we have:

[0103] (7)

[0104] Combining equations (6) and (7), we can obtain:

[0105] (8)

[0106] In the formula: and These represent the water depth in front of the dam corresponding to the actual discharge volume at the end of the breach and the water depth in front of the dam corresponding to the discharge volume at the peak flow time, respectively, in meters;

[0107] In 1982, Ritter proposed the formula for the peak flow of a dam that breaks instantaneously in a rectangular riverbed:

[0108] (9)

[0109] assumed When the peak flow rate is reached, the water depth in front of the dam corresponding to the discharge volume at the peak flow rate is: ,Will Substituting Xie Renzhi's formula (1989), we obtain the formula for calculating peak flow, as shown below:

[0110] (10)

[0111] This represents the final average width of the breach. Regarding... The value of is mainly related to the river channel topography and the upstream slope of the dam. Taking the A landslide dam site as an example, Substituting the value into equation (10) yields The coefficient before the peak flow is close to 1, which is not much different from the calculated value when the coefficient is 0.926. It can be seen that before the peak flow is reached, the water level in the upstream reservoir does not change much, and there is less siltation downstream at this time. Comparing the above equations (9) and (10), the calculated values ​​of the peak flow are not much different. This indicates that the water depth in front of the dam corresponds to the peak flow. The value is reasonable, which further illustrates the assumption. The peak flow rate of the breach is reached at any moment, and the discharge volume is That's reasonable.

[0112] S4.2 Calculation of breach bottom width at peak flow rate

[0113] Determining the breach bottom width during peak flow: Analysis The breach width at any given moment, when the breach flow reaches its peak, is:

[0114] (11)

[0115] (12)

[0116] From equations (11) and (12), we can deduce the width of the ulcer base at this time. Reaching the maximum value As can be seen from the experimental phenomena, in After the peak breach flow (when the breach flow reaches its peak), some minor collapses are still visible on both sides of the breach, but the amount of collapse is much smaller compared to the period before the peak breach flow. Furthermore, since the collapsed dam material on both banks remains above the breach water level after the flood peak and will not be completely washed away, its impact on the calculation of the breach discharge process is minimal. The width of the breach at any given moment ( Approximately equal to the final breach bottom width The expression relating the breach width at peak flow to the final breach width is shown below:

[0117] (13)

[0118] right Let's discuss the possible values ​​of : Figure 3 The paper presents the relationship between the lateral widening (average width) of the erosion section / breach at each stage of a typical test failure process and time. It shows that during the rapid development stage, the breach widening after the flood peak accounts for approximately 1 / 5 to 1 / 6 of the final lateral widening. For example, if the breach widening (average width) at the flood peak (peak flow) is approximately 130 cm, the final lateral widening (average width) is approximately 160 cm, and the breach widening (average width) after the flood peak is 130 cm... Figure 3 (c)). The variation patterns of the breach top width and breach bottom width are similar to... Figure 3 The statistically significant lateral widening (average width) of the erosion cross-section / breach at the dam crest is consistent. Therefore, in equation (13) The value is approximately 4 / 5-5 / 6; furthermore, depending on the actual situation, for soil dams (nearly completely collapsed), Option 1 is acceptable because this type of dam has a longer headward erosion period. When the "steep slope" develops back to the upstream dam slope, the downstream water flow gains greater potential energy, and the breach develops rapidly. By the time the breach flow reaches its peak, the breach has already developed to near its final shape.

[0119] S4.3 Breach depth at peak flow rate (vertical breach depth at peak flow rate) )calculate

[0120] Based on the principle of sediment transport balance and the calculation formula for the lateral widening of the final breach (the top and bottom widths of the final breach), the average volumetric sediment content, the sediment content at the peak flow time, and the projected area of ​​the breach at the peak flow time are derived. Then, based on the principle of trapezoidal similarity, the vertical breach depth at the peak flow time is calculated using the dam shape parameters.

[0121] Let's take equation (4) as an example to analyze the average volumetric sand content. :

[0122] (14)

[0123] but:

[0124] (15)

[0125] parameter The constant, therefore, the form of equation (15) is the same as the average volumetric sand content proposed by Xie Renzhi's formula (1989). The empirical formulas are similar in form, namely:

[0126] (16)

[0127] In the formula: The average erosion coefficient; Soil quality coefficient; For the reservoir capacity in front of the dam, m 3 / s; H is the water depth in front of the dam, in meters.

[0128] The average volumetric sand content is visible. It is largely related to the water depth H in front of the dam, and also to the reservoir capacity in front of the dam. The relationship is inversely proportional because the breach collapse has a significant impact, and its sediment transport capacity is non-linear. The erosion of most dam materials is concentrated within a short period. Therefore, the larger the reservoir capacity, the longer the peak flow time of the breach, and the higher the corresponding average volumetric sediment content. The lower. Now let's compare equations (15) and (16): Unlike equation (16), equation (15) takes into account the characteristic that landslide dams are mostly partially breached. Therefore, the parameters related to breach in the formula do not include the upstream water storage that does not play a role in the entire breach process. The average volumetric sand content is directly proportional to the average scour coefficient, and the average scour coefficient is related to the reservoir capacity and dam material. Therefore, the coefficient before equation (15) takes into account the scour characteristics of the dam body. Under the final breach morphology, The actual discharge volume at the end of the breach corresponds to the water depth in front of the dam. If they are equal, then the average volumetric sand content can be considered equal. The actual discharge volume at the end of the breach corresponds to the water depth in front of the dam. It has a significant impact, and is also related to the actual amount of water discharged at the moment the dam breach ends. They are inversely proportional. This is consistent with the theory in Xie Renzhi's formula (1989). Equation (15) is derived from equation (4), and it serves as the average volumetric sand content. The empirical formula, whose form reflects actual conditions, states that the average volumetric sand content changes throughout the entire process as the breach shape and discharge volume change. Changes have also occurred.

[0129] Equation (15) can be written as:

[0130] (17)

[0131] Furthermore,

[0132] (18)

[0133] Therefore:

[0134] (19)

[0135] because:

[0136] (20)

[0137] Then we have:

[0138] (twenty one)

[0139] (twenty two)

[0140] in, The volumetric sand content at a certain moment;

[0141] Substituting equation (22) into equation (21), we get:

[0142] (twenty three)

[0143] Differentiating both sides of equation (23) yields:

[0144] (twenty four)

[0145] but:

[0146] (25)

[0147] As can be seen from equation (24), when hour, If it does not converge, the rationality of equation (24) can be discussed using the sediment transport rate formula:

[0148] Sediment transport rate:

[0149] (26)

[0150] Equation (26) can also be written as:

[0151] (27)

[0152] In the formula: denoted as ρ, where ρ is the flow velocity of the breach water, in m / s; g is the acceleration due to gravity.

[0153] As shown in equations (7) and (8) above, in the breakdown flow... Before reaching its peak value, the change in water depth corresponding to the outflow volume at the end of the dam breach is not significant. The value does not change significantly. For example, for landslide dam A, the water depth corresponding to the outflow volume at the moment of breach completion changes from the maximum water depth. Reduced to 0.74 , The values ​​differ by only 9%.

[0154] According to the principle of sediment transport balance:

[0155] (28)

[0156] Where: parameters Let m be the effective reservoir capacity upstream of the dam at time t. 3 / s; parameter Let t be the water depth corresponding to the outflow volume in front of the dam. The actual discharge volume at the end of the breach corresponds to the water depth in front of the dam. The ratio; Let be the width of the breach at time t; Let t be the volumetric sediment content of the breach flow at time t; E is the discharge flow rate at the breach. t W is the projected area of ​​the breach at time t; t The actual discharge volume at time t is [value].

[0157] Therefore, the peak flow rate of the breach water flow was reached. At that time, there were:

[0158] (29)

[0159] Where: parameters For the dam to reach its peak flow rate (assumed (Time) The water depth corresponding to the discharge volume in front of the dam at that time The actual discharge volume at the end of the breach corresponds to the water depth in front of the dam. The ratio of .

[0160] According to equation (27), under the final breach condition, the water depth corresponding to the outflow volume in front of the dam at the end of the breach is... The value is very small, while At what moment, the water depth corresponding to the outflow volume in front of the dam is ,therefore:

[0161] (30)

[0162] Substituting equation (30) into equation (29):

[0163] (31)

[0164] When deriving equation (31) using equation (4) as an example, the coefficients in equation (15) take into account the scouring characteristics of the dam body. Therefore, equation (31) is applicable to the calculation when the final vertical failure degree is greater than or equal to 1 / 2 failure.

[0165] When the final vertical collapse is less than 1 / 2 collapse, equations (32), (33) and (34), (35) should be derived from equation (2) as an example:

[0166] (32)

[0167] (33)

[0168] (34)

[0169] (35)

[0170] Analyzing equations (31) and (35), the coefficient terms in the formulas Empirical values ​​can be determined by combining the actual ulcer widening process; parameter items The determination method is shown in equations (4) and (2). Based on the reservoir capacity-water depth relationship and the river width, the parameter terms in the formula can be determined. And coefficient terms, finally obtaining the parameters. .

[0171] When parameter Once determined, the shape of the landslide dam (the length of the dam top along the river channel) can be determined based on the principle of trapezoidal similarity. Length of the dam base along the river channel Dam height Downstream slope angle Given the information, equations (36) and (37) can be used to estimate the result. Constantly descending towards the depths of the collapse ( Figure 2 ).

[0172] (36)

[0173] (37)

[0174] Step S5, the rapid development process of the collapse lasts for a period of time calculate

[0175] S5.1 Determine the flow coefficient Values: Take a value between 1.4 and 1.7 (based on engineering experience; 1.5 is commonly used).

[0176] S5.2 Based on the water balance equation and Xie Renzhi's formula (1989), a unified formula for calculating the peak flow rate before the flood peak is used to estimate the duration of the rapid development stage of the flood breach. :

[0177] From the water balance equation, we get:

[0178] (38)

[0179] Rapid development stage for:

[0180] (39)

[0181] (40)

[0182] In the formula: Here, the flow coefficient is... Take a value between 1.4 and 1.7. It is worth noting that the required parameter in equation (39) It includes the incision volume during the headward erosion stage, but the incision depth and discharge volume during this stage are very small, resulting in minimal error. Sensitivity analysis of the value of s shows that the value of s is relevant to... and The value has little impact, but it is highly sensitive to the duration of rapid development.

[0183] II. Verification of parameters characterizing breach development under various working conditions during the rapid development phase

[0184] Now we will verify equation (39), which contains parameters. time Therefore, when vertical breach depth is difficult to measure, the verification effect of time can also illustrate the rationality of equations (31) and (35). The working conditions used for verification here include working conditions I-1~I-12, II-3~II5, III-2~5, III7 and IV-2~3. Table 1 shows the breach depth at the peak flow time (vertical breach depth at the peak flow time) under the above verification working conditions. Calculated values, and the rapid development phase Calculated and actual values. As shown in Table 1, the vertical breach depth at peak flow time increases with the coarsening of the dam material. The value decreases, accounting for approximately 1 / 2 to 2 / 3 of the final vertical breach depth. This contrasts with the rapid development stage. Calculated values ​​and rapid development stage Actual values ​​show that dams with a final vertical failure rate greater than 1 / 2 (I-1~I-6, II-3, III-2~III-5, IV-1, IV-3) have better predictive performance than dams with a final vertical failure rate less than 1 / 2 (I-7~I-12, II-4~II-5, III-7). In cases where the final vertical failure rate is greater than 1 / 2, case III-3 shows poor verification results, with calculated values ​​exceeding actual values. This is because, in reality, "slender" dams experience severe seepage and collapse during headward erosion, and once they fail, they will rapidly reach peak flow. In cases where the final vertical failure rate is less than 1 / 2: case II-4 shows poor verification results because, in this case, the dam's vertical structure is uneven, and the underlying material d... 50 =0.18mm, top layer material =6 mm, the calculated value is larger than the actual value. In reality, the bottom material has very weak erosion resistance and the failure time is short. The verification results of II-11 and II-12 are not good because under this condition, there are few fine particles in the dam body and the coarse and fine particles have poor adhesion. Under high flow rates (3L / s, 5L / s), once the failure occurs, the dam body material on both sides of the breach will collapse rapidly, the water in the upstream reservoir will be discharged rapidly, and the flood peak time will be brought forward. The dam face of the landslide dam on site is wider and gentler, and the upstream flow is generally small. The dam body is composed of wide-graded materials, of which fine particles account for a large proportion. Therefore, in summary, the calculation methods given in the above formulas (31), (35) and (40) are applicable to most non-special working conditions on site.

[0185] Table 1. Validation results of parameters characterizing breach development under various working conditions during the rapid development phase.

[0186]

[0187] Note: The unit for ulcer depth in the table is meters (m); the unit for time is seconds (s).

[0188] III. Theoretical Basis and Implementation Process

[0189] 3.1 Test Conditions

[0190] This invention conducts generalized experiments, not a reenactment of a specific landslide dam failure, but only to study the patterns and mechanisms. However, to reflect the impact of river channel topography (narrow and deep "V" shaped terrain) on the failure, and considering data availability, a scaled-down river channel model was created, referencing the topography of landslide dam A (98°41′51.60″E, 31°4′54.93″N) from 1.5 km upstream to 2 km downstream of the dam in 2018. Figure 4-5 ).

[0191] This invention fully considers the main influencing factors affecting the failure of landslide dams and conducts a generalized study of their laws and mechanisms. Based on the characteristics of landslide dams, the main influencing factors selected for the experiment include: upstream flow, dam material composition (material gradation, dam structure), dam shape (including length-to-height ratio), and dam density. The specific working conditions and their applications are as follows:

[0192] (1) Upstream flow

[0193] The test conditions for the upstream inflow group include conditions I-1~3, I-4~6, I-7~9, and I-10~12. Based on some field data of upstream inflow from the landslide dam, three upstream inflows were set in the model, with values ​​of 1 L / s, 3 L / s, and 5 L / s (Table 2).

[0194] When studying the impact of upstream flow, the material composition, moisture content, and density of the dam body were kept basically the same in each experimental group. The "control" dam body in Table 2 was generalized as a trapezoid, with its dimensions scaled down to the proportions of the landslide volume of the landslide dam A on November 3, 2018 (1:200 and 1:150). The upper and lower base lengths of the landslide dam under the on-site landslide volume were 195m and 500m, respectively, with a height of 96-100m. Therefore, the upper and lower base lengths of the "control" dam body in this river channel model along the river channel were 1m and 2.5m, respectively, with a height of 0.7m. The width of the dam body perpendicular to the river channel was approximately 2.1m (fully blocked).

[0195] Table 2 Test Condition Settings - Upstream Flow and Dam Gradation

[0196]

[0197] (2) Material composition of the dam body

[0198] The material composition directly affects the erosion resistance and hazard of landslide dams, and is mainly related to the formation mode of the dam body. Landslide dams formed by high-level reverse landslides have a finer particle composition, while those formed by low-level longitudinal landslides contain a certain proportion of coarse particles. The material composition of the dam body includes both the dam material and the dam structure.

[0199] As shown in Table 2, the working conditions for the dam material groups include I-1, I-4, I-7, and I-10 with an upstream inflow of 1 L / s; I-2, I-8, and I-11 with an upstream inflow of 3 L / s; and I-3, I-6, and I-12 with an upstream inflow of 5 L / s. Among these, working condition I-13 initially had an upstream inflow of 5 L / s, but due to the balance between inflow and seepage, failure only occurred when the upstream inflow reached 10 L / s. The main types of landslide dams include rock dams, earth dams, and the common earth-rock hybrid dam. When setting the working conditions for the dam material groups, scaling the particle size distribution of the landslide dam in the field to the river model according to the material scale would result in very small particle sizes in all test groups, failing to reflect the influence of coarse and fine particles on dam failure. Therefore, a generalization treatment is often performed on the dam material. The particle size distribution curves of the dam materials after generalization considering various landslide dam material types are shown in [reference needed]. Figure 6 .

[0200] The aforementioned homogeneous dam design can be used to study the development process and mechanism of landslide dam breaches. Based on the compositional relationships of the landslide dam's materials, the engineering geological structure of the dam body includes not only homogeneous structures but also binary and ternary stacked structures. Under the influence of heterogeneous structures, the discharge volume and final breach morphology after a landslide dam breach differ, thus necessitating the study of the dam structure's impact. Table 3 outlines the working conditions for the dam structure group. There are two types of binary stacked structures. One type is relatively rare, where the bottom layer of the dam body consists of relatively intact rock strata, and the top layer consists of fine-grained soil. For this type of dam structure, the bottom layer uses bricks to simulate intact bedrock strata, while the top layer uses the dam material from control group II-1. The other type typically has a bottom layer composed of fine-grained soil, and the top layer mainly consists of broken stones. For this type of dam structure, the bottom layer uses the dam material from control group II-1, while the top layer uses the dam material from control group II-2. The bottom layer of the ternary stacked structure consists of relatively complete rock strata, the middle layer mainly consists of broken stones, and the top layer mainly consists of fine-grained soil. For this type of dam structure, the bottom layer uses brick blocks to simulate complete bedrock strata, the middle layer uses dam materials from II-2, and the top layer uses dam materials from II-1.

[0201] Table 3 Test Condition Settings - Dam Structure

[0202]

[0203] (3) Dam shape

[0204] Regarding the influence of the shape of the landslide dam, this generalized experiment first designed a "control shape" based on the volume of the secondary landslide body of landslide dam A in 2018. Figure 7 Based on this, the design of the dam shape and working conditions is based on the case of a landslide dam on site (Table 4).

[0205] Table 4 Test Condition Settings - Dam Shape

[0206]

[0207] (4) Dam body density

[0208] Compared to artificial earth-rock dams, landslide dams have a looser structure. This experiment designed three different compaction conditions to reflect the influence of compaction. Under each experimental condition, the control dam shape was a "control shape", the upstream flow rate remained constant (1 L / s), and the water content was the same (Table 5).

[0209] Table 5 Test Condition Settings - Dam Body Compaction

[0210]

[0211] 3.2 Formula Verification

[0212] The parameters for characterizing breach development proposed in this invention are applied to rapidly determine the generalized breach discharge flow process. Multi-dimensional verification is then conducted using engineering examples and classical models to further validate the practicality and reliability of the method. The specific verification process is as follows:

[0213] (I) Verification of the generalized outflow process of the collapse test based on the triangle principle

[0214] The generalized outburst discharge process estimation applies the triangle principle. Specifically, it is assumed that the generalized outburst discharge process and the outburst duration form a triangle, and the area of ​​the triangle is the actual discharge volume. When the total duration of the rapid development phase and the duration when the outburst discharge reaches its peak are known, the height of the triangle (peak flow) can be calculated, and the generalized outburst discharge process can be determined.

[0215] Using the landslide dam A on November 3, 2018 as an engineering example, and following the vertical failure prediction method in patent CN116561529B, the predicted vertical failure of the dam was 2 / 3, which matched the actual vertical failure level. The actual discharge was approximately 488 million cubic meters. 3 (Excluding residual storage capacity). According to equation (39), the rapid development stage... The method determined that the pre-peak duration of the rapid development phase was approximately 9669 seconds (about 3 hours). The dam actually entered the rapid development phase after 2:20 PM on the 13th, reaching its peak flow at 6:00 PM on the 13th, with an actual pre-peak duration of approximately 3 hours and 40 minutes. (Predicted rapid development phase) The value basically matches the actual situation. Therefore, assuming that the area enclosed by the outflow process and the outflow duration forms a triangle, the peak outflow can be roughly estimated at 33644 m³ / h. 3 / s, close to the actual peak flow rate of 31000m³ / s.3 / s( Figure 8 As can be seen, the method for determining parameters characterizing breach development proposed in this invention can basically meet the needs of on-site breach management.

[0216] (II) Embedding Validation Based on a One-Dimensional Dam-Break Unsteady Flow Model

[0217] In the one-dimensional unsteady flow model of dam-break (source model), the cross-section where the dam body is located is treated as the inner boundary of the computational domain, and the weir flow formula is used to calculate it. The advantage of the one-dimensional unsteady flow model of dam-break is that it is convenient to consider factors such as local dam failure and gradual dam failure when solving the discharge process of dam site failure. In the treatment of the breach, this model considers that the development of the breach is mainly determined by four parameters: breach duration, final breach bottom width, final breach depth (final vertical breach depth), and breach slope. This model is mainly used to calculate reservoir dams, and only the initial and final breach parameters are controlled. The breach morphology and duration at peak flow obtained by this invention are embedded into the model calculation, and calculations are carried out on engineering examples and experimental conditions to verify the results. The discharge process of the failure calculated by the model is compared with the actual process to verify the adaptability and accuracy of the parameters of this invention. Specific verification cases are as follows:

[0218] ①Calculation of a landslide dam project example: The upstream flow rate is 600 m³ / s. 3 / s, the length of the dam bottom along the river channel is 700m, the height of the dam at the pass is 96m, and the upstream and downstream slope angles of the dam body are 0.2-0.5; (excavation of the spillway) the initial breach depth is 15m, and the initial breach bottom width is 3m; according to the final vertical breach degree determination method proposed in patent CN116561529B, it is determined that the vertical breach of the dam body is about 2 / 3 under this working condition, and the final vertical breach depth is about 52m; according to formula (4), the final breach bottom width is calculated to be 130m; according to formula (39), formula (36) and formula (13), the rapid development stage is determined. The value is 9669s, and the vertical breach depth and breach width at the peak flow time are approximately 30m and 110m, respectively. The results of the model-calculated breach discharge process are compared with the actual breach discharge process as follows: Figure 9 As shown, the model's calculation accuracy can meet the needs of on-site collapse response.

[0219] ② Calculation test condition I-5: upstream flow rate is 3L / s, dam bottom length along the river channel is 2.5m, dam height is 0.7m, upstream and downstream slope angles of the dam are 0.769; preset initial breach depth is 0.01m, initial breach width is 0.2m; according to the final vertical breach degree determination method proposed in patent CN116561529B, it is determined that the dam body will breach vertically by 2 / 3 under this condition, with a breach depth of about 0.46m; according to formula (4), the final breach bottom width is calculated to be 1m; according to formulas (39), (36) and (13), the rapid development stage is determined. The value is 50 seconds, and the breach depth and bottom width at the peak flood moment are 0.45m and 0.8m, respectively; the model calculation of the breach discharge process is compared with the actual breach discharge process. Figure 10 As shown in (a), the model's calculation accuracy can meet the needs of on-site collapse response.

[0220] ③ Calculation test condition I-8: The upstream flow rate is 3L / s, the length of the dam bottom along the river channel is 2.5m, the dam height is 0.7m, and the upstream and downstream slope angles of the dam are 0.769. The initial breach depth is preset to 0.01m and the initial breach width is 0.2m. According to the final vertical breach degree determination method proposed in patent CN116561529B, the vertical 1 / 2 breach of the dam body under this condition is determined to be about 0.35m deep. According to formula (2), the final breach bottom width is calculated to be 0.8m. According to formulas (39), (36) and (13), the rapid development stage value is determined to be 66s, and the breach depth and breach bottom width at the flood peak are 0.20m and 0.65m, respectively. The model calculation of the breach discharge process and the actual breach discharge process are compared as follows: Figure 10 As shown in (b) of the diagram.

[0221] Based on experimental phenomena and data, this invention proposes a method for determining parameters characterizing breach development beyond the final breach morphology, starting from the physical mechanism and grounded in the principles of sediment transport balance and the triangle principle in the breach discharge process. This method primarily includes the duration of peak discharge during the rapid development phase, the breach morphology at peak value, and the total breach duration during this phase. This avoids several assumptions in model calculations regarding breach duration (1 hour, 2 hours, etc.) and the uniform variation of the breach throughout the entire time period. The results can be used together with the predicted final breach morphology as model input parameters to calculate the breach discharge process. It also facilitates the direct estimation of the generalized breach discharge process during the rapid development phase using parameters characterizing breach development.

[0222] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure, characterized in that, include: Collect basic parameters including dam body shape parameters, river width, upstream river topographic data, and reservoir capacity-water depth relationship curves to determine reservoir capacity characteristic coefficients; Predict the final vertical failure degree of the dam and calculate the final vertical failure depth. Calculate the actual discharge volume at the time of failure and its corresponding water depth in front of the dam, as well as the final breach morphology parameters of the dam. Based on the discharge volume at peak flow, the actual discharge volume at the end of the breach, the water depth in front of the dam corresponding to the actual discharge volume at the end of the breach, and the reservoir capacity characteristic coefficient, calculate the water depth in front of the dam corresponding to the discharge volume at peak flow. The relationship between the breach bottom width at peak flow and the final breach bottom width is established by using empirical coefficients to determine the breach bottom width at peak flow. Based on the principle of sediment transport balance and the final breach bottom width, the average volumetric sediment content, the sediment content at the peak flow time, and the projected area of ​​the breach at the peak flow time are derived. Then, based on the principle of trapezoidal similarity, the vertical breach depth at the peak flow time is calculated through the dam shape parameters. Based on the water balance equation and peak flow calculation formula, combined with the breach projection area, sediment content, ratio of the water depth in front of the dam corresponding to the discharge volume at the peak flow time to the water depth in front of the dam corresponding to the actual discharge volume at the end of the breach, and the flow coefficient determined by engineering experience, the duration of the rapid development stage of the breach is calculated.

2. The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure as described in claim 1, characterized in that, Methods for determining the storage capacity characteristic coefficient include: The relationship between the reservoir capacity and water depth of the landslide dammed lake is fitted into a power function form: W represents the capacity of the landslide dammed lake, and H represents the corresponding water depth; The power function is subjected to a logarithmic transformation, and then linear regression analysis is performed on a logarithmic coordinate system. The intercept of the linear regression line is the reservoir capacity characteristic coefficient. The slope of the straight line is the reservoir capacity characteristic coefficient s.

3. The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure as described in claim 1, characterized in that, Setting the duration of the rapid development phase of the landslide dam failure The peak flow rate is reached at 1 / 3 of the time. The discharge from the reservoir is 1 / 3 of the actual discharge at the end of the breach. This is used to calculate the water depth in front of the dam corresponding to the discharge at the peak flow rate. The expression is: ； in, The actual water discharge at the moment of the breach's end corresponds to the water depth in front of the dam, and s is the reservoir capacity characteristic coefficient.

4. The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure as described in claim 3, characterized in that, The breach width used to determine the peak flow time. The expression is as follows: ； Where r is an empirical coefficient. For partial failure of earth-rock mixed landslide dams, r is taken as 4 / 5 to 5 / 6. For dams with almost complete soil failure, r is taken as 1. The final width of the breach.

5. The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure as described in claim 4, characterized in that, Used to calculate average volumetric sand content Sand content at peak flow rate and the projected area of ​​the breach at peak flow time The expression is as follows: When the final vertical failure rate of the dam body is greater than 1 / 2 of the dam height ； ； ； When the final vertical failure degree of the dam body is ≤1 / 2 of the dam height ； ； ； Where B is the width of the river channel; The actual discharge volume at the end of the breach, parameter The water depth in front of the dam corresponding to the discharge volume at peak flow. The actual discharge volume at the end of the breach corresponds to the water depth in front of the dam. The ratio of .

6. The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure as described in claim 5, is characterized in that, The specific steps for calculating the vertical inrush depth at the peak flow time using the trapezoidal similarity principle are as follows: The length of the dam base along the river channel was calculated using the dam shape parameters. By combining the trapezoidal similarity formulas and substituting the calculated breach projection area at the peak flow time, the vertical breach depth at the peak flow time can be estimated.

7. The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure as described in claim 6, characterized in that, The expression used to calculate the vertical inrush depth at the peak flow moment is as follows: ； ； Among them, the length of the top of the dam along the river channel Length of the dam base along the river channel The mountain pass is high. Downstream slope angle and upstream slope angle , for It is constantly heading towards a deeper collapse.

8. The method for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure as described in claim 7, is characterized in that, Used to calculate the duration of the rapid development phase of the failure. The expression is as follows: ； In the formula: This is the flow coefficient.

9. A device for determining the geometric and temporal characteristic parameters of a landslide dam breach based on overtopping failure, characterized in that, The apparatus is used to implement the steps of the method according to any one of claims 1-8.

10. A method for predicting the outflow process after a dam failure, characterized in that, The outflow process of the landslide dam breach is predicted based on the geometric and temporal characteristic parameters of the breach; wherein the geometric and temporal characteristic parameters of the landslide dam breach are obtained based on the parameter determination method described in any one of claims 1-8.

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