CN117494478B - Calculation method for simulating over-roof dam break flow and break evolution process of core dam - Google Patents

Abstract

The invention discloses a calculation method for simulating the over-roof dam break flow and the break evolution process of a core wall dam, which comprises the steps of determining calculation parameters, setting time steps, calculating the break flow, dam break characteristics, the elevation of the bottom of a break, core wall stress analysis, calculating the exposed length of the core wall, the top width of the break, the bottom width of the break and the like of each time step; the invention establishes a calculating method for the over-roof dam break process of the core wall dam, which can simulate the break-out flow and the break-out state evolution, based on the dam break mechanism of the core wall dam. The calculating method considers the erosion process of dam shell materials and the evolution of the collapse form in the dam break process, simulates the stress state of the core wall based on the combined action of upstream water and soil pressure, judges whether the exposed core wall is damaged or not through a moment balance analysis method, determines the exposed length and the number of times of breakage of the core wall, and the calculating result is more in accordance with the actual dam break process.

Description

A calculation method for simulating the overtop breach flow and breach evolution process of core dams

Technical field

The invention belongs to the technical field of dam breach calculation in water conservancy projects, and is particularly a calculation method for simulating the flow rate and breach evolution process of a core dam overtopping.

Background technique

Core dam is a commonly used earth-rock dam type. It is widely constructed because it uses sand and gravel materials with good water permeability as the dam shell and soil with good impermeability as the anti-seepage core wall. The failure mechanism of core dams is still unclear, and the understanding of the failure process of core dams is insufficient, which provides a great obstacle to emergency rescue and disaster relief of core dam failures.

For understanding the failure mechanism of the core dam, the model test is limited by the site and the scale similarity ratio, and cannot completely restore the failure process of the core dam, and the results obtained are inconsistent with the actual situation. The use of mathematical model calculations can better restore the failure process of core dams, and can completely restore the stress and damage of core dams, providing a low-cost and highly effective way to study the failure mechanism of core dams. Means, such as existing literature: Zhong Qiming et al. [J]. Chinese Science, 2017, 47(9):992-100. Mathematical model of clay core dam overtopping failure process considering different failure modes of the core wall, considering Under the action of overflowing water flow, the core wall will suffer toppling damage and shear failure. However, this document does not consider the development process of the breach before the core wall breaks, nor does it consider the exposed length of the core wall and the number of times of damage, which is different from the actual collapse. The dam process is inconsistent. Failure to consider the exposed length and number of failures before the core wall breaks will result in the development process and trend of the breach flow rate and breach top and bottom width being inconsistent with the actual situation. It cannot well indicate the actual dam breach process and cannot accurately calculate the dam breach flow rate and breach rate. dam development process.

Contents of the invention

In order to solve the problem that the existing technology does not consider the exposed length and the number of times of damage of the core wall before it breaks, and cannot well indicate the actual dam breach process, and cannot accurately calculate the dam breach flow rate and the dam breach development process, the present invention proposes a method that considers the core wall's real-time Calculation method for dam break under stress state. This model adopts time step iteration numerical calculation method.

The technical scheme of the present invention is as follows:

A calculation method for simulating the overtop breach flow and breach evolution process of core dams. The calculation method mainly includes three parts: breach flow calculation, dam breach characteristics calculation, and core wall stress analysis. Specifically, it includes the following steps:

Step 1. Determine the calculation parameters, including core dam body characteristic parameters, core wall characteristic parameters, upstream water level-reservoir surface area relationship curve, time-inflow curve and time-discharge curve.

The dam body characteristic parameters include: dam height, dam top width, dam axis length, upstream dam slope ratio, downstream dam slope ratio and dam shell material characteristic parameters. The dam shell material characteristic parameters include dam shell material cohesion, Dam shell material internal friction angle and dam shell material erosion coefficient, etc. The core wall characteristic parameters include: core wall material cohesion, core wall height, core wall top width, upstream slope ratio, downstream slope ratio and the relative distance between the dam axis and the core wall.

Step 2. Set the time step and calculate the breach flow rate at each time step. The time step can be adjusted as needed, which can be 1s or 2s, including:

Step 2.1. Assign values to the main characteristic points of the dam based on the design data of the initial form, and at the same time read design data such as time-inflow array, upstream water level-reservoir surface area, time-discharge array, etc.

The main characteristic points of the dam body include: reservoir water level, height, upstream dam toe position, dam abutment upstream position, dam abutment downstream position, downstream dam toe position, core wall upstream dam toe position, core wall abutment upstream position, core wall dam The position downstream of the shoulder and the position of the dam toe downstream of the core wall.

Step 2.2. Calculate the elevation change of the upstream reservoir water level based on the time-flow array, taking into account the inflow flow, breach flow, and spillway discharge flow:

In the formula, A _s is the reservoir surface area; z _s is the reservoir water level; t is time; Q _in is the inflow flow, which is a time-inflow array. The corresponding inflow Q _in at each moment is specified by the design. ; Q _b is the breach flow rate; Q _spill is the discharge flow rate of the spillway, which is the discharge value corresponding to each moment in the time-discharge array.

Step 2.3. If the water level of the upstream reservoir is less than or equal to the elevation of the breach bottom, skip the subsequent calculations and calculate the upstream flow and reservoir water level elevation in the next time step; if the upstream reservoir water level is higher than the breach bottom elevation and higher than the downstream water level , use the wide-top weir flow formula to calculate the breach flow rate:

In the formula, b is the width of the breach bottom, calculated by formula (19); H is the water depth at the breach, H = z _s - z _b , calculated at each moment, where z _b is the elevation of the breach bottom, z _s is the reservoir Reservoir water level; m is the breach slope ratio (horizontal/vertical), which is the proposed value; c ₁ and c ₂ are correction coefficients, select c ₁ =1.7m ^0.5 /s, c ₂ =1.1m ^0.5 /s; k _sm is the tail water submersion correction coefficient, which can be calculated by the following formula:

In the formula: z _t is the tail water height.

The elevation of the breach bottom is calculated through formula (13) or formula (7) at each time t, and the elevation change of the breach bottom per unit time is subtracted from the existing elevation to obtain the elevation of the breach bottom at the new time.

Step 3. Calculate the dam failure characteristics at each time step, including calculating the breach bottom elevation;

Affected by the breach flow, the dam top and downstream dam slope were eroded.

If the dam shell material is cohesive soil, the slope at the initial flush pit becomes steeper, and the downstream dam slope angle gradually changes from the initial slope angle β to the internal friction angle φ ₁ of the dam shell material.

The erosion rate of the dam crest material can be calculated by the following formula:

In the formula, E is the erosion rate; k _d is the erosion coefficient, which is often obtained through experimental measurements or empirical formulas; τ _b is the flow shear stress; τ _c is the critical shear stress of the dam material, which can be determined through the Shields curve. . Among them, the calculation formulas of τ _b and k _d are as follows:

In the formula, ρ _w is the density of water; n is the Manning coefficient; R is the hydraulic radius of the breach; A _w is the water flow area. The hydraulic radius and water flow area at the breach are calculated using existing formulas.

In the formula, ρ _d is the dry density of the soil; c % is the clay content.

Then the change in elevation of the breach bottom is the erosion rate of the breach dam shell material per unit time:

When the downstream slope angle reaches the internal friction angle of the dam shell material φ ₁ , under the action of the dam-breaking water flow, traceable erosion continues to develop upstream to the core wall. Assuming that the downstream slope maintains the internal friction angle, the internal friction angle is the critical value of the soil. maximum angle. The following formula can be used to express the traceability erosion process of dam shell materials:

In the formula, C _T is the traceability scour coefficient, q is the single width flow rate of the breach, and He _is the water flow height. These three parameters can be obtained according to the existing formulas.

If the dam shell material is cohesive soil, the erosion amount is:

In the formula, V _b is the volume of the dam shell material eroded by the dam breach flow, x _db is the starting position in the x direction downstream of the breach, x _ub is the end position in the x direction upstream of the breach, E is obtained according to formula (4), b is according to formula ( 19) Obtained, x _db and x _ub are obtained according to the depth of the breach; n _loc represents the location of the breach, n _loc =1 represents unilateral erosion, and n _loc =2 represents bilateral erosion.

Calculate the area of the breach base:

In the formula, b is the bottom width of the breach.

Calculate the projected area of the breach slope on the xz plane:

The projection of the breach slope on the xz plane includes three parts. The first part is the projection of the downstream breach slope. The area is the product of the difference between the downstream end point of the breach and the breach abutment and the breach depth. x _downbrink is the downstream end point of the breach, and x _downcorner is the downstream end of the breach abutment. position; the second part is the product of the difference between the height of the core dam and the elevation of the breach bottom and the width of the top of the core dam, h is the height of the core dam, z _b is the elevation of the breach bottom, Bt is the width of the top of the core wall; the third part is The product of the difference between the upstream abutment of the core dam and the starting point upstream of the breach and the difference between the height of the core dam and the elevation of the bottom of the breach, x _upcorner is the upstream position of the dam abutment, and x _upbrink is the starting point upstream of the breach.

Then the total area of the breach is:

The change in elevation of the breach bottom is:

On the basis of considering the stress of the core wall dam, the present invention considers the exposed length and stress of the core wall after the downstream dam shell material is washed away. At the same time, it calculates the length and number of damage when the core wall breaks. Pattern of fracture development prior to fracture. Before the core wall broke, the bottom of the downstream dam shell material was washed away by the water flow, causing the upper dam shell material to be suspended and the breach to be trapezoidal. The suspended part of the dam shell material is affected by gravity and cohesion. When the cohesion force is insufficient to support the gravity of the suspended part, the suspended part of the dam shell material will undergo shear failure.

Step 4. Stress analysis of the core wall at each time step, including calculation of the core wall exposed length, core wall failure length, number of core wall failures, breach top width, breach bottom width, etc.

The breach at the dam axis continued to develop due to erosion by water flow. Before the collapse of the core wall, the bottom of the downstream dam shell material was eroded by the water flow, causing the upper dam shell material to be suspended and the breach to be trapezoidal. The suspended part of the dam shell material is affected by gravity and cohesion. When the cohesion is not enough to support the suspended part of the gravity, the suspended part of the dam shell material will undergo shear failure. The cohesion and gravity can be expressed as:

In the formula , F _C is the cohesion of the suspended dam shell material, C is the unit cohesion of the dam shell material, F _G is the gravity of the suspended dam shell material, l is the length of the suspended part of the dam shell material, h _l is the height of the suspended part of the slope , γ _s is the bulk density of the dam shell material, p is the porosity, B is the width of the top of the breach, and b is the width of the bottom of the breach.

The value of l can be taken as half of the difference between the top width of the breach and the bottom width of the breach, and the value of h ₁ can be taken as the height of the breach.

After the core wall is destroyed, the erosion of the overflow water makes the breach evolve into an inverted trapezoid. The development increment of the top and bottom width of the breach can be expressed as:

In the formula , φ ₁ is the internal friction angle of the slope dam shell material at the breach.

Then the nth calculation of the top and bottom width of the breach can be expressed as:

In the formula, B _n represents the width of the breach top calculated for the nth time, B _n-1 represents the width of the breach top calculated for the n-1th time, b n represents the width of the breach bottom calculated for the nth time, b _n-1 represents the width of the breach bottom calculated for the nth time _, The width of the breach bottom calculated n-1 times.

After the dam shell material is eroded, the core wall is exposed, and the exposed length of the core wall is calculated by the following formula:

In the _formula , h _k is _the height of the damaged _core wall _; Bottom elevation. According to the downstream slope ratio of the core wall, x _down , x _core , z _b and z _{down can be calculated linearly.}

For the possible damage of the core wall, the moment balance method is used to analyze. The exposed part of the core wall is subject to upstream water and soil pressure, and the moment it experiences is:

In the formula: F _s is the shear force exerted by the breach overflow flow on the top of the core wall; F _w is the water pressure of the reservoir water acting on the core wall; F _e is the earth pressure of the upstream dam shell material acting on the core wall; h _r is The height of the reservoir water level from the failure surface of the core wall.

The moment M _r when the resistance acts on the failure surface of the core wall can be expressed as:

In the formula: A _t is the cross-sectional area of the failed core wall; C ₂ is the cohesion of the clay core wall; W is the weight of the core wall above the failure surface; L ₂ is the width of the bottom of the core wall failure surface. Among them, A _t and W can be expressed as:

In the formula, L ₁ is the width of the top of the core wall failure surface and is the porosity of the core wall material.

According to the upstream water and soil pressure and resistance of the core wall, the critical conditions for its failure are:

For the analysis of the stress state of the exposed core wall, if the failure moment is greater than the resistance moment, the exposed core wall is damaged. The exposed length l _core of the damaged core wall is the failure length, and the number of core wall failures is updated at the same time.

T is the number of times the heart wall is destroyed.

During the calculation process of the program, the post-destruction breach bottom elevation, breach top width, breach bottom width, breach flow rate and dam body characteristic data are iteratively updated.

The beneficial effects of the present invention are:

Based on the dam failure mechanism of the core dam, the present invention establishes a calculation method for the core dam overtopping failure process that can simulate breach flow and breach morphology evolution. The model considers the erosion process of the dam shell material and the evolution of the breach shape during the dam breach process, and simulates the stress state of the core wall based on the joint action of upstream water and earth pressure. It determines whether the exposed core wall is damaged through moment balance analysis. The breaking moment, length and number of breaks of the exposed core wall are determined, and the calculation results are more consistent with the actual dam breach process.

Description of drawings

Figure 1 shows the main characteristic point parameters of the initial shape of the dam body;

Figure 2 shows a schematic diagram of erosion on the dam top and downstream slope;

Figure 3 shows the development process of breach at the dam axis;

Figure 4 shows a schematic diagram of core wall damage;

Figure 5 is the calculation result curve of dam burst flow rate of Sheyuegou Reservoir;

Figure 6 is the calculation curve of the development process of the breach size of the Sheyuegou Reservoir;

Figure 7 compares the breach flow calculated by the existing program and this method.

Detailed ways

The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

Example 1: This method is written into a program using computer language, the case of the core wall dam breach of the Sheyuegou Reservoir is selected, and the overtopping dam breach process is calculated and analyzed.

The specific calculation process includes the following steps:

Step 1. Enter the dam body characteristic parameters and core wall characteristic parameters, and enter the corresponding time-inflow array, water level-reservoir surface area, and time-discharge array according to the water level and time.

The characteristic parameters of the dam body and core wall of Sheyugou Reservoir are shown in Table 1 for details.

Table 1 Characteristic parameters of Sheyuegou Reservoir

Sheyue ditch is an asphalt concrete vertical core wall, and the width of the top of the core wall is the thickness of the center wall in Table 1. The data of time-inflow array, water level-reservoir surface area, and time-discharge array are hydropower station management data.

The program performs iterative calculations based on input parameters, specifically:

Step 2: Calculate the breach flow rate at each time step. In this embodiment, the time step is 1s; specifically, it includes:

The program reads the input data and assigns values to the main feature points of the initial shape of the dam body (input the initial values of these corresponding feature points in the dam body in the initial state). The main feature points are shown in Figure 1. The characteristic points specify the initial shape of the dam body in the program calculation, and play an important role in the breach evolution, flow calculation, core wall stress analysis and damage during the dam failure process. The meaning of each parameter in Figure 1 is shown in Table 2.

Table 2 Main characteristic points of dam body

In each time step, an iterative operation is performed based on the input time-inflow array. Before the water reaches the top, the upstream inflow causes the upstream water level to rise. When the water level of the upstream reservoir is higher than the dam top elevation, the water flow will overflow, and the breach flow rate is calculated according to formulas (1) to (3).

Step 3. Calculate the dam failure characteristics at each time step, including calculating the breach bottom elevation;

Affected by the breach flow, the dam top and downstream dam slope were eroded, as shown in Figure 2. After the upstream water reaches the top, the downstream dam slope angle is washed away by the water flow, and the downstream dam slope angle gradually changes from the initial slope angle β to the internal friction angle φ ₁ of the dam shell material. Calculate the elevation change of the breach bottom after the dam body is eroded by water flow according to formulas (4)-(13).

The erosion of the downstream dam shell material traces its source and develops upstream until the core wall is exposed.

Step 4. Analyze the stress on the core wall at each time step, and calculate the exposed length of the core wall, the number of core wall failures, the top width of the breach, and the width of the breach bottom;

After the core wall was destroyed, the erosion of the overflow water caused the breach to evolve into an inverted trapezoid. The development process of the breach is shown in Figure 3.

After the dam shell material is eroded, the core wall is exposed, as shown in Figure 4. The exposed length of the core wall is represented by formula (20). According to the exposed length of the core wall, the moment balance method is used for analysis. The upstream failure moment is mainly composed of the shear force of the breach overflow flow acting on the top of the core wall, the water pressure of the reservoir water acting on the core wall, and the earth pressure of the upstream dam shell material acting on the core wall. The resistance moment of the core wall is given by formula (22) express.

According to the stress analysis of the exposed core wall, if the failure moment is greater than the resistance moment, the exposed core wall will be destroyed. After the failure, the breach bottom elevation, breach width, breach flow rate, core wall failure length and dam body characteristic data will be updated iteratively, and the core wall will be destroyed at the same time. The number of times increases accordingly.

When the program calculation time reaches the specified time step, the program calculation stops and a result file is output. The file contains the calculation data results of each time step.

According to the output results, the breach flow curve of Sheyuegou Reservoir is shown in Figure 5, and the breach development process is shown in Figure 6. Among them, the comparison of the breach flow rate calculated by the program in the existing literature in the background art and the new program of this method is shown in Figure 7. It can be seen from Figure 7 that the two surges in flow rate of the new program are due to the new program taking into account the exposed core wall. Caused by breakage, this method considers that the core wall can still play the role of retaining soil and water after being exposed, which is more in line with the actual situation. The core wall was suddenly destroyed under the action of water and soil pressure in the upstream, and the breach flow rate surged. Due to the huge water head in the upstream, the calculated flow rate surged, and the calculation results were more consistent with the actual dam breach flow process. The peak flow calculated by the new program is 6851.5 m ³ /s, and the measured peak flow at the Sheyuegou Reservoir dam break site is 6700.0 m ³ /s. The relative error with the peak flow calculated by the program is 2.2%, and the data is closer to the actual flow.

Example 2: Conduct a dam-break flume inversion test based on the dam-break parameters, and compare the program calculation results with the test results, and also compare them with the measured dam-break flow rate at the Sheyuegou dam break site.

The equipment and method of the dam breach flume inversion test are existing technologies. This embodiment does not show the test equipment. In order to demonstrate the test process, the test method is briefly explained here in conjunction with the test process.

Step 1. Determine the water tank test parameters.

The flume erosion equipment used in the test mainly consists of a water supply system, a variable slope flume and a tailwater system. The water tank is 1 m high, 0.3 m wide, and 6 m long. It is connected to the water supply system through a PVC pipe with an inner diameter of 50 mm. The water is continuously supplied by an electromagnetic flowmeter, and a check valve is installed to prevent backflow caused by water pressure when the model stores water. Tempered glass is installed on both sides of the water tank to facilitate observation of test phenomena.

Based on the tank size, determine the model parameters, see Table 3.

Table 3 Model test parameter settings

Step 2: Determine the water tank test dam material and build a model in the water tank.

The on-site sampling gradation of the Sheyuegou Reservoir dam was used as the standard for scale reduction. The maximum test particle size was 20 mm. The equivalent substitution method was used to obtain the model test dam material gradation.

After being completely air-dried and dried, the dam material is divided into 5 particle size groups, namely <1 mm, 1~5 mm, 5~10 mm and 10~20 mm. The soil material has a specific gravity of 2.73 and an initial moisture content of 5%. It is compacted in layers using a compaction hammer. The model compaction degree is 86.9% and the porosity is 27%. In order to facilitate the observation of the test development process, an initial inverted trapezoidal breach was opened on the side of the tempered glass. The top width of the breach was 50 mm, the bottom width was 30 mm, and the breach height was 40 mm.

Step 3. Start the test according to the steps.

The test is carried out in sequence as follows:

(1) Install and fix the pore pressure sensor at the upstream dam toe, connect it to the data acquisition system, and install and fix the camera on the breach side of the model;

(2) Turn on the data acquisition system, water pump and electromagnetic flowmeter. The water supply system flows at a constant flow rate of 0.83 L/s. When the upstream water storage level is reached, the water pump is turned off to saturate the upstream dam body, and then the water pump is turned on to start the test;

(3) When the dam body is no longer damaged and the data measured by the pore pressure sensor is stable, the test is deemed to be over. The water supply system and data acquisition system are shut down, the test data is saved, the model dam body after the test is recorded, and the water tank is cleaned.

Step 4: Convert the flow rate measured in the test according to a similar ratio to obtain the dam break test flow rate of the Sheyuegou Reservoir dam break case, and compare it with the calculated value of the program's output parameter.

After similar conversion, the dam break flow rate measured in the test was 6169.87 m ³ /s. The program calculated the dam break peak flow rate to be 6851.5 m ³ /s. The relative error between the test results and the dam break peak flow rate calculated by the program was -9.9%. , within 10%; the measured peak flow at the Sheyuegou Reservoir dam break site was 6700.0 m ³ /s, and the relative error with the program's calculated dam break peak flow was 2.2%, proving that the program's calculation results have high credibility.

The present invention considers core wall breakage and calculates the change values of several more parameters than existing literature, such as: core wall exposed length, core wall damage length, and core wall damage times. These parameters cannot be known by existing literature methods. In the present invention, the development mode of the breach develops from a straight trapezoid before the core wall is broken to an inverted trapezoid after the core wall is broken. In the existing literature, the breach develops in an inverted trapezoid shape from the beginning to the end, which makes the present invention more realistically simulate the development mode of the breach and is more similar to the actual situation.

Claims (5)

1. A calculation method for simulating the flow rate of a core dam overtopping dam break and the evolution process of a break opening is characterized by comprising the following steps:

step 1, determining calculation parameters including a core dam body characteristic parameter, a core wall characteristic parameter, an upstream water level-reservoir surface area relation curve, a time-inflow curve and a time-outflow curve;

step 2, setting time steps, and calculating the crumple opening flow of each time step, wherein the method specifically comprises the following steps:

step 2.1, assigning values to main feature points of the dam body according to design data of an initial form, and simultaneously reading design data of a time-inflow array, an upstream water level-reservoir area and a time-outflow array;

step 2.2, calculating the elevation change of the water level of the upstream water reservoir according to the time-incoming flow array, wherein the calculation formula is as follows:

in the method, in the process of the invention,A _s the area of the reservoir surface is;z _s is the reservoir water level;ttime is;Q _in the flow is the flow value corresponding to each moment in the time-flow array;Q _b is the flow of the crumple;Q _spill the spillway is used for discharging flow, and the flow discharge value corresponding to each moment in the time-flow discharge array is used for discharging flow;

step 2.3, if the water level of the upstream reservoir is smaller than or equal to the elevation of the bottom of the crumple, calculating after skipping, and calculating the water level elevation of the upstream inflow and reservoir in the next time step; if the water level of the upstream water reservoir is higher than the water level of the downstream water at Cheng Ju, calculating the flow rate of the crumple by adopting a wide top weir flow formula, wherein the calculation formula is as follows:

in the method, in the process of the invention,bthe bottom of the ulcer is wide;Hfor the depth of water at the position of the crumple,H=z _s -z _b whereinz _b For the elevation of the bottom of the crumple,z _s is the reservoir water level; mthe slope ratio of the side slope of the breach is a formulated value;c ₁ 、c ₂ for correction coefficient, selectc ₁ =1.7m ^0.5 /s，c ₂ =1.1m ^0.5 /s；k _sm For the tail water flooding correction coefficient, the following is calculated：

Wherein:z _t is the tail water height;

step 3, calculating dam break characteristics of the dam body in each time step, including calculating the elevation of the bottom of the breach;

if the dam shell material is cohesive soil, the erosion rate of the dam shell material is determined in unit time by the change of the elevation of the bottom of the breach:

if the dam shell material is non-cohesive soil, the height variation of the bottom of the breach is as follows:

in the method, in the process of the invention,Eis the erosion rate;V _b the dam shell material is washed and eroded by dam break water flow;Sthe total area of the crumple is;

the bottom elevation of the crumple at a certain moment is obtained by subtracting the variation of the bottom elevation of the crumple between the moment and the last moment from the bottom elevation of the crumple at the last moment;

step 4, core wall stress analysis in each time step comprises calculating the exposed length of the core wall, the top width of the crumple opening and the bottom width of the crumple opening;

the exposed length of the core wall is calculated by the following formula:

in the middle of， x _down Downstream of exposed core wallxThe end point of the terminal is,x _core downstream of the core wall dam abutmentxThe end point of the direction is defined by the angle,z _b for the elevation of the bottom of the crumple,z _down exposing part of the bottom elevation for the downstream core wall;

the incremental development of the base width of the crumple is expressed as:

the incremental development of the roof width of the crumple is expressed as:

in the middle of，φ ₁ The internal friction angle of the slope angle dam shell material at the position of the crumple is the elevation variation of the bottom of the crumple;n _loc indicating the position of the crumple;

then the firstnThe secondary calculation of the roof and floor widths of the crumple zones can be expressed as:

in the method, in the process of the invention,B _n represent the firstnThe top width of the crumple opening calculated by the time, B _n-1 represent the firstn-1The top width of the crumple obtained by the secondary calculation,b _n represent the firstnThe bottom width of the crumple opening calculated by the time,b _n-1 represent the firstn-1The bottom width of the crumple obtained by the secondary calculation.

2. The method for calculating the flow rate and the break evolution process of the over-roof dam break of the core dam according to claim 1, wherein the dam body characteristic parameters in the step 1 include: dam height, dam length, dam top width, dam axis length, upstream dam slope ratio, downstream dam slope ratio, dam shell material cohesive force, dam shell material internal friction angle and dam shell material erosion coefficient; the core wall characteristic parameters include: core material cohesion, core height, core top width, upstream slope ratio, downstream slope ratio and dam axis and core relative distance.

3. The method for calculating the flow rate and the break evolution process of the over-roof dam break of the core dam according to claim 1, wherein the main characteristic points of the dam body in the step 2.1 comprise: the water level, the height, the upstream dam toe position, the upstream dam abutment position, the downstream dam toe position, the upstream core wall dam abutment position, the downstream core wall dam abutment position and the downstream core wall dam toe position of the reservoir.

4. The method for calculating the flow rate and the evolution process of the breach for the overtopping of the core dam according to claim 1, wherein in the step 3, the dam shell material is eroded by the flow of the breaching waterV _b The calculation formula is as follows:

in the method, in the process of the invention,V _b the erosion volume of the dam shell material by the dam-break water flow is,x _db downstream of the crumplexThe direction is set to be at the initial position,x _ub upstream of the crumplexThe direction end position is set to be at a position,Eis the erosion rate of the dam shell material,bfor the purpose of wide bottom of the crumple,x _db andx _ub obtaining according to the depth of the crumple;n _loc indicating the position of the crumple opening,n _loc =1 indicates a single-sided erosion,n _loc =2 represents double sided erosion; Rthe hydraulic radius of the ulcer is set;A _w is the water flow area.

5. The method for calculating the flow rate and the evolution process of the breach for simulating the overtopping of the core dam according to claim 1, wherein the total area of the breach in the step 3 is as followsSThe calculation formula is as follows:

area of bottom surface of crumpleS _b The calculation formula is as follows:

in the method, in the process of the invention,bthe bottom of the ulcer is wide;

projection area of crumple slope on xz planeS _s The calculation formula is as follows:

wherein:his the height of the core wall dam,z _b for the elevation of the bottom of the crumple,x _downbrink as a downstream end point of the crumple,x _downcorner is a downstream position of the dam abutment, Btis the width of the top of the core wall dam,x _upcorner is the upstream position of the dam abutment,x _upbrink is the upstream origin of the crumple.