CN117828907B - Dam break mathematical model for homogeneous dam and parameter determination method - Google Patents
Dam break mathematical model for homogeneous dam and parameter determination method Download PDFInfo
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Abstract
The invention discloses a dam break mathematical model for a homogeneous dam and a parameter determination method, which comprises the following steps: determining dam body characteristic parameters, dam material characteristic parameters, an upstream water level-reservoir surface area relation curve, a time-incoming flow curve and a time-draining curve; setting a bottom elevation allowable value at the upstream of the crumple; calculating the initial steep bank elevation; setting the calculated total duration and the time step of each calculation; calculating the flow rate, erosion amount, upstream reservoir water level variation, upstream bottom elevation, top width variation and bottom width variation of the crumple opening in each time step; judging whether the abrupt bank is subjected to shearing damage or not; and updating data when shearing damage occurs, continuing to calculate when shearing damage does not occur, judging whether the side slope of the crumple is stable, and finally outputting a calculation result. The dam break mathematical model takes factors such as the water content, compactness and the sticky particle content of soil into consideration when calculating the erosion rate of the steep bank, so that the error of a prediction result is reduced.
Description
Technical Field
The invention belongs to the technical field of dam break calculation of hydraulic engineering, and particularly relates to a dam break mathematical model for a homogeneous dam and a parameter determination method.
Background
The geometric form of the dam body of the homogenizing dam and the physical and mechanical characteristics of the dam material are key factors influencing the dam breaking process of the homogenizing dam, and the difference of the viscosity particle content and the compactness of different dam materials can greatly influence the dam breaking process of the homogenizing dam, and the parameters mainly influence the erosion rate of the steep bank of the homogenizing dam and the erosion resistance of the dam material when the dam breaking mathematical model is calculated.
The prior art: zhong Qiming et al [ J ]. Water conservancy journal, 2016, 47 (12): 1519-1526 discloses a mathematical model study and application of a process of overtopping and dam break of a homogeneous earth dam, wherein a steep bank erosion rate empirical model proposed by Tony L. Wahl in 1998 is adopted for a steep bank moving parameter C T, and the model does not consider factors such as soil water content, compactness, sticky particle content and the like, but the study shows that the factors have influence on the steep bank moving parameter, so that the mathematical model of the paper has poor performance in the actual application process and small application range, and therefore, larger error is generated between the model and the actual situation in the process of predicting the breach flow.
Disclosure of Invention
In order to solve the technical problem that the mathematical model has larger errors in the actual application process because the factors such as the water content, the compactness and the sticky particle content of the soil are not considered in the parameter calculation in the existing mathematical model for the dam break at the top of the homogeneous dam, the invention provides the mathematical model for the homogeneous dam break and the parameter determination method considering the factors such as the water content, the compactness and the sticky particle content of the soil.
In order to achieve the above purpose, the technical measures adopted by the invention are as follows:
a dam break mathematical model and parameter determining method for a homogeneous dam comprises the following steps:
Step 1, determining geometrical characteristic parameters of a dam body, physical and mechanical characteristic parameters of a dam material, an upstream water level-reservoir surface area relation curve, a time-incoming flow curve and a time-draining curve;
step 2, setting a bottom elevation allowable value of the upstream of the crumple;
determining the value of the elevation number of the upstream bottom of the crumple according to whether basic erosion occurs, and if the basic erosion does not occur, taking the value as 0; if basic erosion occurs, the value should be less than 0.
Step 3, calculating the initial abrupt bank elevation;
step4, setting the calculated total duration and the time step of each calculation;
Step 5, calculating the flow rate, erosion amount, upstream reservoir water level variation, upstream bottom elevation, top width variation and bottom width variation of the crumple openings in each time step;
Step 6, respectively calculating the upstream reservoir water pressure F 1, the downstream tail water pressure F 2, the water flow shearing force F 3 on the upper part of the abrupt bank, the water weight F 4 on the upper part of the abrupt bank, the dead weight F 5 of the abrupt bank, the friction force F 6 born by the abrupt bank and the cohesive force F 7 in the soil body of the abrupt bank, if F 1-F2+F3＞F6+F7 is carried out, judging that the abrupt bank is subjected to shearing damage, and carrying out step 7, otherwise, carrying out step 8;
Step 7, updating and calculating the upstream reservoir water level, the upstream bottom elevation of the crumple opening, the top width of the crumple opening and the bottom width of the crumple opening according to the variable quantity calculated in the step 5;
step 8, calculating erosion of the abrupt bank, and updating and calculating the erosion quantity, the water level of the upstream warehouse, the elevation of the upstream bottom of the crumple, the top width of the crumple and the bottom width of the crumple according to the variable quantity obtained by the calculation in the step 5;
Step 9, calculating DeltaZ w / Zw, judging whether DeltaZ w / Zw is smaller than epsilon, wherein epsilon is a calculation convergence condition, and taking 0.0001 or adjusting according to actual conditions; if yes, step 10 is carried out, otherwise, step 5 is returned to continue calculation; Δz w represents the amount of change in the upstream reservoir water level, and Z w represents the upstream reservoir water level;
Step 10, judging whether the side slope of the crumple is stable, if so, judging whether the accumulated calculation time is longer than the set calculation time length, if so, ending the calculation, and outputting calculation results of the crumple flow, the erosion amount, the upstream reservoir water level change amount, the upstream bottom elevation change amount, the crumple top width change amount and the crumple bottom width change amount;
And (5) returning to the step (5) to calculate the next time step if the accumulated calculation time is smaller than the set total calculation time.
Further, in step 3, an initial steep ridge elevation, that is, an initial value of a bottom elevation upstream of the crumple, is calculated, which specifically includes:
Zb=(ldown-ln)sin(αx)
Wherein: fr n is the Froude number; q b is the flow of the crumple, m 3/s;Bt is the top width of the initial crumple, and the width of the crumple on the downstream slope takes the same value; c is the thank you coefficient; z w is the upstream reservoir level, m; z b is the elevation of the upstream bottom of the crumple, m. g is gravity acceleration, m/s 2;ldown is the downstream dam slope length, m; l n is the length of the peak of the downstream dam slope from the initial steep bank position, m; alpha x is the slope angle of the downstream dam slope;
Wherein the thank you coefficient calculation mode is:
Wherein: n is a Manning roughness coefficient, n= (d 50)1/6/12, d represents particle size;
The value of alpha x is a fixed value, is basic data of a homogeneous dam, B t is an initial breach top width, is generally an assumed value, can be selected according to actual conditions, the value of Z W、Zb is given with a calculation initial value, and the calculation initial value is the actual condition when the dam is broken, and is calculated by a program.
Wherein the flow of the crumple is calculated by adopting a water balance formula:
Wherein: q is total leakage flow, m 3/s;Qb is breach flow, m 3/s;Qspill is spillway outflow flow, m 3/s corresponds to the leakage value in each moment in the time-leakage array, and zero is set when no spillway flows; q in is the warehouse-in flow, m 3/s, and corresponds to the incoming flow value at each moment in the time-incoming flow array; a w is the upstream reservoir face area, m 2;Zw is the upstream reservoir water level, m; t is time, s.
Further, when there is only an upstream water level-reservoir capacity relationship curve, a quadratic curve fit is used:
Wherein A w is the upstream reservoir surface area, m 2;Zw is the upstream reservoir water level, m; v w is upstream reservoir capacity, m 3; a1、b1 and c 1 are both fitting coefficients, where a 1 and b 1 need to retain 8 bit decimal places.
Further, if the upstream water level-reservoir capacity and the upstream water level-reservoir surface area relation curve are absent, the following formula is adopted for calculation:
When the area of the surface of a certain water level of the reservoir and the reservoir capacity are known, calculating the values of a 2 and b 2 by adopting two coordinate points (Z w1,Aw1）、（Zw1,Vw1), and when the total reservoir capacity is only available, taking the value of b 2 as 2.0, and taking (Z w2,Vw1) into A W=a2Zw 2 to calculate the value of a 2.
Further, in the step 5, a weir flow formula is adopted for calculating the flow rate of the crumple:
Wherein: σ s is the downstream tailwater inundation coefficient; b d is the bottom width of the crumple, m; z w is the upstream reservoir level, m; z b is the upstream bottom elevation of the crumple, m; beta is the slope ratio of the side slope of the crumple; when (Z d-Zb)/(Zw-Zb) is less than 0.8, the flow is free, and when (Z d-Zb)/(Zw-Zb) is more than or equal to 0.8, the flow is submerged; z d is the downstream tailwater level, m.
Further, the trace-back erosion rate in calculating the erosion amount in step 5 is expressed as dx/dt:
Wherein: c h is a steep bank erosion parameter related to dam material characteristics, and is a key factor for controlling the dam breaking process of the homogeneous dam; q is the single-wide flow of the crumple, m 3/s; h is the height of the steep bank.
Further, the calculation formula of the steep bank erosion parameter C h is:
Wherein: k is a multiple nonlinear regression fitting coefficient, w is the water content of the dam material when the homogeneous dam breaks, w opt is the optimal water content of the homogeneous dam material, w/w opt is characterized as the water holding state of the homogeneous dam material, and c1 is a corresponding estimation coefficient; ρ d is the dam dry density of the homogeneous dam, kg/m 3;ρdm is the maximum dry density of the dam material, kg/m 3,ρd/ρdm is the dam compaction degree of the homogeneous dam, and c2 is the corresponding estimation coefficient; ρ w is the density of water, kg/m 3 ,ρd/ρw is characterized as the relative density of dam material with water as standard substance, c3 is the corresponding estimation coefficient; c c is the content of the dam adhesive particles, the value is 0-1, and c4 is the corresponding estimation coefficient; the corresponding parameter takes the value k= -2.931, c1=0.130, c2=0.315, c3= 2.052, c4=0.117.
Firstly, the erosion rate dx/dt of the abrupt bank has an influence on the flow of the crumple, and the larger the erosion rate dx/dt of the abrupt bank is, the larger the flow of the crumple is; the erosion rate dx/dt of the abrupt bank is influenced by the erosion parameter C h of the abrupt bank, and the positive correlation is formed; the erosion parameter C h of the steep bank is influenced by the moisture content, compactness and the content of the sticky particles of the soil body and is in negative correlation. Therefore, the increase of the moisture content, the compactness and the sticky particle content of the soil body can reduce the flow rate of the crumple, and if the factors are not considered, the calculation accuracy of the flow rate of the crumple can be reduced.
Further, in the step 5, the calculation of the top width variable quantity of the crumple and the bottom width variable quantity of the crumple adopts the following formula:
Wherein: Δb t is the top width increment of the crumple, m; Δb d is the base width increment of the crumple, m; n loc represents the position of the breach, n loc =1 represents that the breach is positioned on the dam abutment, and the breach can only develop towards one direction; n loc =2 indicates that the breach is positioned in the middle of the dam crest, and the breach can develop to two sides; Δz b is the vent depth increment, m.
Further, in step 10, judging whether the crumple side slope is stable, namely judging whether the driving force F d of the sliding wedge body is larger than the anti-sliding force F r, if so, indicating that the crumple side slope is unstable; f d and F r are respectively expressed as:
Wherein: w s is the weight of the sliding wedge, kg; θ is the slope angle after the slope of the crumple is unstable; gamma b is the soil volume weight, N/m 3;Hs is the height of the side slope of the breach, m; phi is the internal friction angle of the soil body; c is the cohesive force of the soil body, kPa; beta is the slope ratio of the ulcer slope.
The invention has the beneficial effects that:
the dam break mathematical model takes factors such as the water content, compactness and the sticky particle content of soil into consideration when calculating the erosion rate of the steep bank, so that the error of a prediction result is reduced.
Drawings
FIG. 1 is a schematic illustration of a homogenous dam overtopping breach formation;
FIG. 2 is a homogenous dam flood peak breach initial pit location;
FIG. 3 is a schematic illustration of a homogenous dam flood peak breach initial pit formation;
FIG. 4 is a schematic diagram of formation of a flood peak break steeply at a dam of homogeneity;
FIG. 5 is a schematic illustration of a flood top collapse of a homogeneous dam for erosion of a steep bank;
FIG. 6 is a schematic view of a sharp shear failure force;
FIG. 7 is a schematic diagram of a dam top breach development process of a homogeneous dam;
FIG. 8 is a schematic diagram of the development process of downstream slope breach of a homogeneous dam;
FIG. 9 is a schematic diagram of analysis of the stability of a dam breach slope;
FIG. 10 is a flow chart of model calculation;
FIG. 11 is a graph of dam level versus reservoir capacity for oil house ditch 1;
FIG. 12 is a graph showing the relationship between water level and reservoir capacity of the Changhan ditch No. 1 and No.2 dams;
FIG. 13 is a graph of the calculated dam break flow rate of the No. 1 dam of the oil house canal;
FIG. 14 is a graph showing the results of calculating the dam break flow rate of the Changhan ditch No. 1 dam;
FIG. 15 is a graph showing the results of calculating the dam break flow rate of the Changhan ditch No.2 dam.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
The method is programmed by a computer language, and the dam break cases of the oil house ditch No. 1, the Changhan ditch No. 1 and the Changhan ditch No. 2 are selected, so that the mathematical model calculation flow of the method is explained.
As shown in fig. 10, the mathematical model calculation flow of the present method includes:
step 1, determining and inputting geometrical characteristic parameters of a dam body, physical and mechanical characteristic parameters of the dam material, an upstream water level-reservoir surface area relation curve, a time-incoming flow curve and a time-discharging flow curve, wherein the parameters are shown in the following table 1;
Table 1 three foundation parameters for a dam
Wherein w/wopt is characterized as a water holding state of the homogeneous dam material; ρ d/ρdm is the dam compaction of the homogeneous dam, and k d is the dam erosion coefficient; τ c is the starting shear stress of the dam; c h is the erosion parameter of the sharp ridge.
Step 2, setting a permissible value of the upstream bottom elevation of the breach, wherein the value of each of the three dam bodies is 0;
Step 3, calculating the initial abrupt bank elevation;
as shown in fig. 1, the homogenous dam overtravel breaks the initial crumple formation, initial steep ridge elevation:
Zb=(ldown-ln)sin(αx)
As shown in fig. 2 and 3, the downstream dam slope erosion by water flow passing through the dam crest is an initial stage of the dam break by the flood peak of the homogeneous dam, and the flow velocity of the flood peak water flowing through the downstream dam slope is gradually increased, so that the downstream dam slope is caused to form an initial pit, and the initial pit forming position is that the point B is a downstream slope abrupt bank forming point:
Wherein: fr n is the Froude number; q b is the flow of the crumple, m 3/s;Bt is the top width of the initial crumple, and the width of the crumple on the downstream slope takes the same value; c is the thank you coefficient; z w is the upstream reservoir level, m; z b is the elevation of the upstream bottom of the crumple, m. g is gravity acceleration, m/s 2;
Wherein the thank you coefficient calculation mode is:
D n in FIG. 2 is the depth of water flow, m, on the downstream dam slope; alpha s is the slope angle of the upstream dam slope; alpha x is the slope angle of the downstream dam slope; l down is the downstream dam slope length, m; and l n is the length of the peak of the downstream dam slope from the initial steep bank position, m.
Wherein the flow of the crumple is calculated by adopting a water balance formula:
Wherein: q is total leakage flow, m 3/s;Qb is breach flow, m 3/s;Qspill is spillway outflow flow, m 3/s corresponds to the leakage value in each moment in the time-leakage array, and zero is set when no spillway flows; q in is the warehouse-in flow, m 3/s, and corresponds to the incoming flow value at each moment in the time-incoming flow array; a w is the upstream reservoir face area, m 2;Zw is the upstream reservoir water level, m; t is time, s.
The model calculation uses a water level-reservoir area relation curve A w -Z, but when only a water level-reservoir capacity relation curve V w -Z is shown in figures 11 and 12, quadratic curve fitting can be used for V w -Z:
a 1、b1 and c 1 are both fitting coefficients, where a 1 and b 1 need to preserve 8-bit decimal places.
If the water level-reservoir capacity and water level-reservoir surface area relation curve is absent, the following formula can be adopted for calculation:
When the area and the storage capacity of a certain water level of the reservoir are known, calculating the values of a 2 and b 2 by adopting two coordinate points (Z w1,Aw1）、（Zw1,Vw1), wherein Z w1 is a specific value of Z w under the condition that the area and the storage capacity of the reservoir are known, and A w1 is a specific value of A w under the condition that the area and the storage capacity of the reservoir are known; when the total storage capacity (the storage capacity corresponding to the check water level) is only available, b 2 suggests that the value is 2.0, and the value of a 2 is calculated by taking (Z w2,Vw1) into A W=a2Zw 2, wherein Z w2 is the specific value of Z w under the condition of only the total storage capacity.
In the method, when the relation between the water level and the area of the reservoir surface is absent, the method for quickly and accurately acquiring the water level and the area of the reservoir surface by adopting other known parameters is adopted, and finally, data A w-Zw is obtained and used for flow calculation.
Step4, setting the calculated total duration and the time step of each calculation;
step 5, calculating the flow rate, erosion quantity, upstream reservoir water level variable quantity, downstream tail water level variable quantity, top width variable quantity and bottom width variable quantity of the crumple mouth in each time step;
in the process of the homogenous dam over-roof dam break, a dam flow formula is adopted for calculating the breach flow:
Wherein: σ s is the downstream tail water inundation coefficient, and the value of σ s is shown in table 2; b d is the bottom width of the crumple, m; z w is the upstream reservoir level, m; z b is the upstream bottom elevation of the crumple, m; beta is the slope ratio of the side slope of the crumple; when (Z d-Zb)/(Zw-Zb) is less than 0.8, the flow is free, and when (Z d-Zb)/(Zw-Zb) is more than or equal to 0.8, the flow is submerged; z d is the downstream tailwater level, m.
Table 2 inundation coefficient sigma s value table
As shown in fig. 3,4 and 5, after the initial pit formation of the downstream slope, upstream tracing erosion is performed in the form of a steep bank, the empty face of the steep bank is vertical, and the tracing erosion rate can be expressed as dx/dt:
Wherein: c h is a steep bank erosion parameter related to a dam material, which is a key factor for controlling the dam breaking process of the homogeneous dam, and is calculated by adopting the steep bank erosion parameter model. In the figure, H represents the dam height.
The process for establishing the calculation model of the erosion parameters C h of the abrupt bank comprises the following steps:
(1) Adopting a multi-element nonlinear regression analysis method, considering nonlinear relations among dam material adhesive particle content c c, water content w, dry density rho d and erosion parameters, wherein the expression of the nonlinear regression model is as follows:
In the middle of ：n=4,Xi=(x1,x2,x3,x4)=(w/wopt,ρd/ρdm,ρd/ρw,cc);
。
Because the direct solution is not suitable for solving the nonlinear regression model, based on the least square method principle, a Gaussian-Newton iteration method is adopted, a Taylor series expansion type is used for approximately replacing the nonlinear regression model, repeated iteration solution is carried out by setting initial values of all estimated coefficients, the regression coefficients are enabled to be continuously approximate to the optimal regression coefficients of the nonlinear regression model, and finally the sum of squares of residual errors of the original model is enabled to be minimum.
(2) The model is subjected to model prediction precision assessment by adopting a goodness of fit R 2 and a root mean square error E rms, and the assessment method comprises the following steps:
Wherein: SSE is the sum of squares of errors; SST is the sum of squares of the dispersion; n is the number of case groups used for model creation, where n=4.
Wherein: i=the number of dependent variables (i.e. the number of measured data sets), y mi is the measured value of the i-th dependent variable; Predicted values for the ith dependent variable; /(I) Is the average of all measured values of the dependent variable; r 2 ranges from 0 to 1, and when R 2 is closer to 1, the fitting degree of the predicted value and the measured value is higher.
According to the invention, 45 groups of experimental data with actual measurement data are adopted, only part of experimental data are displayed because of limited space, and the experimental data are shown in table 3, and a calculation model of the erosion parameters of the steep bank is finally obtained by fitting according to a specific method established by the erosion parameter model of the steep bank, so that the fitting goodness R 2 =0.873 and the root mean square error E rms =0.569 are achieved.
Wherein: k is a multiple nonlinear regression fitting coefficient, w is the water content of the dam material when the homogeneous dam breaks, w opt is the optimal water content of the homogeneous dam material, w/w opt is characterized as the water holding state of the homogeneous dam material, and c1 is a corresponding estimation coefficient; ρ d is the dam dry density of the homogeneous dam, kg/m 3,ρdm is the maximum dry density of the dam material, kg/m 3,ρd/ρdm is the dam compaction degree of the homogeneous dam, and c2 is the corresponding estimation coefficient; ρ w is the density of water, kg/m 3;ρd/ρw is characterized as the relative density of dam material with water as standard substance, c3 is the corresponding estimation coefficient; c c is the content of the dam adhesive particles, the value is 0-1, and c4 is the corresponding estimation coefficient; the corresponding parameter takes the value k= -2.931, c1=0.130, c2=0.315, c3= 2.052, c4=0.117.
TABLE 3 partial actual measurement test data
Compared with the conventional abrupt bank erosion model, the result is shown in table 4, the fitting goodness R 2 of the model is close to 1, and the root mean square error E rms is relatively small, so that the overall prediction accuracy of the model is high.
Table 4 comparison of prediction accuracy for different models
When the dam material is in an unsaturated state, the slope angles of the 'steep bank' and the crumple slope are close to the vertical shape; similarly, for a dam body with higher sticky particle content, the slope angle of the breach slope is in a steep slope form, and the breach slope angle beta is 90 degrees. In the dam break process, the expansion of the top width and the bottom width of the dam crest breach and the erosion of the bottom bed have the following relation, as shown in fig. 7:
The calculation of the top width variable quantity of the crumple and the bottom width variable quantity of the crumple adopts the following formula:
Wherein: b t is the top width of the crumple, and DeltaB t is the top width increment of the crumple, m; b d is the base width of the crumple, and DeltaB d is the base width increment of the crumple, m; n loc represents the position of the breach, n loc =1 represents that the breach is positioned on the dam abutment, and the breach can only develop towards one direction; n loc =2 indicates that the breach is positioned in the middle of the dam crest, and the breach can develop to two sides; Δz b is the vent depth increment, m.
And (3) introducing a correction coefficient considering the characteristics of the crumple to the crumple of the downstream side slope of the homogeneous dam to calculate the top width and the bottom width of the crumple of the downstream side slope. The model assumes that the expansion of the top and bottom widths of the downstream slope crumple zones has the following relationship with the bottom bed erosion, as shown in fig. 8:
Wherein: b d is the bottom width of the crumple, m; b down is the top width of the downstream slope breach, m; b down is the bottom width of the downstream slope breach, m; n loc is a breach position parameter (the breach is positioned in the middle part of the dam body and is 2, and the breach is positioned in the abutment and is 1); z b is the elevation of the upstream bottom of the crumple, m; gamma is the slope angle of the downstream slope breach slope; c b is a correction coefficient.
And 6, after the abrupt bank is developed to a certain degree upstream, under the action of the pressure of the upstream water head and the shearing stress of the water flow on the flood peak, the abrupt bank is sheared and destroyed to collapse, and the stress analysis of the destroyed wedge is shown in fig. 6. The wedge-shaped body receives force mainly including upstream storehouse water pressure F 1, downstream tail water pressure F 2, the upper water flow shear force F 3 of the abrupt bank, the upper water weight F 4 of the abrupt bank, the dead weight F 5 of the abrupt bank, the friction force F 6 that the abrupt bank receives and the internal cohesive force F 7 of the abrupt bank soil body, if F 1-F2+F3＞F6+F7, judge the abrupt bank to shear and destroy, go on step 7, otherwise go on step 8;
wherein at Z d＜Zh, F 2 =0;
Wherein: b d is the bottom width of the crumple, m; ρ w is the water density, kg/m 3; g is gravity acceleration, m/s 2;Zw is the upstream reservoir water level, m; z h is the elevation of the bottom of the downstream of the crumple, m; z b is the upstream bottom elevation of the crumple, m; z d is the downstream tailstock level, m; n is a Manning roughness coefficient; q b is the flow rate of the crumple, and m 3/s;Aw is the cross-sectional area of the water flow of the crumple; r is the hydraulic radius of the crumple and is the ratio of the cross-sectional area of water to the wet circumference; l dt is the length of the top of the steep bank, m; l db is the bottom length of the steep bank, m; h is the height of the steep bank and m; phi is the internal friction angle of the soil body; c is soil cohesive force, kPa.
And 7, after the wedge-shaped body collapses, the erosion mode of the flood top water flow to the rest dam body is changed from the steep bank erosion to the surface erosion, namely the height of the bottom of the breach is continuously reduced. Since the dam material is usually viscous, the erosion rate of the dam material can be calculated by the following formula:
dZb/dt=kd(τb-τc)
Wherein: dZ b/dt is the erosion rate of the bottom bed of the crumple, m/s; k d is the dam erosion coefficient; τ b is the shear stress of water flow, pa; τ c is the starting shear stress of the dam, pa.
Τ c and k d are key factors influencing the development of the crumple and the evolution process of the crumple flow, and the values of τ c and k d have important significance for improving the model prediction precision. The calculation method of k d is as follows:
Wherein: gamma w is the volume weight of water, N/m 3;γd is the dry volume weight of soil body, and N/m 3;cc is the content of sticky particles.
The water flow shear stress τ b can be calculated using the Manning formula:
Wherein: ρ w is the density of water, kg/m 3; g is gravity acceleration, m/s 2; n is the Manning roughness coefficient at the crumple; a w is the sectional area of the water flow of the crumple, m 2; r is the hydraulic radius at the position of the crumple and m.
Updating and calculating the upstream reservoir water level, the upstream bottom elevation of the crumple opening, the top width of the crumple opening and the bottom width of the crumple opening according to the variable quantity calculated in the step 5;
Zw=Zw-1+ΔZw
Zb=Zb-1+ΔZb
Bt =Bt-1+ΔBt
Bd =Bd-1+ΔBd
Wherein Z w represents the upstream reservoir water level at the nth calculation, Z w-1 represents the upstream reservoir water level at the n-1 th calculation, and DeltaZ w represents the variation of the upstream reservoir water level at the n-1 th and nth calculations; z b represents the upstream bottom elevation of the crumple at the nth calculation, Z b-1 represents the upstream bottom elevation of the crumple at the nth-1 calculation, and DeltaZ b represents the variation of the upstream bottom elevation of the crumple at the nth-1 and nth calculations; b t represents the top width of the crumple opening at the nth calculation, B t-1 represents the top width of the crumple opening at the (n-1) th calculation, and DeltaB t represents the variation of the top width of the crumple opening at the (n-1) th and the (n) th calculations; b d represents the bottom width of the crumple at the nth calculation, B d-1 represents the bottom width of the crumple at the n-1 th calculation, and Δb d represents the amount of change in the bottom width of the crumple at the n-1 th and nth calculations.
Step 8, continuously erosion the dam crest breach, and updating and calculating erosion quantity, upstream reservoir water level, upstream bottom elevation of the breach, top width of the breach and bottom width of the breach according to the variable quantity calculated in the step 5;
xn=xn-1+Δx
Zw=Zw-1+ΔZw
Zb=Zb-1+ΔZb
Bt =Bt-1+ΔBt
Bd =Bd-1+ΔBd
Step 9, calculating DeltaZ w / Zw, judging whether DeltaZ w / Zw is smaller than epsilon, wherein epsilon is a calculation convergence condition, and taking 0.0001 or adjusting according to actual conditions; if the delta Z w / Zw is smaller than epsilon, carrying out step 10, otherwise returning to step 5 to continue calculation;
Step 10, judging whether the side slope of the crumple is stable, if so, judging whether the accumulated calculation time is longer than the set calculation time length, if so, ending the calculation, and outputting calculation results of the crumple flow, the erosion amount, the upstream reservoir water level change amount, the upstream bottom elevation change amount, the crumple top width change amount and the crumple bottom width change amount;
With the increasing depth of the breach of the dam crest, the breach side slope may be unstable, and the side slope stability is analyzed by adopting a limit balance method, as shown in fig. 9. When the driving force F d of the sliding wedge body is larger than the anti-sliding force F r, the slope is unstable, namely:
Fd＞Fr
Wherein: f d and F r may be represented as:
Wherein: w s is the weight of the sliding wedge, kg; θ is the slope angle after the slope of the crumple is unstable; gamma b is the soil volume weight, N/m 3;Hs is the height of the side slope of the breach, m; phi is the internal friction angle of the soil body; c is the cohesive force of the soil body, kPa; beta is the slope ratio of the ulcer slope.
The characteristic parameters such as the peak burst flow Q p, the burst peak flow occurrence time T p, the burst top width B t and the like are calculated by adopting the steps. The settlement results are shown in Table 5.
Table 53 sets of actual measurement case verification results
The result shows that the dam break model realizes the accurate prediction of the flow of the crumple, and the prediction precision error of the peak flow of the crumple is within +/-5 percent. For the prediction of the appearance time of the peak flow of the breach of the oil house ditch No. 1 dam and the burst of the Changhan ditch No. 1 dam, the calculation error of the model is less than +/-10%, and for the prediction of the burst No. 2 dam, the relative error is within +/-20%. As the Changhan ditch No. 1 dam lacks the measurement data of the top width of the crumple, comparison is not carried out here, and the relative error of the prediction result of the model on the crumple width is within +/-35%.
Claims (3)
1. A dam break mathematical model and parameter determining method for a homogeneous dam is characterized by comprising the following steps:
Step 1, determining geometrical characteristic parameters of a dam body, physical and mechanical characteristic parameters of a dam material, an upstream water level-reservoir surface area relation curve, a time-incoming flow curve and a time-draining curve;
step 2, setting a bottom elevation allowable value of the upstream of the crumple;
Step 3, calculating an initial abrupt bank elevation, namely an initial value of the upstream bottom elevation of the crumple, specifically comprising:
Zb=(ldown-ln)sin(αx)
Wherein: fr n is the Froude number; q b is the flow of the crumple, m 3/s;Bt is the top width of the initial crumple, and the width of the crumple on the downstream slope takes the same value; c is the thank you coefficient; z w is the upstream reservoir level, m; z b is the upstream bottom elevation of the crumple, m; g is gravity acceleration, m/s 2;ldown is the downstream dam slope length, m; l n is the length of the peak of the downstream dam slope from the initial steep bank position, m; alpha x is the slope angle of the downstream dam slope;
Wherein the thank you coefficient calculation mode is:
Wherein: n is a Manning roughness coefficient, n= (d 50)1/6/12, d represents particle size;
Wherein the flow of the crumple is calculated by adopting a water balance formula:
Wherein: q is total leakage flow, m 3/s;Qb is breach flow, m 3/s;Qspill is spillway outflow flow, m 3/s corresponds to the leakage value in each moment in the time-leakage array, and zero is set when no spillway flows; q in is the warehouse-in flow, m 3/s, and corresponds to the incoming flow value at each moment in the time-incoming flow array; a w is the upstream reservoir face area, m 2;Zw is the upstream reservoir water level, m; t is time, s;
when there is only an upstream water level-reservoir capacity relationship curve, a quadratic curve fit is used:
wherein A w is the upstream reservoir surface area, m 2;Zw is the upstream reservoir water level, m; v w is upstream reservoir capacity, m 3;a1、b1 and c 1 are fitting coefficients, where a 1 and b 1 require 8 bit decimal places to be preserved;
If the upstream water level-reservoir capacity and the upstream water level-reservoir surface area relation curve are absent, the following formula is adopted for calculation:
When the area of a certain water level of the reservoir and the reservoir capacity are known, calculating the values of a 2 and b 2 by adopting two coordinate points (Z w1,Aw1）、（Zw1,Vw1), and when the total reservoir capacity is only available, taking the value of b 2 as 2.0, and carrying (Z w2,Vw1) into A W=a2Zw 2 to calculate the value of a 2; z w1 is the specific value of Z w under the condition that the area of the warehouse surface and the storage capacity are known, A w1 is the specific value of A w under the condition that the area of the warehouse surface and the storage capacity are known, and Z w2 is the specific value of Z w under the condition that the total storage capacity is only available
Step4, setting the calculated total duration and the time step of each calculation;
Step 5, calculating the flow rate, erosion amount, upstream reservoir water level variation, upstream bottom elevation, top width variation and bottom width variation of the crumple openings in each time step;
And calculating the flow of the burst orifice by adopting a weir flow formula:
Wherein: σ s is the downstream tailwater inundation coefficient; b d is the bottom width of the crumple, m; z w is the upstream reservoir level, m; z b is the upstream bottom elevation of the crumple, m; beta is the slope ratio of the side slope of the crumple; when (Z d-Zb)/(Zw-Zb) is less than 0.8, the flow is free, and when (Z d-Zb)/(Zw-Zb) is more than or equal to 0.8, the flow is submerged; z d is the downstream tailstock level, m;
the trace-source erosion rate when calculating erosion amount is expressed as dx/dt:
Wherein: c h is a steep bank erosion parameter related to dam material characteristics, and is a key factor for controlling the dam breaking process of the homogeneous dam; q is the single-wide flow of the crumple, m 3/s; h is the height of the steep bank;
the calculation formula of the steep bank erosion parameter C h is as follows:
；
Wherein: k is a multiple nonlinear regression fitting coefficient, w is the water content of the dam material when the homogeneous dam breaks, w opt is the optimal water content of the homogeneous dam material, w/w opt is characterized as the water holding state of the homogeneous dam material, and c1 is a corresponding estimation coefficient; ρ d is the dam dry density of the homogeneous dam, kg/m 3,ρdm is the maximum dry density of the dam material, kg/m 3,ρd/ρdm is the dam compaction degree of the homogeneous dam, and c2 is the corresponding estimation coefficient; ρ w is the density of water, kg/m 3 ,ρd/ρw is characterized as the relative density of dam material with water as standard substance, c3 is the corresponding estimation coefficient; c c is the content of the dam adhesive particles, the value is 0-1, and c4 is the corresponding estimation coefficient; the corresponding parameter takes the value of k= -2.931, c1=0.130, c2=0.315, c3= 2.052, c4=0.117;
Step 6, respectively calculating the upstream reservoir water pressure F 1, the downstream tail water pressure F 2, the water flow shearing force F 3 on the upper part of the abrupt bank, the water weight F 4 on the upper part of the abrupt bank, the dead weight F 5 of the abrupt bank, the friction force F 6 born by the abrupt bank and the cohesive force F 7 in the soil body of the abrupt bank, if F 1- F2+ F3＞F6+ F7 is carried out, judging that the abrupt bank is subjected to shearing damage, and carrying out step 7, otherwise, carrying out step 8;
Step 7, updating and calculating the upstream reservoir water level, the upstream bottom elevation of the crumple opening, the top width of the crumple opening and the bottom width of the crumple opening according to the variable quantity calculated in the step 5;
step 8, calculating erosion of the abrupt bank, and updating and calculating the erosion quantity, the water level of the upstream warehouse, the elevation of the upstream bottom of the crumple, the top width of the crumple and the bottom width of the crumple according to the variable quantity obtained by the calculation in the step 5;
Step 9, calculating DeltaZ w / Zw, judging whether DeltaZ w / Zw is smaller than epsilon, wherein epsilon is a calculation convergence condition, and taking 0.0001 or adjusting according to actual conditions; if yes, step 10 is carried out, otherwise, step 5 is returned to continue calculation; Δz w represents the amount of change in the upstream reservoir water level, and Z w represents the upstream reservoir water level;
Step 10, judging whether the side slope of the crumple is stable, if so, judging whether the accumulated calculation time is longer than the set calculation time length, if so, ending the calculation, and outputting calculation results of the crumple flow, the erosion amount, the upstream reservoir water level change amount, the upstream bottom elevation change amount, the crumple top width change amount and the crumple bottom width change amount;
And (5) returning to the step (5) to calculate the next time step if the accumulated calculation time is smaller than the set total calculation time.
2. The dam-break mathematical model and parameter determining method for homogeneous dam according to claim 1, wherein the calculating of the variation of the top width of the breach and the variation of the bottom width of the breach in step 5 adopts the following formula:
Wherein: Δb t is the top width increment of the crumple, m; Δb d is the base width increment of the crumple, m; n loc represents the position of the breach, n loc =1 represents that the breach is positioned on the dam abutment, and the breach can only develop towards one direction; n loc =2 indicates that the breach is positioned in the middle of the dam crest, and the breach can develop to two sides; Δz b is the vent depth increment, m.
3. The dam break mathematical model and parameter determining method for homogeneous dam according to claim 1, wherein in step 10, it is determined whether the breach slope is stable, i.e. whether the driving force F d of the sliding wedge is greater than the anti-sliding force F r, if so, it is indicated that the breach slope is unstable; f d and F r are respectively expressed as:
Wherein: w s is the weight of the sliding wedge, kg; θ is the slope angle after the slope of the crumple is unstable; gamma b is the soil volume weight, N/m 3;Hs is the height of the side slope of the breach, m; phi is the internal friction angle of the soil body; c is the cohesive force of the soil body, kPa; beta is the slope ratio of the ulcer slope.
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