CN107816009B - A method of inquiring into multistage compound cross-section stage discharge relation - Google Patents
A method of inquiring into multistage compound cross-section stage discharge relation Download PDFInfo
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Abstract
The present invention proposes a kind of universal method for inquiring into multistage compound cross-section stage discharge relation, comprising the following steps: section is divided into M+N+1 sub- sections, and is further classified as 7 class components by the measurement data for obtaining target section；Resistance is carried out to each sub- section and divides fk=fbk+fvk, wherein fvk=4 λkCDDkmkhkFor the resistance coefficient that vegetation towing generates, the Manning coefficient of each sub- section is calculatedThe apparent shear stress for calculating each element, establishes the momentum balance relationship of each sub- section, to obtain the matrix equation of tridiagonal coefficient matrix；Using " chasing method " solution matrix equation, the mean velocity in section of each sub- section is obtained, and then obtains the stage discharge relation of the section.Method proposed by the present invention has unified expression formula, convenient for being calculated using Excel or programming, the stage discharge relation for all multistage compound cross-sections that can be applied to including second level compound cross-section is inquired into, and is a kind of calculating simplicity but calculation method with high accuracy.
Description
Technical field
The invention belongs to hydraulic engineering technical field, specifically one kind inquires into multistage compound cross-section stage discharge relation
Method.
Background technique
For the bed-forming role for adapting to different flow, natural river is mostly the compound cross-section of second level or multistage.In addition, city river
Stream is also often designed to the compound cross-section of second level or multistage, to mitigate influence of the flood control measure to river corridor landscape, and increases edge
The access and open riverfront of bank resident.Compound cross-section is usually made of a deeper major trough and relatively shallower one or more beaches,
Transfer passages of the major trough as dry season, beach are only just used as flood passage channel when flood period Flood Plain Flow occurring.Due to section
Discontinuously, for beach usually by vegetative coverage, roughness is big compared with major trough in addition, thus the flow velocity of major trough is often big compared with beach, leads to beach
There are momentum-exchanges between slot.Momentum-exchange between swale will increase resistance to water-flow, and then reduce section conveyance capacity.Therefore, single
One method of section, section split plot design etc. do not consider that the calculation method of momentum-exchange between swale cannot accurately inquire into compound cross-section
Stage discharge relation.For this purpose, many scientific workers are dedicated to the research of compound cross-section stage discharge relation calculation method, propose
Many calculation methods with high accuracy, are roughly divided into hydraulic method (such as apparent stress method, zero stress interface method), statistics
Method (such as multivariate regression models) and artificial intelligence approach (such as artificial neural network, genetic algorithm) three categories.However, this
What a little methods were proposed both for second level compound cross-section, seldom pay close attention to the calculation method of multistage compound cross-section stage discharge relation.
In the flood-control management of natural river, stage discharge relation is rapidly and accurately established, forecasts the flood under crest discharge
Water level and corresponding floodplain can just take rationally effective flood defence policies.In the engineering design of city river improvement,
Establishing stage discharge relation is to carry out section design, especially determines major trough groove depth, beach width, greening scheme (as set than selecting
Diameter, vegetation density etc.) etc. key parameters basis.Therefore, in order to reasonably be managed to river, there is an urgent need to one kind to inquire into
The calculation method of multistage compound cross-section stage discharge relation.
Summary of the invention
The purpose of the present invention is to propose to a kind of methods for inquiring into multistage compound cross-section stage discharge relation, can be easy, fast
Speed accurately inquires into multistage compound cross-section stage discharge relation including second level compound cross-section.Pass through following technical proposal
It realizes.
The present invention provides such a calculation method, a method of inquiring into multistage compound cross-section stage discharge relation, is
Above-mentioned technical problem is solved, the technical solution used in the present invention is as follows:
Step 1: the geometric dimension analysis of target section.Obtain the profileometry data (X of target sectioni, Zi) (i=1,
2 ..., K), XiTarget cross section starting point X is arrived for i-th point1Distance, ZiFor the elevation of the point, K is the quantity of section survey point；
It chooses elevation and changes obvious point, section is divided into M+N+1 sub- sections (such as Fig. 1 institute by the vertical line put by these
Show), wherein the maximum sub- section of the depth of water is known as major trough, remaining is known as beach, and M is the number of beach (sub- section) on the left of major trough
Amount, N are the quantity of beach (sub- section) on the right side of major trough, and M, N are natural number, and M+N >=1.Son is successively labeled as from starting point side
Section k (1≤k≤K-1).Sub- section (k=M, M+2) close to major trough is known as level-one beach, and it is flat that bed elevation is known as level-one
The beach depth of water, the sub- section (k=M-1, M+3) close to level-one beach are known as second level beach, and bed elevation is known as the flat beach water of second level
It is deep, and so on.The width b of each sub- section is read respectivelyk, terrace height dk, the gradient of beach side slope, the left grade of side slope of major trough
SLkWith the right grade of side slope S of major troughRk, such as Fig. 1.
Step 2: determining the Manning roughness coefficient of each section.The Manning roughness coefficient of sub- section k is calculated using following formula:
In formula: nkFor the Manning roughness coefficient of sub- section k；RkFor the hydraulic radius of sub- section k, removed by the area of sub- section k
It is obtained with the wetted perimeter of the sub- section；G is acceleration of gravity, is usually taken to be 9.81m/s2；fkFor total Darcy- of sub- section k
Weisbach resistance coefficient.Since vegetation density can be used for defining unvegetated situation for 0, according to additive property principle, Darcy-
Weisbach resistance coefficient resistance coefficient caused by vegetation drag and bed surface coefficient of frictional resistance form, i.e.,
fk=fbk+fvk (2)
In formula: fbkFor the bed surface coefficient of frictional resistance of sub- section k, fvkFor resistance caused by vegetation drag on sub- section k
Coefficient
fvk=4 λkCDDkmkhk (3)
In formula: DkFor the diameter of plant on sub- section k；hkFor the depth of water of sub- section k；mkFor on unit area on sub- section k
The quantity of plant, i.e. vegetation density, for the plant of rule plantation, vegetation density is the inverse of line-spacing and spacing in the rows product, i.e. mk
=1/ (LxkLyk), Lxk、LykFor the line-spacing and spacing in the rows of plant on sub- section k；CDForce coefficient is pulled for vegetation；λkTo consider vegetation
The correction factor of degree is flooded, calculation formula is as follows:
Wherein: SDkFor the degree of flooding of vegetation on sub- section k, is defined as:
In formula: hvFor the height of plant on sub- section k；
Step 3: the basic element composition of identification target section.Arbitrary multistage compound cross-section can be by the element in Fig. 2
It constitutes.For example, section shown in FIG. 1 is by I, M-1 element VI of 1 element, IV, N-1 element VII of 1 element and 1 element
The total M+N+1 basic element of II is constituted.The concrete condition that sub- section is divided according to target section, control is chosen each in Fig. 2
The corresponding element of sub- section.The sub- cross-sectional area A of each component is calculated separately according to table 1k, wetted perimeter PkWith hydraulic radius Rk, and
Determine the height h of its left and right sides interfaceLkAnd hRk。
The hydraulic parameters of the multistage compound cross-section constitution element of table 1
Step 4: calculating apparent shear stress coefficient.The momentum-exchange between adjacent element is measured using apparent shear stress,
Its calculation formula is
In formula:Apparently cutting between respectively sub- section k and the sub- section k-1 and sub- section k+1 in right side in its left side
Stress；ρ is the density of water；hLk, hRkFor the sub- section k and sub- section k-1 in its left side and the sub- section k+1 interface height in right side；
uk-1,uk,uk+1For sub- section k-1, the mean flow rate of k, k+1；ξK, k-1, ξK, k+1The respectively sub- section k and sub- section k-1 in its left side
With the apparent shear stress coefficient of the sub- section k+1 in right side.Second level compound cross-section research shows that the value of apparent shear stress coefficient is big
The small relative water depth between adjacent sub- section, relative width, the breadth depth ratio of relative roughness and major trough are related.It is multiple for multistage
Formula section, using the j grades of flat beach depth of waters as boundary (beach j=M-k+1, right side beach j=k-M-1 on the left of major trough), lower than being considered as its
" new major trough " is considered as " new point bar " (being detailed in Fig. 1) higher than it, estimates apparent shear stress coefficient using formula (7)
Wherein: r is intermediate variable；H is the depth of water of new major trough；B is that (including half major trough and left side are all for rivers and canals left half
Point bar) width；BMrFor the overall width of new major trough；hrFor the depth of water of new point bar；Dr is the flat beach depth of water of new point bar；nrFor new side
The roughness on beach；nr+1For the roughness of new major trough；ψ is proportionality coefficient related with section symmetry and vegetation.
For unvegetated symmetrical compound cross-section, ψ=4.5 × 10-4；For unvegetated asymmetric compound cross-section, ψ=6.3 × 10-4；
There are the symmetrical compound cross-section of vegetation, ψ=1.0 × 10 for beach-4；There is the asymmetric compound cross-section of vegetation for beach, ψ=
1.4×10-4。
Step 5: design factor matrix.The longitudinal slope for determining section is measured than drop S0, according to the element of the target section of identification
Composition, calculates separately the following parameter of each sub- section:
Wherein: Ik,Jk,Xk,YkFor the intermediate variable of calculating, nk,Rk,ξk,k-1,ξk,k+1,hLk,hRk, the meaning of g is the same.
The difference of square of flow velocity between apparent shear stress and sub- section is directly proportional.Remember that sub- section k is adjacent with its arranged on left and right sides
The direction coefficient of apparent shear stress is respectively α between sectionkAnd βk。αkAnd βkThe value between -1,0 and 1, point or less three kinds of feelings
Condition determines value: 1. sub- section biggish for flow velocity, apparent shear stress are the resistances of the sub- section, i.e. apparent shear stress
With gravity along the contrary of component is flowed to, the direction of apparent shear stress is expressed as "+1 " in direction；2. son lesser for flow velocity
Apparent shear stress between section, with adjacent sub- section is power, i.e. the direction of apparent shear stress and gravity edge flows to component
Direction it is identical, be expressed as " -1 "；3. there is no adjacent sub- section to Mr. Yu side, it is expressed as " 0 ".According to above-mentioned regulation, in Fig. 2
Shown in 7 kinds of element αkAnd βkValue be shown in Table 1.When with method proposed by the present invention, to element belonging to each sub- section
After classification is identified, the value of α and β can be determined according to table 1.For example, group section k belongs to element IV, by table 1, αk=1, βk
=1；Group section k belongs to element V, by table 1, αk=1, βk=0, and so on.
According to the composition of target section, the direction coefficient of the apparent shear stress of each sub- section is successively determined according to table 1, and is counted
Calculate following parameters
ak=αkXk,bk=Ik-αkXk-βkYk,ck=βkYk (9)
Step 6: establishing matrix equation.For multistage compound cross-section as shown in Figure 1, solution matrix is triple diagonal matrix
Element is
Φ X=J (10)
In formula:For flow velocity matrix；J=(J1 J2 … JM+N+1)TFor momentum matrix；Φ is
Three diagonal coefficient matrixes
Step 7: formula (11) being solved using " chasing method ", obtain the mean flow rate u of each sub- sectionk, respectively multiplied by corresponding
Sub- cross-sectional area Ak, obtain the flow Q of each sub- sectionk.According to total flow equation, the total flow Q of target section is calculated, i.e.,
Q=AUT (12)
In formula: U=(u1 u2 … uM+N+1)T, A=(A1 A2 … AM+N+1)T。
Good effect of the present invention:
The present invention has following advantages and effect compared with prior art: 1) being vertically divided into multistage compound cross-section more
A sub- section is classified as 7 major class according to the border condition of anyon section and its adjacent sub- section, any one multistage is multiple
Formula section can be made up of this 7 kinds of elements the method for " playing with building blocks ", and therefore, method proposed by the present invention can be applied to own
Multistage compound cross-section (including second level compound cross-section)；2) method of the bright proposition of we is sufficiently examined when calculating Manning resistant coefficient
Beach has been considered usually by the actual conditions of vegetative coverage, and vegetation extra coefficient of resistance is considered using vegetation degree of flooding correction factor
Change with fluctuation in stage, improves the precision of calculating；3) method proposed by the present invention has unified expression formula, convenient for using
Excel or programming are calculated；4) compared with the conventional methods such as the single method of section, section split plot design, computational accuracy is higher, with
Two, three-dimensional hydraulic method is compared with artificial intelligence approach, required time (time including being ready for data) and consumption
The human and material resources taken are less, are a kind of calculating simplicity but calculation method with high accuracy.
Detailed description of the invention
Fig. 1 is that the method for the present invention multistage compound cross-section divides schematic diagram；
Fig. 2 is the component schematic diagram of the method for the present invention multistage compound cross-section；
Fig. 3 is the symmetrical compound cross-section schematic diagram of the unvegetated second level of beach of embodiment 1；
Fig. 4 is the stage discharge relation for the embodiment 1 inquired into using proposition method of the present invention；
Fig. 5 is that beach has the asymmetric compound cross-section schematic diagram of the three-level of vegetation in embodiment 2；
Fig. 6 is the stage discharge relation for the embodiment 2 inquired into using proposition method of the present invention.
Specific embodiment
Embodiment 1
Certain section is the unvegetated symmetrical compound cross-section (as shown in Figure 3) of beach, major trough bottom width bm=0.75m, groove depth d=
0.15m, slope coefficient S=1, the wide b of point barf=2.25m, major trough and beach are all made of concrete lining and form, relative smooth, break
The bed sloped of section where face is 1.027 ‰, inquires into the stage discharge relation of the section.
The step of stage discharge relation of the section is inquired into using technical solution of the present invention is as follows:
Step 1: section is vertically divided into 3 sub- sections by selected point C and F, is successively denoted as k=1,2,3, then b1=b3
=2.25m, b2=1.50m, d1=d3=0.15m.
Step 2: major trough and its equal relative smooth of the beach of two sides, and without vegetative coverage, that is, take mk=0, obtain 3 sub- sections
Manning roughness coefficient be 0.010s/m1/3, i.e. n1=n2=n3=0.010s/m1/3。
Step 3: the sub- section obtained according to division, the section are made of 1 element I, 1 element IV and 1 element II,
That is the element of target section is configured to " I+IV+II ".The depth of water h of group section 2 (major trough)2When≤d=0.15m, water flow is whole
It is transported by major trough, stage discharge relation is directly inquired by Manning formula, and as H > 0.15, water flow overbank is compound cross-section, by water
Deep H successively increases 0.01m or 0.02m, and the cross-sectional area A of each sub- section is calculated according to table 1k, wetted perimeter PkWith hydraulic radius Rk.By
Table 1 differentiates that sub- section 2 belongs to element IV, and the height with the sub- section interface in the left and right sides is respectively hL2=h2-1=h1, hR2=
h2+1=h3, calculated result is shown in Table 2 in detail.
Table 2 is the calculating process and result that the present invention is used for example 1
| H(m) | 0.160 | 0.170 | 0.180 | 0.190 | 0.200 | 0.220 | 0.240 | 0.260 | 0.280 | 0.300 |
| h1(m) | 0.010 | 0.020 | 0.030 | 0.040 | 0.050 | 0.070 | 0.090 | 0.110 | 0.130 | 0.150 |
| A1(=A3)(m2) | 0.041 | 0.082 | 0.123 | 0.164 | 0.205 | 0.287 | 0.369 | 0.451 | 0.533 | 0.615 |
| A2(m2) | 0.266 | 0.284 | 0.302 | 0.320 | 0.338 | 0.374 | 0.410 | 0.446 | 0.482 | 0.518 |
| hL2(=hR1=hR2=hL3)(m) | 0.010 | 0.020 | 0.030 | 0.040 | 0.050 | 0.070 | 0.090 | 0.110 | 0.130 | 0.150 |
| ξ12(=ξ21=ξ23=ξ32) | 0.082 | 0.044 | 0.031 | 0.024 | 0.021 | 0.016 | 0.014 | 0.012 | 0.011 | 0.010 |
| Q1(=Q3)(m3/s) | 0.008 | 0.023 | 0.042 | 0.065 | 0.097 | 0.170 | 0.261 | 0.348 | 0.460 | 0.595 |
| Q2(m3/s) | 0.196 | 0.210 | 0.226 | 0.247 | 0.264 | 0.309 | 0.361 | 0.497 | 0.526 | 0.578 |
| Q(m3/s) | 0.211 | 0.255 | 0.310 | 0.378 | 0.459 | 0.649 | 0.884 | 1.193 | 1.446 | 1.769 |
Step 4: calculating apparent shear stress coefficient.The section beach is symmetrical and without vegetative coverage, therefore proportionality coefficient ψ=
4.5×10-4, j=1 (an only terrace) is enabled, then solves apparent shear stress coefficient by formula (7).According to ξ21And ξ23Depth of water H's
Change and change, value is shown in Table 2.
Step 5: design factor matrix.The longitudinal slope of target section is than drop S0=1.027 × 10-3, calculated separately by formula (8)
Ik, Jk、XkAnd Yk.It is formed according to the element of the target section of identification, the direction coefficient of each sub- section: sub- section 1 is determined by table 1
(element I): α1=0, β1=-1；Sub- section 2 (element IV): α2=1, β2=1；Sub- section 3 (element II): α3=-1, β3=0.
A is calculated by formula (9)k、bkAnd ck。
Step 6: establishing matrix equation.The tridiagonal coefficient matrix Φ being calculated according to step 5, establishes matrix equation.
Step 7: formula (A2) being solved using " chasing method ", obtains the mean flow rate u of each sub- sectionk, respectively multiplied by corresponding
Cross-sectional area Ak, obtain the flow Q of each sub- sectionk.According to total flow equation, the total flow Q of target section is calculated, is shown in Table 2 Hes in detail
Fig. 4.
Fig. 4 is the stage discharge relation for 1 section of example inquired into using mode proposed by the present invention, and uses measured data
Data verifies calculated result, shows that computational accuracy of the invention is higher.
Embodiment 2
Certain river is beach by vegetative coverage, the asymmetric compound cross-section of three-level, as shown in Figure 5.The target section beam overall
Degree is 100m, wherein the wide b of second level point bar1=25m, the high d in terrace1=1.4m, the wide b of first order point bar2=25m, the high d in terrace2=
1.0m, the wide b of major trough3=50m, slope coefficient are 0.Rule kind is implanted with rigid vegetation on second level beach, the high 1.2m of plant, directly
Diameter 0.06m, line-spacing 0.25m, spacing in the rows 0.5m, the bed sloped of section where section are 0.4 ‰, inquire into the stage-discharge of the section
Relationship.
The step of inquiring into the stage discharge relation of section shown in embodiment 2 using technical solution of the present invention is as follows:
Step 1: target section is vertically divided into 3 sub- sections by selected point C and E, successively be labeled as k=1,2,3,
Then b1=b2=25m, b3=50m, d1=13.6m, d2=10.6m.
Step 2: beach has vegetative coverage, hv=1.2m, D=0.06m, Lx=0.25m, Ly=0.5m, vegetation density m1
=m2=1/0.25/0.5=8, major trough is without vegetative coverage, i.e. m3=0.Increased according to the roughness of formula (4) beach with the raising of water level
Add, see Table 3 for details for the beach roughness under different water levels.
Table 3 is the calculating process table that the present invention is applied to example 2
| H(m) | 1.10 | 1.20 | 1.40 | 1.60 | 1.80 | 2.00 | 2.20 | 2.40 | 2.60 | 2.80 | 3.00 | 3.20 | 3.40 |
| h1(m) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.20 | 0.40 | 0.60 | 0.80 | 1.00 |
| h2(m) | 0.10 | 0.20 | 0.40 | 0.60 | 0.80 | 1.00 | 1.20 | 1.40 | 1.60 | 1.80 | 2.00 | 2.20 | 2.40 |
| A1(m2) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5 | 10 | 15 | 20 | 25 |
| A2(m2) | 2.5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 30 | 35 | 40 | 45 | 50 |
| A3(m2) | 55 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 |
| n1 | - | - | - | - | - | - | - | 0 | 0.039 | 0.061 | 0.080 | 0.096 | 0.112 |
| n2 | 0.026 | 0.039 | 0.061 | 0.080 | 0.096 | 0.112 | 0.126 | 0.127 | 0.128 | 0.129 | 0.130 | 0.131 | 0.132 |
| ξ12(=ξ21) | - | - | - | - | - | - | - | - | 0.003 | 0.002 | 0.002 | 0.001 | 0.001 |
| ξ23(=ξ32) | 0.007 | 0.005 | 0.003 | 0.003 | 0.002 | 0.002 | 0.002 | 0.002 | 0.003 | 0.002 | 0.002 | 0.001 | 0.001 |
| Q1(m3/s) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.7 | 1.8 | 2.6 | 3.4 | 4.2 |
| Q2(m3/s) | 0.4 | 0.9 | 1.8 | 2.7 | 3.5 | 4.4 | 5.3 | 6.8 | 8.3 | 10 | 11.8 | 13.5 | 15.2 |
| Q3(m3/s) | 57.0 | 65.8 | 84.9 | 105.8 | 128.4 | 152.7 | 178.5 | 205.9 | 249.1 | 278.8 | 312.0 | 347.1 | 383.9 |
| Q(m3/s) | 57.4 | 66.7 | 86.7 | 108.5 | 131.9 | 157.1 | 183.8 | 212.7 | 258.1 | 290.6 | 326.4 | 364.0 | 403.3 |
Step 3: the sub- section obtained according to division, the section are made of 1 element I, 1 element VI and 1 element V,
That is the element of target section is configured to " I+VI+V ".As H≤d=1.0m, water flow is all transported by major trough, stage discharge relation
Directly inquired by Manning formula；As 1.0m < H≤2.4m, water flow overbank to level-one beach compound cross-section；As H > 2.4m, water
Overbank is flowed to second level beach.Depth of water H is successively increased into 0.1m or 0.2m, the cross-sectional area A of each sub- section is calculated according to table 1k, it is wet
All PkWith hydraulic radius Rk.Differentiate that sub- section 2 belongs to element IV by table 1, distinguishes with the height of the sub- section interface in the left and right sides
For hL2=h2-1=h1, hR2=h2+1=h2, calculated result is shown in Table 2 in detail.
Step 4: calculating apparent shear stress coefficient.The section beach is asymmetric and has vegetative coverage, therefore proportionality coefficient ψ=
1.4×10-4.As j=1, it is higher than d2Sub- section 1 (second level beach) and sub- section 2 (level-one beach) be considered as " new point bar ", it is low
In d2Sub- section 3 (major trough) be " new major trough "；As j=2, it is higher than d1+d2Sub- section 1 (second level beach), be considered as " new side
Beach " is lower than d1+d2Sub- section 2 (level-one beach) and sub- section 3 (major trough) be " new major trough ", table is calculated separately using formula (7)
Shearing stress coefficient is seen, is shown in Table 3.
Step 5: design factor matrix.The longitudinal slope of target section is than drop S0=0.4 × 10-3, I is calculated separately by formula (8)k,
Jk、XkAnd Yk.It is formed according to the element of the target section of identification, the direction coefficient of each sub- section is determined by table 1: sub- 1 (member of section
Plain I): α1=0, β1=-1；Sub- section 2 (element VI): α2=1, β2=-1；Sub- section 3 (element V): α3=1, β3=0.By formula
(9) a is calculatedk、bkAnd ck。
Step 6: establishing matrix equation.The triple diagonal matrix Φ being calculated according to step 5, establishes matrix equation.
Step 7: formula (A2) being solved using " chasing method ", obtains the mean flow rate u of each sub- sectionk, respectively multiplied by corresponding
Cross-sectional area Ak, obtain the flow Q of each sub- sectionk.According to total flow equation, the total flow Q of target section is calculated, is shown in Table 3 Hes in detail
Fig. 6.
Claims (5)
1. a kind of method for inquiring into multistage compound cross-section stage discharge relation, which comprises the following steps:
Step 1: the geometric dimension analysis of target section is implemented as follows:
Obtain the profileometry data X of target sectioni, Zi, i=1,2 ..., K, XiTarget cross section starting point X is arrived for i-th point1Away from
From ZiFor the elevation of the point, K is the quantity of section survey point；
It chooses elevation and changes obvious point, section is divided into M+N+1 sub- sections by the vertical line put by these, wherein water
Deep maximum sub- section is known as major trough, remaining is known as beach, and M is the quantity of the sub- section of beach on the left of major trough, and N is on the right side of major trough
The quantity of the sub- section of beach, M, N are natural number, and M+N >=1；
Sub- section k, 1≤k≤M+N+1 are successively labeled as from starting point side；
Sub- section close to major trough is known as level-one beach, and bed elevation is known as the flat beach depth of water of level-one, close to the son of level-one beach
Section is known as second level beach, and bed elevation is known as the flat beach depth of water of second level, and so on；
The width b of each sub- section is read respectivelyk, terrace height dk, the gradient of beach side slope, the left grade of side slope S of major troughLkAnd major trough
Right grade of side slope SRk；
Step 2: it determines the Manning roughness coefficient of each section, is implemented as follows:
The Manning roughness coefficient of sub- section k is calculated using following formula:
In formula: nkFor the Manning roughness coefficient of sub- section k；RkFor the hydraulic radius of sub- section k, by the area of sub- section k divided by this
The wetted perimeter of sub- section obtains；G is acceleration of gravity；fkFor total Darcy-Weisbach resistance coefficient of sub- section k；
Step 3: the basic element composition of identification target section is implemented as follows:
Arbitrary multistage compound cross-section can be made of one or more of following seven kinds of elements:
Element I: left side offshore beach；Element II: right side offshore beach；Element III: left side offshore major trough；Element IV: offshore master
Slot；Element V: right side offshore major trough；Element VI: left side offshore beach；Element VII: right side offshore beach；
The concrete condition of sub- section is divided according to target section, chooses the corresponding element of each sub- section；
Calculate separately the sub- cross-sectional area A of each componentk, wetted perimeter PkWith hydraulic radius Rk, and determine its left and right sides interface
Height hLkAnd hRk；
Step 4: apparent shear stress coefficient is calculated, is implemented as follows:
The momentum-exchange between adjacent element is measured using apparent shear stress, its calculation formula is
In formula:Apparently cutting between respectively sub- section k and the sub- section k-1 and sub- section k+1 in right side in its left side is answered
Power；ρ is the density of water；hLk, hRkFor the sub- section k and sub- section k-1 in its left side and the sub- section k+1 interface height in right side；uk-1,
uk, uk+1For sub- section k-1, the mean flow rate of k, k+1；ξK, k-1, ξK, k+1The respectively sub- section k and sub- section k-1 in its left side and the right side
The apparent shear stress coefficient of the sub- section k+1 in side；
Step 5, design factor matrix is implemented as follows:
The longitudinal slope for determining section is measured than drop S0, according to the element of the target section of identification form, calculate separately each sub- section with
Lower parameter:
Wherein: Ik,Jk,Xk,YkFor the intermediate variable of calculating, nkFor the Manning roughness coefficient of sub- section k, g is acceleration of gravity, hLk
And hRkFor the height of interface at left and right sides of each component, RkFor the hydraulic radius of each component, ξK, k-1, ξK, k+1Respectively
For the apparent shear stress coefficient of sub- section k and its left side sub- section k-1 and the sub- section k+1 in right side；
The direction coefficient for remembering apparent shear stress between sub- section k and its arranged on left and right sides adjacent sections is respectively αkAnd βk；Group is disconnected
Face k belongs to element I, αk=0, βk=-1；Group section k belongs to element II, αk=-1, βk=0；Group section k belongs to element
III, αk=0, βk=1；Group section k belongs to element IV, αk=1, βk=1；Group section k belongs to element V, αk=1, βk=0；
Group section k belongs to element VI, αk=1, βk=-1；Group section k belongs to element VII, αk=-1, βk=1；
According to the composition of target section, the direction coefficient of the apparent shear stress of each sub- section is successively determined, and calculate following parameters
ak=αkXk,bk=Ik-αkXk-βkYk,ck=βkYk；
Step 6: matrix equation is established, is implemented as follows:
For multistage compound cross-section, the matrix equation that coefficient matrix is triple diagonal matrix is solved
Φ X=J
In formula:For flow velocity matrix；J=(J1 J2…JM+N+1)TFor momentum matrix；Φ is three diagonal
Coefficient matrix
Step 7: three diagonal coefficient matrix Φ being solved using chasing method, obtain the mean flow rate u of each sub- sectionk, respectively multiplied by phase
The sub- cross-sectional area A answeredk, obtain the flow Q of each sub- sectionk；According to total flow equation, the total flow Q of target section is calculated, i.e.,
Q=AUT
In formula: U=(u1 u2…uM+N+1)T, A=(A1 A2…AM+N+1)T。
2. the method according to claim 1 for inquiring into multistage compound cross-section stage discharge relation, it is characterised in that:
In step 2, since vegetation density can be used for defining unvegetated situation for 0, according to additive property principle, Darcy-
Weisbach resistance coefficient resistance coefficient caused by vegetation drag and bed surface coefficient of frictional resistance form, i.e.,
fk=fbk+fvk
In formula: fbkFor the bed surface coefficient of frictional resistance of sub- section k, fvkFor resistance coefficient caused by vegetation drag on sub- section k
fvk=4 λkCDDkmkhk
In formula: DkFor the diameter of plant on sub- section k；hkFor the depth of water of sub- section k；mkFor plant on unit area on sub- section k
Quantity, i.e. vegetation density, for the plant of rule plantation, vegetation density is the inverse of line-spacing and spacing in the rows product, i.e. mk=1/
(LxkLyk), Lxk、LykFor the line-spacing and spacing in the rows of plant on sub- section k；CDForce coefficient is pulled for vegetation；λkTo consider that vegetation is flooded
The correction factor of degree, calculation formula are as follows:
Wherein: SDkFor the degree of flooding of vegetation on sub- section k.
3. the method according to claim 2 for inquiring into multistage compound cross-section stage discharge relation, it is characterised in that:
In step 2, degree of the flooding S of vegetation on sub- section kDk, is defined as:
In formula: hvFor the height of plant on sub- section k, hkFor the depth of water of sub- section k.
4. the method according to claim 1 for inquiring into multistage compound cross-section stage discharge relation, it is characterised in that:
In step 4, for multistage compound cross-section, the depth of water is divided as boundary using j grades, is considered as new major trough lower than it, higher than its view
For new point bar, apparent shear stress coefficient is estimated using following formula
Wherein: r is intermediate variable；H is the depth of water of new major trough；B is rivers and canals left half, including all point bars of half major trough and left side
Width；BMrFor the overall width of new major trough；hrFor the depth of water of new point bar；Dr is the flat beach depth of water of new point bar；nrFor new point bar
Roughness；nr+1For the roughness of new major trough；ψ is proportionality coefficient related with section symmetry and vegetation.
5. the method according to claim 4 for inquiring into multistage compound cross-section stage discharge relation, it is characterised in that:
In step 4, for unvegetated symmetrical compound cross-section, ψ=4.5 × 10-4；For unvegetated asymmetric compound cross-section, ψ
=6.3 × 10-4；There are the symmetrical compound cross-section of vegetation, ψ=1.0 × 10 for beach-4；There is the asymmetric multiple of vegetation for beach
Formula section, ψ=1.4 × 10-4。
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