A method for determining the water surface line of natural rivers in hilly and mountainous areas

Abstract

The present invention discloses a method for determining the water surface line of natural river channels in hilly and mountainous areas, which includes the following steps: determining the calculation type of the river channel water surface line, dividing the river channel into calculation river reaches and arranging the positions of calculation cross-sections, determining the cross-section positions for dividing the calculation river reaches according to the requirements of the river reach type, where the water flow at both ends of the river reach is gradually varied flow or the critical water depth position; successively calculating the water surface line for each river reach, and choosing to calculate from the downstream water level boundary upwards for each river reach; for a single calculation river reach, determining the flow regime of the river reach by calculating the Froude number at the known water level end to determine the direction of water surface line calculation, and solving the calculation formula corresponding to the river reach type. The method of the present invention uses the Froude number to judge and calculate separately for the calculation river reaches with flow regimes belonging to rapid flow and slow flow respectively, and finds the critical flow position between the connection of rapid flow and slow flow and inserts a calculation cross-section during the calculation process to avoid the situation of no solution in the calculation equation.

Description

Technical Field

[0001] The present invention relates to the field of water surface line calculation, and particularly to a method for measuring the water surface line of natural rivers in hilly and mountainous areas. Background Art

[0002] The calculation of the river water surface line refers to the process of dividing river reaches and calculating various hydraulic elements of the river to obtain the water surface line along the river under the conditions of river topography and upstream and downstream boundary conditions. The main purpose of calculating the river water surface line is to derive the highest water level along the river and the maximum cross-sectional discharge, which serves as the basic conditions in water conservancy work such as river regulation and flood disaster risk control. The importance of the accuracy of the water surface line calculation results is self-evident.

[0003] Among many water surface line calculation methods, methods such as solving the differential equation of steady non-uniform gradually varied flow and solving the Saint-Venant equations have withstood a large number of practical tests, and their calculation accuracy in cases of small and medium-sized rivers (one-dimensional generalization) is sufficient to guide actual projects. However, both the Saint-Venant equations and the differential equation of steady non-uniform gradually varied flow are based on the assumption of gradually varied flow for equation construction or parameter simplification. When rapid variation flow occurs, the local head loss cannot be calculated. If the original formula is still used for calculation, the result accuracy cannot be guaranteed. At the same time, whether the river bottom slope is gentle slope, steep slope or critical slope is closely related to the derivation direction of the water surface line of the calculated river reach. Whether starting from the upstream or downstream section of the calculated river reach for recursion, situations where it cannot be derived may be encountered, and it is necessary to further analyze whether the water flow is rapid or slow before making a judgment (Liu Zengmei, Wu Junxiao, Chen Ming. Feasibility study on the derivation direction of the water surface line of rivers and canals [J]. Journal of Water Resources and Hydraulic Engineering, 2011(01):76 - 83. DOI:10.16198 / j.cnki.1009 - 640x.2011.01.005.).

[0004] In water conservancy practice, the river channel slope in plain areas is relatively small, and the water flow regime is mainly in the form of gradually varied flow. Conventional water surface line calculation is simple and shows good accuracy. For the much larger number of mountainous rivers, due to the relatively large riverbed slope, relatively fast water flow velocity, the non-negligible lateral water level difference in the cross-section of river bends, and relatively large changes in river cross-section and riverbed slope, the water flow regime frequently switches between rapid and gradually varied flow, and there are more river reaches with rapid variation flow compared to plain rivers. Therefore, more problems arise in the calculation of the water surface line of mountainous rivers and canals in water conservancy planning and design. In addition, the levee project level of hilly and mountainous river channels (channels) is generally relatively low, usually below level 3, and the levee top freeboard usually does not exceed 1.0m (even 0.6m), and the possibility that the error of the calculated water surface line result exceeds the levee top freeboard cannot be ignored.

[0005] In summary, when calculating the water surface profile of rivers in hilly and mountainous areas, factors such as the conversion of flow patterns and directions, abrupt changes in cross-sections, and local head losses must be considered to ensure that the accuracy of the calculated water surface profile meets the requirements. Therefore, it is necessary to explore a method for calculating the water surface profile that suits the characteristics of rivers in hilly and mountainous areas to provide good technical support for the comprehensive treatment of rivers in these areas. Summary of the Invention

[0006] To solve the above problems, the present invention provides a method for measuring the water surface profile of natural rivers in hilly and mountainous areas. Considering the complex flow patterns, undulating river beds, and abrupt changes in flow directions of rivers in mountainous areas, it can simultaneously consider situations of abrupt flow changes such as bends, tributary confluences, and weirs on the river, as well as situations where the river channel boundary suddenly changes, and there are deep pools or dead water areas. Most rivers in mountainous areas are small and medium-sized rivers with relatively small widths, which can be regarded as one-dimensional water surface profile calculation problems. The method for measuring the water surface profile of natural rivers in hilly and mountainous areas provided by the present invention calculates the one-dimensional water surface profile by solving the differential equation of steady non-uniform gradually varied flow, and at the same time calculates the lateral super elevation at the bend position to make up for the limitations of one-dimensional water surfaces. For each special and unconventional river channel type (such as tributary confluences, hydraulic jumps, weirs, etc.), special hydraulic formulas are derived from the energy equation for calculation to ensure the accuracy of the calculated water surface profile.

[0007] At the same time, when the method for measuring the water surface profile of natural rivers in hilly and mountainous areas provided by the present invention solves cases with complex flow patterns and the switching between rapid and slow flows, to avoid the situation where the difference equation has no solution and cannot be deduced, the critical flow transition position and the calculation direction of the water surface profile for each divided river reach are determined based on the Froude number, and the calculation river reach is re-divided according to the existing cross-section data. Calculation cross-sections are inserted at the critical flow transition to grasp the connection status of the water surface profile flow pattern.

[0008] The present invention is achieved by at least one of the following technical solutions.

[0009] A method for measuring the water surface profile of natural rivers in hilly and mountainous areas includes the following steps:

[0010] Step 1: According to the data of the entire river calculation area, determine the calculation type of the river water surface profile, and divide the river into multiple calculation river reaches and arrange the positions of calculation cross-sections according to each calculation type;

[0011] Step 2: According to the arrangement of the river calculation cross-sections, measure the river cross-section data and river characteristic parameters. The river cross-section data includes two-dimensional x / y coordinates sufficient to describe the cross-section shape, the maximum cross-section discharge at the inflow cross-section position, and the average water level corresponding to the outflow cross-section position during the corresponding period. The river characteristic parameters include bend curvature, building dimensions, etc.;

[0012] Step 3: Starting from the first downstream calculation river reach, calculate the water surface profile upstream reach by reach. Calculate the Froude number using the known water level at the downstream cross-section of each reach to determine whether the flow at this cross-section is rapid or subcritical, and then determine the direction of water surface profile calculation for this reach;

[0013] Step 4: Select the model corresponding to the river reach calculation type. Substitute the data according to the direction of water surface profile calculation to calculate the water level at the upstream cross-section of this reach, and conduct error checking until the calculation accuracy requirement is met. If the model has no solution, add a calculation cross-section between the two cross-sections to shorten the calculation interval for solution;

[0014] Step 5: Calculate the Froude number at the upstream cross-section of the reach and judge the flow regime: If the flow regimes are different before and after, add an additional calculation cross-section between the two cross-sections and return to Step 4. The calculation cross-section is added at the junction of rapid and subcritical flows through trial calculation to make the Froude number equal to 1. If there are multiple solutions and different flow regime discriminations, select the solution with the same flow regime as the downstream cross-section. If the flow regimes are the same before and after, it is considered that the cross-section water level calculation is correct;

[0015] Step 6: Starting from the downstream, repeat Steps 3 to 5 for each calculation reach one by one until the water surface profile calculation of the entire river channel is completed.

[0016] Furthermore, in Step 1, the river reach calculation types include gradually varied flow regular reaches, sharp bends, hydraulic jumps, hydraulic drops, water retaining structures, and confluence inlet types of braided streams.

[0017] Furthermore, in Step 3, when the Froude number is greater than 1, the flow is rapid, and the water surface profile is calculated from upstream to downstream. Conversely, when the Froude number is less than 1, the flow is subcritical, and the water surface profile should be calculated from downstream to upstream.

[0018] Furthermore, in Step 3, when the Froude number is greater than 1 and the flow is rapid, according to the direction of water surface profile calculation from the upstream cross-section water level to the downstream cross-section water level, assuming there are K reaches, k ∈ K, substitute the water level Z u(k) [[ID=2o]]of the upstream cross-section of the k-th reach into the following corresponding formula model for trial calculation of the water level Z d(k) of the downstream cross-section, and substitute it into the calculation formula model of this reach for trial calculation and solution until the error between the water level Z d(k) of the downstream cross-section and the calculation result Z u(k-1) (the water level of the same cross-section) of the previous reach is within the allowable range, then assume the water level Z u(k) of the upstream cross-section is the required value; conversely, when the Froude number is less than 1 and the flow is subcritical, according to the direction of water surface profile calculation from the downstream cross-section water level to the upstream cross-section water level, directly substitute the calculation result Z u(k-1) of the previous reach into Z d in the following corresponding calculation formula model to solve for the water level Z u(k) of the upstream cross-section of this reach.

[0019] Furthermore, when calculating the water levels at both ends of the computational reach in Step 4, if the water flow in a certain reach is determined to be rapid flow, the water surface profile direction for calculating the downstream section water level based on the upstream section water level shall be adopted.

[0020] Furthermore, the water flows at both ends of the computational reach are both gradually varied flows or critical water depth positions.

[0021] Furthermore, in Steps 2, 4 and 5, if there are no measured cross-section data at the selected cross-section, the river channel cross-section data shall be supplemented. If there is no water level data downstream, the cross-section water level downstream shall be deduced first using the cross-section with water level data.

[0022] Furthermore, in Step 4,

[0023] The water surface profile model for a general reach is:

[0024]

[0025] In the formula: Z u and Z d are the water levels of the upstream and downstream cross-sections, in m;

[0026] A u and A d are the cross-sectional flow areas of the upstream and downstream cross-sections, in m 2 ;

[0027] K u and K d are the discharge moduli of the upstream and downstream cross-sections, in m / s;

[0028] ξ is the local head loss;

[0029] α is the velocity distribution coefficient;

[0030] Δs is the distance between the upstream and downstream cross-sections, in m;

[0031] Q is the cross-sectional discharge, in m 3 / s;

[0032] g is the acceleration due to gravity;

[0033] The water surface profile model for a curved reach where the local head loss in the bend cannot be ignored includes calculating the longitudinal water level change including the local head loss and the transverse water surface super elevation; the longitudinal water surface profile is calculated according to the water surface profile calculation formula in the case of no bend, i.e., letting ξ = 0, and the equivalent roughness coefficient is used to reflect the local head loss in the bend, specifically including:

[0034] a) The longitudinal water surface profile of the river channel bend is:

[0035]

[0036]

[0037] In the formula: b is the width of the river channel, which should be the water surface width for a trapezoidal cross-section, in m;

[0038] r is the bending radius of the curved axis of the river channel, in m;

[0039] l is the length of the river channel bend, in m;

[0040] ζ is an intermediate variable;

[0041] R and C are the hydraulic radius and Chezy coefficient respectively, taking the average value of the upstream and downstream cross-sections;

[0042] b) The lateral water surface elevation is:

[0043]

[0044] In the formula: Δh1 is the value of the water surface elevation in the bend under the action of the inertial centrifugal force, in m;

[0045] Δh2 is the value of the water surface elevation generated by the inertial head-on impact of the straight-section flow before the bend, in m;

[0046] v is the average flow velocity in the bend, taking the average value of the upstream and downstream cross-sections, in m / s;

[0047] β1 is the included angle between the normal line at the intersection of the straight-section axis at the inlet and the concave bank of the bend section;

[0048] The water surface line model for the river reach with a water weir, a spillway dam, and a bridge backwater is:

[0049]

[0050] In the formula: Q is the cross-section discharge, σ s is the submergence coefficient; ε is the side contraction coefficient; m is the discharge coefficient; B is the width of the gate opening, in m; n is the number of gate openings; H0 is the total head at the weir crest, in m;

[0051] For the water surface line model of the river reach where there is a tributary confluence with a relatively large flow ratio and cannot be ignored within the required accuracy, the water levels of the two branches upstream are deduced from the downstream confluence water level:

[0052]

[0053]

[0054] Among them, the local resistance loss calculation formula is:

[0055]

[0056]

[0057] In the formula: Z 11 、Z21 , Z 31 are the water level elevations of the two upstream branches and the downstream main stream respectively, in m;

[0058] v 11 , v 21 , v 31 are the flow velocities of the two upstream branches and the downstream main stream respectively, in m / s;

[0059] A 11 , A 21 , A 31 are the cross-sectional areas of the two upstream branches and the downstream main stream respectively, in m 2 ;

[0060] h j1-3 , h j2-3 are the local head losses at which the two branches flow into the main stream respectively, in m;

[0061] α 11 , β 21 , α 31 are the flow velocity distribution coefficients of the two upstream branches and the downstream main stream;

[0062] Calculation for the occurrence of hydraulic jump in an artificial open channel:

[0063]

[0064] In the formula: h c1 , h c2 are the distances from the centroids of the pre-jump and post-jump sections of the hydraulic jump to the water surface;

[0065] A1 and A2 are the cross-sectional areas of the pre-jump and post-jump sections of the hydraulic jump.

[0066] Furthermore, for the cases of sudden changes in the river channel boundary, presence of deep pools or dead water areas, the local head loss is calculated by determining the local head loss coefficient ξ≠0 in the calculation, and the cross-sectional data after deducting the dead water area from the cross-section is used to substitute into the water surface profile model of the general river reach to obtain the corresponding cross-sectional water level.

[0067] Furthermore, in step four, after the water surface profile of each river reach is calculated, error judgment is carried out. The error calculation for the subcritical flow reach is:

[0068]

[0069]

[0070] In the formula, Δs and s are the distances between the upstream and downstream cross-sections and the calculated value of the cross-section distance respectively, in m; Δ is the allowable error, in m; E su , E sdTo represent the sum of the elevation head and the velocity head at the upstream and downstream cross-sections respectively, by substituting the cross-section data into E s The calculation formula gives that E s is the sum of the elevation head and the velocity head at the cross-section, m; j represents the bottom slope of the calculated river reach; represents the average hydraulic gradient of the calculated river reach; h represents the water level of the calculated cross-section, m; A represents the cross-sectional area of the calculated cross-section, m 2 ; Q represents the discharge passing through the calculated cross-section, m 3 / s.

[0071] Furthermore, in step four, after the water surface profile of each river reach is calculated, an error judgment is carried out. The basic formula for error calculation in a rapid flow reach is:

[0072] |Z′ d -Z d |≤Δ

[0073] In the formula: Z d represents the actual value of the water level at the downstream cross-section of the river reach or the result of the previous calculated river reach; Z′ d represents the trial value of the water level at the downstream cross-section of the river reach; Δ represents the allowable error.

[0074] Furthermore, the division position of the calculated cross-section should be selected at the position of gradually varied flow. The cross-section layout and measurement need to follow the following principles:

[0075] (1) Where there are water weirs, overflow dams, and bridges, a measurement cross-section shall be arranged at its location and at the upstream and downstream respectively, and the water flow on the front and rear cross-sections shall meet the conditions of gradually varied flow: the cross-section in front of the weir is 5 - 20 m away from the weir head, and the water flow of the cross-section behind the weir is 5 - 30 m away from the weir head. The data of the cross-section where the weir head, overflow dam, and bridge are located include the weir type, weir width, weir crest elevation, number of gate openings, shape and size of the pier;

[0076] (2) Where there are tributary inflows, measurement cross-sections shall be arranged before and after the inflow and at the front of the tributary confluence. The distance between the measurement cross-sections before and after the confluence does not exceed 20 m from the confluence, and the tributary confluence does not exceed 10 m;

[0077] (3) Where there are bends, measurement cross-sections shall be arranged before and after the jump;

[0078] (4) Where there are hydraulic jumps, measurement cross-sections shall be arranged at the entrance and exit of the bend, and the length and bending radius of the center axis of the bend shall be measured;

[0079] (5) Measurement cross-sections shall be arranged both before and after the sudden expansion or sudden contraction of the cross-sectional shape and size of the river channel. The cross-section before the mutation is arranged before the streamline changes from relatively smooth to unsmooth, and the cross-section after the mutation is arranged after the streamline changes from unsmooth to relatively smooth;

[0080] (6) Measuring cross-sections shall be arranged at locations where the bottom slope, cross-sectional shape, size, and roughness of the river channel change, as well as before and after such locations.

[0081] Compared with the existing technologies, the beneficial effects of the present invention are as follows:

[0082] (1) The present invention provides a water surface profile calculation method for mountainous rivers with more complex terrain and flow patterns. Each calculation river reach type is analyzed and corresponding calculations are adopted. Considering the lateral elevation difference problem of the bend flow under high flow velocities, and to avoid the situation where the formula has no solution and cannot be deduced, the critical and subcritical flow connection positions and the water surface profile calculation directions of each divided river reach are determined based on the Froude number, thus overall realizing a higher-precision calculation of the water surface profiles of natural river channels in hilly and mountainous areas.

[0083] (2) Starting from the application perspective, the method of the present invention specifically studies a series of problems that are often encountered and must be solved in the calculation of the water surface profiles of hilly and mountainous rivers, such as how to determine the switching between critical flow and subcritical flow, the calculation methods of the water surface profiles (longitudinal and lateral) of bend flows, the hydraulic calculation methods of several common rapidly varied flows (hydraulic jump, hydraulic drop, tributary confluence, and the presence of buildings in the river channel, etc.). Based on the conventional water surface profile calculation method, improvements are made according to the characteristics of mountainous rivers to ensure the accuracy of the calculated results of the water surface profiles of hilly and mountainous rivers, facilitating better guidance of engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a flowchart of the method for measuring the water surface profiles of natural river channels in hilly and mountainous areas in the second embodiment of the present invention;

[0085] Figure 2 It is a schematic diagram of the confluence of the main stream and tributaries used for the parameter description in the calculation formula of the tributary confluence reach;

[0086] Figure 3a It is a schematic diagram of the calculated result of the main stream water surface profile in the embodiment of the present invention;

[0087] Figure 3b It is a schematic diagram of the calculated result of the water surface profile of tributary 1 in the embodiment of the present invention;

[0088] Figure 3c It is a schematic diagram of the calculated result of the water surface profile of tributary 2 in the embodiment of the present invention;

[0089] Figure 4a It is a water surface profile calculation result diagram of Tonggukeng in the embodiment of the present invention without considering the flow pattern connection in the calculated water surface profile;

[0090] Figure 4b It is a water surface profile calculation result diagram of Tonggukeng in the embodiment of the present invention considering the flow pattern connection in the calculated water surface profile. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0091] This section conducts research on the method of the present invention using a specific research area example. Further detailed descriptions do not constitute any limitation to the present invention. For different research areas and river basins with different hydraulic conditions, the methods used need to be adaptively adjusted and cannot be generalized. At the same time, any limited modifications within the scope of the claims of the present invention are still within the scope of the claims of the present invention. Subsequently, two embodiments will be used to demonstrate the application process of the method of the present invention. The water surface profile derivation method of the present invention only derives the water level at the moment of the maximum flow rate of the river channel, rather than the water level change during the entire flood discharge process of the river channel.

[0092] Embodiment 1

[0093] Such as Figure 1 A method for measuring the water surface profile of natural river channels in hilly and mountainous areas as shown. Based on the conventional water surface profile derivation method, in view of the various characteristics of complex flow patterns and undulating river beds in mountainous rivers, separate hydraulic calculations are carried out for river reaches with various characteristic terrains (bends, tributaries, water retaining structures, etc.) in the river channel, and a clear distinction is made between the calculation directions of rapid flow and slow flow reaches, including the following steps:

[0094] Step 1: Review the data of the entire river calculation area, determine the calculation type of the river channel water surface profile, divide the calculation river reaches for the river channel according to the requirements of each calculation type, and arrange the positions of the calculation cross-sections. The water flow at both ends of the calculation river reach should be either gradually varied flow or critical water depth position;

[0095] Common river reach calculation types include gradually varied flow regular river reaches, as well as common rapidly varied flow types such as sharp bends, hydraulic jumps, hydraulic drops, water retaining structures, and confluence inlets of bifurcated streams.

[0096] Specifically, the division position of the calculation cross-section should be selected at the gradually varied flow position. The layout and measurement of the cross-section need to follow certain principles. For non-general river reaches:

[0097] [[ID=2 O]](1) Wherever there are water weirs, overflow dams, or bridges, a measurement cross-section must be arranged at its location and in front and behind (or upstream and downstream). Moreover, the water flow on the front and rear cross-sections must meet the conditions of gradually varied flow. The cross-section in front of the weir can generally be about 5 - 20 m away from the weir head, and the water flow on the cross-section behind the weir is generally about 5 - 30 m away from the weir head. Moreover, a detailed understanding of the cross-section where the weir head, overflow dam, or bridge is located is required. The corresponding cross-section data includes weir type, weir width, weir crest elevation, number of sluice holes, shape and size of the pier, etc.;

[0098] (2) Wherever a tributary converges, measurement cross-sections must be arranged near the front and rear of the convergence and at the front of the tributary confluence. Generally, the measurement cross-sections before and after the convergence can meet the conditions of gradually varied flow within no more than 20 m from the confluence, and the tributary confluence can meet the conditions of gradually varied flow even within no more than 10 m;

[0099] (3) At any place with a bend, measurement sections need to be arranged before and after the jump. The length of the hydraulic jump can be calculated using existing hydraulic formulas.

[0100] (4) At any place with a hydraulic jump, measurement sections need to be arranged at the inlet and outlet of the bend, and the length of the central axis of the bend and the bending radius also need to be measured.

[0101] (5) Measurement should be carried out before and after any sudden expansion or contraction of the cross-sectional shape and size of the river channel. The cross-section before the mutation is arranged just before the streamline changes from relatively smooth to non-smooth, and the cross-section after the mutation is arranged just after the streamline changes from non-smooth to relatively smooth.

[0102] (6) Measurement sections should be arranged at places where there are obvious changes in the bottom slope, cross-sectional shape, size, roughness rate, etc. of the river channel that cannot be ignored, and measurement sections should also be arranged before and after nearby.

[0103] Step 2: According to the arrangement of the calculated cross-sections of the river channel, measure the river channel cross-section data and river channel characteristic parameters. The river channel cross-section data includes two-dimensional x / y coordinates sufficient to describe the cross-sectional shape, the maximum cross-sectional discharge at the inflow cross-section position, and the average water level corresponding to the outflow cross-section position during the corresponding period. The river channel characteristic parameters include bend curvature, building size, etc.

[0104] Step 3: Starting from the first calculated river reach downstream, calculate the water surface profile section by section upstream. Calculate the Froude number using the known water level at the downstream cross-section of each river reach to determine whether the flow at this cross-section is rapid or subcritical, and then determine the direction of water surface profile calculation for this calculated river reach.

[0105] If the Froude number is greater than 1, the flow is rapid, and the direction of water surface profile calculation is to calculate the downstream cross-section water level based on the upstream cross-section water level. Assume there are K river reaches, k ∈ K. Substitute the upstream cross-section water level Z u(k) into the following corresponding formula model to trial-calculate the downstream cross-section water level Z d(k) , substitute it into the calculation formula model of this river reach to trial-solve until the downstream cross-section water level Z d(k) and the calculation result Z u(k-1) (water level of the same cross-section) of the previous river reach have an error within the allowable range. Then assume that the upstream cross-section water level Z u(k) is the required value; conversely, if the Froude number is less than 1, the flow is subcritical, and the direction of water surface profile calculation is to calculate the upstream cross-section water level based on the downstream cross-section water level. Then directly substitute the calculation result Z u(k-1) of the previous river reach into Z d in the following corresponding calculation formula model to solve for the upstream cross-section water level Z u(k) of this river reach.

[0106] Step 4: Select the corresponding water surface profile calculation model according to the river section calculation type. Substitute the data of the upstream or downstream section according to the water surface profile derivation direction, and finally calculate the water level of the upstream section of the calculation river section, and conduct error checking until the calculation accuracy requirement is met. If the calculation model has no solution, add a calculation section between the two sections to shorten the calculation distance for solution; if there are multiple solutions and the flow patterns are different, select the solution with the same flow pattern as the downstream section;

[0107] Specifically, in Step 4, when calculating a general river section with a straight and regular river course, no tributary inflow or negligible flow rate, and no water-blocking structures, the model used for water surface profile calculation is:

[0108]

[0109] In the formula: Z u and Z d are the water levels of the upstream and downstream sections, in m;

[0110] A u and A d are the cross-sectional water areas of the upstream and downstream sections, in m 2 ;

[0111] K u and K d are the discharge moduli of the upstream and downstream sections, in m / s;

[0112] ξ is the local head loss, and for gradually varied flow, ξ = 0;

[0113] α is the velocity distribution coefficient, and for gradually varied flow, α = 1;

[0114] Δs is the distance between the upstream and downstream sections, in m;

[0115] Q is the cross-sectional discharge, in m 3 / s;

[0116] g is the acceleration due to gravity, taking 9.81 m / s 2 ;

[0117] When calculating a river section with a large curvature such that the local head loss in the bend cannot be ignored, it is necessary to calculate the longitudinal water level change including the local head loss and the lateral water surface elevation; the longitudinal water surface profile is calculated according to the water surface profile calculation formula in the case of no bend, i.e., by setting ξ = 0, and the equivalent roughness coefficient is used to reflect the local head loss in the bend, and the longitudinal water level and the lateral water surface elevation are calculated respectively:

[0118] a) The model used for calculating the longitudinal water surface profile of a river channel bend is:

[0119]

[0120]

[0121] In the formula: b is the width of the river channel, which should be the water surface width for a trapezoidal cross-section, in m;

[0122] r is the bending radius of the curved axis of the river channel, in m;

[0123] l is the length of the river channel bend, in m;

[0124] ζ is an intermediate variable;

[0125] R and C are the hydraulic radius and Chezy coefficient respectively, taking the average value of the upstream and downstream cross-sections;

[0126] b) The model adopted for calculating the lateral water surface elevation is:

[0127]

[0128] In the formula: Δh1 is the value of the water surface elevation in the bend under the action of the inertial centrifugal force, in m;

[0129] Δh2 is the value of the water surface elevation generated by the inertial impact of the straight-section flow before the bend, in m;

[0130] v is the average flow velocity in the bend, taking the average value of the upstream and downstream cross-sections, in m / s;

[0131] β1 is the included angle between the axis of the inlet straight section and the normal line at the intersection of the concave bank of the bend section, in degrees;

[0132] When calculating the cross-section flow rate of a river reach with a weir, a spillway dam, and a bridge water backwater, the model adopted is:

[0133]

[0134] In the formula: σ s is the submergence coefficient;

[0135] ε is the side contraction coefficient;

[0136] m is the discharge coefficient;

[0137] B is the width of the gate opening, in m;

[0138] n is the number of gate openings;

[0139] H0 is the total head at the weir crest, in m;

[0140] When calculating a river reach where there is a tributary confluence with a relatively large flow rate and cannot be ignored within the required accuracy, the water levels of the two branches upstream are determined by the downstream confluence water level:

[0141]

[0142]

[0143] Among them, the local resistance loss calculation formula is:

[0144]

[0145]

[0146] Where: Z 11 、Z 21 、Z 31 are the water level elevations of the two upstream branches and the downstream main stream respectively, in m;

[0147] v 11 、v 21 、v 31 are the flow velocities of the two upstream branches and the downstream main stream respectively, in m / s;

[0148] A 11 、A 21 、A 31 are the cross-sectional areas of flow of the two upstream branches and the downstream main stream respectively, in m 2 ;

[0149] h j1-3 、h j2-3 are the local head losses at the confluence of the two branches into the main stream respectively, in m;

[0150] α 11 、α 21 、α 31 are the flow velocity distribution coefficients of the two upstream branches and the downstream main stream respectively;

[0151] Calculation for the case of hydraulic jump occurring in an artificial open channel:

[0152]

[0153] Where: h c1 、h c2 are the distances from the centroid of the pre-jump and post-jump cross-sections to the water surface; A1 and A2 are the cross-sectional areas of flow of the pre-jump and post-jump cross-sections respectively;

[0154] For the case of sudden change in the river channel boundary, presence of deep pools or dead water areas, the local head loss is calculated by determining the local head loss coefficient ξ≠ in the calculation, and the cross-sectional data after deducting the dead water area from this cross-section is used to substitute into the general river reach water surface line calculation formula.

[0155] Specifically, after the water surface line of each river reach is calculated in step four, error judgment is carried out. The error in the subcritical flow reach is:

[0156]

[0157]

[0158] Where s and Δs represent the calculated and measured values of the river section length, respectively, in m;

[0159] Δ represents the allowable error, m;

[0160] e s is the sum of the section height head and the flow velocity head, E su 、E sd To represent the sum of the upstream and downstream section height head and the flow velocity head, the section data is substituted into E s The calculation formula can be obtained, m;

[0161] i represents the bottom slope of the calculated river section;

[0162] is the average hydraulic gradient of the calculated river section;

[0163] h is the water level of the calculation section, m;

[0164] A is the water flow area of the calculated section, m 2 ;

[0165] Q is the flow rate of the calculated section, m 3 / s;

[0166] The error in the rapid river section is:

[0167] |Z′ d -Z d |≤Δ

[0168] Where: Z d , Z′ d To indicate the actual water level value of the lower section of the river or the result of the last calculated river section;

[0169] Z′ d Step 5: Calculate the Froud number of the upper section of the river and determine the flow pattern:

[0170] If the flow pattern is different before and after, an additional calculation section should be added between the two sections and return to step 4. The calculation section should be added at the junction of rapid and slow flow through trial calculation to make the Froud number 1. If there are multiple solutions with different flow patterns, choose the solution with the same flow pattern as the next section. If the flow pattern is the same before and after, the water level calculation of the section is considered correct and proceed to the next step.

[0171] Step 6: Repeat steps 3 to 5 for each calculated river section starting from the downstream until the water surface line calculation of the entire river is completed.

[0172] Example 2

[0173] For a certain river channel and its tributaries in the southern region, the water surface line derivation area includes two parts: the main stream and the tributaries. The basic data of the river channel cross-sections are shown in Table 1, and the cross-section data and building information will not be elaborated here.

[0174] Table 1 Basic Data Table of River Channel Cross-sections

[0175]

[0176]

[0177] Based on the above conditions, use the method for determining the water surface line of natural river channels in hilly and mountainous areas described in this embodiment to derive the water surface line. On the basis of the conventional water surface line derivation method, in view of the various characteristics of complex flow patterns and undulating river beds in mountainous rivers, conduct separate hydraulic calculations for river reaches with various characteristic terrains (such as bends, tributaries, water retaining buildings, etc.) in the river channel, and clearly distinguish the calculation directions for rapid flow and slow flow reaches. The following is the specific implementation process:

[0178] S1. According to the collected river channel cross-section data (river channel plane topographic maps, river channel cross-sectional data, control section water level data, river channel roughness coefficients, etc.) and river channel characteristic positions (such as bends, tributaries, water retaining building locations), divide the calculation reaches. The water flow at both ends of the calculation reaches should be gradually varied flow; the required initial conditions for the upstream are the maximum cross-sectional discharge, and the initial conditions for the downstream are the average water levels corresponding to the corresponding time periods.

[0179] S2. Determine the calculation type of each reach according to the data of each reach, including gradually varied flow conventional reaches and common rapidly varied flow types such as sharp bends, hydraulic jumps, hydraulic drops, water retaining buildings, and confluence inlets of bifurcated streams. Determine the cross-section positions for dividing the calculation reaches according to the requirements of each reach calculation type. The water flow at both ends of the calculation reaches should be gradually varied flow or critical water depth positions.

[0180] S3. Start from the first calculation reach downstream and calculate the water surface line upward in sequence. Calculate the Froud number using the known water level at the downstream cross-section of each reach to judge whether the water flow at this cross-section is rapid flow or slow flow, and then determine the water surface line derivation direction of this calculation reach.

[0181] S4. Select the formula corresponding to the reach calculation type, substitute the data according to the water surface line derivation direction to calculate the water level at the upstream cross-section of this reach, and conduct error checking until the calculation accuracy requirements are met. If the calculation equation has no solution, another calculation cross-section needs to be added between the two cross-sections to shorten the calculation interval for solution.

[0182] S5. Calculate the Froude number of the upper cross-section of the calculated river reach and determine the flow regime. If the flow regimes before and after are different, additional calculation cross-sections need to be added between the two cross-sections and return to step four. The calculation cross-sections should be added through trial calculations at the junction of rapid and slow flows to make the Froude number equal to 1. If the flow regimes before and after are the same, it is considered that the cross-section water level calculation is correct and proceed to the next step.

[0183] S6. Starting from the downstream, repeat steps three, four, and five for each calculated river reach one by one until the water surface profile of the entire river channel is calculated.

[0184] The comparison between the calculated results of the water surface profile obtained by using the method for measuring the water surface profile of natural river channels in hilly and mountainous areas described in the present invention and the measured data ensures relatively high accuracy. The calculated results of the main stream water surface profile are shown in Table 2, and the calculated results of the water surface profile of tributary 1 are shown in Table 3. The schematic diagram of the calculated results of the water surface profile in this embodiment is listed in Figures 3a to 3c .

[0185] Table 2 Comparison of calculated results of the main stream water surface profile Peak flood flow: 90m 3 / s Downstream highest water level: 38m

[0186]

[0187]

[0188] It can be seen from the calculation of the main stream (Table 2) that the Froude numbers of all cross-sections of the main stream do not exceed 1, indicating that most of the river reach is in a slow flow state along the way. Therefore, the water surface profile calculation can be directly carried out from the first downstream cross-section upwards in sequence.

[0189] However, during the calculation process of tributary 1 (Table 3), the Froude number of the cross-section at mileage 0m is greater than 1, while the Froude number of the cross-section at mileage 100m is less than 1, indicating that a flow regime transition occurs between the river channels from 0 to 100m. A cross-section needs to be inserted at the flow regime transition position to ensure the calculation accuracy. It can be seen that if the cross-section is not inserted and the water level between the cross-section at 0m and the cross-section at 100m is interpolated, the water surface profile between mileage 0 - 100m will far exceed the height of the river dike design, and the calculation results of this water surface profile will not be able to guide water conservancy work. Therefore, cross-section 2 is added in the calculation, and through repeated trial calculations, it is determined that cross-section 2 should be added at mileage 50m. It can be seen that the Froude number of the cross-section at mileage 0m is close to 1, that is, this place can be regarded as the position where the rapid and slow flow regimes of the water flow change.

[0190] Of course, in the embodiment, a river reach with a relatively obvious slope change is selected for display to illustrate the effect. When selecting the calculated river reach, the flow regime transition here should be able to be visually distinguished. However, in actual production projects, the flow regime transitions that are not obvious are usually difficult to visually judge. Therefore, judging the flow regime of each cross-section is a necessary step to ensure the calculation accuracy.

[0191] Table 3 Comparison Table of Calculation Results of Water Surface Profile of Tributary 1 Peak Discharge: 15 m 3 / s Downstream Highest Water Level: 41.375 m Type: Inflow Branch Location: 5500 m

[0192]

[0193]

[0194] To further illustrate the effect and necessity of distinguishing the cross - section flow regime through the Froud number in each calculation reach, Example 3 is specifically added for illustration.

[0195] Example 3 is taken from a section of the river course in Tonggukeng, Huadu District, Guangzhou City, which connects the upstream reservoir and the downstream urban inland river. The slope of the river reach changes greatly, and the flow regime switches between rapid and slow flows. Table 4 is the result table directly calculated from the existing cross - section water levels, while Table 5 is the result table calculated from the supplemented cross - sections at the connection of rapid and slow flows.

[0196] Table 4 Calculation Results of Water Surface Profile of Tonggukeng (Without Considering Water Flow Connection)

[0197] Peak Discharge: 50 m 3 / s Downstream Highest Water Level: 37 m

[0198]

[0199]

[0200] Table 5 Calculation Results of Water Surface Profile of Tonggukeng (Considering Water Flow Connection)

[0201] Peak Discharge: 50 m 3 / s Downstream Highest Water Level: 37 m

[0202]

[0203]

[0204] In the example of Tonggukeng, from mileage 200 m to mileage 900 m is a relatively long continuous rapid flow section, and the cross - section Froud numbers are all greater than or approximately equal to 1. Both ends of the rapid flow section are slow flow sections. Therefore, from top to bottom, this river reach can be divided into three sections: slow - rapid - slow, and it is necessary to consider the flow regime connection problem to control the calculation accuracy.

[0205] It is not difficult to see from the comparison between Table 4 and Table 5 that in the scheme considering the connection of flow patterns, two cross-sections are added at mileage 170m and mileage 950m. The cross-section at 170m is located at the place where slow flow changes to rapid flow, and a hydraulic drop phenomenon occurs. Therefore, the cross-section at 170m is used to control the water level at the drop sill. The cross-section at 950m is added at the place where rapid flow changes to slow flow, and the Froude number is approximately 1. Figure 4b And Figure 4a Figure 4 is a comparison diagram of the water surface line calculation results of whether the connection of water flow is considered in the third embodiment. It is not difficult to find by comparing the two that if the connection of water flow is not considered, whether interpolation is used at the two ends of the water level at mileage 170m or mileage 950m, the error in the water level line calculation is sufficient to affect the construction of river dikes.

[0206] Application effect of the method for measuring the water surface line of natural rivers in hilly and mountainous areas according to the present invention:

[0207] Analyzing from the calculation results of the second embodiment, the method described in the present invention can achieve better accuracy in the calculation of the water surface line of rivers in hilly and mountainous areas. After a small adjustment of the interval roughness coefficient, the overall error is below 0.10m, which is sufficient to guide engineering practice. Then, from the results of the third embodiment, for the calculation of the water surface line of the reach with rapid flow, considering the connection of water flow patterns is extremely important for ensuring the calculation accuracy and will directly affect engineering applications. The above effects are sufficient to show that the method described in the present invention can solve a series of problems that are often encountered and must be solved in the calculation of the water surface line of rivers in hilly and mountainous areas, such as how to determine the switching between rapid flow and slow flow, the calculation method of the water surface line (longitudinal and transverse) of curved channel flow, etc., and has the characteristics of high accuracy, simple process, etc. and good application potential.

[0208] The preferred embodiments of the present invention disclosed above are only used to help explain the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments to better explain the principle and practical application of the present invention, so that those skilled in the art in the relevant technical field can understand and utilize the present invention well. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A method for determining the water surface line of natural river channels in hilly and mountainous areas, characterized in that: It includes the following steps: Step 1: Determine the calculation type of the channel water surface line based on the data of the entire river calculation area. Divide the channel into multiple calculation reaches according to each calculation type and arrange the positions of the calculation sections; Step 2: According to the layout of the channel calculation sections, measure the channel section data and channel characteristic parameters. The channel section data includes two-dimensional x / y coordinates sufficient to describe the section shape, the maximum section discharge at the inflow section position, and the average water level corresponding to the outflow section position during the corresponding period. The channel characteristic parameters include the bend curvature and the building size; Step 3: Start from the first calculation reach downstream and calculate the water surface line section by section upstream. Calculate the Froud number using the known water level at the downstream section of each reach to determine whether the flow at this section is a rapid flow or a subcritical flow, and then determine the direction of water surface line calculation for this calculation reach; Step 4: Select the model corresponding to the reach calculation type. Substitute the data according to the direction of water surface line calculation to calculate the water level at the upstream section of the reach, and conduct error checking until the calculation accuracy requirement is met. If the model has no solution, add a calculation section between the two sections to shorten the calculation interval for solution; for cases where the river channel boundary changes suddenly, there are deep pools or dead water areas, calculate the local head loss by determining that the local head loss coefficient ξ≠0 during the calculation, and substitute the section data after deducting the dead water area from the section cross-sectional area into the water surface line model of the general reach to obtain the corresponding section water level; Step 5: Calculate the Froud number at the upstream section of the calculation reach and judge the flow regime: If the flow regimes are different before and after, add an additional calculation section between the two sections and return to Step 4. The calculation section is added at the junction of rapid and subcritical flows through trial calculation to make the Froud number equal to 1; if there are multiple solutions and different flow regime discriminations, select the solution with the same flow regime as the downstream section; if the flow regimes are the same before and after, it is considered that the section water level calculation is correct; Step 6: Repeat Steps 3 to 5 for each calculation reach one by one starting from the downstream until the calculation of the entire river channel water surface line is completed.

2. A method for measuring the water surface line of natural river channels in hilly and mountainous areas according to claim 1, characterized in that: In Step 1, the reach calculation types include gradually varied flow regular reaches, sharp bends, hydraulic jumps, hydraulic drops, water retaining structures, and confluence types of braided streams.

3. A method for measuring the water surface line of natural rivers in hilly and mountainous areas according to claim 1, characterized in that: In Step 3, when the Froud number is greater than 1, the flow is a rapid flow, and the water surface line is calculated from upstream to downstream. Conversely, when the Froud number is less than 1, the flow is a subcritical flow, and the water surface line should be calculated from downstream to upstream.

4. A method for determining the water surface line of natural rivers in hilly and mountainous areas according to claim 1, characterized in that: The flows at both ends of the calculation reach are gradually varied flows or critical water depth positions.

5. A method for measuring the water surface line of natural rivers in hilly and mountainous areas according to claim 1, characterized in that: In Steps 2, 4, and 5, if there are no measured section data at the selected section, supplement the measurement of the river channel section data. If there is no water level data downstream, first use the section with water level data to calculate the section water level downstream.

6. A method for measuring the water surface line of natural rivers in hilly and mountainous areas according to claim 1, characterized in that: In Step 4, the water surface line model for the general reach is: where: Z u , Z d are the water levels of the upstream and downstream cross-sections, in m; A u and A d are the cross-sectional flow areas of the upstream and downstream sections, in m 2 ; K u and K d are the discharge moduli of the upstream and downstream cross-sections, m / s; ξ is the local head loss; α is the velocity distribution coefficient; Δs is the distance between the upstream and downstream sections, m; Q is the sectional discharge, m 3 / s; g is the acceleration due to gravity; The water surface line model for the curved reach where the local head loss of the bend cannot be ignored includes calculating the longitudinal water level change and the lateral water surface elevation including the local head loss; the longitudinal water surface line is calculated according to the water surface line calculation formula in the case of no bend, i.e., when ξ = 0, and the equivalent roughness coefficient is used to reflect the local head loss of the bend, specifically including: a) The longitudinal water surface line of the river channel bend is: In the formula: b is the width of the river channel, which should be the water surface width for a trapezoidal cross-section, in m; r is the bending radius of the bending axis of the river channel, in m; l is the length of the river channel bend, in m; ζ is an intermediate variable; R and C are the hydraulic radius and Chezy coefficient respectively, taking the average value of the upstream and downstream cross-sections; b) The lateral water surface elevation is: In the formula: Δh1 is the value of the water surface elevation in the bend under the action of inertial centrifugal force, in m; Δh2 is the value of the water surface elevation generated by the inertial impact of the straight section flow before the bend, in m; v is the average flow velocity in the bend, taking the average value of the upstream and downstream cross-sections, in m / s; β1 is the intersection angle between the axis of the inlet straight section and the normal line at the intersection point of the concave bank of the bend section; The water surface line model for the river reach with weirs, overflow dams and bridge backwaters is: where Q is the sectional discharge, σ s is the submergence coefficient; ε is the side contraction coefficient; m is the discharge coefficient; B is the width of the sluice opening, m; n is the number of sluice openings; H0 is the total head above the weir crest, m; For the water surface line model of the river reach where there are tributaries with a relatively large flow proportion and cannot be ignored within the required accuracy, the water levels of the two branches upstream are deduced from the downstream confluence water level: Among them, the local resistance loss calculation formula is: where: Z 11 , Z 21 , Z 31 are respectively the water level elevations of the two upstream branches and the downstream main stream, in m; v 11 、 v 21 、 v 31 are used to denote the flow velocities of the two upstream branches and the downstream main stream, m / s; A 11 and A 21 and A 31 represent the cross-sectional areas of the two upstream branches and the downstream main stream, in m 2 ; h j1-3 and h j2-3 respectively represent the local head losses of the two branch streams flowing into the main stream, in m; ɑ 11 and α 21 and α 31 are the velocity distribution coefficients referring to the upstream two branches and the downstream main stream. Calculate the situation of hydraulic jump occurring in the artificial open channel: where: h c1 , h c2 represent the distances from the centroids of the cross-sections before and after the hydraulic jump to the water surface; A1 and A2 represent the cross-sectional areas of the water flow before and after the hydraulic jump.

7. A method for measuring the water surface line of natural rivers in hilly and mountainous areas according to claim 1, characterized in that: In step four, after the water surface line of each river reach is calculated, error judgment is carried out. The error calculation for the subcritical flow river reach is: Where Δs and s represent the distance between the upstream and downstream cross-sections and the calculated value of the cross-section distance respectively, in m; Δ represents the allowable error, in m; E su and E sd represent the sum of the elevation head and the velocity head of the upstream and downstream cross-sections respectively. By substituting the cross-section data into the E s calculation formula, E s is the sum of the elevation head and the velocity head of the cross-section, in m; $i$ represents the bottom slope of the calculated river reach; represents the average hydraulic gradient of the calculated river reach; $h$ represents the water level of the calculated cross-section, m; $A$ represents the cross-sectional area of flow of the calculated cross-section, m 2 ; $Q$ represents the discharge of the calculated cross-section, m 3 / s.

8. A method for measuring the water surface line of natural rivers in hilly and mountainous areas according to claim 1, characterized in that: In step four, after the water surface line of each river reach is calculated, error judgment is carried out. The basic formula for the error calculation of the supercritical flow river reach is: |Z′ d -Z d |≤Δ where: Z d represents the actual value of the water level at the downstream section of the river reach or the result of the previous calculated river reach; Z' d represents the trial value of the water level at the downstream section of the river reach; Δ represents the allowable error.

9. A method for measuring the water surface line of natural river channels in hilly and mountainous areas according to claim 1, characterized in that: The position for dividing the cross-section should be selected at the position of gradually varied flow. The cross-section layout and measurement follow the following principles: (1) Where there are weirs, overflow dams, and bridges, one measurement cross-section must be arranged at its location and upstream and downstream respectively, and the water flow on the front and rear cross-sections should meet the conditions of gradually varied flow: the cross-section in front of the weir is 5 - 20 m away from the weir head, and the water flow of the cross-section behind the weir is 5 - 30 m away from the weir head. The data of the cross-section where the weir head, overflow dam, and bridge are located include the weir type, weir width, weir crest elevation, number of sluice openings, shape and size of the pier; (2) Where there are tributaries joining, measurement cross-sections are arranged before and after the joining and in front of the tributary confluence. The measurement cross-sections before and after the joining are not more than 20 m away from the confluence, and the tributary confluence is not more than 10 m; (3) Where there are bends, measurement cross-sections are arranged before and after the jump; (4) Where there is a hydraulic jump, measurement cross-sections are arranged at the inlet and outlet of the bend, and the length and bending radius of the center axis of the bend are measured; (5) Measurement cross-sections should be arranged before and after the sudden expansion or sudden contraction of the river channel cross-section shape and size. The cross-section before the mutation is arranged before the streamline changes from relatively smooth to unsmooth, and the cross-section after the mutation is arranged after the streamline changes from unsmooth to relatively smooth; (6) Measurement cross-sections should be arranged at the places where the river bottom slope, cross-section shape, size and roughness coefficient change and before and after them.

Images