CN116720418B - Calculation method for mountain hill region channel mountain flood sand evolution bed load sand conveying rate - Google Patents
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Abstract
The invention provides a calculation method of a mountain area channel mountain flood sand evolution bed load sand conveying rate, which comprises the following steps: s1, taking a hilly area channel to be subjected to bed load sand conveying rate calculation as a target channel; s2, a target channel generalization model is established, and a plurality of measurement sections are arranged along the journey in the generalization model; s3, simulating the sediment particle transferring process in the generalization model under the action of water flow by adopting a CFD-DEM coupling model to obtain the time-dependent change relation of the position of the sediment particles in the generalization model; s4, linearly fitting the dimensionless sand transmission rate and dimensionless time of each measured section by adopting Weibull function fitting, obtaining a corresponding shape parameter lambda and a corresponding proportion parameter eta for each measured section, and obtaining lambda and [ x ]]Linear fitting is performed on η and [ x ]]Performing linear fitting; for arbitrary cross sections, the cross sections are represented by λ, η and [ x ]]The shape parameter lambda and the scale parameter eta are determined from the linear fitting relation of (b) and the formula f (t) = (lambdat) λ‑1 /η λ )exp[‑(t/η) λ ]Obtaining the change relation of the bed load sand conveying rate of the section along with time.
Description
Technical Field
The invention belongs to the field of disaster prevention and reduction of mountain torrent sand disasters in a mountain area, and relates to a calculation method of a mountain torrent sand-modeling bed load sand-transporting rate in the mountain area.
Background
In recent years, some potential disaster bodies such as cracks are generated on channel slopes in southwest hilly areas of China, a large amount of loose piles are formed, and under the influence of factors such as rainfall, the loose piles enter channels in a manner of collapse, landslide, debris flow and the like. Especially in a period of time after the earthquake occurs, sediment supply conditions and the form of a river bed can be influenced, so that river blockage and rapid increase of sand content in flood are caused, and factors such as a channel bed surface and water level of a hilly area are rapidly changed, so that negative influence is brought to flood control of a downstream branch ditch or a main river channel, and flood control safety is seriously influenced. Currently, research on channel sediment transport is mainly focused on the total amount of erosion produced sand, and research on a sand transport process along a section of a journey, ditch bed evolution and a mountain torrent sand coupling disaster-causing mechanism is not yet enough. Therefore, the research of the quantitative calculation method for the sand delivery of the channel edge Cheng Duanmian of the hilly area is an important task for preventing and controlling river water sand disasters of the hilly area.
Currently, students at home and abroad have carried out a series of researches on the non-uniform sand bed load sand conveying rate. For example: einstein carries out grouping calculation on the formula extension of the uniform sand bed load sand transfer rate established according to the statistical rule, and has a good fitting effect on low-intensity sand transfer. The Meyer-peter establishes a sand conveying rate formula based on a large amount of experimental data by taking the drag force as a main parameter, and has strong applicability. The Ackers-white is also based on a large amount of experimental data and introduces dimensionless parameters to obtain a calculation formula of the sand carrying capacity of the full sand, but larger errors can be generated for a riverbed with higher fine sand content. Wilcock and Crowe correct the bed surface shearing force and obtain a grouping sand conveying rate formula based on the bed surface composition, but the calculation accuracy of the formula can be affected by the severe change of the bed surface composition. Liu Xingnian and Chen Yuanxin derive the group sand transfer rate formula by introducing the concept of exposure height, but the formula is applicable when the bed surface composition is stable. Because most bed load sand conveying rate formulas are obtained through water tank experimental data, the formulas still need to be calibrated by selecting proper actual measurement data in practical application. The channel of the large-ratio river reach and even the hilly area is relatively deficient in actual measurement data, so that the accurate calibration and practical application of the conventional sand conveying rate formula are limited. In addition, because particles frequently collide in the movement process of the bed load in the hilly area channel, the sand conveying rate can be changed, and therefore the accuracy of the existing formula on the calculation of the bed load sand conveying rate is limited.
Disclosure of Invention
The method aims at solving the problems that the influence of frequent or severe collision among particles in the motion process of the bed load in the hilly area ditch on the sand conveying rate is not considered in the prior art, so that the calculation accuracy of the existing bed load sand conveying rate formula on the bed load sand conveying rate in the hilly area ditch is limited, the existing bed load sand conveying rate formula is limited, the actual measurement data of large-ratio river reach and the hilly area ditch are relatively deficient, the existing bed load conveying rate formula is difficult to calibrate accurately, and the space-time change of the bed load on each section along the journey is difficult to solve in the existing hilly area ditch bed load conveying calculation. The invention provides a calculation method of the mountain-region channel mountain flood sand evolution bed load sand conveying rate, which is used for improving the accuracy of the calculation of the mountain-region channel bed load sand conveying rate while realizing the calculation of the bed load sand conveying rates of different sections of the channel along the channel, so as to provide more accurate process data for the sediment replenishment calculation of the mountain-region river, and further provide more scientific and reliable references for the flood control and disaster reduction design of the downstream channel of the mountain region.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a calculation method of a mountain hill region channel mountain flood sand evolution bed load sand conveying rate comprises the following steps:
s1, taking a hilly region channel to be subjected to load sand conveying rate calculation as a target channel, wherein a target river section consists of a channel sediment accumulation section and a channel sediment conveying and moving section which are mutually connected, the ratio drop of the channel sediment accumulation section is larger than that of the channel sediment conveying section, and loose accumulation bodies are arranged in the channel sediment accumulation section;
s2, establishing a target channel generalization model in open source software Gmsh according to topographic information of a target channel and grading information of sediment particles of a loose pile body, wherein the generalization model comprises a channel sediment pile section and a channel sediment conveying and moving section which are mutually connected, the loose pile body is piled in the channel sediment pile section, and the sediment particles in the loose pile body are in a repose angle state; the joint of the channel sediment accumulation section and the channel sediment conveying and moving section is marked as a slope changing point; arranging a plurality of measurement sections along the way in the generalized model;
s3, simulating the sediment particle transferring process in the generalization model under the action of water flow by adopting a CFD-DEM coupling model to obtain data of the position and the speed of the sediment particles in the generalization model along with time;
s4, (1) obtaining sediment Mass of each measuring section passing through the measuring section at the moment T according to the simulation of the step S3, passing through the sediment total Mass of the measuring section from 0 to T, obtaining the non-dimensional accumulated Mass [ M ], the non-dimensional time [ T ] and the non-dimensional sediment rate [ Mass rate ] of the section according to the conversion of (4) to (6) from the sediment Mass passing rate of each measuring section at the moment 0 to T,
[T]＝t×(g/H) 1/2 (5)
in the formulae (4) to (6) [ M ] c ]Mass of silt passing through the section from the start of simulation to the time t, [ M ] r ]To accumulate the total mass of sediment passing through the section in the simulation process [ M ]]Accumulating mass for section without dimension [ T ]]Is a dimensionless time, [ Mass rate ]]Is the non-dimensional sand conveying rate, t is time, the unit is s, g is the gravity acceleration, and g is 9.81m/s 2 H is the height difference between the lower end of the loose pile and the slope changing point before the simulation starts,the unit is m;
the horizontal distance x of the generalized model is dimensionless according to the formula (7) to obtain a dimensionless horizontal distance [ x ],
[x]＝x/H (7)
in the formula (7), x is a dimensionless horizontal distance, x is a horizontal distance, and the horizontal distance is calculated from the top end of the loose stack, and the unit is m; h is the height difference between the lower end of the loose stack and the slope changing point before simulation starts, and the unit is m;
(2) carrying out linear fitting on the dimensionless sand transmission rate [ Mass rate ] and the dimensionless time [ T ] of each measured section by adopting Weibull function fitting with an expression as shown in a formula (10), obtaining a corresponding shape parameter lambda and a corresponding proportion parameter eta for each measured section, namely obtaining a series of [ x ] and lambda and eta corresponding to the x, carrying out linear fitting on lambda and [ x ] to obtain a linear fitting relation of lambda and [ x ], and carrying out linear fitting on eta and [ x ] to obtain a linear fitting relation of eta and [ x ];
lnln[1-F(t)] -1 ＝λlnt-λlny (10)
in the formula (10), lambda is a shape parameter, eta is a proportion parameter, and t is time;
(3) for any section, determining a shape parameter lambda by a linear fitting relation between lambda and [ x ], determining a proportion parameter eta by a linear fitting relation between eta and [ x ], further obtaining a time-dependent change relation of the bed load sand conveying rate of the section by a formula (9),
f(t)＝(λt λ-1 /η λ )exp[-(t/η) λ ] (9)
in the formula (9), λ is a shape parameter, η is a scale parameter, and t is time.
In step S3 of the method for calculating the sediment transport rate of the mountain flood sand evolution bed load of the hilly area channel, the CFD-DEM coupling model is adopted to simulate the sediment particle transport process in the generalization model under the action of water flow, and the adopted water flow is determined according to the historical rainfall data at the target channel. For example, the water flow rate employed is determined by: flood control indexes are designed according to the region where the target channel is located, the flood flow in a specific recurring period is determined by combining historical rainfall data and hydrologic analysis, the flood flow in the specific recurring period is taken as an original flow, and the original flow is scaled according to a model scale, so that the water flow adopted in the generalized model is obtained.
In the step S2 of the method for calculating the transition sediment transport rate of the channel mountain flood sand in the hillside area, at least 5 measurement sections are arranged along the journey in the generalized model.
In the technical scheme of the calculation method of the channel mountain flood sand evolution bed load sand transfer rate in the hilly area, the CFD-DEM coupling model is adopted to simulate the sediment particle transfer process in the generalized model under the action of water flow, and the method comprises the following steps:
(1) Reading a channel generalization model;
(2) During the calculation cycle of the DEM model, contact and overlap between particles is detected and force and momentum of each particle is calculated using the hertz contact model. Determining the motion state of each particle according to the calculated force and momentum by utilizing Newton's second law, and updating the speeds and positions of all particles;
(3) All particle information is sent to a CFD calculation cycle through a coupling module of the CFD-DEM coupling model;
(4) Next performing a CFD solution cycle, identifying particles in each grid, and determining the volume fraction and average particle velocity of the grid while calculating the fluid force experienced by each particle;
(5) Transferring the fluid forces of all particles back to the DEM model;
(6) Checking whether all time steps have been performed, and if the calculation has not been completed, re-performing steps (2) - (5) until the calculation is completed;
(7) And finishing calculation and outputting a result.
Compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
1. the invention provides a calculation method of a mountain region channel mountain flood sand evolution bed load sand transmission rate, which is used for determining the change relation of the mountain region channel bed load sand transmission rate along with time based on a CFD-DEM (computational fluid dynamics-discrete element) coupling model. The method can better capture the collision phenomenon in the sediment particle movement process, so that the method can solve the problems that the existing sediment transport rate formula has limited calculation accuracy on the sediment transport rate in the hillside channel, can improve the calculation accuracy of the sediment transport rate in the hillside channel, further provide more accurate process data for the sediment replenishment calculation of the hillside river, and provide more scientific and reliable references for the flood control and disaster reduction design of the downstream channel of the hillside.
2. The method provided by the invention is based on a CFD-DEM coupling model to simulate the sediment particle transfer process in the generalized model under the action of water flow, so that the calculation of the bed load sand transfer rate of the hillside channel along different sections is realized, namely, the method provided by the invention can calculate the bed load transfer process of the hillside channel along different sections, and the real-time capture of the bed load space-time change is realized. The method can solve the problem that the existing method for calculating the bed charge transfer in the channel of the hilly area by combining hydrologic calculation with bed charge movement rules only can obtain the total bed charge transfer, but cannot solve the time-space change condition of the bed charge of each section along the journey.
3. Because the process of bed charge transfer in the hilly area channel influences the downstream water and sand movement and the ditch bed evolution, the detailed process of bed charge transfer in the channel can be calculated by the method, for example, the calculation of bed charge transfer rate of different sections along the hilly area channel can be realized, and based on the method, more accurate process data can be provided for the sediment replenishment calculation of the hilly area river, and more scientific and reliable references can be provided for the flood control and disaster reduction design of the downstream channel of the hilly area.
4. Because the movement of the bed load in the hilly area channel is essentially different from the movement of the traditional river bed load, the method can better capture the collision phenomenon in the movement process of sediment particles in the hilly area channel through the simulation based on the CFD-DEM coupling model, and can reveal the microscopic mechanism of the bed load transportation in the hilly area channel.
Drawings
FIG. 1 is a comparison of the results of numerical simulation and calculation of the relationship of the sedimentation velocity of sediment particles over time using a CFD-DEM coupling model and a theoretical formula.
Fig. 2 is a typical hillside channel image.
Fig. 3 is a schematic diagram of a hillside channel generalization model.
Figure 4 shows the grading of silt particles.
The two diagrams (A) and (B) of FIG. 5 show the mean square displacement Deltax of the silt particles as they move in the channel 2 And the variance sigma of the horizontal displacement of the particles 2 Time-dependent changes.
FIG. 6 shows the movement of sediment particles after the loose packed bodies in the generalized model are washed by water flows at different times, wherein the washing times of the graphs (A) - (E) are respectively 0s, 2s, 4s, 8s and 20s.
Two graphs (A) and (B) of FIG. 7 are respectively the change condition of the non-dimensional mass and the non-dimensional sand conveying rate on a typical measurement section along with the non-dimensional time.
Fig. 8 is a result of linear fitting of the dimensionless sand ratio [ Mass rate ] and dimensionless time [ T ] of a measured section of x=5.5 m using a Weibull function.
FIG. 9 is a non-dimensional sand rate [ Mass rate ] of 10 measured sections using Weibull function]And dimensionless time [ T ]]Linear fitting deterministic coefficient R for linear fitting 2 。
Fig. 10 is a plot of the shape parameter λ and the scale parameter η in the fitted Weibull function as a function of the dimensionless horizontal distance [ x ].
Detailed Description
The method for calculating the transition sediment transport rate of the mountain hill region channel mountain flood sediment evolution is further described through the following embodiments. It is to be noted that the following examples are given solely for the purpose of illustration and are not to be construed as limitations on the scope of the invention, since numerous insubstantial modifications and variations of the invention will become apparent to those skilled in the art in light of the above disclosure, and yet remain within the scope of the invention.
According to the invention, a CFD-DEM coupling model is utilized to simulate and calculate the movement process of loose accumulation bodies in a hilly area channel, so that the bed-load transfer processes of different measurement sections are mainly analyzed and discussed, and the change relation of the bed-load sand transfer rate of any section along with time is determined on the basis of the simulated calculation.
1. Verifying applicability and accuracy of CFD-DEM coupling model
Firstly, the applicability and accuracy of a CFD-DEM coupling model to simulate the movement process of sediment particles in water are required to be verified.
Reference [ Zhao T, dai F, xu NW. Coupled DEM-CFD investigation on the formation of landslide dams in narrow rivers [ J ]].Landslides,2017,14(1):189-201.]In (3) the particle diameter is 0.002m, and the density is 2650kg/m 3 For example, the settling process of the sediment particles in water is simulated by adopting a CFD-DEM coupling model, namely, the numerical simulation of the time-dependent change process of the settling speed (settling speed) of the sediment particles is performed by adopting the CFD-DEM coupling model, and the result is shown as data points (simulation results) in fig. 1.
The sedimentation process of single spherical particles in water can be described by an equation shown in a formula (1), wherein the sedimentation velocity (sedimentation velocity) of sediment particles in water is theoretically calculated according to the formula (1) according to the time change relation, and the calculation result is shown as a curve (theoretical result) in fig. 1:
in the formula (1), r is the radius of the sediment particles, ρ s Is the density of silt particles, ρ f Is of fluid density, C d U as drag coefficient r Is the relative velocity of the silt particles and the fluid.
As can be seen from fig. 1, in the sedimentation process, the drag force suffered by the sediment particles gradually increases, the acceleration of the sediment particles gradually decreases, the movement speed of the sediment particles shows a change trend of increasing firstly and then tending to stabilize, and the movement speed of the sediment particles finally stabilizes at 0.245m/s. Comparing the "simulation result" and the "theoretical result" in fig. 1, it can be known that the numerical simulation result is better matched with the theoretical calculation result, which indicates that it is feasible to simulate and calculate the movement problem of the sediment particles in the water flow through the CFD-DEM coupling model.
2. Calculating sediment particle transporting process in hilly area channel by adopting CFD-DEM coupling model
(1) Establishing a hilly area channel generalization model
And taking the hillock area channel to be subjected to the calculation of the bed load sand conveying rate as a target channel, and establishing a hillock area channel generalization model according to the target channel topography. The method comprises the following steps:
an image of a typical hilly area channel is shown in fig. 2, taking the typical hilly area channel as an example, illustrating the establishment process of a generalized model, and as can be seen from fig. 2, the upstream of the hilly area channel is a triangular section and is formed by loose accumulation bodies, and the channel is named as a channel sediment accumulation section; the downstream section of the hillside channel is rectangular, when the mountain floods come on, loose accumulation bodies at the upstream of the hillside channel can be transported along the channel under the pushing of water flow, and the part of the channel is named as a channel sediment transport section. The target channel consists of a channel sediment accumulation section and a channel sediment conveying and moving section which are mutually connected.
And measuring the topographic information of the target channel, wherein the topographic information comprises the information such as the ratio drop, the size and the section shape of the channel sediment accumulation section and the channel sediment conveying and moving section, the size and the shape of loose accumulation bodies in the channel sediment accumulation section and the like.
And establishing a hilly area channel generalization model shown in fig. 3 in open source software Gmsh according to the topographic information of the target channel. When constructing the generalized model, firstly, the position information, the line, the surface and the body composition information of the points are written into an input file containing all necessary geometric information; then, the input file is imported into open source software Gmsh, a grid is created according to the required model dimension by using a grid module, and output is stored to obtain a generalized model. The generalization model consists of a channel sediment accumulation section and a channel sediment transport section which are mutually connected, wherein the ratio of the channel sediment accumulation section is reduced to 26.8 percent (the gradient is 15 degrees), the horizontal distance (the horizontal distance is calculated from the top end of the accumulation body) is 2.0m, and the section shape is an isosceles triangle with the bottom edge length of 0.2m and the height of 0.3 m; the ratio of the sediment transport sections of the channel is reduced to 1%, the horizontal distance is 5.7m, an isosceles triangle is connected with a rectangular river channel by using a section of variable cross section transition section with the length of 1.2m, and the remaining 4.5m is a rectangular river channel area with the width of 0.2m and the height of 0.3 m. The structure of the variable cross-section transition section is as follows: the starting point is the vertex of an isosceles triangle, the bottom edge is 0.2m long and the height is 0.3m, and in the horizontal distance of 1.2m, the isosceles triangle is gradually transited into a rectangular river channel, the length of the bottom edge is increased, and the height is kept unchanged. The design realizes the smooth transition of the cross section shape of the channel, and is more in line with the practical characteristics of the variable cross section of the channel in the hilly area.
Since the composition of loose-packed bodies in mountain areas is generally gravel-pebble wide-graded sediment, the grading information of sediment particles of the loose-packed bodies is adopted in the simulation, and the grading of the particles is shown in fig. 4. The loose deposit is formed by natural phenomena such as landslide, and in the absence of a pushing action of water flow, the loose deposit cannot be transported for a long distance, is deposited upstream of a hill region channel, and is generally in an angle of repose state. Therefore, when the generalized model is constructed, loose accumulation bodies are arranged at the sediment accumulation section of the generalized model, the loose accumulation bodies are accumulated within the range of 0m to 1m of horizontal distance, and sediment particles in the loose accumulation bodies are in a repose angle state.
In the generalized model, a plurality of measurement sections are arranged, as can be seen from fig. 2, the periphery of the channel sediment transport section in the hilly area is usually located with a protection object, so the invention focuses on the change of sediment transport rate of different sections along the channel sediment transport section, and therefore the measurement sections are arranged in the channel sediment transport section, and the concrete steps are as follows: the horizontal distance starting section is denoted as x=0m section, from x=0m section, 10 measurement sections are arranged along the course at x=3.0m, x=3.5m, x=4.0m, x=4.5m, x=5.0m, x=5.5m, x=6.0m, x=6.5m, x=7.0m and x=7.5m for monitoring the bed sand transporting process.
And when the CFD-DEM coupling method is adopted for analog calculation in the follow-up process, the adopted water flow is 2.1L/s.
(2) Simulating the process of transporting bed load in generalized model by adopting CFD-DEM coupling model
And simulating the sediment particle transferring process in the generalization model under the action of water flow by adopting a CFD-DEM coupling model to obtain data of the position, the speed and the like of the sediment particles in the generalization model, which change with time. In the simulation calculation process, the CFD part selects OpenFOAM as calculation software for simulating water flow, and the DEM part selects LIGGGHTS as calculation software for simulating sediment particle movement. The process of simulation using OpenFOAM includes preparing a geometric model, mesh generation, setting boundary conditions and initial conditions, selecting appropriate physical models and numerical methods, and running several parts of the simulation. The computation process involves a number of modules and functions, such as using boundaryfields for defining boundary conditions, turbinacemodels for providing turbulence models, fvschemas and fvsolutions for defining numerical formats and solver settings, etc. In this embodiment, the fluid computation portion uses a standard k- ε turbulence model, and computes the flow of fluid in conjunction with a fluid volume fraction (VOF) two-phase flow model. The operation of simulation using light includes preparing input files, setting particle models and interaction force fields, defining boundary conditions, setting simulation time and time steps, running simulations, and using post-processing tools for result analysis and visualization.
The process of transporting the bed load in the generalized model is analyzed below to determine the transporting characteristics of the bed load in the hilly area channel and the differences of the transporting characteristics of the bed load in the hilly area channel and the common river channel.
Calculating the mean square displacement delta x of the particles when the sediment particles move in the channel according to the formula (2) 2 The variation over time, then the particle horizontal displacement variance sigma is calculated according to equation (3) 2 The results of the time-dependent changes are shown in two graphs (A) and (B) of FIG. 5,
Δx 2 ＝<|x(t+Δt)-x(t)| 2 > (2)
in the formulae (2) to (3), Δx 2 Is the mean square displacement of the particles,<>representing the mean value of the internal expression, t being the time, here in particular the simulation time, Δt being the time variation, x (t) being the horizontal position of the particle at time t, x (t+Δt) being the horizontal position of the particle at time t+Δt, σ 2 For the horizontal displacement variance of the particles, x 1 ,x 2 ,…,x i For the horizontal position coordinate of each sediment particle at a certain moment, i is the total number of sediment particles,the average value of the horizontal position coordinates of all the silt particles at the moment.
Δx or Δx 2 The change of delta t can be used for representing that sediment particles are in a convection state or a diffusion state. If the sediment particles are in a convection state, delta x-delta t, and if the sediment particles are in a diffusion state, delta x 2 Deltat. Therefore, the two straight lines with slopes of 2 and 1 in the double logarithmic coordinate axis of the graph (a) of fig. 5 represent the normal convection state and the normal diffusion state of the silt particles, respectively. As can be seen from FIG. 5 (A), the Δx of the silt particles was calculated over a period of time from the start of the simulation 2 No growth occurs and the silt particles remain in a steady state. After that, after the water flows through the top of the loose pile, the sediment particles are in super-convection state, then are converted into convection state, and finally are converted into normal diffusion state.
The movement condition of the channel bed load in the hilly area shown in fig. 5 (a) is different from the movement condition of the channel bed load in the river channel, which indicates that the bed load is under the action of gravity and water flow on the sediment accumulation section of the channel in the hilly area, and the average movement speed in the horizontal direction is greater than the movement speed of the sediment particles in the river channel.
In addition, as can be seen from the graph (a) of fig. 5, when the movement of the silt particles occurs, the movement distance of the silt particles with larger particle size is larger than that of the silt particles with smaller particle size at any time.
As can be seen from the graph (B) of FIG. 5, the variance σ of the horizontal displacement of the silt particles having a particle diameter of 3mm is in addition to 2 The horizontal displacement variance sigma of the sediment particles with other particle diameters after the sediment particles are moved and are always in an increasing state 2 The trend is presented of increasing followed by decreasing and finally increasing again. Variance sigma of horizontal displacement 2 The falling is caused by the influence of the slow down and the widening of the channel gradient at the variable slope, so that sediment particles are accumulated, and the horizontal displacement variance sigma is caused 2 A drop occurs. Then the sediment particles are restarted under the pushing action of the water flow, and the horizontal displacement variance sigma 2 Rise again and are in a normal diffuse state.
The movement of the sediment particles after the loose-packed bodies in the generalized model are washed by water flows at different times is shown in fig. 6, the washing times (i.e. simulation times) of the graphs (a) - (E) in fig. 6 are respectively 0s, 2s, 4s, 8s and 20s, the graph (a) in fig. 6 also shows the positions of the x=0m section and the measurement section arranged along the way, the black solid lines in the graphs (B) - (D) in fig. 6 represent the water surface lines, the lower part is water flow, and the upper part is air. As can be seen from fig. 6, the loose stack remains stable when the water flow has not yet topped up, and after the water flow has passed over the top surface of the loose stack, a large amount of silt particles are transported downstream of the channel by the water flow. When sediment particles enter the sediment transport section of the channel, the water flow speed is greatly reduced due to the influence of the slow down and the widening of the gradient of the channel, so that sediment particles are deposited in the channel. Then, when the flow field tends to be stable, the deposited sediment particles move again under the action of water flow, the volume of the loose stack body is gradually reduced, and the mass of the sediment particles conveyed to the downstream is gradually increased.
(3) Calculation method for determining bed load sand conveying rate
(1) The dimensionless data is processed to further calculate the dimensionless sand transmission rate, so that the method is a common data processing means. According to the simulation of the step (2), obtaining the sediment Mass of each measuring section passing through the measuring section at the time T, passing through the total sediment Mass of the measuring section from 0 to T, obtaining the dimensionless accumulated Mass [ M ], dimensionless time [ T ] and dimensionless sediment transport rate [ Mass rate ] of the section according to the conversion of the sediment Mass passing rate of each measuring section from 0 to T according to the steps (4) to (6),
[T]＝t×(g/H) 1|2 (5)
in the formulae (4) to (6) [ M ] c ]Mass of silt passing through the section from the start of simulation to the time t, [ M ] r ]To accumulate the total mass of sediment passing through the section in the simulation process [ M ]]Accumulating mass for section without dimension [ T ]]Is a dimensionless time, [ Mass rate ]]Is the non-dimensional sand conveying rate, t is time, the unit is s, g is the gravity acceleration, and g is 9.81m/s 2 H is the difference in height from the lower end of the loose stack to the slope change point before the simulation starts, the unit is m, and the values of H in different generalized models are different, and in the embodiment, H is 0.268m.
As can be seen from fig. 2, the periphery of the channel sediment transport section in the hilly area is usually located with a protection object, so the invention focuses on examining the change of the sediment transport rate of different measurement sections of the channel sediment transport section along the way. Two graphs (A) and (B) of FIG. 7 respectively show the change of the dimensionless mass and the dimensionless sand conveying rate on the typical measurement section along the journey with the dimensionless time. As can be seen from fig. 7, the increase of the dimensionless mass has monotonicity and the value range is [0,1]; the dimensionless sand conveying rate shows a biased unimodal property, and the area of a graph surrounded by the curve and the horizontal axis is 1. In view of the above characteristics, the invention uses Weibull functions to fit the obtained dimensionless sand transmission rate data.
The horizontal distance x of the generalized model is dimensionless according to the formula (7) to obtain a dimensionless horizontal distance [ x ],
[x]＝x/H (7)
in the formula (7), x is a dimensionless horizontal distance, x is a horizontal distance, and the horizontal distance is calculated from the top end of the loose stack, and the unit is m; h is the height difference between the lower end of the loose stack and the slope changing point before simulation starts, and the unit is m;
(2) the distribution function and the density function of the standard Weibull function are expressed as the following formulas (8) (9):
F(t)＝1-exp[-(tη) λ ] (8)
f(t)＝(λt λ-1 /η λ )exp[-(t/η) λ ] (9)
in the formulas (8) to (9), λ is a shape parameter, and η is a ratio parameter.
For ease of fitting, the distribution function of the Weibull function shown in equation (8) is converted as follows to a linear form of equation (10):
the method comprises the steps of linearly fitting the dimensionless sand transmission rate [ Mass rate ] and the dimensionless time [ T ] of each measurement section by adopting a Weibull function with an expression as shown in a formula (10), obtaining a corresponding shape parameter lambda and a corresponding proportion parameter eta for each measurement section, namely obtaining a series of [ x ] and lambda and eta corresponding to the [ x ], linearly fitting the lambda and the [ x ] to obtain a linear fitting relation of lambda and [ x ], and linearly fitting the eta and the [ x ] to obtain a linear fitting relation of eta and [ x ].
lnln[1-F(t)] -1 ＝λlnt-λlnη (10)
In the formula (10), lambda is a shape parameter, eta is a proportion parameter, and t is time;
for example, for a measurement section with x=5.5m, a dimensionless horizontal distance [ x ] =20.5 is obtained according to formula (7), and according to the dimensionless sand rate [ Mass rate ] data of the measurement section at different moments, the dimensionless sand rate [ Mass rate ] and the dimensionless time [ T ] of each measurement section are linearly fitted by using a Weibull function as shown in formula (10), and the result is shown in fig. 8. The data points in fig. 8 represent "simulated sand rate", that is, the dimensionless sand rate [ Mass rate ] data of the measured section with x=5.5m at different moments, and the curve in fig. 8 represents "fitted sand rate", that is, the curve obtained by fitting the "simulated sand rate" data by using Weibull function fitting shown in (10). From this fitted curve, the shape parameter λ and the scale parameter η corresponding to the measured cross section of x=5.5m can be obtained.
The fitting process is also performed on the other 9 measurement sections by referring to the fitting process of the measurement sections with x=5.5m, and the shape parameter λ and the proportion parameter η corresponding to each measurement section are obtained. That is, through the foregoing operation, 10 measurement sections (each measurement section corresponds to one dimensionless horizontal distance [ x ]) and the corresponding shape parameter λ and scale parameter η are obtained in total.
FIG. 9 is a non-dimensional sand ratio [ Mass ratio ] of the 10 measured sections using the Weibull function shown in FIG. 10]And dimensionless time [ T ]]Linear fitting deterministic coefficient R after linear fitting 2 As can be seen from FIG. 9, the Weibull function has a good fitting effect on the process of transporting the bed load of the channel in the hilly region, R 2 > 0.84. Meanwhile, as can be seen from the combination of fig. 8, the Weibull function is adopted to fit the process of transporting the sand by the channel bed load in the hilly area, and the fitting function not only has good performance on the fitting deterministic coefficient, but also can well express the actual change condition of the sand transporting rate.
Performing linear fitting on the 10 groups of dimensionless horizontal distances [ x ] obtained through the process and the 10 corresponding shape parameters lambda to obtain a linear fitting relation shown in a formula (11); and (3) performing linear fitting on the 10 groups of dimensionless horizontal distances [ x ] obtained through the process and the 10 corresponding proportional parameters eta to obtain a linear fitting relation formula shown in the formula (12). The fitting results are shown in fig. 9.
λ＝0.476[x]+0.267 (11)
η＝9.76[x]-71.3 (12)
In the formulas (11) to (12), λ is a shape parameter, η is a scale parameter, and [ x ] is a dimensionless horizontal distance.
For this example, since each measurement section is arranged at the channel silt transport section, the linear fitting relations of the above formulas (11) - (12) are applicable to the case of [ x ] > 11.2.
As can be seen from fig. 9, the shape parameter λ and the scale parameter η have a significant linear correlation with the non-dimensionalized horizontal distance [ x ], and the slopes of the two fitting lines are significantly different from 0 at the level of 0.05 through analysis of variance. .
(3) For any section, a given section means that [ x ] is known, a shape parameter lambda is determined by a linear fitting relation of lambda and [ x ], a proportion parameter eta is determined by a linear fitting relation of eta and [ x ], and then a change relation of a bed load sand conveying rate of the section with time is obtained by a formula (9),
f(t)＝(λt λ-1 /η λ )exp[-(t/η) λ ] (9)
in the formula (9), lambda is a shape parameter, eta is a proportion parameter, t is time, and f (t) is a transition mass dimensionless sand conveying rate corresponding to the moment t.
Claims (4)
1. The calculation method of the mountain hill region channel mountain flood sand evolution bed load sand conveying rate is characterized by comprising the following steps:
s1, taking a hilly region channel to be subjected to load sand conveying rate calculation as a target channel, wherein a target river section consists of a channel sediment accumulation section and a channel sediment conveying and moving section which are mutually connected, the ratio drop of the channel sediment accumulation section is larger than that of the channel sediment conveying section, and loose accumulation bodies are arranged in the channel sediment accumulation section;
s2, establishing a target channel generalization model in open source software Gmsh according to topographic information of a target channel and grading information of sediment particles of a loose pile body, wherein the generalization model comprises a channel sediment pile section and a channel sediment conveying and moving section which are mutually connected, the loose pile body is piled in the channel sediment pile section, and the sediment particles in the loose pile body are in a repose angle state; the joint of the channel sediment accumulation section and the channel sediment conveying and moving section is marked as a slope changing point; arranging a plurality of measurement sections along the way in the generalized model;
s3, simulating the sediment particle transferring process in the generalization model under the action of water flow by adopting a CFD-DEM coupling model to obtain the time-dependent change relation of the position of the sediment particles in the generalization model;
s4, (1) obtaining sediment Mass of each measuring section passing through the measuring section at the moment T according to the simulation of the step S3, passing through the sediment total Mass of the measuring section from 0 to T, obtaining the non-dimensional accumulated Mass [ M ], the non-dimensional time [ T ] and the non-dimensional sediment rate [ Mass rate ] of the section according to the conversion of (4) to (6) from the sediment Mass passing rate of each measuring section at the moment 0 to T,
[T]＝t×(g/H) 1/2 (5)
in the formulae (4) to (6) [ M ] c ]Mass of silt passing through the section from the start of simulation to the time t, [ M ] r ]To accumulate the total mass of sediment passing through the section in the simulation process [ M ]]Accumulating mass for section without dimension [ T ]]Is a dimensionless time, [ Mass rate ]]Is the non-dimensional sand conveying rate, t is time, the unit is s, g is the gravity acceleration, and g is 9.81m/s 2 H is the height difference between the lower end of the loose stack and the slope changing point before simulation starts, and the unit is m;
the horizontal distance x of the generalized model is dimensionless according to the formula (7) to obtain a dimensionless horizontal distance [ x ],
[x]＝x/H (7)
in the formula (7), x is a dimensionless horizontal distance, x is a horizontal distance, and the horizontal distance is calculated from the top end of the loose stack, and the unit is m; h is the height difference between the lower end of the loose stack and the slope changing point before simulation starts, and the unit is m;
(2) carrying out linear fitting on the dimensionless sand transmission rate [ Mass rate ] and the dimensionless time [ T ] of each measured section by adopting Weibull function fitting with an expression as shown in a formula (10), obtaining a corresponding shape parameter lambda and a corresponding proportion parameter eta for each measured section, namely obtaining a series of [ x ] and lambda and eta corresponding to the x, carrying out linear fitting on lambda and [ x ] to obtain a linear fitting relation of lambda and [ x ], and carrying out linear fitting on eta and [ x ] to obtain a linear fitting relation of eta and [ x ];
ln ln[1-F(t)] -1 ＝λln t-λlnη (10)
in the formula (10), lambda is a shape parameter, eta is a proportion parameter, and t is time;
(3) for any section, determining a shape parameter lambda by a linear fitting relation between lambda and [ x ], determining a proportion parameter eta by a linear fitting relation between eta and [ x ], further obtaining a time-dependent change relation of the bed load sand conveying rate of the section by a formula (9),
f(t)＝(λt λ-1 /η λ )exp[-(t/η) λ ] (9)
in the formula (9), λ is a shape parameter, η is a scale parameter, and t is time.
2. The method for calculating the channel mountain flood sand evolution bed load sand conveying rate in a hilly area according to claim 1, wherein in the step S3, when a CFD-DEM coupling model is adopted to simulate the sediment particle conveying process in a generalization model under the action of water flow, the adopted water flow is determined according to the historical rainfall data at a target channel.
3. The method for calculating the channel mountain flood sand evolution bed load sand transfer rate in a hilly area according to claim 2, wherein in step S3, the flow rate of water flow adopted when the transporting process of sediment particles in a generalized model under the action of water flow is simulated by adopting a CFD-DEM coupling model is determined by the following steps: flood control indexes are designed according to the region where the target channel is located, the flood flow in a specific recurring period is determined by combining historical rainfall data and hydrologic analysis, the flood flow in the specific recurring period is taken as an original flow, and the original flow is scaled according to a model scale, so that the water flow adopted in the generalized model is obtained.
4. A method for calculating a sand transfer rate of a mountain hill region channel mountain flood sand evolution bed load according to any one of claims 1 to 3, wherein in step S2, at least 5 measurement sections are arranged along the way in a generalized model.
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