CN103422461B - Method for judging 'bottom tearing' scour caused by hyper-concentration floods - Google Patents

Abstract

The invention belongs to the technical field of sediment dynamics, and relates to a hydrological forecasting method, in particular to a method for judging 'bottom tearing' scour caused by hyper-concentration floods. The IPC number is E02B1/00. The method includes the following steps: first, carrying out a bending test on sticky mud blocks at a 'bottom tearing' stream segment, second, building a 'bottom tearing' scour sticky mud block breakage and tearing model, analyzing various loads acting on the sticky mud blocks, determining the most unfavorable load combination and building a sticky mud block critical breakage balance equation, and third, calculating various forces acting on the sticky mud blocks and solving the equation to determine the sticky mud block breakage and tearing critical flow velocity. The method is the only method that 'bottom tearing' scour critical judging indexes are calculated with sticky mud block breakage strength conditions considered, the accurate forecasting method is provided for judging whether a certain flood causes the 'bottom tearing' phenomenon, decision bases are provided for flood prevention, and real-time data acquisition on 'bottom tearing' scour becomes possible.

Description

A Distinguishing Method for High Sediment Concentration Flood "Uncovering the River Bottom" Scour

technical field

The invention relates to a hydrological forecasting method, in particular to a method for discriminating scour caused by high-water-content floods, which belongs to the technical field of sediment dynamics. The IPC international patent classification number is E02B1/00.

Background technique

The phenomenon of "exposing the bottom of the river" by high-sediment floods is a landscape on the Yellow River, which generally occurs in the main stream of Xiaobei in the middle reaches of the Yellow River and the lower reaches of the Weihe River. When high-sediment floods pass through this river section, the denser and stronger cement blocks (river bed sediments) that have been deposited for a certain period of time in the early stage are lifted up by the water and exposed to the water surface, with an area of several square meters or even more than ten square meters. The clods of mud stand upright like a wall perpendicular to the direction of the water flow, and then "plop" into the water (some clods of mud stand upright for two or three minutes before falling into the water), and are quickly swallowed by the flood. A large number of mud clods rise and fall on the surface of the river, tumbling down the current, the river is full of flowers, surging, and the sound of water is deafening. "Uncovering the river bottom" scour is a phenomenon produced by the interaction between high-sediment flow and special riverbed boundary. The scouring of "exposing the river bottom" often leads to a strong downcut of the river bed. Sometimes a flood peak can wash the river bed several meters deep, resulting in a sharp drop in the river bed and water level. Flood control of the Yellow River brought enormous pressure.

In the 1970s, the phenomenon of "uncovering the bottom of the river" attracted the attention of water conservancy workers at home and abroad, and conducted research on this issue. At present, the research methods of "exposing the bottom of the river" are divided into three categories: the first category is to use the actual measurement data of the prototype hydrological station to study and analyze the water and sediment conditions of the "exposing the river bottom" phenomenon in the main stream of the Yellow River and the Weihe River. Because the water and sediment conditions of high-sediment rivers vary greatly along the course, it is inaccurate to use the measured data of the upstream and downstream hydrological stations of the "Jiehedi" river section as the calculation data for the scouring water and sediment conditions of the "Jiehedi". The conditions for the formation of the "bottom" phenomenon are relatively special, and its occurrence is relatively random. It is difficult to capture the measured data of "exposing the bottom of the river" with strong followability in practice, which also leads to the limitation of the length of statistical data. Therefore, this method The proposed water and sediment conditions for the phenomenon of "exposing the bottom of the river" are not convincing. The second type of method is to use the concept of water flow sediment-carrying capacity to study the water and sediment conditions when the clay block is started. However, the sediment-carrying capacity reflects the migration of the sediment during the downstream transportation process, and cannot reflect the instantaneous lifting of the clay block. The relationship between the dynamic mechanics and the lifting of clay blocks is also very different from that of a single sediment particle. Therefore, it is debatable whether the concept of sand-carrying capacity can be used to reflect the problem of "uncovering the river bottom". The third type of research method is experimental research. This method uses the flume test to simulate the scour phenomenon of "uncovering the river bottom", and constructs two mechanical models for the unraveling of clay blocks: one is that the bottom of the clay block is eroded by water flow, and when the mud block moves along the When the continuous part (fixed end) with the river bed rotates upward, the front end of the clay block is in a cantilever state; the other is to build a mechanical analysis model by considering only the adhesion between the boundary of the clay block and the river bed without considering the erosion and scour conditions, but this Both models are based on the calculation of water and sand conditions under the condition that the whole piece of clay block is uncovered, and neither considers the influence of the structural strength (flexural strength) of the clay block itself.

Due to the different research means, methods, objects, and research emphases in the current research on "exposing the river bottom", there is still a lack of unified understanding of the criteria, indicators, and mechanism of "exposing the river bottom". The conditions for the phenomenon of "exposing the bottom of the river" are relatively special, and its occurrence is relatively random. It is difficult to capture the measured data of "exposing the bottom of the river" in practice, which also leads to the current phenomenon of "exposing the bottom of the river". research is restricted.

Whether the riverbed sediment block can be lifted up, or whether the phenomenon of "exposing the river bottom" can be produced mainly depends on the comprehensive results of various conditions, including the previous riverbed sedimentation shape and adjustment, sediment density and relative roughness, and sedimentation. The formation of the block and the thickness of the layers, the boundary conditions of the silt block, the mechanical strength of the silt block itself, the magnitude of the flood peak flow and sediment concentration, the duration of the flood process, the shape parameters of the river channel, the strength of the vertical fluctuation pressure of the layer, Phase distribution and phase superposition probability of pulsating pressure on the upper and lower surfaces of sediment blocks.

Judging from the current research results of "exposing the river bottom" scouring problem, no research literature has been found that comprehensively considers the above-mentioned influencing factors of "exposing the river bottom" scour when deriving the critical discriminant conditions for "exposing the river bottom" scour. The present invention utilizes the test data of the mechanical strength of the clay block scoured by "exposing the river bottom", and considers the comprehensive influencing factors of "exposing the river bottom" scour, and deduces the critical discrimination formula for "exposing the river bottom" scour.

Contents of the invention

In the present invention, under the condition of considering the comprehensive influencing factors of "exposing the river bottom" scour, a mechanical analysis model for the breaking and uncovering of the clay block is constructed, and by using the test data of the flexural strength of the clay block, the phenomenon of "exposing the river bottom" caused by the breaking of the clay block is calculated. critical flow conditions. The technical scheme that the present invention takes is:

A high-sediment flood "exposing the river bottom" scour discrimination method, comprising the following steps:

(1) The flexural strength test of the clay block in the scour-prone river section of "Jiehe Bottom":

The test soil samples are clay blocks taken from the scouring-prone river section of "Jiehedi". First, the test soil samples are reshaped. The clay block is crushed, put into a container and stirred with water to make the sediment flocculate and deposit, and the sample of the clay block is formed by air-drying, and the moisture content of the sample of the clay block is controlled by using the air-drying time; then, different groups of the clay block are tested Sample, using the flexural testing machine to measure the flexural strength;

The test method is as follows:

Put the clay block sample horizontally on the two supporting cylinders of the flexural testing machine, the long axis of the specimen is perpendicular to the supporting cylinders of the flexural testing machine, and pass the load of the flexural testing machine at a rate of 50N/s±10N/s The vertical load is evenly applied to the horizontal surface of the prism until the sample of the clay block is broken; the flexural strength M of the sample of the clay block is calculated by formula (1),

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1.5</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; L</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, F _f - the load applied vertically to the middle of the top plane of the specimen when it breaks, the unit is N;

L- the distance between the supporting cylinders, the unit is mm;

B- the side length of the square section of the prism, the unit is mm;

Taking the average value of the flexural strength of a group of three cement block samples as the test result, the relationship equation between the flexural strength of the cement block and the water content is established by using the experimental results, and the relationship equation is used to calculate the "exposed river bottom" scour-prone river The flexural strength M _s at the saturated water content of the cement blocks in the section;

(2) Constructing a mathematical model of the force of the clay block breaking and uncovering when the "exposing the bottom of the river" is scoured:

F _D is the frontal thrust of water flow: $f_{\mathrm{D.}}=\frac{{\mathrm{\&gamma;}}_m{C}_{\mathrm{D.}}}{2}{V}_b^2\mathrm{bcg}---\left(2\right)$

In the formula, V _b is the water flow velocity at the bottom of the clay block, C _D is the drag coefficient, γ _m is the muddy water density, b is the width of the clay block, and c is the thickness of the clay block.

F _D ' is the reaction force of F _D on the fracture surface: $f_{\mathrm{D.}}^{\&prime;}=\frac{{\mathrm{\&gamma;}}_m{C}_{\mathrm{D.}}}{2}{V}_b^2\mathrm{bcg}---\left(3\right)$

τ is the water drag force on the upper surface of the cement block: $\mathrm{\&tau;}=\frac{{\mathrm{\&gamma;}}_m{C}_{\mathrm{D.}}}{2}{V}_b^2\mathrm{lbg}---\left(4\right)$

The weight of G _s clay block is: G _s = γ _s lbcg (5)

In the formula, γ _s is the bulk density of the cement block, l is the length of the erosion cantilever, g is the acceleration of gravity, and other symbols are the same as before.

P ₁ is the water pressure on the clay block: P ₁ =γ _m lbhg (6)

In the formula, h is the water depth at the surface of the cement block, and other symbols are the same as before.

P ₂ is the buoyancy of the clay block: P ₂ =γ _m lb(h+c)g (7)

Maximum water flow pulsation lifting force: $f_{d\max }={\mathrm{K\&gamma;}}_{m}J{V}_b^2\mathrm{lb}---\left(8\right)$

In the formula, K is the linear coefficient, the unit is kg m s, and the value range is 3 to 4.2, and J is the slope of the water surface.

(3) Considering the most unfavorable load combination conditions, establish the moment balance equation of each force on the y-axis:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&tau;c</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\frac{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; bc</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

(4) Solve the equation to obtain the critical velocity V _b :

Firstly, substitute equations (2)-(8) in steps (2) and (3) into equation (9) to solve, and obtain equation (10):

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cg</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; KJ</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; lcg</span>}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

The length of the erosion cantilever that the cement block is washed out in the time period of Δt adopts the empirical formula:

$\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.013</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In the formula, C ₁ is the scour coefficient of the river bed, τ _s is the drag force on the sediment particles around the cement block, τ _c is the critical starting shear stress when the river bed sediment is scoured, and γ _c is the bulk density of the river bed sediment.

${\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.16</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

$\frac{{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; A</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

In the formula, _ρm is the density of high-sediment flood, D is the average particle size of movable sediment around the clay block, A is the comprehensive influence coefficient, and its value ranges from 0.015 to 0.034, the median value is 0.0245, and the coefficient ξ takes The value is 0-1, d _m is the average particle size of the erosion sediment, d _i is the particle size of the eroded sediment,

Simultaneous equations (10), (11), (12) and (13) are solved to obtain V _b , which is the critical flow velocity for "exposing the bottom of the river" scour _;

(5), judging whether a certain flood produces the scouring phenomenon of "exposing the bottom of the river".

When a high-sediment flood occurs in the upper reaches of the "Jiehedi" scouring-prone river, according to the observation data of the flood flow velocity and sediment concentration at the upstream hydrological observation station of the river, the flood when the flood reaches the river is calculated. Actual riverbed flow velocity, sediment concentration and scouring time length, and then use the method of step (4) to calculate the critical flow velocity V _b of "exposing the river bottom" scour, when the actual riverbed flow velocity is greater than the critical flow velocity V _b , it will occur The scouring phenomenon of "exposing the bottom of the river", otherwise, the scouring phenomenon of "exposing the bottom of the river" will not occur.

The discrimination method of the present invention can more accurately predict whether high water content floods will produce "exposing the river bottom" scouring phenomenon, provide decision-making basis for flood control and flood fighting, and also provide possibility for real-time data collection of "exposing the river bottom" scouring.

Detailed ways

The key steps of the present invention are to carry out the flexural strength test on the clay block in the "exposing the river bottom" section; considering the comprehensive influence factors of "exposing the river bottom" scour to construct the mathematics of the breaking and exposing model of the clay block, and to solve the model. Its specific implementation steps are as follows:

(1) The flexural strength test of clay blocks in the scour-prone river section of "Jiehe Bottom".

The test soil sample is the clay block of the Yellow River "Jiehe Bottom" scour-prone section. Firstly, according to the formation mechanism of the flocculation deposition of clay blocks in the "Jiehedi" scouring-prone river section, the soil samples retrieved from the "Jiehedi" scouring-prone section were remodeled. The returned clay blocks are crushed, put into a container and stirred with water to make the sediment flocculate and deposit, and the clay blocks are formed by air-drying as samples, and the moisture content of the samples of the clay blocks is controlled by using different air-drying times. For different groups of clay block samples, the flexural strength was measured using a flexural testing machine.

The test method is as follows:

Put the clay block sample horizontally on the two supporting cylinders of the flexural testing machine, the long axis of the specimen is perpendicular to the supporting cylinders of the flexural testing machine, and pass through the loading and unloading of the flexural testing machine at a rate of about 50N/s±10N/s. The load cylinder applies the vertical load evenly on the horizontal plane of the prism until the cement block sample breaks. The calculation formula of the flexural strength M is as formula (1), and the unit is Newton/square millimeter (MPa).

$\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1.5</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}\mathrm{<span\; class="notranslate">\; L</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the formula, F _f - the load applied vertically to the middle of the top plane of the specimen when it breaks, the unit is N;

L- the distance between the supporting cylinders, the unit is mm;

B- The side length of the square section of the prism, in mm.

The average value of the flexural strength of a group of three cement block samples is taken as the test result. Based on the experimental results, the relationship equation between the flexural strength and water content of the clay block is established, and the flexural strength M _s of the clay block at saturated water content in the "Jiehe bottom" scour-prone river section is calculated from the relationship equation.

(2) Construct the mathematic model of the force of the clay block when it is broken and uncovered during the scour of "Jiehe bottom", and calculate the load on the clay block.

F _D water frontal thrust: $f_{\mathrm{D.}}=\frac{{\mathrm{\&gamma;}}_m{C}_{\mathrm{D.}}}{2}{V}_b^2\mathrm{bcg}---\left(2\right)$

In the formula, V _b is the water flow velocity at the bottom of the clay block, C _D is the drag coefficient with a value of 1, γ _m is the muddy water bulk density, b is the width of the clay block, and c is the thickness of the clay block.

F _D ' is the reaction force of F _D : $f_{\mathrm{D.}}^{\&prime;}=\frac{{\mathrm{\&gamma;}}_m{C}_{\mathrm{D.}}}{2}{V}_b^2\mathrm{bcg}---\left(3\right)$

τ' is the vertical shear force at the fractured section of the clay block, which does not produce a moment on the y-axis and can be ignored.

τ is the water drag force on the upper surface of the cement block: $\mathrm{\&tau;}=\frac{{\mathrm{\&gamma;}}_m{C}_{\mathrm{D.}}}{2}{V}_b^2\mathrm{lbg}---\left(4\right)$

τ” is the drag force of the water flow on the lower surface of the cement block, which does not produce a moment on the y-axis and can be ignored.

Clay block weight G _s : G _s = γ _s lbcg (5)

In the formula, γ _s is the bulk density of the cement block, l is the length of the cantilever of the brush, g is the acceleration of gravity, and other symbols are the same as before.

Water pressure P ₁ on the clay block: P ₁ = γ _m lbhg (6)

In the formula, h is the water depth at the surface of the cement block, and other symbols are the same as before.

The buoyancy P ₂ of the clay block: P ₂ =γ _m lb(h+c)g (7)

Maximum water flow pulsation lifting force: $f_{d\max }={\mathrm{K\&gamma;}}_{m}J{V}_b^2\mathrm{lb}---\left(8\right)$

In the formula, K is the linear coefficient, the unit is kg m s, and the value range is 3 to 4.2, and J is the slope of the water surface.

(3) Considering the most unfavorable load combination conditions, establish the moment balance equation of each force on the y-axis

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&tau;c</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; G</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\frac{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; bc</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

(4) Solve the equation to obtain the flow velocity V _b , which is the critical flow velocity at which the scour of "exposing the bottom of the river" occurs:

Substituting formulas (4), (5), (6), (7), and (8) into formula (9), we can get:

${\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cg</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; KJ</span>}{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; lcg</span>}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

The length of the erosion cantilever that the cement block is washed out in the time period of Δt adopts the empirical formula:

$\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.013</span>}{\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In the formula, C ₁ is the scour coefficient of the river bed, τ _s is the drag force on the sediment particles around the cement block, τ _c is the critical starting shear stress when the river bed sediment is scoured, and γ _c is the bulk density of the river bed sediment.

${\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}^{<span\; class="notranslate">\; \&prime;</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; D.</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\frac{{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 12</span>}<span\; class="notranslate">\; )</span>$

In the formula, C _D ' is the drag force coefficient, the value is 0.4, α _D is the area coefficient of the sediment particles, the value is ρ _m is the density of water, d _i is the size of the eroded sediment particles, and other symbols are the same as before. Substituting d _i with the average particle size D of the movable sediment around the clay block, the formula (12) is sorted out to get:

${\mathrm{<span\; class="notranslate">\; \&tau;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.16</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Critical starting shear stress τ _c of riverbed sediment: $\frac{{\mathrm{\&tau;}}_c}{({\mathrm{\&gamma;}}_c-{\mathrm{\&gamma;}}_m)d_i}=A(1+\mathrm{\&xi;}\frac{d_m}{d_i})---\left(14\right)$

In the formula, A is the comprehensive influence coefficient, its value ranges from 0.015 to 0.034, and the median value is 0.0245; ξ is the coefficient related to the exposure of sediment particles, and its value is 0 to 1; d _m is the erosion sediment The average particle size of d _i is the particle size of the eroded sediment.

Substituting equations (13) and (14) into equation (11), the calculation formula for the cantilever length 1 of the brush can be obtained:

$\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 0.16</span>}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; A</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 0.013</span>}\mathrm{<span\; class="notranslate">\; A</span>}{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

Considering that the particle size of the erodible sediment particles around the clay block is on the order of 10 ^-5 (m), the value range of A is on the order of 10 ^-2 , and Therefore, in formula (15) Substituting d _i with the average particle size D of movable sediment around the clay block, formula (15) can be expressed as:

$\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 0.16</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; AD</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 16</span>}<span\; class="notranslate">\; )</span>$

Will l as a variable, formula (10) and formula (16) are solved simultaneously: Substituting formula (10) into formula (16) and sorting out:

${\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;tAD</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&xi;</span>}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;tADcg</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; KJ</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&xi;\&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&xi;\&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&rho;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 0.32</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.16</span>}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

make $a^{,}=-\frac{C_1\mathrm{\&Delta;tAD}}{2}(2{\mathrm{\&gamma;}}_c+2\mathrm{\&xi;}{\mathrm{\&gamma;}}_c-{\mathrm{\&gamma;}}_m-{\mathrm{\&xi;\&gamma;}}_m),$ $b^{,}=-\frac{C_1\mathrm{\&Delta;tADcg}}{2\mathrm{KJ}}({\mathrm{\&gamma;}}_c+\mathrm{\&xi;}{\mathrm{\&gamma;}}_c-{\mathrm{\&gamma;}}_m-{\mathrm{\&xi;\&gamma;}}_m),$

c'＝-C ₁ ΔtD ² ρ _m c[0.32M _s +0.16(γ _s -γ _m )], Then formula (17) is transformed into:

(l') ³ +pl'+q＝0 (18)

In the formula, $p=(\frac{{\left(a^{,}\right)}^2}{3}+b^{,}),$ $q=\frac{2{\left(a^{,}\right)}^3-{9a}^{,}{b}^{,}+27c^{,}}{27}$

According to the formula for finding the root of the cubic equation in one variable:

$\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ]</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \}</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; q</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; p</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ]</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \}</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; a</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Substituting 1 into formula (10), we can find $V_b^2=f(C_1,\mathrm{\&Delta;t},{\mathrm{\&gamma;}}_c,{\mathrm{\&gamma;}}_{\mathrm{the\; s}},{\mathrm{\&gamma;}}_m,c,J,K,m_{\mathrm{the\; s}},\mathrm{D.}).$

(5), judging whether a certain flood produces the scouring phenomenon of "exposing the bottom of the river".

When a high-sediment flood occurs in the upper reaches of the "Jiehedi" scouring-prone river, according to the observation data of flood flow velocity and sediment concentration at the upstream hydrological observation station of this river section, and according to the hydrological observation data of this river section for many years, it can be It is easy to calculate the actual riverbed flow velocity, sediment concentration and scouring time when the flood reaches the river section, and then use the method of step (4) to calculate the critical flow velocity V _b for "exposing the river bottom" scouring. When the actual river bed flow velocity is greater than the critical flow velocity _Vb , the scour phenomenon of "exposing the river bottom" will occur; otherwise, the scour phenomenon of "exposing the river bottom" will not occur.

Claims (1)

1. A high-sediment flood "exposing the river bottom" scour discrimination method, comprising the following steps: (1) The flexural strength test of the clay block in the scour-prone river section of "Jiehe Bottom": The test soil samples are clay blocks taken from the scouring-prone river section of "Jiehedi". First, the test soil samples are reshaped. The clay block is crushed, put into a container and stirred with water to make the sediment flocculate and deposit, and the sample of the clay block is formed by air-drying, and the moisture content of the sample of the clay block is controlled by using the air-drying time; then, different groups of the clay block are tested Sample, using the flexural testing machine to measure the flexural strength; The test method is as follows: Put the clay block sample horizontally on the two supporting cylinders of the flexural testing machine, the long axis of the specimen is perpendicular to the supporting cylinders of the flexural testing machine, and pass the load of the flexural testing machine at a rate of 50N/s±10N/s Cylindrical vertical load is evenly added on the horizontal plane of prism, until the cement block sample is broken; Utilize formula (1) to calculate the flexural strength M of the cement block sample; In the formula, F _f - the load applied vertically to the middle of the top plane of the specimen when it breaks, the unit is N; L- the distance between the supporting cylinders, the unit is mm; B- the side length of the square section of the prism, the unit is mm; Taking the average value of the flexural strength of a group of three cement block samples as the test result, the relationship equation between the flexural strength of the cement block and the water content is established by using the experimental results, and the relationship equation is used to calculate the "exposed river bottom" scour-prone river The flexural strength M _s at the saturated water content of the cement blocks in the section; (2) Constructing a mathematical model of the force of the clay block breaking and uncovering when the "exposing the bottom of the river" is scoured: F _D is the frontal thrust of water flow: In the formula, V _b is the water velocity at the bottom of the clay block, _CD is the drag coefficient, γ _m is the muddy water bulk density, b is the width of the clay block, and c is the thickness of the clay block; F′ _d is the reaction force of F _D on the fracture surface: τ is the water drag force on the upper surface of the cement block: The weight of G _s clay block is: G _s = γ _s lbcg (5) In the formula, γ _s is the bulk density of the clay block, l is the length of the erosion cantilever, and g is the acceleration of gravity; P ₁ is the water pressure on the clay block: P ₁ =γ _m lbhg (6) In the formula, h is the water depth at the surface of the cement block; P ₂ is the buoyancy of the clay block: P ₂ =γ _m lb(h+c)g (7) Maximum water flow pulsation lifting force: In the formula, K is the linear coefficient, the unit is kg m s, and the value range is 3 to 4.2, and J is the slope of the water surface; (3) Considering the most unfavorable load combination conditions, establish the moment balance equation of each force on the y-axis: (4) Solve the equation to obtain the critical velocity V _b : First, formulas (2)-(9) in steps (2) and (3) are solved simultaneously to obtain formula (10): The length l of the erosion cantilever that the cement block is washed out in the time period Δt adopts the empirical formula: In the formula, C ₁ is the scour coefficient of the river bed, τ _s is the drag force on the sediment particles around the clay block, τ _c is the critical starting shear stress when the river bed sediment is scoured, and γ _c is the bulk density of the river bed sediment; In the formula, _ρm is the density of high-sediment flood, D is the average particle size of movable sediment around the clay block, A is the comprehensive influence coefficient, and its value ranges from 0.015 to 0.034, the median value is 0.0245, and the coefficient ξ takes The value is 0-1, d _m is the average particle size of the erosion sediment, and d _i is the particle size of the eroded sediment; Simultaneous equations (10), (11), (12) and (13) are solved, and V _b can be obtained, and this V _b is the critical flow velocity for "exposing the bottom of the river" to be scoured; (5), judging whether a certain flood has produced the scour phenomenon of "exposing the river bottom": When a high-sediment flood occurs in the upper reaches of the "Jiehedi" scouring-prone river, according to the observation data of the flood flow velocity and sediment concentration at the upstream hydrological observation station of the river, the flood when the flood reaches the river is calculated. Actual riverbed flow velocity, sediment concentration and scouring duration, and then use the method of step (4) to calculate the critical flow velocity V _b of "exposing the river bottom" scour, when the actual riverbed flow velocity is greater than the critical flow velocity V _b , it will occur The scouring phenomenon of "exposing the bottom of the river", otherwise, the scouring phenomenon of "exposing the bottom of the river" will not occur.