Method for calculating riprap drift distance of net bag in underwater foot protection construction
By establishing the vertical and horizontal motion equations after the net bag throws the rocks fall into the water, combining the physical parameters of water depth and flow rate, the drift distance of the net bag throws is directly calculated, which solves the problem of difficult to ensure the accuracy of the stone throwing construction in the river bank protection project, and achieves efficient and accurate construction operations.
Patent Information
- Application Number
- CN202411543404.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-31
- Publication Date
- 2025-03-14
AI Technical Summary
In the river bank protection project, due to the rapid flow of the river and the deep water depth during the underwater foot protection construction, there are large deviations in the landing point of the net-pocket stone throwing and the over-water throwing point, which makes it difficult to ensure the construction accuracy. The existing methods rely on on-site trial throwing measurements, with large errors and large workloads.
By establishing the vertical and horizontal motion equations after the net bag throws the rock into the water, combining the physical parameters of water depth and flow velocity, the drift distance of the net bag throws the rock into the water is directly calculated. The method includes establishing a vertical direction motion equation to determine the water depth and sinking time, and establishing a horizontal direction motion equation to calculate the horizontal displacement and drift distance.
This method does not require on-site trial throwing, and can accurately calculate the drift distance of the net bag throwing stone, improve the construction accuracy and efficiency, and reduce construction costs.
Smart Images
Figure CN119622163A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of river channel regulation engineering, and particularly relates to a method for calculating the drift distance of underwater foot protection net bag riprap in the construction of river channel bank protection engineering. Background Art
[0002] In the underwater foot protection construction of bank protection projects, it is often necessary to use a riprap boat to throw net bag riprap and other foot protection materials from above the water surface to the bottom of the riverbed. Due to the rapid flow and deep water in the river channel, there is often a large deviation between the landing point of the net bag riprap on the riverbed and the throwing point on the water. In order to ensure the accuracy of the throwing construction, a certain drift distance needs to be reserved above the water surface. In existing engineering practices, the drift distance is generally determined by on-site throwing tests. This method determines the landing point of the net bag riprap by comparing the measured terrain before and after the test throwing. Since the size of the net bag riprap for the test throwing is smaller than the underwater riverbed terrain, after the net bag riprap sinks to the bottom of the river, the thickness increased by about 0.5 to 1.5m relative to the original riverbed. The underwater terrain measurement error is large, and it is difficult to accurately determine the riprap position; and the water depth and flow rate along the same engineering bank section often vary greatly. If the test throwing is carried out in sections, the workload is large. Therefore, it is necessary to establish the general relationship between the drift distance of net bag stone throwing and water depth and flow velocity through theoretical deduction, so as to directly calculate the drift distance of net bag stone throwing through the relevant physical parameters of net bag stone throwing and the easily measurable physical quantities such as water depth and flow velocity of the river channel in the throwing area. Summary of the invention
[0003] The present invention aims to provide.
[0004] To achieve the above objectives, the technical solution of the present invention is:
[0005] A method for calculating the drift distance of a net bag riprap in underwater foot protection construction, the method comprising:
[0006] Establishing a motion equation in the vertical direction after the net bag throws the stone into the water, and obtaining a functional relationship between the vertical displacement y(t) and time t after the net bag throws the stone into the water through the motion equation in the vertical direction;
[0007] When the net bag riprap sinks to the riverbed, the vertical displacement y(t) of the net bag riprap is equal to the water depth H;
[0008] After obtaining the water depth H value, the time t from the net bag riprap entering the water to sinking to the riverbed is calculated based on the functional relationship between the vertical displacement of the net bag riprap after falling into the water and time;
[0009] Establishing a motion equation in the horizontal direction after the net bag throws the stone into the water, and obtaining a functional relationship between the horizontal displacement x(t) and time t after the net bag throws the stone into the water through the motion equation in the horizontal direction;
[0010] The drift distance of the net bag throwing stones is calculated by the time t from the net bag throwing stones entering the water to sinking to the riverbed, as well as the functional relationship between the horizontal displacement of the net bag throwing stones after falling into the water and time.
[0011] Furthermore, the motion equation of the net bag after the stone falls into the water in the vertical direction is as follows:
[0012]
[0013] In the formula, ρs is the density of the net bag riprap; V is the volume of the net bag riprap; is the differential, is the sinking speed of the net bag riprap in the plumb direction; t is the time after the net bag riprap falls into the water, assuming that the time t0 at the time of entry into the water is 0; is the density of water; g is the acceleration of gravity; is the drag force coefficient; Ay is the area of the stream-facing surface of the net bag riprap along the y direction.
[0014] Furthermore, by solving the formula (5), the general solution of the flow velocity expression in the y direction after the net bag throws the stone into the water is obtained as formula (6):
[0015]
[0016] Where, is the sinking speed of the net bag riprap in the vertical direction; ρs is the density of the net bag riprap; is the density of water; g is the acceleration of gravity; V is the volume of the net bag riprap; is the drag force coefficient; Ay is the surface area of the net bag riprap along the y direction; t is the time after the net bag riprap falls into the water; C1 is a constant;
[0017] By integrating formula (6) along time t, the functional relationship between the displacement y(t) of the net bag riprap in the y direction and time t is obtained as shown in formula (8):
[0018]
[0019] Wherein: is the falling depth of the net bag riprap in the y direction; ρs is the density of the net bag riprap; is the density of water; g is the acceleration due to gravity; V is the volume of the net bag riprap; is the drag coefficient; Ay is the surface area of the net bag riprap along the y direction; t is the time after the net bag riprap falls into the water; C1 is a constant, when H0 is equal to 0, C1 is equal to 0; in formula (8), when y(t) is equal to the water depth H, according to the known water depth H, the time t when the net bag riprap falls to the riverbed can be calculated by formula (8).
[0020] Furthermore, the motion equation of the net bag after the stone falls into the water in the horizontal direction is as follows:
[0021]
[0022] Solve the horizontal motion equation formula (9) and substitute the boundary conditions t0=0, ux0=0 to obtain the relationship between the flow velocity of the net bag riprap in the horizontal direction and time as shown in formula (10):
[0023]
[0024] Where, ρs is the density of the net bag riprap; V is the volume of the net bag riprap; d is the differential; ux is the horizontal speed of the net bag riprap after entering the water, which is a function of time t; CD is the drag coefficient; Ax is the horizontal flow area of the net bag riprap; Uw is the average flow velocity of the water flow at water depth;
[0025] Furthermore, the calculation method of the net bag riprap drift distance x(t) is: integrate both sides of formula (10) along time t, and obtain the relationship between the horizontal drift distance x(t) and time t after the net bag riprap enters the water as shown in formula (11):
[0026]
[0027] Where x(t) is the horizontal drift distance or displacement of the net bag after the stone enters the water; Uw is the average velocity of the water flow; t is the time after the net bag falls into the water; ρs is the density of the net bag; V is the volume of the net bag; ρw is the density of water; C D is the drag coefficient; Ax is the horizontal flow area of the net bag riprap;
[0028] In formula (8), when y(t) is equal to the water depth H, the time t when the net bag throws the stone into the water can be calculated according to the known water depth H. Substitute the time t from the net bag throwing the stone into the water to the time it sinks into the riverbed into the horizontal drift distance and time formula (11) to calculate the drift distance after the net bag throws the stone into the water.
[0029] The beneficial effects of the present invention are:
[0030] The invention provides a method for calculating the drift distance of net bag riprap in the construction of a bank protection project. The method only needs to measure the average flow velocity of each riprap area, the water depth, the distance between the riprap starting point and the water surface, the volume of the net bag riprap, and the projection area of the flow-facing surface in the x and y directions, so as to calculate the drift distance of the net bag riprap after it falls into the water, without the need for on-site riprap tests, thereby saving costs for the construction of the bank protection project and improving the construction efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] Figure 1 A schematic diagram of a net bag riprap provided by an example of the present invention.
[0032] Figure 2 A schematic diagram of a coordinate system for a net bag throwing stone into water provided in an embodiment of the present invention.
[0033] Figure 3 This is a force analysis diagram of a net bag throwing stones into water provided by an example of the present invention.
[0034] Figure 4 A plan view of each riprap area for net bags taking into account the drift distance before and after the drift distance is provided in an embodiment of the present invention.
[0035] In the figure: filling stones 1; net bag 2; net bag riprap 3; riverbed 4; track line 5; nearshore side 6. DETAILED DESCRIPTION
[0036] In order to make the purpose, technical solutions and advantages of the invention clearer, the present invention is further described below with reference to the accompanying drawings.
[0037] like Figure 1 As shown, the filling stones 1 are placed in the net bag 2 to form the net bag riprap 3 according to the embodiment of the present invention.
[0038] In such Figure 2 In the coordinate system shown, the functional relationship between the vertical displacement of the net bag and the time after the stone falls into the water is established.
[0039] A force analysis is conducted on the process of a net bag throwing stones into water, and the motion equation is established. The shot put in a stationary state is only affected by buoyancy and gravity, but the shot put in a moving state, in addition to buoyancy and gravity, is also affected by the water flow resistance in the opposite direction of movement. The buoyancy size remains unchanged, and the buoyancy size is related to the volume of the shot put, and the water flow resistance is related to the speed of movement.
[0040] like Figure 3 As shown in the figure, when the net bag throws the stone into the water and sinks, the net bag throws the stone in the vertical direction (y direction) and is subjected to gravity G and buoyancy F 浮 and the vertical flow resistance F Dy Among them, gravity, buoyancy and water flow resistance can be calculated using the following formulas:
[0041] G=ρ s Vg (1)
[0042] F 浮 =ρ w Vg (2)
[0043]
[0044] Where G is the weight of the net bag throwing stones; ρ s is the density of the net bag riprap; V is the volume of the net bag riprap; g is the acceleration of gravity; F 浮 is the buoyancy of the net bag throwing stones; ρ w is the density of water; F Dy C is the water flow resistance of the net bag riprap in the vertical direction; Dis the drag coefficient. The drag force refers to the resistance of water. The drag coefficient is a priori constant parameter, which is common in hydraulics and fluid mechanics. For a relatively uniform spherical net bag riprap, it can be taken as 1; A y is the surface area of the net bag riprap along the y direction. If the net bag riprap is assumed to be a sphere with a radius of r, then A y =πr 2 ;u y It is the sinking speed of the net bag throwing stones in the plumb direction.
[0045] In the present invention, the motion equation of the net bag during the process of throwing stones into the water is as follows:
[0046]
[0047] In the formula, ρ s is the density of the riprap; V is the volume of the riprap; d is the differential symbol; u y is the sinking speed of the net bag riprap in the vertical direction; t is the time after the net bag riprap falls into the water; G is the gravity of the net bag riprap; F 浮 F is the buoyancy of the net bag throwing stones; Dy It is the water flow resistance that the net bag throw stones encounter in the vertical direction.
[0048] Substituting the formulas of gravity, buoyancy and water flow resistance in formulas (1)-(3) into formula (4), the motion equation of the net bag throwing stones into the water is obtained as shown in formula (5):
[0049]
[0050] In the formula, ρ s is the density of the net bag riprap; V is the volume of the net bag riprap; d is the differential, u y is the sinking speed of the net bag riprap in the vertical direction; t is the time after the net bag riprap falls into the water, assuming that the time of entering the water is t0 = 0; ρ w is the density of water; g is the acceleration due to gravity; C D is the drag force coefficient; Ay is the flow-facing surface area of the net bag riprap along the y direction.
[0051] Solving the equation of motion, formula (5), we can obtain the flow velocity expression in the y direction after the net bag throws the stone into the water, as shown in formula (6):
[0052]
[0053] In the formula, u y is the sinking speed of the net bag riprap in the vertical direction; ρ s is the density of the riprap in the net bag; ρ w is the density of water; g is the acceleration due to gravity; V is the volume of the net bag riprap; C Dis the drag force coefficient; Ay is the surface area of the net bag throwing stones along the y direction; t is the time after the net bag throwing stones fall into the water.
[0054] C1 is a constant, assuming that the net bag throws the stone from Figure 2 If the ball is thrown from the height H0 above the water surface as shown, the speed when it enters the water is For example, when the water is at time t0 = 0, the initial boundary condition Substituting the flow velocity expression of the net bag riprap into the water in the y direction, the expression of the constant C1 is obtained as shown in formula (7):
[0055]
[0056] The flow velocity expression of the net bag riprap in the y direction after entering the water, that is, formula (6), is integrated along time t to obtain the falling depth y(t) of the net bag riprap in the y direction as shown in formula (8):
[0057]
[0058] From the falling depth expression, it can be seen that the falling depth y(t) is a function of time t, where y(t) is the falling depth of the net bag riprap in the y direction; ρs is the density of the net bag riprap; ρ w is the density of water; g is the acceleration due to gravity; V is the volume of the net bag riprap; C D is the drag force coefficient; Ay is the area of the upstream surface of the net bag stone along the y direction; t is the time after the net bag stone falls into the water; C1 is a constant, when H0 is equal to 0, C1 is equal to 0.
[0059] When falling to the bottom of the riverbed 4, y(t)=H.
[0060] In formula (8), when y(t) is equal to the water depth H, based on the known water depth H, formula (8) can be used to calculate the time t when the net bag throws the stone to the riverbed at 4 o'clock; the water depth H is the actual measured value on site.
[0061] In order to derive the functional relationship between the horizontal displacement and time during the process of throwing stones from the net bag into the water, the motion equation in the horizontal direction is established as shown in formula (9):
[0062]
[0063] In the formula, ρ s is the density of the riprap; V is the volume of the riprap; d is the differential; u x is the horizontal speed of the net bag after the stone enters the water, which is a function of time t; C D is the drag coefficient; A x is the horizontal flow area of the net bag riprap. If the net bag riprap is assumed to be a sphere with a radius of r, then Ax = πr2 ; U w It is the depth-average flow velocity of water. The flow velocity of water at different water depths (y coordinates) is different. The depth-average (also called vertical average) flow velocity is generally used in hydraulics and fluid mechanics. A velocimeter is used on-site to measure the flow velocity at different water depths, and then the weighted average is taken to obtain the Uw value.
[0064] Solve the horizontal motion equation (9) and substitute the boundary conditions t0=0, u x0 =0, the boundary condition refers to t=0, u in formula (9) x = 0, and the horizontal flow velocity u of the net bag riprap is obtained x The relationship between (t) and time is shown in formula (10):
[0065]
[0066] The relationship between the velocity and time of the net bag riprap in the horizontal direction is integrated along the time t on both sides, and the relationship between the horizontal drift distance x(t) and the time t after the net bag riprap enters the water is obtained as shown in formula (11):
[0067]
[0068] Where Uw is the average velocity of the water depth; t is the time after the net bag throws the stone into the water; ρ s is the density of the riprap in the net bag; V is the volume of the riprap in the net bag; ρ w is the density of water; C D is the drag coefficient; A x is the horizontal frontal area of the net bag riprap; Figure 2 In the figure, trace 5 is the running track of the net bag riprap in the water. When the net bag riprap sinks to the riverbed 4, the horizontal displacement x(t) of the net bag riprap is the drift distance.
[0069] In formula (8), when y(t) is equal to the water depth H, the time t when the net bag throws the stone into the riverbed can be calculated according to the known water depth H; the time t from the net bag throwing the stone into the water to the time it sinks into the riverbed is substituted into the horizontal drift distance and time formula (11), and the drift distance x(t) after the net bag throws the stone into the water can be calculated. According to the calculated drift distance x(t) and the measured water flow direction, the position of each throwing area is moved in the opposite direction of the flow direction by the corresponding drift distance x(t) as the throwing point.
[0070] The drift distance of the net bag throwing stone is related to the water depth. The farther from the shore, the greater the drift distance. In practical applications, the river throwing area needs to be divided into multiple sub-areas according to the distance from the shore, and the drift distance of each sub-area is calculated separately. Figure 4As shown in the figure, the water level during the construction period is 7m. According to the measured topography, the net bag riprap area of the bank protection project can be divided into four riprap areas with different average water depths along the direction from the nearshore to the river channel. The water depths of the four different riprap areas are 10m, 17m, 24m, and 29m from the nearshore side 6 to the far side.
[0071] The average velocity of the measured water depth in the throwing area is Ux = 3m / s. The volume of the net bag throwing stones is V = 3m 3 , its shape is considered as a sphere, then
[0072] The density of riprap is ρ s =1900kg / m 3 The density of water is ρ w =1000kg / m 3 According to relevant experimental research, the drag coefficient C of the water flow on the net bag riprap D =1.0. When the caisson method is used for casting, the height of the net bag throwing stones into the water is H0=0, and the corresponding C1=0. Substituting the above parameters into the functional relationship between the horizontal displacement of the net bag throwing stones and time, the time required for the net bag throwing stones to sink to the bottom of the river after entering the water can be obtained through trial calculation. The trial calculation results show that the time of each throwing area is t1=6.94s, t2=5.86s, t3=4.35s, and t4=2.84s. Further, substituting the time obtained by trial calculation into the functional relationship between the horizontal drift distance and time after the net bag throwing stones enter the water, the drift distances of each throwing area are x(t)1=13.02m, x(t)2=10.40m, x(t)3=6.91m, and x(t)4=3.73m. According to the drift distances calculated above and the measured water flow direction, the position of each throwing area is moved by the corresponding drift distance in the opposite direction of the flow direction, and the following is obtained: Figure 4 The figure shows the range of the net bag for each throwing area after considering the drift distance. For the hanging throwing construction method, the net bag's entry height into the water is generally not 0. Assuming the entry height H0 = 1m, taking throwing area 1 as an example, the drift distance x(t)1 = 11.91m can be calculated.
[0073] Through this embodiment, it can be found that when the water depth is deep and the water flow speed is high, the drift distance of the net bag riprap can reach more than 10m, which has a very obvious impact on the construction accuracy. Therefore, the influence of the drift distance must be considered in the net bag riprap construction process. Compared with the caisson construction method, when the hanging throwing construction method is adopted, since the net bag riprap starting point is a certain distance from the water surface, it takes a shorter time for the net bag riprap to sink to the bottom of the riverbed after falling into the water, so the calculated drift distance is smaller.
[0074] Finally, it should be noted that the contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field. The above description is only the preferred embodiment of the present invention and is not used to limit the present invention. Although the present invention is described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions recorded in the aforementioned embodiments, or to replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.
Claims
1. A method for calculating the drift distance of net bag riprap in underwater foot protection construction, characterized in that: The method comprises: Establishing a motion equation in the vertical direction after the net bag throws the stone into the water, and obtaining a functional relationship between the vertical displacement y(t) and time t after the net bag throws the stone into the water through the motion equation in the vertical direction; When the net bag riprap sinks to the riverbed, the vertical displacement y(t) of the net bag riprap is equal to the water depth H; After obtaining the water depth H value, the time t from the net bag riprap entering the water to sinking to the riverbed is calculated based on the functional relationship between the vertical displacement of the net bag riprap after falling into the water and time; Establishing a motion equation in the horizontal direction after the net bag throws the stone into the water, and obtaining a functional relationship between the horizontal displacement x(t) and time t after the net bag throws the stone into the water through the motion equation in the horizontal direction; The drift distance of the net bag throwing stones is calculated by the time t from the net bag throwing stones entering the water to sinking to the riverbed, as well as the functional relationship between the horizontal displacement of the net bag throwing stones after falling into the water and time.
2. The method for calculating the drift distance of net bag riprap in underwater foot protection construction according to claim 1 is characterized in that: The motion equation of the net bag after the stone falls into the water in the vertical direction is as follows: In the formula, ρ s is the density of the net bag riprap; V is the volume of the net bag riprap; d is the differential, u y is the sinking speed of the net bag riprap in the vertical direction; t is the time after the net bag riprap falls into the water, assuming that the time of entering the water is t0 = 0; ρ w is the density of water; g is the acceleration due to gravity; C D is the drag force coefficient; Ay is the flow-facing surface area of the net bag riprap along the y direction.
3. The method for calculating the drift distance of net bag riprap in underwater foot protection construction according to claim 2 is characterized in that: By solving the formula (5), the general solution of the flow velocity expression in the y direction after the net bag throws the stone into the water is obtained as formula (6): In the formula, u y is the sinking speed of the net bag riprap in the vertical direction; ρ s is the density of the riprap in the net bag; ρ w is the density of water; g is the acceleration due to gravity; V is the volume of the net bag riprap; C D is the drag coefficient; Ay is the surface area of the net bag riprap along the y direction; t is the time after the net bag riprap falls into the water; C1 is a constant; By integrating formula (6) along time t, the functional relationship between the displacement y(t) of the net bag riprap in the y direction and time t is obtained as shown in formula (8): Where y(t) is the falling depth of the net bag riprap in the y direction; ρs is the density of the net bag riprap; ρ w is the density of water; g is the acceleration due to gravity; V is the volume of the net bag riprap; C D is the drag coefficient; Ay is the surface area of the net bag riprap along the y direction; t is the time after the net bag riprap falls into the water; C1 is a constant, when H0 is equal to 0, C1 is equal to 0; in formula (8), when y(t) is equal to the water depth H, according to the known water depth H, the time t when the net bag riprap falls to the riverbed can be calculated by formula (8).
4. The method for calculating the drift distance of net bag riprap in underwater foot protection construction according to claim 1 is characterized in that: The motion equation of the net bag after the stone falls into the water in the horizontal direction is as follows: Solve the horizontal motion equation (9) and substitute the boundary conditions t0=0, u x0 = 0, and the horizontal flow velocity u of the net bag riprap is obtained x The relationship between (t) and time is shown in formula (10): In the formula, ρ s is the density of the riprap; V is the volume of the riprap; d is the differential; u x is the horizontal speed of the net bag after the stone enters the water, which is a function of time t; C D is the drag coefficient; A x is the horizontal flow area of the net bag riprap; U w It is the depth-average velocity of the water flow.
5. The method for calculating the drift distance of net bag riprap in underwater foot protection construction according to claim 1 is characterized in that: The calculation method of the net bag riprap drift distance x(t) is: integrate both sides of formula (10) along time t, and obtain the relationship between the horizontal drift distance x(t) and time t after the net bag riprap enters the water as shown in formula (11): Where U w is the average velocity of the water depth; t is the time after the net bag throws the stone into the water; ρ s is the density of the riprap in the net bag; V is the volume of the riprap in the net bag; ρ w is the density of water; C D is the drag coefficient; Ax is the horizontal flow area of the net bag riprap; In formula (8), when y(t) is equal to the water depth H, the time t when the net bag throws the stone into the water can be calculated according to the known water depth H. Substitute the time t from the net bag throwing the stone into the water to the time it sinks into the riverbed into the horizontal drift distance and time formula (11) to calculate the drift distance after the net bag throws the stone into the water.