Experimental Study of Roughness Reduction of Large Aqueducts in the Middle Route of the South-to-North Water Diversion Project

Abstract

The roughness of the aqueduct in the Middle Route of the South-to-North Water Diversion Project has increased due to factors such as the natural aging of concrete and biological attachment. To increase the flow capacity of the project, a roughness reduction test was carried out in April 2021 by installing a nano-rubber coating on the Fangshui River aqueduct, which consists of three aqueduct bodies arranged in parallel. Before and after the test, as well as two years after the test, three field observations were conducted. The analysis revealed that compared to aqueduct body 2, which was only cleaned of surface attachments, after excluding the difference in the background roughness, the nano-rubber coating reduced the roughness of aqueduct body 1 by 0.0013 (10.00%). After two years of operation, the roughness was 0.0010 (7.41%) lower, indicating that the nano-rubber coating had a good and lasting effect on the roughness reduction. The roughness field observation results are sensitive to flow rate and water level measurement errors. For aqueducts with a low head and a high flow rate similar to those of the Fangshui River aqueduct, non-contact measuring instruments should be preferentially utilized, and sufficiently accurate flow rate measurements should be ensured to improve the accuracy of the roughness calculation.

1. Introduction

The Middle Route of the South-to-North Water Diversion Project is the largest inter-basin water transfer project in the world, with a total length of 1432 km. It primarily uses open channel flow for water conveyance and started full operation in December 2014. As of the end of March 2023, the cumulative water transfer to northern China had exceeded 55 billion m³, benefiting over 85 million people directly and resulting in significant social, economic, and ecological benefits [1]. Roughness is a comprehensive coefficient that measures the influences of the flow surface coarseness degree and flow cross-section variation of water conveyance structures on flow resistance. It is one of the key technical parameters for the design and operation of water conveyance systems [2,3]. The Middle Route of the South-to-North Water Diversion Project includes 27 large aqueducts. After years of operation, these aqueducts have been affected by adverse factors such as freeze–thaw cycles, concrete carbonation, and sedimentation. As a result, concrete spalling and algal and freshwater mussel attachment have occurred on the aqueduct surfaces, leading to an increase in surface roughness, reducing the flow capacity of the project [4], and posing a threat to water supply safety. Therefore, it is necessary to conduct research on roughness reduction.

Motion resistance is an essential fluid characteristic, and its mechanism analysis, simulation, and regulation are widely studied [5,6,7,8,9,10,11]. The method of coating the flow surface with drag-reduction materials to reduce the roughness and enhance protective capabilities was first applied to long-distance oil and gas pipelines, such as the Zeepipe pipeline in Norway [12] and the Alliance pipeline between Canada and the United States [13], both of which were internally coated with epoxy resin. In the field of hydraulic engineering, materials such as polyurethane (PU) and polyvinyl chloride (PVC) have been widely used in aqueduct and channel renovation projects due to their excellent anti-seepage and roughness-reduction properties [14,15,16]. In recent years, a new type of nano-modified, inorganic, water-based, permeable, crystalline material called nano-rubber has been used in the field of drag reduction materials [17] to enhance the strength and smoothness of concrete surfaces, suppress the growth of bacteria and algae, and improve the flow capacity. Compared to traditional materials such as PU and PVC, nano-rubber has the advantages of a simple construction process, short construction period, and strong resistance to detachment and erosion, and it has been applied in projects such as the No. 9 Water Plant Water Transfer Tunnel in Beijing [18], the water conservancy hub project in Guangxi [19], and the Xiangyang Sluice in the Chaobai River in Beijing [20]. In April 2021, a test of the roughness reduction ability of nano-rubber coating was conducted on the Fangshui River aqueduct as a pilot test in the South-to-North Water Diversion Project.

Roughness is a hydraulic parameter that cannot be directly measured and can only be indirectly estimated [21,22,23]. The Middle Route of the South-to-North Water Diversion Project is a typical low-head, high-flow water transfer project. The aqueduct has a distributed head of only about 0.2 m, and hence, the estimation of its roughness requires a high measurement accuracy [24,25,26]. Taking the Fangshui River aqueduct as the research object, three field observations were conducted to evaluate the effectiveness and durability of the nano-rubber coating in reducing roughness. This study aimed to provide a reference for selecting appropriate drag-reduction materials for the Middle Route of the South-to-North Water Diversion Project and gain experience from the field observations of the roughness, which can be applied to similar water transfer projects with high-flow, low-head aqueducts.

2. Materials and Methods

2.1. Overview of the Fangshui River Aqueduct

The Fangshui River aqueduct is located in the Tang County section (Baoding City, Hebei Province) of the South-to-North Water Diversion Project. The inverted-siphon check gate of the Tang River is located 25.7 km upstream, and the inverted-siphon check gate of the Puyang River is located 13.2 km downstream. The structure of the Fangshui River aqueduct is shown in Figure 1, including the three aqueduct bodies arranged symmetrically and in parallel. The aqueduct has a designed maximum flow rate of 160 m³/s, which corresponds to a distributed head of 0.16 m. The inlet section consists of a 40 m long transition section and a 20 m long check gate chamber section, with a maximum operating water level of 69.99 m before the gate. The outlet section consists of a 10 m long maintenance gate chamber section and a 40 m long outlet transition section, with a maximum operating water level of 69.83 m before the gate. The aqueduct body section is 240 m long and has a rectangular cross-section and dimensions of 7 m × 5.2 m. During normal operation, the check gate is involved in adjusting the water level and flow rate in the aqueduct, while the maintenance gate is in standby mode with the gate fully open.

2.2. Application of Drag-Reduction Coating

Nano-rubber is a type of nano-modified, inorganic, water-based, permeable, crystalline material. It is a colorless, odorless, completely transparent aqueous solution with a viscosity of less than 15 mPa·s. The size of the nano silica gel particles contained in it mainly ranges from 3 to 50 nm [16]. This material reacts with the calcium hydroxide in concrete to generate calcium silicate hydrate (C-S-H) gel [27], which fills the gaps in the concrete and forms a dense layer, thereby enhancing the surface strength of the concrete, protecting the alkaline environment of the concrete, and inhibiting the intrusion of deteriorating factors such as water, salt, acids, alkalis, carbon dioxide, and microorganisms. Therefore, from a mechanistic perspective, the nano-rubber has the functions of repairing the microstructure of the concrete surface and reducing the roughness of the flow surface.

To verify the drag reduction performance of the nano-rubber, a roughness reduction test was conducted in April 2021 using the Fangshui River aqueduct as a pilot project [28]. To facilitate comparison with the roughness reduction effect of the nano-rubber coating, aqueduct body 1 was cleaned of surface attachments (including those on the sidewalls and floor slabs) and then coated with nano-rubber, aqueduct body 2 was only cleaned of surface attachments, and aqueduct body 3 was left in its original state. Figure 2 shows the process of cleaning the attachments from the aqueduct surface and coating it with nano-rubber.

2.3. Calculation of Roughness and Error Analysis

During steady water transfer, the flow in the aqueduct can be considered to be a constant, non-uniform, open channel flow. The energy conservation equation is applied to the upstream measurement cross-section (denoted by subscript 1) and the downstream measurement cross-section (denoted by subscript 2) in Figure 1.

$$z_1+{\alpha }_1\frac{v_1^2}{2g}=z_2+{\alpha }_2\frac{v_2^2}{2g}+h_{\mathrm{f}}+h_{\mathrm{j}}$$

(1)

where z is the water level of the cross-section; v is the average flow velocity of the cross-section; α is the kinetic energy correction factor; h_f is the frictional head loss between the upstream and downstream measurement cross-sections; and h_j is the local head loss. The cross-section of the aqueduct is regular and smooth, so h_j can be ignored, and α is taken as 1. h_f is calculated as follows:

$$h_{\mathrm{f}}=\frac{Q^2{n}^2}{{(\overline{A}{\overline{R}}^{2/3})}^2}L$$

(2)

where Q is the flow rate, n is the roughness and L is the distance between cross-sections 1 and 2, and $\overline{A}{\overline{R}}^{\frac{2}{3}}=\frac{A_1{R}_1{}^{\frac{2}{3}}+A_2{R}_2{}^{\frac{2}{3}}}{2}$, in which A is the cross-sectional area, and R is the hydraulic radius.

Substituting Equation (2) into Equation (1) yields:

$$n=\frac{\overline{A}{\overline{R}}^{\frac{2}{3}}}{Q}\sqrt{s_0+\frac{y_1-y_2}{L}+(\frac{1}{A_1{}^2}-\frac{1}{A_2{}^2})\frac{Q^2}{2gL}}$$

(3)

where y is the water depth of the cross-section and s₀ is the bed slope.

The absolute error of the calculated roughness can be expressed as follows:

$$\mathrm{\Delta }n=\sqrt{{\left(\frac{\partial n}{\partial Q}\mathrm{\Delta }Q\right)}^2+{\left(\frac{\partial n}{\partial y_1}\mathrm{\Delta }{y}_1\right)}^2+{\left(\frac{\partial n}{\partial y_2}\mathrm{\Delta }{y}_2\right)}^2+{\left(\frac{\partial n}{\partial s_0}\mathrm{\Delta }{s}_0\right)}^2+{\left(\frac{\partial n}{\partial L}\mathrm{\Delta }L\right)}^2}$$

(4)

The partial derivatives are calculated as follows:

$$\frac{\partial n}{\partial Q}=-\frac{n}{Q}+\frac{1}{2gLQn}{\left(\overline{A}{\overline{R}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^2\left(\frac{1}{A_1^2}-\frac{1}{A_2^2}\right)$$

(5)

$$\frac{\partial n}{\partial y_1}=\frac{n{R}_1^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{6\overline{A}{\overline{R}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\left(5B_1-4R_1\right)+\frac{1}{2Q^{2}Ln}{\left(\overline{A}{\overline{R}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^2\left(1-\frac{Q^2{B}_1}{g{A}_1^3}\right)$$

(6)

$$\frac{\partial n}{\partial y_2}=\frac{n{R}_2^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{6\overline{A}{\overline{R}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}\left(5B_2-4R_2\right)+\frac{1}{2Q^{2}Ln}{\left(\overline{A}{\overline{R}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^2\left(1-\frac{Q^2{B}_2}{g{A}_2^3}\right)$$

(7)

$$\frac{\partial n}{\partial s_0}=\frac{{\left(\overline{A}{\overline{R}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^2}{2Q^{2}n}$$

(8)

$$\frac{\partial n}{\partial L}=\frac{{\left(\overline{A}{\overline{R}}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^2}{2Q^{2}n{L}^2}\left(y_1-y_2\right)$$

(9)

where B is the width of the cross-section, and the other variables are the same as in the previous equations.

2.4. Field Observation Schemes

2.4.1. Field Observation in 2021

• Scheduling scheme

(1) Before the test, the upstream Tang River inverted-siphon check gate and the downstream Puyang River inverted-siphon check gate were adjusted to maintain a stable water level and flow rate in the Fangshui River aqueduct. At this time, the aqueduct had a water depth of about 3.5 m and a flow rate of about 105 m³/s.

(2) The check gate of aqueduct body 2 was closed, and the check gates of aqueduct bodies 1 and 3 were fully open. After the flow stabilized, the water levels and flow rates of the upstream and downstream measurement cross-sections of aqueduct body 1 were measured and recorded as Condition #1_2021_Before.

(3) The check gate of aqueduct body 1 was closed, and the check gates of aqueduct bodies 2 and 3 were fully open. After the flow stabilized, the water levels and flow rates of the upstream and downstream measurement cross-sections of aqueduct body 2 were measured and recorded as Condition #2_2021_Before. Aqueduct body 1 was cleaned of surface attachments and coated with nano-rubber.

(4) The check gate of aqueduct body 2 was closed, and the check gates of aqueduct bodies 1 and 3 were fully open. After the flow stabilized, the water levels and flow rates of the upstream and downstream measurement cross-sections of aqueduct body 1 were measured and recorded as Condition #1_2021_After. Aqueduct body 2 was cleaned of surface attachments.

(5) The check gate of aqueduct body 1 was closed, and the check gates of aqueduct bodies 2 and 3 were fully open. After the flow stabilized, the water levels and flow rates of the upstream and downstream measurement cross-sections of aqueduct body 2 were measured and recorded as Condition #2_2021_After.

(6) After the completion of all of the measurements, the upstream and downstream check gates were adjusted to restore the channel to its normal operating state.

2.

Observation scheme

(1) Observation instruments. The instruments used in 2021 included a radar water level gauge, electromagnetic flowmeter, electronic level, and electronic rangefinder (

Table 1. Observation instruments and performance parameters.

No.	Type	Model or Specification	Main Performance Indicators	Measurements	Year of Observation
1	Radar water level gauge	HZ-RLS-26L-50	Range: 0.25–15 m; Range hole: 0.25 m; Range accuracy: ±2 mm	Water level	2021/2023
2	ADCP	SonTek RiverSurveyor	Velocity measurement range: ±10 m/s; Resolution: 0.001 m/s; Accuracy: ±1%	Discharge	2023
3	Remotely controlled, unmanned ship system	Nortek USV	Scope of application: rivers or channels with a velocity of 0–5 m/s	/	2023
4	Electronic level	Leica SPRINTER 100/100M	Elevation measurement accuracy: 2.0 mm; Distance measurement accuracy: standard deviation = 1‰ of the measured value; Distance measurement range: 2–80 m	Elevation	2021/2023
5	Rangefinder	Leica D5	Measuring range: 0.05–200 m; Measuring accuracy: ±1.0 mm	Distance	2021/2023
6	Electromagnetic flowmeter	ACM2-RS	Measuring range: ±2.50 m/s; Measuring accuracy: ±0.005 m/s or ±2% (0–±1 m/s); Resolution: 0.001 m/s;	Flow velocity	2021

).

(2) Arrangement of measurement points. According to Equation (3), estimating the roughness requires measuring several quantities, including the distance between the upstream and downstream measurement cross-sections, the dimensions of the aqueduct at these cross-sections, the floor elevation, the water depth, and the flow rate. The inlet of the Fangshui River aqueduct is a 40 m long transition section, where the flow gradually narrows and converges to produce a zigzag flow that causes fluctuations in the flow at the inlet section of the aqueduct. The magnitude of these fluctuations increases as the flow increases. Therefore, the upstream and downstream measurement cross-sections were arranged at locations far from the turbulent flow, where the flow was relatively smooth. Specifically, they were located approximately 7 m downstream of the check gate and 3 m upstream of the maintenance gate.

(3) Water level measurement. The installation of the radar water level gauge is shown in Figure 3a, and its horizontal alignment was calibrated using the built-in level. The reference zero point was determined using a level gauge from the secondary reference point measurement of the South-to-North Water Diversion Project. The radar water level gauge was powered by a 12 V direct current (DC) power supply, and the measurement data were recorded using its built-in software. The water level was measured at a frequency of 0.5 Hz, with a sampling time of approximately 900 s. The instrument performance and measurement scheme met the requirements of the Specifications for Water Measurement of Irrigation Canal System (GBT 21303-2017) [29].

(4) Flow rate measurement. The flow velocity distribution at the cross-section was measured using an electromagnetic flowmeter, and the flow rate of the aqueduct was calculated using the velocity-area method. The area of the cross-section was measured before the nano-rubber coating was applied. During the velocity measurement, it was difficult to fix the measuring rod due to the large torque exerted on it by the flow impact (Figure 3b). The actual distribution of the velocity measurement points is shown in Figure 4a. The flow in the aqueduct was simulated using the FLOW-3D software to obtain the velocity distribution at the cross-section (Figure 4b). Based on comparison with the distribution of the velocity measurement points, the formula for calculating the average velocity $\overline{V}$ at the cross-section can be obtained:

$$\overline{V}=\frac{3{\overline{V}}_1+2{\overline{V}}_2+{\overline{V}}_3+{\overline{V}}_4+2{\overline{V}}_5+3{\overline{V}}_6}{12}$$

(10)

where ${\overline{V}}_i$ is the average velocity of the ith vertical line.

2.4.2. Field Observation in 2023

1.

Scheduling scheme

(1) Before the test, the upstream Tang River inverted-siphon check gate and the downstream Puyang River inverted-siphon check gate were adjusted to maintain a stable water level and flow rate in the Fangshui River aqueduct. At this time, the aqueduct had a water depth of about 4.0 m and a flow rate of about 87 m³/s.

(2) The check gate of aqueduct body 2 was closed, and the check gates of aqueduct bodies 1 and 3 were fully open. After the flow stabilized, the water levels and flow rates at the upstream and downstream measurement cross-sections of aqueduct body 1 were measured and recorded as Condition #1_2023_After.

(3) The check gate of aqueduct body 2 was fully open, and the check gates of aqueduct bodies 1 and 3 were partially closed symmetrically so that the flow rate in aqueduct body 2 approached its designed maximum water transfer capacity. After the flow stabilized, the water levels and flow rates at the upstream and downstream measurement cross-sections of aqueduct body 2 were measured and recorded as Condition #2_2023_After.

(4) After the completion of all of the measurements, the upstream and downstream check gates were adjusted to restore the channel to its normal operating state.

2.

Observation scheme

The measurement point layout, instruments, and scheme for the water level measurements were the same as those used in 2021. The flow rate measurements were carried out using a measurement system consisting of an acoustic Doppler current profiler (ADCP) and a remotely controlled, unmanned vessel (Table 1). In addition, the total flow in the aqueduct was measured by setting up a flow rate measurement point downstream of the aqueduct in a section with a smooth flow, which was located approximately 100 m from the outlet of the aqueduct.

Referring to the ADCP flow rate measurement specifications in the Code for Discharge Measurement of Acoustic Doppler Current (SL337-2006) [30], four to seven rounds of measurements were conducted at each cross-section (Figure 5), with a sampling time of 40–160 s. The measurement data were recorded using the built-in software for the instrument. The arithmetic mean of the measured flow rates and the deviation of the return flow rate in each half round from the mean were calculated. The measurements were repeated if the deviation was greater than 5%. The analysis showed that the deviation of the return flow rate from the mean during each half round was within 2%, which is stricter than the requirement of the ADCP flow rate measurement specifications.

3. Field Observation Results

3.1. Results and Errors for 2021

Due to space limitations, only part of the measurement results before the cleaning of the surface adherents are presented here. The velocity history of each measurement point on vertical line 1 at the downstream measurement cross-section of aqueduct body 2 is shown in Figure 6a, and the water level histories at the upstream and downstream measurement cross-sections for aqueduct bodies 1 and 2 are shown in Figure 6b.

For 2021, the water depths, average flow velocities, flow rates, and calculated roughness values for the upstream and downstream measurement cross-sections before and after the cleaning of the surface attachments (i.e., coating with nano-rubber) on aqueduct bodies 1 and 2 are presented in

Table 2. Field observation results for the Fangshui River aqueduct in 2021.

Working Condition	Aqueduct Body	Water Depth at the Upstream Measurement Cross-Section (m)	Water Depth at the Downstream Measurement Cross-Section (m)	Cross-Sectional Average Flow Velocity (m/s)	Flow Rate (m3/s)	Roughness
#1_2021_Before	#1	3.519	3.470	2.217	53.216	0.0130
#1_2021_After	#1	3.462	3.441	2.305	54.859	0.0105
#2_2021_Before	#2	3.476	3.438	2.079	49.530	0.0132
#2_2021_After	#2	3.468	3.443	2.110	50.342	0.0120

. Before the cleaning, aqueduct body 1 had a roughness of 0.0130, which decreased to 0.0105 (a decrease of 19.23%) after cleaning and coating with nano-rubber. Before and after the cleaning, the roughness of aqueduct body 2 was 0.0132 and 0.0120 (a decrease of 9.09%), respectively.

Based on the measurement accuracies of the various measuring instruments (Table 1), as well as the measurement results of the hydraulic parameters and structural parameters of each cross-section, the absolute error and relative error of the calculated roughness were obtained. Under four measurement conditions in 2021, the calculated roughness had an absolute error of 0.00043–0.00051 and a relative error of 3.33–4.57%.

3.2. Results and Errors for 2023

The measurement results of the flow rate in the aqueduct are presented in

Table 3. Field observation results of flow rate measurements in 2023 (m³/s).

Working Condition	Aqueduct Body #1	Aqueduct Body #2	Aqueduct Body #3	Aqueduct Outlet
#1_2023_After	45.431	0.000	42.748	87.794
#2_2023_After	10.907	/	10.376	86.933

. The water level histories for the upstream and downstream measurement cross-sections are shown in Figure 7. During the measurement of the flow rate in aqueduct body 2 under Condition #2_2023_After, it was difficult to enter the aqueduct due to the unmanned vessel’s inability to reach the rated speed. Instead, the flow rates in aqueduct bodies 1 and 3 and the total flow rate at the aqueduct’s outlet were measured. The flow rate in aqueduct body 2 was then calculated based on flow conservation, resulting in a value of 65.650 m³/s. To verify the accuracy of this method, during the measurement of the flow rate in aqueduct body 1 under Condition #1_2023_After, the sum of the flow rates of all of the aqueduct bodies and the flow rate at the aqueduct’s outlet were calculated. The difference between the two values was only 0.385 m³/s, which corresponds to a closure error of 0.44%.

The water depths, average flow velocities, flow rates, and calculated roughness values at the upstream and downstream measurement cross-sections in aqueduct bodies 1 and 2 in 2023 are presented in

Table 4. Field observation results for the Fangshui River aqueduct in 2023.

Working Condition	Aqueduct Body	Water Depth at the Upstream Measurement Cross-Section (m)	Water Depth at the Downstream Measurement Cross-Section (m)	Cross-Sectional Average Flow Velocity (m/s)	Flow Rate (m3/s)	Roughness
#1_2023_After	#1	4.015	4.012	1.631	45.431	0.0135
#2_2023_After	#2	4.202	4.135	2.269	65.650	0.0147

. The roughness values of aqueducts 1 and 2 were 0.0135 and 0.0147, respectively. The error analysis indicates that the absolute errors of this calculation were 0.00039 and 0.00085, respectively, corresponding to relative errors of 6.28% and 2.64%, respectively.

4. Discussion

4.1. Error Sensitivity Analysis

Taking aqueduct body 1 in 2023 as an example, the curves of the relationships between the calculated roughness value and the measured flow rate, water depth at the upstream measurement cross-section, and spacing between the measurement cross-sections were calculated using Equation (4) and plotted (Figure 8, Figure 9 and Figure 10). It can be seen that they all exhibited linear relationships. With a change of 0.0001 in the roughness, the corresponding changes in the flow rate, water level, and section spacing were 0.327 m³/s, 0.0007 m, and 3.401 m, respectively. Based on the performance evaluation of the commonly used measuring instruments, it was found that the calculation error of the roughness had a high sensitivity to the accuracies of the flow rate and water level measurements and a low sensitivity to the accuracy of the distance measurement. In the three field observations, the water level gauge and rangefinder had a measurement accuracy of 0.001 m, which basically meets the above requirements. For the 2021 observations, the flow rate was measured using the velocity-area method, and the estimated measurement error was 5% (approximately 2.5 m³/s), which is lower than the above requirements. For the 2023 observations, the flow rate was measured using an ADCP, and the estimated measurement accuracy was 1% (approximately 0.5 m³/s), which is close to the above accuracy requirements. Improving the accuracy of the flow rate measurement contributes to enhancing the accuracy of the roughness calculation.

4.2. Comparison of Results from Field Observations

The calculated roughness values for 2021 and 2023 are compared in

Table 5. Comparison of roughness calculation results.

Item	2021		2023	Notes
	Before Reduction	Immediately after Reduction	Two Years after Reduction
Roughness of aqueduct body 1	0.0130	0.0105	0.0135	Cleaning and coating
Roughness of aqueduct body 2	0.0132	0.0120	0.0147	Cleaning
Difference in the roughnesses of aqueduct bodies 1 and 2	0.0002	0.0015	0.0012	Including the difference in background roughness
	0	0.0013	0.0010	Excluding the difference in background roughness

. The analysis shows that the coating with the roughness reduction material in 2021 led to a decrease in the roughness of aqueduct body 1 by 0.0013 (10.00%) after excluding the difference in the background roughness compared to that of aqueduct body 2, demonstrating a good immediate roughness reduction effect. After two years of operation, the roughness was reduced by 0.0010 (7.41%) after excluding the difference in the background roughness. Due to its ability to repair the microstructure of the concrete surface and reduce the attachment of pollutants, the nano-rubber still exhibited a significant roughness reduction effect after two years of operation. Admittedly, its roughness reduction effect decreased slightly compared to that when it was initially applied in 2021.

The reliabilities of the roughness calculation results for 2021 and 2023 were compared. As can be seen from the previous analysis, the roughness calculation error was mostly attributed to the flow rate measurements. In 2021, the traditional velocity-area method was used, which is a contact measurement method. It was difficult to fix the flow rod due to the high flow velocity at the bottom of the aqueduct, so the velocities at some of the measurement points could not be directly obtained and were indirectly estimated using a FLOW-3D numerical model. In 2023, the ADCP was used for the flow rate measurements. This is a non-contact measurement method. The instrument has a high measurement accuracy and a convenient operation scheme, and the measurement results were cross-checked based on the flow conservation principle. As a result, the roughness calculation results for 2023 are more reliable.

5. Conclusions

The Fangshui River aqueduct in the Middle Route of the South-to-North Water Diversion Project is a large aqueduct consisting of three aqueduct bodies positioned in parallel. In April 2021, a roughness reduction test was conducted. Aqueduct body 1 was cleaned of surface attachments and coated with nano-rubber, aqueduct body 2 was only cleaned of surface attachments, and aqueduct body 3 was left in the original state. Field observations were conducted before and after the test and two years into operation to track and evaluate the effect of the roughness reduction. The findings of the study can be summarized in the following four points:

(1) In 2021, aqueduct body 1 had a roughness of 0.0130 before cleaning and 0.0105 after cleaning and application of the nano-rubber coating, demonstrating a reduction of 19.23%. Aqueduct body 2 had a roughness of 0.0132 before cleaning and 0.0120 after cleaning, i.e., a reduction of 9.09%. Compared to that of aqueduct body 2 after cleaning, the roughness of aqueduct body 1 after cleaning and application of the nano-rubber coating, excluding the difference in the background roughness, was 0.0013 lower, corresponding to a reduction of 10.00%, indicating that the nano-rubber had a good immediate effect in reducing the roughness.

(2) In 2023, the roughnesses of aqueduct bodies 1 and 2 were 0.0135 and 0.0147, respectively. After excluding the difference in the background roughness, the roughness of aqueduct body 1 was 0.0010 (7.41%) lower than that of aqueduct body 2, demonstrating that the nano-rubber still has a good effect in reducing the roughness after two years despite a slight decrease in the degree of roughness reduction.

(3) The relative error of the roughness calculation during the three field observations was 2.64–6.28%, indicating that the calculation results are reliable. The calculated roughness was highly sensitive to the errors in the flow rate and water level measurements and was less sensitive to the error in the section spacing measurements. Taking aqueduct body 1 as an example, in order to achieve a roughness calculation accuracy of 0.0001, the measurement errors of the flow rate, water level, and section spacing should be controlled within 3.270 m³/s, 0.007 m, and 3.401 m, respectively. Improving the accuracy of the flow rate measurement contributes more to enhancing the accuracy of the roughness calculation.

(4) For water conveyance projects with a large flow rate and a low head similar to those of the Fangshui River aqueduct, when developing a scheme for field roughness observation, it is advised that working conditions with a high flow velocity be chosen, that the measurement cross-sections be located away from the turbulent zones near check gates and transition sections, and that non-contact instruments with a high precision be preferentially used for the flow rate and water level measurements.

This research contributes to the understanding of roughness reduction in large aqueducts. Continuing follow-up observations and obtaining more test data are work that should be accomplished, which are essential for a more solid assessment.