# Experimental Study on Calculation Method of Drainage Capacity of Drainage Facilities Affected by Overtopping on Artificial Island

Authors: Long-zai Ge; Han-bao Chen; Hai-yuan Liu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The drainage capacity design of offshore artificial island and inland urban drainage facilities have a great differences in the boundary conditions involved. Therefore, in order to ensure the safety and reliability of the drainage facilities of the Shenzhen-Zhongshan channel’s East artificial island under extreme weather conditions, the coastline of the Southwest open section of the artificial island is identified as a subject for carrying out the research study. This island is affected by offshore waves and the superposition of rainstorms, therefore the calculation method of drainage capacity of artificial island drainage facilities is demonstrated in the article. Through the physical model testing based on soft computing techniques, some recommendations are suggested for preserving the environment, where the optimization schemes are meeting the design requirements of wave and landscape based on correlations between them. Secondly, the adjustment of drainage capacity is suggested to analyze the overtopping of waves on the island and then the final scheme meeting the drainage capacity is obtained. By introducing the comprehensive influence coefficientk of overtopping volume and current velocity caused by overtopping under the action of superimposed waves, a new calculation method and simple calculation formula suitable for the drainage capacity in the artificial island are proposed. The proposed method is verified by the drainage capacity test results of the southeast shoreline. The results show that the proposed method has good accuracy and can provide reference for the design and estimation of drainage capacity of similar projects to preserve the environment. The research results based on mathematical problems in engineering not only solve the practical problems of major projects of Shenzhen China channel but also provide valuable inputs for similar projects.


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## Body

## 1. Introduction

The Shenzhen-Zhongshan channel is an important sea traffic project in China after the Hong Kong Zhuhai Macao Bridge project [1]. The project is responsible for constructing an ultra large cross sea bridge, deep-water artificial island, and underwater interworking [2]. In order to carry out the research study on the project by considering environmental aspects, proper collection of records is required and then some innovative methods should be applied to analyze the collected data for decision making. The drainage capacity of an artificial island has unprecedented scale, extremely complex construction conditions, and new comprehensive technical difficulties [3]. The East artificial island, one of the projects adopts the scheme of “one body and two wings.” The island is equipped with the main line tunnel, four ramp tunnels, a rescue wharf, and relevant auxiliary facilities. The length of the island wall structure is about 3178.5 m and the elevation of the land area is 4.9 M. The plane layout of the project is shown in Figure 1.Figure 1
Project layout and test research scope.The East artificial island is located close to Shenzhen with shallow water depth and small wave height but it is affected by short waves (SW) adversely. On the premise of ensuring the structural safety of the island wall of the East artificial island, the SW direction of the least favorable wave is selected from the perspective of ecological sea use, landscape esthetic effect, and economy. The rationality of the elevation of the East artificial island is evaluated through the overall wave model test. The drainage capacity of the open drain behind the embankment is studied thoroughly. Based on the drainage capacity design of the offshore artificial island and inland urban drainage facilities, there are great differences in the boundary conditions involved. Therefore, in order to ensure the safety and reliability of the drainage facilities of the “century project,” the East artificial island of Shenzhen-Zhongshan channel under extreme weather conditions is studied on the basis of data collected in a real time environment. The coastline of the southwest open section of the artificial island most affected by offshore waves is selected [4–8]. The outer side of the island wall is designed by the coexistence of riprap slope, vertical buttress, rescue wharf, and other complex structures. The external seawater depth is high and the incident waves are very large; the drainage capacity of the inner drainage facilities is to be studied due to the influence of overtopping which needs to be paid more attention. The research in this article is focusing on the environmental aspect of the artificial island where the impact of overtopping of sea waves is studied and remedial solutions based on soft computing method for better drainage of water are proposed.It is the first time in China to test and verify the drainage capacity of drainage facilities on the offshore artificial island due to wave crossing superimposed storm rainfall, and there is no mature case abroad for reference. However, for the research on overtopping or drainage capacity of an artificial island, the former has been studied by a large number of scholars while the latter has only individual research results.In [23], the authors have combined the comparison of the results of various means such as normative formula and physical model test. They have obtained the method of reasonable top elevation of artificial island wave retaining wall under multiple influencing factors; according to the structural characteristics of artificial island revetment. In [3], the authors have proposed the calculation method of overtopping considering the slope shoulder reduction coefficient K. They have given a solution against overtopping and measured its performance using evaluation techniques. In [4], the authors have proposed a reasonable elevation determination method for the artificial island of Hong Kong, Zhuhai, and Macao by comparing the standard differences in overtopping volume in domestic and foreign specifications. In [5], the authors have used physical model tests under different wave directions and water levels to obtain the results of wave climbing and overtopping on the top of the artificial island embankment. In [6], the authors have studied the overtopping of a new scheme of sectional design for the elevation of the artificial island of Dalian Maritime airport, and obtained the reasonable elevation and type of the artificial island. A study on the current velocity generated by overtopping is presented by many authors [7–9]. The authors in reference [10] have presented the new calculation formulas of the velocity and water thickness on the top of the overtopping dike under the action of a single wave.In [11], the authors have analyzed the process of breakwater damage caused by overtopping flow through an indoor flume test. In [12], the authors have analyzed and studied the damage of overtopping flow to the back slope through a large-scale model test and analyzed the influence degree and scope of overtopping flow. For the drainage capacity of an artificial island, the authors have proposed the method of combining overall and local tests, combined with the wave overtopping superposition actual rainfall simulation analysis method [13] which can significantly improve the accuracy of simulation. However, in the research results, there is no further demonstration of the calculation method of wave overtopping affecting the drainage capacity of drainage facilities.For the calculation method of drainage capacity of drainage facilities, there are many research results in urban construction. The calculation methods are mainly surface confluence and pipe network runoff. There are often two methods of hydrology and hydraulics in the calculation of surface confluence. Hydrological methods mainly include the reasoning method [14], isochronal method [15], unit hydrograph method [16], and nonlinear reservoir methods. Literature [14] only considers the catchment time which is relatively simple, widely used, and has obvious drawbacks. In [16], the instantaneous unit hydrograph method proposed by Nash is the most widely used but this method needs the measured rainfall-runoff data to determine the parameters before it can be applied to the areas without data. Hydraulic methods mainly include dynamic wave [17, 18], diffusion wave [19, 20], motion wave method [21, 22], as well as improved nonlinear motion wave method and nonlinear regulation method. For the research results using the pipe network runoff method, the more successful calculation methods include the rainstorm management calculation software proposed by the US Environmental Protection Agency in 1978 [23], and the runoff module in the rainstorm software developed by the American Association of engineers [24]. These models can truly simulate the rainfall runoff and the rainwater runoff in the pipeline.In [25], the authors have proposed the research on the calculation method of runoff yield in urban impervious and semi permeable areas. In [26], China’s research in this field started relatively late and the measured data are scarce. In [27, 28], the authors have proposed the intelligent models based on the systematic research on the rainstorm runoff of urban airports. In [29], the authors have developed the urban water logging risk analysis model system (USRAMS) to evaluate the drainage capacity of pipe network and analyze the water logging risk.Summarizing the above calculation methods of drainage capacity of urban rainwater pipe network, and the calculation methods are as follows devised by formulas (1) and (2):(1)Qint=Qa−Qe,(2)Qa=φ∗F∗q,where Qint is the discharge flow at the outlet, m3; Qa is the flow into the drainage outlet within the area F, m3 which can be calculated by formula (2); Qe is the flow not discharged in time, m3; and φ is the runoff coefficient. For asphalt pavement and cement concrete pavement, φ=0.90; F is the designed catchment area, m2 and q is the design intensity of rainstorm, m3/(m.s).Although there are great differences in the design conditions of drainage capacity between offshore artificial islands and inland urban drainage facilities, the calculation of drainage capacity of artificial island drainage facilities is not only related to the land but also different from the land. It is mainly reflected in (1) the same points can be calculated by the collected water area method (2) The artificial island is built in the open waters of the open sea with poor wave cover and nonlinear overtopping where the falling water body over the wave is instantaneously concentrated, and the falling water body has a certain kinetic energy which is easy to lead to floodplain. The distribution of overtopping along the island is uneven and the size design of drainage facilities is uncertain.Therefore, to sum up the research results, based on the coastline of the open section in the southwest of east artificial island, the test is first carried out to determine the wave overtopping volume under different wave retaining wall elevations with extreme wave conditions and then the reasonable elevation of the wave retaining wall from the perspective of landscape esthetic effect is analyzed. Then, based on the above wave overtopping results and superimposing the rainstorm rainfallQ with a return period of 100a, rechecking of the drainage capacity of the design scheme is performed for the drainage facilities on the inner side of the island to verify whether the drainage capacity meets the design requirements or not. Finally, using urban road drainage facilities on land on the basis of the research results, the calculation method of drainage capacity under the influence of rainstorm is introduced with the comprehensive influence coefficient k of overtopping amount and current velocity caused by overtopping under the action of superimposed waves. A new calculation method and simple calculation formula suitable for the drainage capacity of the artificial island are proposed which are verified by the test results of the drainage capacity of shoreline 5#∼8# outfall on the southeast side of the project. The results show that the formula has good accuracy and can provide reference for the design and estimation of drainage capacity of similar projects. At the same time, the research results can not only solve the practical problems of major projects of Shenzhen-Zhongshan channel but also provide valuable basic data and reference for the construction of artificial island in China in the future. However, the newly proposed formula for calculating the drainage capacity of artificial island involves many influencing factors, but it is suggested that it is necessary to carry out the corresponding wave overall physical model test for further inspection and verification for major projects.The next section elaborates on the proposed method.


## 2. Proposed Model

The model is suggested for the preservation of marine life in the ocean-based environment and for the construction of model of the artificial island by keeping multiple factors in the proposed model as mentioned in this section.


### 2.1. Structural Section Type of Revetment and Outfall in Open Section

Four drainage outlets are arranged along the open section and their dimensions along with the plane layout are shown in Figure1. The drainage outlet directly passes through the 5t Accropode armor on the slope of the island wall and is connected with the open sea. Its bottom elevation is located between the designed high water level and extreme high water level to ensure the smooth discharge of water bodies on the island. Figure 2 shows the structural section.Table 1
Test wave elements.
Retum period water levelH1% (m)H5% (m)Hs (m)H (m)T (s)L (m)E.H.W.L 3.61 m (300a)3.502.992.591.757.145.1E.H.W.L 3.34 m (100a)3.262.772.401.626.739.4Figure 2
Plane and section layout of drainage outlet, (a) plane layout of drainage outlet and open drainage ditch in the island, (b) structural section 2-2 of drainage outlet.
(a)(b)


### 2.2. Determination of Test Conditions

(1)
Test water level: Select the extreme return period 100a and 300a water levels (considering sea level rise) which are 3.34 m and 3.61 m, respectively.(2)
Test wave elements: Select the most unfavorable SW wave direction and reproduce 100a and 300a wave elements corresponding to water level as shown in Table1.(3)
Rainstorm rainfall in the island: The test mainly considers the influence of wave crossing on the drainage capacity, so the constant value of rainstorm is considered. It projects that the outfall 1#∼4# is, respectively, 0.47 m³/s, 0.749 m³/s, 0.778 m³/s, and 0.525 m³/s.(4)
Setting of overtopping pump: Drainage capacity is set to 9.33 m³/s.


### 2.3. Test Design and Manufacturing Method

#### 2.3.1. Instruments and Equipment

The test was carried out in the basin of wave and current test hall of Tianjin Research Institute for Water Transport Engineering, M.O.T. The basin is 70.0 m long, 42 m wide, and 1.0 m high. Water supply and drainage system shall be equipped at both ends of the test tank. The bottom is made of smooth concrete and wave absorptions use are porous materials along each basin boundary. The wave is generated by the movable plate irregular wave-making machine with the maximum wave-making depth of 0.6 m, wave height of 0∼0.2 m, and wave period of 0.5∼3.0 s.The wave-making principle is as follows: according to certain parameters corresponding to the waves required for the test, the computer completes the calculation of the wave-making control signal, transmits the wave-making control signal to the servo driver through the interface circuit, the servo driver controls the rotation of the servo motor, and the electric cylinder converts the rotation of the output shaft of the servo motor into the linear movement of the push rod of the electric cylinder. Then the motion is transmitted to the wave pushing plate through the lever mechanism to drive the wave pushing plate to produce the desired water wave.Measuring equipment: in physical model testing, wave sensor and SG2008 type wave height measuring and analyzing systems are used to analyze wave height, wave period, and wave spectrum. The accuracy of wave sensor is ≤ 1 mm. The water level is measured by needle measurement and a camera is used to record the wave surface process and rising waves.


#### 2.3.2. Model Design and Production

The design is carried out in accordance with the technical code for simulation test of Water Transportation Engineering (JTS/T231-2021) [30], and the normal fixed bed is adopted according to the gravity similarity criterion with a scale of 1:40. The model terrain is copied by the pile point method which is 1.0 m × 1.0 m pile points. The artificial island simulation is made by section control method, the open drainage ditch and outlet channel are made of the gray plastic plate and the gravity flow drainage pipe is simulated with PVC pipe. Roughness is an important simulation in this test. The floodplain range of overtopping water body has a great relationship with the roughness value of open drainage ditch. Therefore, the model is roughened. The weight and geometric dimension errors in the manufacturing process meet the requirements of the test regulations. The effect of the model is shown in Figure 3.Figure 3
The effect of the model against overtopping.


### 2.4. Test Method

Wave simulation: irregular wave is adopted, and the wave spectrum is JOP spectrum (γ=3.3). Intermittent wave generation is adopted for wave making to eliminate multiple reflections of waves.


#### 2.4.1. Simulation of Constant Rainfall

The cube overflow water tank is adopted, and four faucet valves are set on the side wall of the water tank. The rainfall of different drainage outlets is simulated by adjusting the opening of different valves and each faucet is connected with the drainage opening through a hose.


#### 2.4.2. Measurement of Water Surface Change in Drainage Ditch

SetP1 ∼ P8 monitoring points along the open ditch (see Figure 4).Figure 4
Division of overtopping measurement area.


#### 2.4.3. Measurement of Overtopping Volume

Due to the special shape of the artificial island, there are overtopping differences in different sections. In order to accurately measure the overtopping volume of each section, a total of 19 sections, K1 ∼ K19 are set from south to north as shown in Figure4. The length of each section is shown in Table 1. For the collection method of overtopping water body in each section, the overtopping volume of each complete wave train is measured through the collecting tank, the water is weighed and converted into volume, and then converted into plasma. Finally, the average overtopping volume per unit length and unit time is obtained. Specifically, it is calculated according to formula (3):(3)Q=VB∗t,where Q is the average overtopping volume per unit width, m3/(m.s); V is the total water volume of overtopping under the action of one wave train, m3; B is the length of water receiving area for collecting overtopping volume, m; and t is the duration of one wave train, s.


## 2.1. Structural Section Type of Revetment and Outfall in Open Section

Four drainage outlets are arranged along the open section and their dimensions along with the plane layout are shown in Figure1. The drainage outlet directly passes through the 5t Accropode armor on the slope of the island wall and is connected with the open sea. Its bottom elevation is located between the designed high water level and extreme high water level to ensure the smooth discharge of water bodies on the island. Figure 2 shows the structural section.Table 1
Test wave elements.
Retum period water levelH1% (m)H5% (m)Hs (m)H (m)T (s)L (m)E.H.W.L 3.61 m (300a)3.502.992.591.757.145.1E.H.W.L 3.34 m (100a)3.262.772.401.626.739.4Figure 2
Plane and section layout of drainage outlet, (a) plane layout of drainage outlet and open drainage ditch in the island, (b) structural section 2-2 of drainage outlet.
(a)(b)


## 2.2. Determination of Test Conditions

(1)
Test water level: Select the extreme return period 100a and 300a water levels (considering sea level rise) which are 3.34 m and 3.61 m, respectively.(2)
Test wave elements: Select the most unfavorable SW wave direction and reproduce 100a and 300a wave elements corresponding to water level as shown in Table1.(3)
Rainstorm rainfall in the island: The test mainly considers the influence of wave crossing on the drainage capacity, so the constant value of rainstorm is considered. It projects that the outfall 1#∼4# is, respectively, 0.47 m³/s, 0.749 m³/s, 0.778 m³/s, and 0.525 m³/s.(4)
Setting of overtopping pump: Drainage capacity is set to 9.33 m³/s.


## 2.3. Test Design and Manufacturing Method

### 2.3.1. Instruments and Equipment

The test was carried out in the basin of wave and current test hall of Tianjin Research Institute for Water Transport Engineering, M.O.T. The basin is 70.0 m long, 42 m wide, and 1.0 m high. Water supply and drainage system shall be equipped at both ends of the test tank. The bottom is made of smooth concrete and wave absorptions use are porous materials along each basin boundary. The wave is generated by the movable plate irregular wave-making machine with the maximum wave-making depth of 0.6 m, wave height of 0∼0.2 m, and wave period of 0.5∼3.0 s.The wave-making principle is as follows: according to certain parameters corresponding to the waves required for the test, the computer completes the calculation of the wave-making control signal, transmits the wave-making control signal to the servo driver through the interface circuit, the servo driver controls the rotation of the servo motor, and the electric cylinder converts the rotation of the output shaft of the servo motor into the linear movement of the push rod of the electric cylinder. Then the motion is transmitted to the wave pushing plate through the lever mechanism to drive the wave pushing plate to produce the desired water wave.Measuring equipment: in physical model testing, wave sensor and SG2008 type wave height measuring and analyzing systems are used to analyze wave height, wave period, and wave spectrum. The accuracy of wave sensor is ≤ 1 mm. The water level is measured by needle measurement and a camera is used to record the wave surface process and rising waves.


### 2.3.2. Model Design and Production

The design is carried out in accordance with the technical code for simulation test of Water Transportation Engineering (JTS/T231-2021) [30], and the normal fixed bed is adopted according to the gravity similarity criterion with a scale of 1:40. The model terrain is copied by the pile point method which is 1.0 m × 1.0 m pile points. The artificial island simulation is made by section control method, the open drainage ditch and outlet channel are made of the gray plastic plate and the gravity flow drainage pipe is simulated with PVC pipe. Roughness is an important simulation in this test. The floodplain range of overtopping water body has a great relationship with the roughness value of open drainage ditch. Therefore, the model is roughened. The weight and geometric dimension errors in the manufacturing process meet the requirements of the test regulations. The effect of the model is shown in Figure 3.Figure 3
The effect of the model against overtopping.


## 2.3.1. Instruments and Equipment

The test was carried out in the basin of wave and current test hall of Tianjin Research Institute for Water Transport Engineering, M.O.T. The basin is 70.0 m long, 42 m wide, and 1.0 m high. Water supply and drainage system shall be equipped at both ends of the test tank. The bottom is made of smooth concrete and wave absorptions use are porous materials along each basin boundary. The wave is generated by the movable plate irregular wave-making machine with the maximum wave-making depth of 0.6 m, wave height of 0∼0.2 m, and wave period of 0.5∼3.0 s.The wave-making principle is as follows: according to certain parameters corresponding to the waves required for the test, the computer completes the calculation of the wave-making control signal, transmits the wave-making control signal to the servo driver through the interface circuit, the servo driver controls the rotation of the servo motor, and the electric cylinder converts the rotation of the output shaft of the servo motor into the linear movement of the push rod of the electric cylinder. Then the motion is transmitted to the wave pushing plate through the lever mechanism to drive the wave pushing plate to produce the desired water wave.Measuring equipment: in physical model testing, wave sensor and SG2008 type wave height measuring and analyzing systems are used to analyze wave height, wave period, and wave spectrum. The accuracy of wave sensor is ≤ 1 mm. The water level is measured by needle measurement and a camera is used to record the wave surface process and rising waves.


## 2.3.2. Model Design and Production

The design is carried out in accordance with the technical code for simulation test of Water Transportation Engineering (JTS/T231-2021) [30], and the normal fixed bed is adopted according to the gravity similarity criterion with a scale of 1:40. The model terrain is copied by the pile point method which is 1.0 m × 1.0 m pile points. The artificial island simulation is made by section control method, the open drainage ditch and outlet channel are made of the gray plastic plate and the gravity flow drainage pipe is simulated with PVC pipe. Roughness is an important simulation in this test. The floodplain range of overtopping water body has a great relationship with the roughness value of open drainage ditch. Therefore, the model is roughened. The weight and geometric dimension errors in the manufacturing process meet the requirements of the test regulations. The effect of the model is shown in Figure 3.Figure 3
The effect of the model against overtopping.


## 2.4. Test Method

Wave simulation: irregular wave is adopted, and the wave spectrum is JOP spectrum (γ=3.3). Intermittent wave generation is adopted for wave making to eliminate multiple reflections of waves.


### 2.4.1. Simulation of Constant Rainfall

The cube overflow water tank is adopted, and four faucet valves are set on the side wall of the water tank. The rainfall of different drainage outlets is simulated by adjusting the opening of different valves and each faucet is connected with the drainage opening through a hose.


### 2.4.2. Measurement of Water Surface Change in Drainage Ditch

SetP1 ∼ P8 monitoring points along the open ditch (see Figure 4).Figure 4
Division of overtopping measurement area.


### 2.4.3. Measurement of Overtopping Volume

Due to the special shape of the artificial island, there are overtopping differences in different sections. In order to accurately measure the overtopping volume of each section, a total of 19 sections, K1 ∼ K19 are set from south to north as shown in Figure4. The length of each section is shown in Table 1. For the collection method of overtopping water body in each section, the overtopping volume of each complete wave train is measured through the collecting tank, the water is weighed and converted into volume, and then converted into plasma. Finally, the average overtopping volume per unit length and unit time is obtained. Specifically, it is calculated according to formula (3):(3)Q=VB∗t,where Q is the average overtopping volume per unit width, m3/(m.s); V is the total water volume of overtopping under the action of one wave train, m3; B is the length of water receiving area for collecting overtopping volume, m; and t is the duration of one wave train, s.


## 2.4.1. Simulation of Constant Rainfall

The cube overflow water tank is adopted, and four faucet valves are set on the side wall of the water tank. The rainfall of different drainage outlets is simulated by adjusting the opening of different valves and each faucet is connected with the drainage opening through a hose.


## 2.4.2. Measurement of Water Surface Change in Drainage Ditch

SetP1 ∼ P8 monitoring points along the open ditch (see Figure 4).Figure 4
Division of overtopping measurement area.


## 2.4.3. Measurement of Overtopping Volume

Due to the special shape of the artificial island, there are overtopping differences in different sections. In order to accurately measure the overtopping volume of each section, a total of 19 sections, K1 ∼ K19 are set from south to north as shown in Figure4. The length of each section is shown in Table 1. For the collection method of overtopping water body in each section, the overtopping volume of each complete wave train is measured through the collecting tank, the water is weighed and converted into volume, and then converted into plasma. Finally, the average overtopping volume per unit length and unit time is obtained. Specifically, it is calculated according to formula (3):(3)Q=VB∗t,where Q is the average overtopping volume per unit width, m3/(m.s); V is the total water volume of overtopping under the action of one wave train, m3; B is the length of water receiving area for collecting overtopping volume, m; and t is the duration of one wave train, s.


## 3. Test Results and Analysis

This section highlights the results obtained from the suggested methodology.


### 3.1. Results of Overtopping Test in Open Section

The maximum overtopping of the rescue Wharf at the inner concave top is 24.07 × 10−3 m3/(m.s), minimum at both ends which is affected by the concentration of wave energy on the inner concave Island wall in the open section of the East artificial island. Figure 5(a) shows the overtopping phenomenon. According to the overtopping standard and design requirements, the elevation of each section along the open section of the design scheme is optimized with the proposed scheme. The optimized elevation is shown in Table 2.Figure 5
Overtopping and overtopping water body floodplain on the open section of the island: (a) overtopping phenomenon, and (b) overtopping water body floodplain.
(a)(b)Table 2
Overtopping results under different conditions (unit: 10−3 m3/(m.s)).
NoB (m)Section typeDesign schemeOptimization schemeElevation of CAP (m)OvertoppingElevation of CAP (m)OvertoppingReturn period 100aReturn period 300aReturn period 100aReturn period 300aK164.4M = 1.5 slope7.50.001.227.00.191.51K240.07.51.8712.207.02.0117.03K340.0Vertical structure7.86.9215.247.58.5127.07K440.07.84.9113.107.510.9325.16K540.07.81.866.297.510.1121.15K640.07.81.344.207.53.039.72K740.0M = 1.5 slope vertical structure7.52.537.197.53.129.18K840.07.59.9024.077.511.9521.78K940.07.03.7512.216.56.6020.95K1045.07.03.0011.706.56.9025.01K1140.0m = 1.5 slope7.56.4623.607.55.0322.99K1240.07.52.6216.617.52.9816.59K1340.07.51.628.777.52.219.05K1440.07.51.649.727.51.9810.35K1540.07.52.6611.207.53.2813.57K1640.07.51.578.337.51.949.94K1740.07.52.436.787.52.607.79K1840.07.50.454.617.51.285.13K1984.87.50.251.887.50.632.72With the change of elevation, it is concluded that the overtopping at the island wall and concave apex of the vertical section is the largest with a maximum of 27.07 × 10−3 m3/(m.s). When compared with the existing design scheme, the overtopping volume increases by 12.5% but still needs more improvements in the design by considering unseen parameters because nature is very uncertain. Table 2 shows the overtopping results.


### 3.2. Drainage Capacity Test Results of Open Section

Based on the results of overtopping under the above optimal scheme of open section, the drainage capacity test is carried out. The results are as follows (Table3).(1)
In the design scheme of the outfall under the action of extreme wave conditions in the return period of 300a, the drainage capacity results are analyzed. Due to the short distance between the wave retaining wall and the open drainage ditch, the small slope of 1%, the small size of the open drainage ditch, and the concentration of the overtopping water body caused by a single large wave, results in a high velocity of overtopping water. The basic drainage of each outfall is not timely, resulting in the floodplain phenomenon. Figure5(b) shows the results and more quantitative information is revealed in Table 3.(2)
The first optimization scheme is proposed. Combined with the overtopping forms of different sections in the design scheme, the optimized scheme is designed and proposed for the range of 1#∼2# section of the outfall where due to the small amount of floodplain water, the 0.98 m wave retaining wall at the exit of the existing tunnel is used for water retaining. For the range of 3#∼4# section of the outfall, the slope ratio between the wave retaining wall and the open ditch increased from 1% to 2.5%, and the width of the slope increased from 19.0 m to 36.0 m. According to the test, the wave action meets the requirements after a return period of 100a but the extreme return period of 300a still does not meet the requirements. The flood plain mode of water flow across the embankment is the same as that of the design scheme. Table3 depicts the results.(3)
Put forward the second optimization scheme: increase the 0.98 m wave retaining wall to 1.50 m, set a second open drainage ditch at the 36 m slope top of the slope with the size of 0.8 m deep and 1.0 m wide. Connect the first and second open ditches with∅=0.6m pipes every 20 m. According to the test, the second optimization scheme meets the requirements, and the test results of drainage capacity are shown in Table 3.Table 3
Summary of west drainage and floodplain in different schemes.
NoDrain opening conditionDesign schemeOptimization scheme IOptimization scheme IIReturn period 100aReturn period 300aReturn period 100aReturn period 300aReturn period 300aFloodplainFloodplainFloodplainFloodplainFloodplainK1∼K34# openingYesYesNoYesNoK4∼K83#+ overtopping pump openingYesYesNoYesNoK9∼K142# openingYesYesNoYesNoK15∼K191# openingNoYesNoYesNoThe drainage capacity test of the artificial island caused by overtopping shows that it is quite different from that caused by the single rainstorm. The interpretations are as follows:(1)
The uneven distribution of waves along the embankment leads to an obvious difference in the overtopping of each section of the embankment and the overtopping water body has obvious nonlinearity.(2)
A single large wave causes the instantaneous concentration of the water body falling over the wave, and the flow velocity of the wave crossing flow is large, resulting in the short-term drainage of the open ditch and the formation of floodplain accident.(3)
When splashing over waves happen, the seawater contains salinity which requires high anti-corrosion maintenance of drainage pumps and facilities. Based on the study of drainage capacity, attention should be paid to the design of drainage facilities of the artificial island.


### 3.3. Calculation Method of Drainage Capacity

As the research on the influence of artificial island overtopping to drainage capacity is still unanswerable at present. The calculation method of overtopping volume and drainage capacity is proposed by using the research results. In order to facilitate the drainage capacity design of similar artificial island projects in the future, the calculation method is proposed to specify the drainage capacity of the artificial island. Using the more mature calculation methods of urban road rainfall drainage capacity in formulas (2) and (3), and referring to the research results of Zhang Zhi-qiang [31], Feng Hang-hua [32], and Hu Wei-fen [33], for the new calculation formula of drainage capacity of the artificial island project is devised in this article. It is necessary to consider superimposing the overtopping amount on the basis of rainfall flow. In addition, the impact of current velocity impact caused by overtopping waves needs to be considered. Therefore, the influence coefficient k is introduced. Therefore, formula (2) is finally transformed as formula (4):Note, floodplain phenomenon occurs, that is, the drainage in the open ditch is not timely.(4)Qk=k∗φ∗F∗q+qw,(5)q=167A11+ClgPt+bN,(6)qw=0.07Hc′/H1/3exp0.5−b12H1/3BKAH1/32TP0.3m+thdH1/3−2.82lngTP2m2πH1/3,where q is the design rainstorm intensity m3/(m.s), according to the rainstorm intensity formula commonly used in China [34]. P is the design return period, A1, C, b, and N are local parameters which are calculated and determined according to the statistical method and t is the design rainfall duration, where qw is the overtopping volume which can be calculated by the formula of code for hydrology of ports and waterways [35] (JTS154-2015), and it is stipulated that the corresponding calculation formula shall be used for different wave retaining types. Since this is the type with wave retaining wall, formula (6) shall be used for calculation, where Hc is the height of the crest of the wave retaining wall above the still water surface m, H1/3 is the effective wave height, b1 is the front shoulder width of the wave retaining wall, B is the empirical coefficient, KA is the influence coefficient of armor structure, Tp is the period of spectral peak s; m is the slope coefficient; d is the depth of water in front of the building, and G is the weight acceleration in m/s2.Derivation of the relationship between the discharge capacities of the outlet: the amount of water received by the outlet includesQa and Qe. Qa is the amount of rainwater and overtopping per unit time on the catchment area of the outlet and Qe is the flow that is not discharged in time at the outlet. Then change formula (1) to obtain formula (8) as follows:(7)Qint=Qa+Qe−Q3,where Q3 represents the amount of water that cannot be discharged in time. The amount of water that can be discharged by the drainage outlet is set, that is, the discharge capacity is Qr to ensure smooth drainage, and the following formula (8) must be met.(8)Qr≥Q.Therefore, if the discharge of each outlet is unobstructed (Qe  = 0, Q3  = O), there is Qr ≥ Qa, where Qa is the amount of water at the outlet which depends on the design rainstorm intensity, catchment area, pavement longitudinal slope, overflow section of street ditch bonding, and overtopping volume.In this regard, the influence coefficientk in the calculation formula (4) of water volume at the outlet is proposed to be determined. The rainstorm flow q of 1#∼4# outlet provided in this design is, respectively, 0.47 m³/s, 0.749 m ³/s, 0.778 m³/s, and 0.525 m³/s. The overtopping qw measured in the test of each representative section in Table 1 results. At the same time, using the water surface change process line of water level monitoring points arranged in the open drainage ditch (see Figure 6), the water surface height change ∆h and the water passing section s of the open drainage ditch (available according to the design section size) during each overtopping volume are obtained. This way, Q4 can be calculated by substituting all known parameters. Transform formula (4) to obtain the calculation expression of K value (9)k=Q4φ∗F∗q+qw,where φ=0.90, the area F value can be calculated according to the divided collection wave crossing section.Figure 6
The water surface change process line of monitoring points in open drainage ditch.According to formula (9), combined with the rainwater volume at each outlet, the comprehensive influence coefficient k is finally calculated to be 1.25. Therefore, the calculation formula (10) applicable to the drainage capacity of the artificial island can be deduced as follows:(10)Q=1.25∗φ∗F∗q+qw.To sum up, the calculation formula of artificial island drainage capacity is deduced, that is, based on the rainfall collection flow formula of mature urban road pavement, the superimposed overtopping amount is proposed. The influence coefficientk of overtopping flow is considered which is suitable for a new calculation formula of artificial island drainage capacity flow.In order to check the accuracy of formula (10), the test results of the drainage capacity of the coastline 5#∼8# outfalls on the southeast side of the industrial island are used for verification. At this time, the test conditions are as follows (Figure 7):(1)
The rainstorm in the return period of 100a is set asq=0.50 m3/(m.s), the elevation of the wave retaining wall of the artificial island is 6.0 m, and the wave overtopping qw of the section represented by each drainage outlet is collected under the action of sea waves in the return period of 300a. Meanwhile, formula (10) is used for estimation and the two results are produced (see Figure 7).(2)
The oblique line in the figure is an ideal line of 45°. Through comparison, it can be seen that the calculated value of discharge (Q) is slightly greater than the test value but the correlation between the two is up to 0.91. It shows that the newly proposed calculation formula (10) can accurately predict the discharge (Q) value of the drainage capacity of the offshore artificial island after the superposition of overtopping and rainstorm.Figure 7
Verification results of test values and calculated values.


## 3.1. Results of Overtopping Test in Open Section

The maximum overtopping of the rescue Wharf at the inner concave top is 24.07 × 10−3 m3/(m.s), minimum at both ends which is affected by the concentration of wave energy on the inner concave Island wall in the open section of the East artificial island. Figure 5(a) shows the overtopping phenomenon. According to the overtopping standard and design requirements, the elevation of each section along the open section of the design scheme is optimized with the proposed scheme. The optimized elevation is shown in Table 2.Figure 5
Overtopping and overtopping water body floodplain on the open section of the island: (a) overtopping phenomenon, and (b) overtopping water body floodplain.
(a)(b)Table 2
Overtopping results under different conditions (unit: 10−3 m3/(m.s)).
NoB (m)Section typeDesign schemeOptimization schemeElevation of CAP (m)OvertoppingElevation of CAP (m)OvertoppingReturn period 100aReturn period 300aReturn period 100aReturn period 300aK164.4M = 1.5 slope7.50.001.227.00.191.51K240.07.51.8712.207.02.0117.03K340.0Vertical structure7.86.9215.247.58.5127.07K440.07.84.9113.107.510.9325.16K540.07.81.866.297.510.1121.15K640.07.81.344.207.53.039.72K740.0M = 1.5 slope vertical structure7.52.537.197.53.129.18K840.07.59.9024.077.511.9521.78K940.07.03.7512.216.56.6020.95K1045.07.03.0011.706.56.9025.01K1140.0m = 1.5 slope7.56.4623.607.55.0322.99K1240.07.52.6216.617.52.9816.59K1340.07.51.628.777.52.219.05K1440.07.51.649.727.51.9810.35K1540.07.52.6611.207.53.2813.57K1640.07.51.578.337.51.949.94K1740.07.52.436.787.52.607.79K1840.07.50.454.617.51.285.13K1984.87.50.251.887.50.632.72With the change of elevation, it is concluded that the overtopping at the island wall and concave apex of the vertical section is the largest with a maximum of 27.07 × 10−3 m3/(m.s). When compared with the existing design scheme, the overtopping volume increases by 12.5% but still needs more improvements in the design by considering unseen parameters because nature is very uncertain. Table 2 shows the overtopping results.


## 3.2. Drainage Capacity Test Results of Open Section

Based on the results of overtopping under the above optimal scheme of open section, the drainage capacity test is carried out. The results are as follows (Table3).(1)
In the design scheme of the outfall under the action of extreme wave conditions in the return period of 300a, the drainage capacity results are analyzed. Due to the short distance between the wave retaining wall and the open drainage ditch, the small slope of 1%, the small size of the open drainage ditch, and the concentration of the overtopping water body caused by a single large wave, results in a high velocity of overtopping water. The basic drainage of each outfall is not timely, resulting in the floodplain phenomenon. Figure5(b) shows the results and more quantitative information is revealed in Table 3.(2)
The first optimization scheme is proposed. Combined with the overtopping forms of different sections in the design scheme, the optimized scheme is designed and proposed for the range of 1#∼2# section of the outfall where due to the small amount of floodplain water, the 0.98 m wave retaining wall at the exit of the existing tunnel is used for water retaining. For the range of 3#∼4# section of the outfall, the slope ratio between the wave retaining wall and the open ditch increased from 1% to 2.5%, and the width of the slope increased from 19.0 m to 36.0 m. According to the test, the wave action meets the requirements after a return period of 100a but the extreme return period of 300a still does not meet the requirements. The flood plain mode of water flow across the embankment is the same as that of the design scheme. Table3 depicts the results.(3)
Put forward the second optimization scheme: increase the 0.98 m wave retaining wall to 1.50 m, set a second open drainage ditch at the 36 m slope top of the slope with the size of 0.8 m deep and 1.0 m wide. Connect the first and second open ditches with∅=0.6m pipes every 20 m. According to the test, the second optimization scheme meets the requirements, and the test results of drainage capacity are shown in Table 3.Table 3
Summary of west drainage and floodplain in different schemes.
NoDrain opening conditionDesign schemeOptimization scheme IOptimization scheme IIReturn period 100aReturn period 300aReturn period 100aReturn period 300aReturn period 300aFloodplainFloodplainFloodplainFloodplainFloodplainK1∼K34# openingYesYesNoYesNoK4∼K83#+ overtopping pump openingYesYesNoYesNoK9∼K142# openingYesYesNoYesNoK15∼K191# openingNoYesNoYesNoThe drainage capacity test of the artificial island caused by overtopping shows that it is quite different from that caused by the single rainstorm. The interpretations are as follows:(1)
The uneven distribution of waves along the embankment leads to an obvious difference in the overtopping of each section of the embankment and the overtopping water body has obvious nonlinearity.(2)
A single large wave causes the instantaneous concentration of the water body falling over the wave, and the flow velocity of the wave crossing flow is large, resulting in the short-term drainage of the open ditch and the formation of floodplain accident.(3)
When splashing over waves happen, the seawater contains salinity which requires high anti-corrosion maintenance of drainage pumps and facilities. Based on the study of drainage capacity, attention should be paid to the design of drainage facilities of the artificial island.


## 3.3. Calculation Method of Drainage Capacity

As the research on the influence of artificial island overtopping to drainage capacity is still unanswerable at present. The calculation method of overtopping volume and drainage capacity is proposed by using the research results. In order to facilitate the drainage capacity design of similar artificial island projects in the future, the calculation method is proposed to specify the drainage capacity of the artificial island. Using the more mature calculation methods of urban road rainfall drainage capacity in formulas (2) and (3), and referring to the research results of Zhang Zhi-qiang [31], Feng Hang-hua [32], and Hu Wei-fen [33], for the new calculation formula of drainage capacity of the artificial island project is devised in this article. It is necessary to consider superimposing the overtopping amount on the basis of rainfall flow. In addition, the impact of current velocity impact caused by overtopping waves needs to be considered. Therefore, the influence coefficient k is introduced. Therefore, formula (2) is finally transformed as formula (4):Note, floodplain phenomenon occurs, that is, the drainage in the open ditch is not timely.(4)Qk=k∗φ∗F∗q+qw,(5)q=167A11+ClgPt+bN,(6)qw=0.07Hc′/H1/3exp0.5−b12H1/3BKAH1/32TP0.3m+thdH1/3−2.82lngTP2m2πH1/3,where q is the design rainstorm intensity m3/(m.s), according to the rainstorm intensity formula commonly used in China [34]. P is the design return period, A1, C, b, and N are local parameters which are calculated and determined according to the statistical method and t is the design rainfall duration, where qw is the overtopping volume which can be calculated by the formula of code for hydrology of ports and waterways [35] (JTS154-2015), and it is stipulated that the corresponding calculation formula shall be used for different wave retaining types. Since this is the type with wave retaining wall, formula (6) shall be used for calculation, where Hc is the height of the crest of the wave retaining wall above the still water surface m, H1/3 is the effective wave height, b1 is the front shoulder width of the wave retaining wall, B is the empirical coefficient, KA is the influence coefficient of armor structure, Tp is the period of spectral peak s; m is the slope coefficient; d is the depth of water in front of the building, and G is the weight acceleration in m/s2.Derivation of the relationship between the discharge capacities of the outlet: the amount of water received by the outlet includesQa and Qe. Qa is the amount of rainwater and overtopping per unit time on the catchment area of the outlet and Qe is the flow that is not discharged in time at the outlet. Then change formula (1) to obtain formula (8) as follows:(7)Qint=Qa+Qe−Q3,where Q3 represents the amount of water that cannot be discharged in time. The amount of water that can be discharged by the drainage outlet is set, that is, the discharge capacity is Qr to ensure smooth drainage, and the following formula (8) must be met.(8)Qr≥Q.Therefore, if the discharge of each outlet is unobstructed (Qe  = 0, Q3  = O), there is Qr ≥ Qa, where Qa is the amount of water at the outlet which depends on the design rainstorm intensity, catchment area, pavement longitudinal slope, overflow section of street ditch bonding, and overtopping volume.In this regard, the influence coefficientk in the calculation formula (4) of water volume at the outlet is proposed to be determined. The rainstorm flow q of 1#∼4# outlet provided in this design is, respectively, 0.47 m³/s, 0.749 m ³/s, 0.778 m³/s, and 0.525 m³/s. The overtopping qw measured in the test of each representative section in Table 1 results. At the same time, using the water surface change process line of water level monitoring points arranged in the open drainage ditch (see Figure 6), the water surface height change ∆h and the water passing section s of the open drainage ditch (available according to the design section size) during each overtopping volume are obtained. This way, Q4 can be calculated by substituting all known parameters. Transform formula (4) to obtain the calculation expression of K value (9)k=Q4φ∗F∗q+qw,where φ=0.90, the area F value can be calculated according to the divided collection wave crossing section.Figure 6
The water surface change process line of monitoring points in open drainage ditch.According to formula (9), combined with the rainwater volume at each outlet, the comprehensive influence coefficient k is finally calculated to be 1.25. Therefore, the calculation formula (10) applicable to the drainage capacity of the artificial island can be deduced as follows:(10)Q=1.25∗φ∗F∗q+qw.To sum up, the calculation formula of artificial island drainage capacity is deduced, that is, based on the rainfall collection flow formula of mature urban road pavement, the superimposed overtopping amount is proposed. The influence coefficientk of overtopping flow is considered which is suitable for a new calculation formula of artificial island drainage capacity flow.In order to check the accuracy of formula (10), the test results of the drainage capacity of the coastline 5#∼8# outfalls on the southeast side of the industrial island are used for verification. At this time, the test conditions are as follows (Figure 7):(1)
The rainstorm in the return period of 100a is set asq=0.50 m3/(m.s), the elevation of the wave retaining wall of the artificial island is 6.0 m, and the wave overtopping qw of the section represented by each drainage outlet is collected under the action of sea waves in the return period of 300a. Meanwhile, formula (10) is used for estimation and the two results are produced (see Figure 7).(2)
The oblique line in the figure is an ideal line of 45°. Through comparison, it can be seen that the calculated value of discharge (Q) is slightly greater than the test value but the correlation between the two is up to 0.91. It shows that the newly proposed calculation formula (10) can accurately predict the discharge (Q) value of the drainage capacity of the offshore artificial island after the superposition of overtopping and rainstorm.Figure 7
Verification results of test values and calculated values.


## 4. Discussion

The new formula for calculating the drainage capacity of an artificial island involves many influencing factors, so the parameters of the formula need to be adjusted and modified.(1)
For example, rainstorm intensityq with the great change of climate in the world in recent years, there is an obvious change in rainfall in the intensification of short-term rainstorm. Therefore, A1, C, b, and N parameters in formula (5) should be corrected according to the sea area where the project is located and the rainfall of recent years.(2)
Overtopping quantityqw as given in reference [35] can be used for calculation according to the requirements of the specification for different types of wave retention and different wave incident conditions. However, the calculation formula is different, but it is not universally applicable. It is necessary to use the physical model test of wave section to measure the overtopping amount. It needs to be adjusted and modified according to the specific project.(3)
For different types of outlets, such as setting horizontal and vertical grate, the formula of discharge capacity still needs to be adjusted. Therefore, for major projects, it is suggested that it is necessary to carry out corresponding wave overall physical model tests for further inspection and verification.


## 5. Conclusions

Based on the huge difference of boundary conditions involved in the drainage capacity design of offshore artificial island and inland urban drainage facilities, an optimized calculation method is proposed. In order to ensure the safety and reliability of the drainage facilities of the “century project,” the East artificial island of Shenzhen-Zhongshan channel under extreme weather conditions is examined and correspondingly the overall physical model and research method of wave is adopted. Using the mature calculation formula of drainage capacity of the drainage facilities under the influence of rainstorm and the influence factork of overtopping, a new estimation method of drainage capacity of artificial island drainage facilities on the sea is proposed. The proposed method is verified by the test results of drainage capacity of shoreline 5#∼8# outfall on the southeast side of the project. The results show that the formula has good accuracy and can provide reference for the design and estimation of drainage capacity of similar projects. Under extreme sea conditions, affected by the concentration of concave wave energy in the open section of the artificial island, the overtopping amount at the top of the embankment is greater than that at both sides with a maximum of 24.07 × 10−3 m3/(m.s). After multiple optimization and adjustment of the elevation of the wave retaining wall, the optimal scheme is meeting the design requirements and providing the optimal solution. Based on the results of overtopping under the optimal scheme, the floodplain and drainage are not timely in the design scheme of the open ditch outlet in the island under extreme sea conditions. After the optimization measures such as increasing the slope, setting the second open ditch and wave retaining wall, the drainage capacity requirements can be met. Therefore, due to the combination of overtopping and rainfall, there are obvious differences in engineering drainage design between artificial island and separate rainfall environment. By introducing the comprehensive influence coefficient k of overtopping volume and current velocity caused by overtopping under the action of superimposed waves, a new calculation method and simple calculation formula suitable for the drainage capacity in the artificial island are proposed which are verified by the drainage capacity test results. The results show that the formula has good accuracy and can provide reference for the design and estimation of drainage capacity of similar projects. At the same time, the calculation formula involves many influencing factors and the parameters can vary from project to project and location to location. It is suggested that the influencing parameters to be taken as per the sea conditions and sea area for protecting the marine environment and for measuring the safety features for the public.



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*Source: 2655727-2022-09-16.xml*