The rapid urbanization effect is like a catalyst, greatly accelerating the hydrological cycle. This makes heavy rainfall events occur frequently, and the risk of urban waterlogging continues to rise [1,2]. The vulnerability of the stormwater network to heavy rain and the risk of water accumulation in the region have always been regarded as uncertain issues [3]. In order to analyze such problems, a series of hydrological and hydrodynamic models have been developed, such as InfoWorksICM, PCSWMM, MIKE, etc. [4]. As a relatively mature stormwater model, the MIKE model has been widely used in engineering and academic fields. Since the MIKE model contains multiple calculation modules, its application directions are also different. Some researchers simply use a module of the MIKE model for modeling. For example, Gao Guoming [5] used the MIKE21 module to simulate and analyze the evolution process of river water to the interior of the city after a river dam breaks. Chen Xuan [6] built a river basin model based on MIKE11 to realize flood storage and dispatch. Li Pinliang [7] focused on the performance of the rainwater pipe network under various rainfall through MIKE URBAN. On the other hand, some scholars have coupled multiple modules of the MIKE model to perform 1D-2D dynamic hydrological analysis. For example, Yao Siyang [7] coupled the MIKE11 and MIKE21 modules to analyze the flood risk in the area around the river bank under multiple scenarios. Ren Meifang [8] coupled MIKE URBAN and MIKE 21 in MIKE FLOOD, and analyzed waterlogging in a typical urban area such as overpass bridges.
The above literature shows that there are relatively few studies on coupling one-dimensional pipe network and two-dimensional surface modeling based on MIKE FLOOD, and most researchers focus on the watershed scale and administrative regions. This may be because the pipe network in a larger area involves greater data processing difficulties. In addition, the two-dimensional surface model has higher requirements for terrain accuracy. Therefore, when model engineers build 1D-2D coupled models, it is often difficult to guarantee the accuracy of the water grid (the pixel size is generally above 10m). Residential district is an important part of the city, and its regional importance is relatively high. Therefore, it is necessary to carry out the safety analysis of the rainwater system and the risk analysis of water accumulation. Most of the previous studies used SWMM or MIKE URBAN model as a tool for safety analysis of rainwater systems, but they could not simulate the actual situation of water accumulation in the community. With the help of the small scale of the residential area, it is possible to realize a high-precision two-dimensional surface model by finely dividing the measured elevation points. Therefore, this paper constructs a high-precision 1D-2D coupling model of residential quarters based on MIKE FLOOD. It is expected to provide ideas for coupling modeling of residential quarters, and further provide safety assessment and waterlogging risk analysis for rainwater systems in residential quarters.
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1.1 MIKE URBAN
MIKE URBAN is an important tool for urban pipe network analysis, including two modules: surface runoff calculation and pipe network confluence calculation. MIKE URBAN assumes that the water flow on the surface and the pipe network is a homogeneous and incompressible fluid, and that the water flow does not flow in two dimensions at the same time. Therefore, MIKE URBAN is essentially a one-dimensional model. Based on the premise of mass and energy conservation equations, its core governing equation is the Saint-Venant equation:
（1）
In the formula, -flow, -side flow, m3/s; -momentum correction coefficient; -hydraulic radius, m.
1.2 MIKE21
The MIKE21 model is a two-dimensional surface model that can simulate the two-dimensional flow of water on the surface. When modeling the MIKE21 model, it is necessary to generalize the two-dimensional surface into a triangular or rectangular grid to establish a digital elevation model DEM. In the hydrodynamic calculation, the gravitational acceleration of the falling water flow is ignored, and the model is solved according to the Navier-Stokes equation, the equation is as follows:
Continuity equation:
（2）
Momentum equation:
（3）
In the formula, -flow velocity in direction; -flow velocity in direction; -water depth; -water level; -component of flow velocity; -gravitational acceleration; -viscosity coefficient.
1.3 MIKE FLOOD coupling model
After MIKE URBAN and MIKE21 run independently, the coupling of one-dimensional pipe network and two-dimensional surface model can be completed through manhole connection in MIKE FLOOD to realize the dynamic exchange process of water volume.
2.1. Natural profile of the study area
2.1.1 Analysis of underlying surface in the study area
The research is a residential area, located in Yantian District, Shenzhen City, covering an area of 61,729 square meters. According to the characteristics of the current underlying surface, the regional underlying surface is divided into six categories: roof, water body, pavement, green space, bare soil, and road surface. After using the GIS data function to segment and classify different underlying surfaces, the area of green space (including ecological grass slopes and green spaces) is about 16227m2, the area of roofs is 20182m2, and the area of bare soil (including mounds and sand dunes) is 969m2. The pavement area is 32872m2, the pavement area (including site roads and sports fields) is 10959m2, and the water body area is 1576m2. Among them, green space accounted for 19.60%, roofs accounted for 24.37%, bare soil accounted for 1.17%, pavement accounted for 39.60%, and pavement accounted for 13.23%.
Fig. 1 Analysis of the underlying surface in the study area
Fig.1 Analysisof underlying surface in the study area
2.1.2 Vertical analysis of the study area
In order to obtain a high-precision DEM model of the research area, the elevation layout and elevation measurement of the residential area were carried out in the early stage of the project. Subsequently, the elevation points were made into a high-precision grid of 1.5m*1.5m by Kriging interpolation method in Arcgis. The vertical elevation of the plot has a strong influence on the surface runoff production and confluence process and the two-dimensional evolution of ponding water when the MIKE model is coupled, and the slope can reflect the flow velocity and direction of surface runoff to a certain extent. Therefore, it is necessary to conduct vertical elevation analysis and slope analysis for the study area. Figure 2-a is a 3D elevation map of the research area. It is not difficult to find that the overall terrain of the residential area is from northwest to southeast, and the elevation of the southeast area is about 3.68m because it is adjacent to the artificial lake. The maximum elevation of the research area is 8.94m, and most of the area is located in the southwest corner. , with the help of the 3D Analyst tool, the slope map of the study area can be obtained, as shown in Figure 2-b. The slope map shows that the slope fluctuations in the study area are not very large, and the slopes in most areas are below 6.36°. It can also be seen from Figure 2-b that there are many strips or circular slope lines in the study area, which may be due to the presence of many landscape slopes, mountain protective retaining walls, and concave track and field fields in the community. In general, with the help of high-precision DEM model, the vertical topography of the study area can be embodied.
Figure 2 Vertical analysis of the study area
Fig.2 Verticalanalysis of the study area
2.2 Construction of one-dimensional pipe network model
2.2.1 Design rainfall
Taking the Chicago rain pattern as the design rainfall pattern, the latest rainstorm intensity formula in Yantian District, Shenzhen is used to calculate:
（4）
In the formula, rain intensity, L/( s hm2); rainfall duration, min; return period, a.
In this modeling, the rain peak coefficient is 0.35, and the rainfall duration is 120 minutes.
2.2.2 Pipe network generalization
The pipe network data used for modeling in this paper comes from the CAD construction drawings of the research area. In the actual construction process, each node and pipeline may deviate from the design drawings. For this reason, the project team conducted field research and corrections on the location, pipe diameter and inspection well depth of the pipe network in the residential area before modeling. According to statistics, the existing drainage pipes in the research area are 8733m, including 5865m of rainwater pipes and 2868m of sewage pipes. Before modeling, it is necessary to convert the pipe network data in CAD format into shp data in Arcgis and establish the modeling parameter attribute table of pipe network and nodes. Subsequently, in MIKE URBAN, the space and data attributes of the pipe network system are matched one by one to complete the conversion from GIS data to MIKE data. In the end, the pipeline network in the study area was generalized into 711 pipeline sections and 132 inspection wells in total.
2.2.3 Division of subcatchments
MIKE URBAN provides the function of automatic division of sub-catchments, and its division method is based on the principle of Thiessen polygons. Although the automatic division method saves the cumbersome steps of outlines of structures and buildings, it is difficult to estimate parameters such as runoff coefficient and impermeability of subcatchments due to the lack of underlying surface attributes. For this reason, this paper adopts the method of automatic and manual division, and manually divides the underlying surfaces such as roofs and sports fields on the basis of Thiessen polygon division. In addition, before running the model, the impermeability of each subcatchment needs to be calculated. In the underlying surface analysis, the land use in the study area is divided into six categories. Therefore, in the URBAN model, the impermeability rates of roofs, roads, pavements, bare soil, green spaces, and water bodies are set to 95%, 85%, 60%, 45%, 15%, and 0 in sequence, and the sub-catchments are completed Weighted average calculation of impermeability. In the end, the research area was generalized into 580 sub-catchments, and the overview of sub-catchments and pipe networks is shown in Figure 3:
Figure 3 Pipe network and sub-catchments
Fig.3 Pipenetwork and sub-catchment area
2.3 Construction of 2D surface model
The 2D surface model is based on DEM, but MIKE cannot recognize the DEM data in GIRD format. Therefore, it is necessary to convert the GRID elevation to ASCII code in Arcgis first, and then use MIKE ZERO to output the DEM as a MIKE21 terrain file in dfs2 format. Considering the obstructive effect of buildings on two-dimensional water flow and the ability of roads to discharge surface runoff, the layers of buildings and roads are overlaid with the natural terrain as the base map. Finally, the building layer was set to be raised to 30m based on the base map, and the road layer was set to be lowered by 0.15m. The accuracy of the model is still 1.5m*1.5m.
2.4 Model Validation
The coupling model was verified by the method of literature 9 [9], and the rainfall data came from the "20180606" field rainfall in Yantian District, with a total rainfall of 432.5 mm. The calibration results show that the average relative errors of the outflow curves of the three discharge outlets in the study area are 6.68%, 7.21%, and 8.56%, and the Nash coefficients are 0.81, 0.79, and 0.77, respectively; the average relative error of the two-dimensional water depth is 12.36 %. The calibration data shows that the coupling model has good fitting accuracy and can be used for subsequent analysis.
3.1 Pipe network and runoff analysis
3.1.1 Rainwater runoff analysis
Since the design return period of the municipal pipe network generally does not exceed 5 years, the rainfall of 1a, 3a and 5a is taken as the boundary rainfall condition when analyzing the pipe network and runoff. After the runoff model simulation is completed, statistical reports such as the maximum, minimum, and cumulative flow of each subcatchment can be obtained. The runoff coefficient of each sub-catchment is obtained through result loading and calculation tools. Table 1 and Figure 4 are the statistical data of rainwater runoff in the community and the runoff coefficients of each catchment area:
Figure 4 Classification of runoff coefficients in each subcatchment
Fig.4Classification of runoff coefficients in each sub-catchment area
After simulation analysis, the runoff coefficient of the subcatchment increases with the increase of rainfall. However, the author found that if the same runoff coefficient classification interval points are used to classify each catchment area, the runoff coefficient distribution map of the study area will hardly change. Therefore, this paper takes the 5-year rainfall as an example, uses the natural breakpoint method to classify and evaluate the runoff coefficient, and draws Figure 4. It can be seen from Figure 4 that most of the catchment areas in the study area are classified as level 4, that is, the runoff coefficient is between 0.49 and 0.64. The smallest level of runoff coefficient appears in the southwest and northeast corners of the study area, ranging from 0.03 to 0.24, indicating that the underlying surface types of these two areas are relatively consistent and the vegetation coverage in this area may be relatively high. Due to the good impermeability of the roof, the building is classified as a Class 5 runoff coefficient with a value higher than 0.65.
In order to further analyze the system and runoff conditions, the author draws Table 1:
Table 1 System rainwater runoff statistics
Tab.1 SystematicRain Water runoff statistics
| return period |
Maximum runoff flow (m3/s) |
Total water storage capacity (mm) |
Total infiltration (mm) |
Comprehensive runoff coefficient |
| 1a |
1.26 |
0.833 |
7.950 |
0.47 |
| 3a |
1.68 |
1.124 |
8.108 |
0.52 |
| 5a |
2.25 |
1.313 |
8.165 |
0.62 |
It can be seen from Table 1 that all indicators are positively correlated with the return period. Although the return intervals were two years apart, the increases across indicators were uneven. Among them, from 1a to 3a and 3a to 5a, the increases of the maximum runoff of the system were 33.33% and 25.33%, respectively, the increases of the total water storage were 25.89%, 14.39%, and the increases of the total infiltration were 1.95% and 0.70% respectively , the increase of comprehensive runoff coefficient was 9.62% and 16.13% respectively. The above data show that only the second increase of the comprehensive runoff coefficient is greater than the first increase, indicating that after 3 years, the infiltration and water storage of most subcatchments reached saturation, and the surface runoff increased significantly. Especially the total infiltration, under each return period, the growth rate is within single digits. The difference between the first increase and the second increase of the total water storage also reached 11.60%, indicating that when the rainfall occurs once every 3 years, the water storage in the surface depressions will almost reach the maximum value.
3.1.2 Evaluation of drainage capacity of pipe network
The evaluation of the drainage capacity of the pipe network is of great significance to the subsequent analysis of the causes of flood-prone points and the engineering measures to be adopted. In this paper, the evaluation is based on the maximum fullness of the pipeline. When the maximum fullness of the pipeline is greater than 1, it is considered that the drainage design capacity of the pipeline is not met; when the maximum fullness of the pipeline is less than or equal to 1, the pipeline is considered to meet the drainage design capacity. The rainfall of different return periods 1a, 3a and 5a is used to evaluate the drainage capacity of the pipeline, and the drainage capacity of the pipeline network is divided into 4 levels, as shown in Figure 5. The drainage capacity statistics of the pipe network are shown in Table 2.
Figure 5 Drainage Capacity Diagram of Pipe Network
Fig.5Drainage capacity diagram of pipe network
Table 2 List of drainage capacity of pipe network
Tabl.2 Summary of drainage capacity of pipe networks
| drainage capacity |
≤1a（m） |
1a-3a（m） |
3a-5a（m） |
≥5a（m） |
total |
| tube chief |
2427 |
814 |
109 |
4297 |
7437 |
| Proportion |
33.0% |
11.0% |
1.5% |
54.5% |
100% |
It can be seen from Figure 5 and Table 2 that the design return period of most pipe networks in the study area exceeds 5 years, and the percentage is 54.5%. The pipe network with a return period of 5a or more is mainly concentrated near the discharge outlet, which shows that the drainage load near the discharge outlet has been considered in the design and planning stage of this community, and there is room for the design return period of the pipe network. In addition, there are also some scattered pipe networks above 5a in other areas, which may be due to the small runoff in the catchment area where the pipe network connects or the relatively large slope of the pipe network with better drainage capacity. In addition to the pipe network with a return period of 5 years or more, the proportion of the pipe network with a return period of less than or equal to 1 year is also relatively large, which is 33%. This shows that the pipeline network planning in the study area is not so balanced, showing the characteristics of polarization. Because there are many bottlenecks in the pipe network, the overall rainwater system is prone to bottlenecks. It can also be seen from Table 2 that the proportion of 3a-5a pipe network is very small, 1.5%, which indicates that the design return period of the pipe network in the study area does not have a good transition.
3.2 Analysis of accumulated water in the study area
3.2.1 Analysis of ponding depth
Under the low return period, the overflow situation of the pipeline network nodes is not yet obvious. But when the study area encountered a 50a rainstorm, the nodes were almost completely overloaded. Therefore, based on the Mike Flood platform, this project couples the one-dimensional drainage pipe network model (MIKE URBAN) with the two-dimensional surface runoff model (MIKE 21), and considers that surface water is caused by the pipe network overflowing to the surface of. In the waterlogging simulation analysis, take 50a rainstorm as an example, and set the simulation time to 24h in MIKE FLOOD. The water accumulation distribution map of the study area is shown in Figure 6:
Figure 6 Depth of accumulated water in the study area
Fig.6Depth of water in the study area
From the result map of the maximum water accumulation depth, it can be found that surface water accumulation points or areas mostly appear in some road pavement and along the line, low-lying areas and other areas. Most of the submerged areas are concentrated in the middle and lower parts. The reason is that some areas have relatively low-lying terrain, small pipe diameters, reverse slopes, etc., which are more prone to water accumulation. In the study area, there are six waterlogged areas with a depth of more than 0.3m, most of which are caused by low-lying terrain and small pipe diameters. In particular, the depth of accumulated water in a certain area in the northern part of the study area is more than 1.2m. After the longitudinal section analysis and field investigation of the pipe network, it was found that the pipe network in this area has serious reverse slope phenomenon and extremely poor drainage. Under the dual effects of slope and topography, the accumulation of water in this area is the most serious. On the whole, although local water accumulation is serious in the study area, there is no widespread water accumulation in large areas. The ponding area near the discharge outlet of the pipe network is relatively large, but the depth of the ponding water is below 0.15m, which has little impact on the travel of vehicles and pedestrians.
3.2.2 Analysis of water accumulation duration
The duration of water accumulation reflects the continuous effect of water accumulation. Figure 7 shows the distribution of water accumulation duration in the study area:
Figure 7 Duration of water accumulation in the study area
Fig.6The length of water in the study area
The water accumulation unit in Figure 7 is h, and it can be found that the temporal and spatial distributions of the maximum water accumulation duration and the maximum water accumulation depth are not consistent. In other words, the duration of water accumulation in an area with a large depth of water is not necessarily large. As shown in Figure 6, in the area with the maximum water accumulation depth greater than 1.2m, the water accumulation time is only between 9.0h and 11.0h, and the maximum water accumulation depth occurs in the northeast area. This shows that the local pipe network with a large water depth may have a large continuous discharge capacity even though the instantaneous overflow is large. On the whole, the duration of water accumulation in the study area is mostly less than 10 hours, and the duration of water accumulation in some areas is more than 19 hours. Among them, the overall waterlogging time in the northeast region is higher than that in other regions, which may be due to the high impermeability and the low density of the pipe network in this region.
In this paper, a high-precision MIKE model is used to construct a 1D-2D coupling model at the residential area scale, and based on this, the drainage capacity of the pipe network in the study area and the situation of surface water accumulation are analyzed. Overall, this paper draws the following conclusions:
(1) The high-precision MIKE model is suitable for stormwater simulation at the residential area scale, but it needs to be based on a high-precision digital elevation model (DEM). To this end, it is necessary to carry out fine preliminary elevation layout and survey work. Since the minimum width of the roadway in the community is 3.5m, it is recommended that the grid pixel of the MIKE model be controlled below 3.5m*3.5m.
(2) The MIKE model can truly reflect the transmission load of the pipe network in the study area, and then assist engineers and scientific researchers to analyze the drainage capacity of the pipe network in the planning and renovation stages. The simulation results of this case show that although the design return period of more than half of the pipe networks is greater than or equal to 5 years, the overall drainage pipe network design is not balanced, and there are a large number of stuck pipe networks.
(3) The 50-year two-dimensional inundation simulation results of the study area show that the depth of water accumulation in most areas of the study area is below 0.3m, and the water accumulation time is mostly below 10h. The overall risk of waterlogging in the community is not high, but the depth of water in some areas is more than 1.2m, and the time of water accumulation is close to 24 hours. The MIKE model can be used for the next step of reconstruction plan design and result analysis.
Application of Mathematical Models in Water Environment Impact Assessment, Flood Control Assessment and Sewage Outlet Demonstration Project https://mp.weixin.qq.com/s?__biz=MzU0MDQ3MDk3NA==&mid=2247549489&idx=2&sn=f2ce353d22481ef7261b661452d49616&chksm=fb3af9e0cc4d7 0f6a1a270812e18f2dff83ea34a30289733dbc80282cb009783c2fa44c34a9b&scene=21#wechat_redirect Transferred from "Journal of Hydraulic and Architectural Engineering"