CN113836725A - Integrated drainage design method for special rainfall, runoff and pipe network of airport - Google Patents

Integrated drainage design method for special rainfall, runoff and pipe network of airport Download PDF

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CN113836725A
CN113836725A CN202111131015.8A CN202111131015A CN113836725A CN 113836725 A CN113836725 A CN 113836725A CN 202111131015 A CN202111131015 A CN 202111131015A CN 113836725 A CN113836725 A CN 113836725A
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马耀鲁
潘国瑞
王近
廖源铭
赵亮
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PowerChina Kunming Engineering Corp Ltd
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Abstract

The invention relates to a special rainfall, runoff and pipe network integrated drainage design method for an airport, which comprises four steps of site external hydrological environment analysis, airport drainage confluence analysis, local fine analysis and parameter informatization scheme presentation; the four steps are sequentially performed by 1) site external hydrological environment analysis, 2) airport drainage sink flow analysis, 3) local refinement analysis and 4) parameter informatization scheme presentation. The method comprehensively considers key problems of field macroscopic drainage line design, local gully water quantity fine evaluation and the like, cooperates with the drainage capacity and the structural stability of the drainage structure and even related professional design, strengthens further integration with related professionals, and can perform data interaction with related professionals of airport design.

Description

Integrated drainage design method for special rainfall, runoff and pipe network of airport
Technical Field
The invention relates to the field of airport design, in particular to a special integrated drainage design method for rainfall, runoff and pipe networks of an airport.
Background
The airport drainage design is an important component of airport design, and is closely matched with the terrain and the road surface of an airport on the basis of the overall planning of the airport, so that the problems of flight safety and strength of each part of a flight field are jointly solved. Because no software tool specially designed and analyzed for airport drainage exists at present, in the actual production design, in order to ensure safety, over-design is often carried out to a certain degree, and the cost is invisibly increased; on the contrary, if the estimation of the water displacement of the airport surface area is insufficient, the water accumulation phenomenon occurs, and the later-period remediation (operation and maintenance cost) is also improved. Therefore, the airport drainage problem is very important but lacks certain rationality, and reasonable drainage design needs to be established on the basis of accurate expression and quantification of the drainage process. The drainage process of the airport surface area is obviously influenced by time and space, the time-varying process of rainfall conditions is one of the most obvious factors influencing the drainage of the airport surface area in time, and the rainfall intensity is mainly used for measurement; in the aspect of space, not only is the overall macroscopic drainage process in a surface area crucial, but also the design of a local refined drainage scheme is also worth paying attention, and reasonable drainage scheme facilities need to be analyzed from the aspects of time and space, and also pay attention to the cooperative cooperation with related specialties (rock and soil, structures and the like).
The traditional calculation method (manual hydraulic calculation) is not perfect for the expression of the time-space dynamic change of the drainage process, which leads to certain deficiency of the procedural description of drainage; secondly, the current drainage design process is not deeply fused with BIM technology of relevant majors of airports, and the consistency of the drainage capacity design of drainage structures and the structure thereof and even the majors of rock soil, structure and the like needs to be further enhanced.
Disclosure of Invention
The invention aims to solve the defects of the problems and provides a special rainfall, runoff and pipe network integrated drainage design method for an airport for realizing space-time expression of a drainage process and performing data interaction among specialties.
The invention is realized by adopting the following technical scheme.
According to terrain data, design rainfall data and engineering characteristics, following a research idea of 'macro-microscopic-fine', providing an airport special rainfall, runoff and pipe network integrated drainage design method, wherein the design method comprises four steps of site external hydrological environment analysis, airport drainage sink flow analysis, local fine analysis and parameter informatization scheme presentation;
the four steps are sequentially performed by 1) site external hydrological environment analysis, 2) airport drainage sink flow analysis, 3) local fine analysis and 4) parameter informatization scheme presentation;
the method comprises the following steps that 1), the hydrological environment outside the site is analyzed, namely, the hydrological environment around the airport is evaluated, and the surrounding hydrological environment comprises special landforms; obtaining the area of a potential flooding area and the length of a drainage line under the design of an optimal control strategy;
specifically, according to the flow direction judgment criterion of "D8", that is, gridding the ground surface in a two-dimensional plane, it is considered that the water flow in a certain grid flows to the grid with the highest height in the eight adjacent grids on the ground surface, relative to the grid. And connecting the grids by using a solid line according to the principle that the flowing water always flows to a low position, namely obtaining the spatial distribution of the river network in the research area, and further determining the length of the drainage line under the design of an optimal control strategy.
Step 2), airport drainage sink flow analysis, namely, the drainage process analysis is carried out on airport surface areas, and the water volume space-time change rule under a single precipitation event is analyzed;
in particular, according to the principle of water balance.
Wherein, the flow production part:
for impervious ground surfaces, the following formula is followed: when there is no depression on the earth's surface, R1P-E; when there is depression on the earth's surface, R2=P-D;R1、R2Water yield on the earth surface is mm; p is rainfall, mm; e is evaporation capacity, mm; d is the depression storage amount, mm;
for permeable surfaces, rainfall losses include pooling and infiltration according to the following formula: r3=(i-f)t;R3Water yield on the earth surface is mm; i is rainfall intensity, mm/s; f is the infiltration strength, mm/s.
A confluence portion:
solving by using a continuous equation and a Manning equation according to the nonlinear reservoir model,
the continuous equation:
Figure BDA0003280531460000031
in the formula: v is the surface water collection amount, m3(ii) a h is water depth m; t is time, s; a is the surface area, m2(ii) a i is the net rain intensity, mm/s; q is the flow, m3/s。
The manning equation is:
Figure BDA0003280531460000032
in the formula: w: width of sub-basin, m; n: a Mannich coefficient; h isp: the ground water storage depth is mm; s0: the sub-basin slope.
The step 3) local fine analysis, namely scheme comparison and optimization are carried out by adjusting local parameter information;
specifically, for the description of the water flow inside the airport drainage pipe network (ditch), the solution is carried out according to a one-dimensional Saint-Venn equation set.
Figure BDA0003280531460000033
Figure BDA0003280531460000034
In the formula, x: a one-dimensional spatial variable; bs: water surface width, m; g: acceleration of gravity, m/s2;As: cross sectional area of water flow, m2;ib: a bottom slope; k: flow modulus, m2And s. And 4) displaying the result in various forms by using the parameter informatization scheme in the step 4), wherein the result is quantitatively described in a drainage area and a drainage evolution process, and a time series curve and a chart of the result, a slope diagram and an analysis result of statistical frequency are provided.
Specifically, the flooding result at the surface pipe network node is led into BIM software (such as but not limited to DHI-MIKE) as a water volume boundary condition to quantitatively describe the evolution process of the surface water. The surface flooding results are visually viewed by BIM software (such as but not limited to DHI-MIKE, Tecplot, etc.).
The invention provides a method for analyzing the outside hydrological environment of a site in the step 1), wherein the special landform comprises gully and pipeline downward penetration.
The airport surface area in the step 2) airport drainage production convergence analysis comprises a road surface and an open trench.
The local parameter information in the step 3) local fine analysis comprises the gradient of the catchment area, the water-permeable area ratio of the catchment area and the size of the ditch pipe.
The method comprises the following steps that 1) the external hydrological environment of the site is analyzed, the GIS hydrological analysis technology is utilized to preliminarily quantify the possibly occurring flood outside the site, and the scale and the size of a drainage system are reasonably designed; the method has the advantages that the flooding area of the natural channel/river channel system is accurately drawn, and the optimal control strategy design is provided on the premise of ensuring the drainage requirement of the drainage line. And (3) combining GIS hydrological analysis: the slope and the terrain elevation divide a catchment area, and open ditches and pipe network drainage structures are arranged; analyzing the water quantity change process of the airport surface area under a single precipitation event, and comprehensively treating the produced flow and confluence of each sub-basin by the runoff module part; and water quantity transmission is carried out through a pipe network and an open channel drainage facility, and the water quantity of runoff generated by each sub-basin at any time with different time step lengths, and the flow and water depth conditions of water in each pipeline and river channel are tracked and simulated.
The airport drainage production and sink flow analysis in the step 2) comprises the steps of utilizing a water quantity balance principle and a nonlinear reservoir model, building an airport drainage numerical analysis model according to terrain conditions, dividing a surface area catchment area according to the terrain conditions of a design scheme, and arranging drainage structures such as open ditches, blind ditches and the like; calculating the runoff process of the road surface by adopting a hydraulic calculation method, and solving the confluence process in the ditch or pipeline by a one-dimensional Saint-Venn equation set; the integrated design of rainfall-runoff-pipe network for airport drainage is to perform simulation analysis on the drainage process of airport surface areas (road surfaces, open ditches and the like) and combine GIS hydrological analysis: the slope and the terrain elevation divide a catchment area, and open ditches and pipe network drainage structures are arranged; analyzing the water quantity change process of the airport surface area under a single precipitation event, and comprehensively treating the produced flow and confluence of each sub-basin by the runoff module part; water quantity transmission is carried out through drainage facilities such as a pipe network and an open channel, and the water quantity of runoff generated by each sub-basin at any time with different time step lengths, the flow quantity and the water depth condition of water in each pipeline and a river channel are tracked and simulated.
The local fine analysis in the step 3) comprises the steps of carrying out quantitative evaluation on the drainage capacity of the existing drainage scheme under the extreme rainfall condition; carrying out local treatment: the single water outlet is used for refining the drainage time-space change analysis, and rechecking the stability of the drainage structure from the aspect of rock soil and structure from the aspect of water power.
The parameter informatization scheme in the step 4) is presented by integrating GIS space analysis technology, water (power) calculation analysis, drainage result visualization and BIM deepening application functions, exerting the advantages of the GIS and BIM technology in airport drainage design and simultaneously providing a parameter informatization scheme presentation solution for the airport drainage design process; editing data input by a research area, simulating hydrological and hydraulic change conditions, and displaying results in various forms, including carrying out color coding on a drainage area and a system drainage route, and providing time sequence curves and graphs of the results, a slope diagram and analysis results of statistical frequency; the water quantity time-varying process of the overload node is used as a boundary condition to be input into the earth surface model, so that the influence of topographic relief on the overflow of the overload water quantity earth surface is accurately expressed, and a parameter informatization scheme is provided for local fine adjustment.
The design method of the invention also comprises the following steps of 5) establishing a data management system: BIM and GIS technologies are fused to conduct data standardized management, index parameters such as node positions, node water volumes and overload time are recorded, a data base is provided for building a long-term information management platform, the target has the functions of scene presence, result inquiry, condition adjustment, data traceability and information warehousing, and the requirements of data inquiry, comparison, traceability, archiving and transfer are met.
The invention has the beneficial effects that:
1. the method realizes the quick hydraulic calculation, the parameterization scheme design and comparison selection, the excellent visual dynamic display and the like in the airport drainage design process. The problem that the drainage time-varying process cannot be described in detail in the traditional hydraulic calculation method is solved, the manual calculation cost is greatly saved, and the design efficiency is improved by more than one time.
2. The data analysis is more flexible, and the time-space change process of the water quantity and the water level of the macroscopic field region drainage and the local drainage node can be considered simultaneously. In addition to simulating water flow in gullies, the device can also simulate water flow in closed/open channel pipelines with various shapes; the (complete) kinetic wave equation is applied for the confluence calculation. Different forms of water flow may be described, such as backwater, overflow, reverse flow, and surface water volume prediction, among others.
3. The integrated design advantages of rainfall-runoff-pipe network drainage of the airport are exerted, the application of GIS technology and BIM forward design in airport design is further perfected, a standard parameterized data information interaction interface is established, and design cooperation barriers of drainage specialties and other related specialties are opened.
4. The functions of scene availability, result inquiry, condition adjustment, data traceability, information warehousing and the like can be realized, and the requirements of data inquiry, comparison, traceability, filing and transfer are met. The method is applied to the design process of a certain airport at present, obtains better effect and provides data reference for the comparison of multiple schemes of drainage lines.
The invention is further explained below with reference to the drawings and the detailed description.
Drawings
FIG. 1 is a schematic topographical view of an embodiment of the present invention;
FIG. 2 is a schematic view of a slope/flow analysis according to an embodiment of the present invention;
FIG. 3 is a schematic view of the positioning of the catchment area and the drainage point according to the embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a statistical analysis of the area of the channeling basin according to an embodiment of the present invention;
FIG. 5 is a schematic view of a "rainfall-runoff-pipe network" integrated model in an embodiment of the invention;
FIG. 6 is a schematic diagram illustrating node risk partitioning for a field according to an embodiment of the present invention;
FIG. 7 is a schematic plan view of an overflow node according to an embodiment of the present invention;
fig. 8 is a diagram of the flooding process according to the embodiment of the present invention (t ═ 5 min);
fig. 9 is a diagram of the flooding process according to the embodiment of the present invention (t ═ 10 min);
fig. 10 is a diagram of the flooding process according to the embodiment of the present invention (t ═ 15 min);
fig. 11 is a diagram of the flooding process according to the embodiment of the present invention (t ═ 20 min);
fig. 12 is a diagram of the flooding process of the embodiment of the present invention (t ═ 25 min);
FIG. 13 is a diagram illustrating a spatial distribution of river networks in a research area according to the flow direction judgment criteria "D8" in accordance with the present invention;
FIG. 14 is a schematic diagram of a technical scheme of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. The specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The embodiment provides a rainfall, runoff and pipe network integrated drainage design method special for an airport, and is used for solving the drainage design problem in the engineering of newly-built airports and reconstructed and expanded airports. The method is composed of four modules of site external hydrological environment analysis, airport drainage confluent analysis, local fine analysis and parameter informatization scheme presentation, and the specific implementation process is as follows:
1. site external hydrological environment analysis
Depending on the construction project of a new airport, the method analyzes the terrain and hydrological environment around the site and is beneficial toBy using an Arc Hydro Tool, through analysis such as terrain (figure 1), slope/flow direction (figure 2), runoff accumulation, river network grading, catchment area division, drainage point positioning (figure 3) and the like, the spatial distribution of the river network in a research area (figure 13) is obtained according to a flow direction judgment criterion of D8, and a potential catchment area-gully is positioned according to terrain change and confluence characteristics (figure 4). Accumulating and calculating the catchment area in the gully range by using a spatial statistical analysis tool to obtain the gully area (563.7 ten thousand meters)2) And preliminarily determining the length of the drainage line under the design of the optimal control strategy.
2. Integrated design of drainage rainfall-runoff-pipe network for airport
Taking a certain airport as an example, dividing a ground catchment area according to the hydrological analysis and the topographic conditions, setting a pipe network and corresponding nodes according to a design scheme, and setting a rainfall-runoff-pipe network integrated model of the airport as shown in fig. 5. In order to better analyze the time-space variation process of the drainage, the rainfall condition adopts constant rainfall intensity. Calculating the surface flow rate according to the water balance principle; solving the earth surface confluence by utilizing a continuous equation and a Manning equation according to the nonlinear reservoir model; and (4) calculating the water discharge amount of the water flow in the airport drainage pipe network (ditch) according to a one-dimensional Saint-Venn equation set. When the rainfall intensity is set to be 5mm/h and the rainfall duration is 3h, a part of nodes (figure 8) are selected, the water quantity in the nodes is increased rapidly when the rainfall starts, the nodes reach a steady state in a rapid time, and the water quantity of the nodes falls back obviously when the rainfall is finished. From the upstream to the downstream of the pipe network, the node water amount is reduced in sequence. In the process of reducing the node water volume after the rainfall is finished, the reduction of the downstream node water volume is slightly delayed compared with the upstream node water volume under the influence of space factors (relative position, spacing and the like). The water quantity of the downstream node comprises not only the upstream water inflow quantity, but also the surface water quantity of the catchment area corresponding to the position of the downstream node. Therefore, downstream nodes are relatively more susceptible to overloading.
Under certain rainfall intensity, the rainfall duration is prolonged or the rainfall intensity is increased, the overload sequence of potential flooding nodes is simulated, the number of the flooding nodes in the field area in the whole rainfall process is calculated and compared (table 1), and according to the times of the flooding nodes appearing under different rainfall intensities, the pipe network nodes in the field area are divided into flooding areas with different risks (figure 6), so that reference basis is provided for setting of related flood control measures.
TABLE 1 Water volume at overload node
Figure BDA0003280531460000081
3. Local refinement analysis and parameter informatization scheme presentation
Editing data input by a research area, simulating hydrological and hydraulic change conditions, and displaying results in various forms, including carrying out color coding on drainage areas and system drainage routes, and providing time series curves and graphs of results, slope maps and analysis results of statistical frequency. The water quantity time-varying process of the overload node is used as a boundary condition to be input into the earth surface model, so that the influence of topographic relief on the overflow of the overload water quantity earth surface is accurately expressed, and a parameter informatization scheme is provided for local fine adjustment.
When the node water volume is overloaded, the water volume overflowing from the node can form local confluence in the field area, so that local flooding is caused. In order to obtain the submerged evolution process, the time-varying process of the node overload water volume in the SSA calculation result is used as a water volume boundary condition, BIM software (such as but not limited to DHI-MIKE) is introduced to quantitatively describe the evolution process of the surface water, and then a field surface flow field model is established (fig. 7). Through the effective connection of the two results, the accurate quantitative expression of the surface flood inundation process of the field is realized (fig. 8-12), and the surface flood inundation result is visually checked through BIM software (such as but not limited to DHI-MIKE, Tecplot and the like). Accordingly, the submerging range and the submerging water depth are determined, and corresponding treatment measures are made for potential local flooding.
TABLE 2 Water volume at overload node
Figure BDA0003280531460000091
4, building a data management system integrating BIM and GIS technologies
BIM and GIS technologies are fused for data standardized management, and output data (node positions, water quantities, water depths, flow rates and the like) are stored according to corresponding format requirements (table 1) so as to meet the requirements of data query, comparison, tracing, filing and handover.
TABLE 3 data filing table
Figure BDA0003280531460000092
The case analysis shows that the method not only can realize the spatial distribution simulation of the drainage process of the field on the medium and macro scale, but also has good simulation precision and strong operability based on the actual rainfall and actual terrain data. The method comprehensively considers key problems of field macroscopic drainage line design, local gully water quantity fine evaluation and the like, cooperates with the drainage capacity and the structural stability of the drainage structure and even related professional design, strengthens further integration with related professionals, and can perform data interaction with related professionals of airport design.
The foregoing is only a part of the specific embodiments of the present invention and specific details or common general knowledge in the schemes have not been described herein in more detail. It should be noted that the above-mentioned embodiments do not limit the present invention in any way, and all technical solutions obtained by means of equivalent substitution or equivalent transformation for those skilled in the art are within the protection scope of the present invention. The scope of the claims of the present application shall be determined by the contents of the claims, and the description of the embodiments and the like in the specification shall be used to explain the contents of the claims.

Claims (10)

1. A method for designing rainfall, runoff and pipe network integrated drainage special for airports is characterized by comprising four steps of site external hydrological environment analysis, airport drainage confluent flow analysis, local fine analysis and parameter informatization scheme presentation;
the four steps are sequentially performed by 1) site external hydrological environment analysis, 2) airport drainage sink flow analysis, 3) local fine analysis and 4) parameter informatization scheme presentation;
the method comprises the following steps that 1), the hydrological environment outside the site is analyzed, namely, the hydrological environment around the airport is evaluated, and the surrounding hydrological environment comprises special landforms; obtaining the area of a potential flooding area and the length of a drainage line under the design of an optimal control strategy;
step 2), airport drainage sink flow analysis, namely, the drainage process analysis is carried out on airport surface areas, and the water volume space-time change rule under a single precipitation event is analyzed;
the step 3) local fine analysis, namely scheme comparison and optimization are carried out by adjusting local parameter information;
and 4) displaying the result in various forms by using the parameter informatization scheme in the step 4), wherein the result is quantitatively described in a drainage area and a drainage evolution process, and a time series curve and a chart of the result, a slope diagram and an analysis result of statistical frequency are provided.
2. The integrated drainage design method for rainfall, runoff and pipe networks special for airports as claimed in claim 1, wherein the special landform in the step 1) of analyzing the outside hydrological environment of the site comprises gully and pipeline underpass.
3. The integrated drainage design method for rainfall, runoff and pipe networks special for airports as claimed in claim 1, wherein the airport surface areas in the step 2) of airport drainage confluence analysis comprise a road surface and an open trench.
4. The method for designing integrated drainage of rainfall, runoff and pipe networks specially used for airports as claimed in claim 1, wherein the local parameter information in the local refinement analysis in the step 3) comprises the gradient of the catchment area, the ratio of the water permeable area of the catchment area and the size of the ditch pipe.
5. The method for designing integrated drainage of rainfall, runoff and pipe networks special for airports according to claim 1, wherein the step 1) of analyzing the hydrological environment outside the site is to preliminarily quantify the possible flood outside the site by using a GIS hydrological analysis technology and reasonably design the scale and the size of a drainage system; accurately drawing a flood area of a natural channel/river channel system, and providing an optimal control strategy design on the premise of ensuring the drainage requirement of a drainage line; specifically, according to the flow direction judgment criterion of 'D8', namely meshing the earth surface on a two-dimensional plane, it is considered that the water flow in a certain grid flows to the grid with the highest height in eight adjacent grids on the earth surface relative to the grid; and connecting the grids by using a solid line according to the principle that the flowing water always flows to a low position, namely obtaining the spatial distribution of the river network in the research area, and further determining the length of the drainage line under the design of an optimal control strategy.
6. The airport special rainfall, runoff and pipe network integrated drainage design method as claimed in claim 1, wherein the airport drainage production and collection flow analysis of step 2) is that an airport drainage numerical analysis model is built according to terrain conditions by using a water balance principle and a nonlinear reservoir model, a surface catchment area is divided according to the terrain conditions of a design scheme, and open-ditch and blind-ditch drainage structures are arranged; and calculating the runoff process of the road surface by adopting a hydraulic calculation method, and solving the confluence process in the ditch or the pipeline by a one-dimensional Saint-Venn equation set.
7. The airport-specific rainfall, runoff and pipe network integrated drainage design method as set forth in claim 1, wherein the step 3) of local refinement analysis is that the existing drainage scheme is subjected to quantitative evaluation of drainage capacity under extreme rainfall conditions; carrying out local treatment: the single water outlet is used for refining the drainage time-space change analysis, and rechecking the stability of the drainage structure from the aspect of rock soil and structure from the aspect of water power.
8. The airport-specific rainfall, runoff and pipe network integrated drainage design method of claim 1, wherein the parameter informatization scheme of step 4) is presented by integrating GIS space analysis technology, water (dynamic) force calculation analysis, drainage result visualization and BIM deepening application functions, editing data input in a research area, simulating hydrology and hydraulic change conditions, and displaying results in various forms, including color coding of drainage areas and system drainage routes, providing time series curves and graphs of results, slope maps and analysis results of statistical frequency; the water quantity time-varying process of the overload node is used as a boundary condition to be input into the earth surface model, so that the influence of topographic relief on the overflow of the overload water quantity earth surface is accurately expressed, and a parameter informatization scheme is provided for local fine adjustment.
9. The airport special rainfall, runoff and pipe network integrated drainage design method as claimed in claim 1, 3 or 5, wherein the airport drainage sink flow analysis of step 2) is specifically based on the water balance principle,
wherein, the flow production part:
for impervious ground surfaces, the following formula is followed:
when there is no depression on the earth's surface, R1=P-E;
When there is depression on the earth's surface, R2=P-D;
R1、R2Water yield on the earth surface is mm; p is rainfall, mm; e is evaporation capacity, mm; d is the depression storage amount, mm;
for permeable surfaces, rainfall losses include pooling and infiltration according to the following formula:
R3=(i-f)t;
R3water yield on the earth surface is mm; i is rainfall intensity, mm/s; f is infiltration strength, mm/s;
a confluence portion:
solving by using a continuous equation and a Manning equation according to the nonlinear reservoir model,
the continuous equation:
Figure FDA0003280531450000031
in the formula: v is the surface water collection amount, m3(ii) a h is water depth m; t is time, s; a is the surface area, m2(ii) a i is the net rain intensity, mm/s; q is the flow, m3/s;
The manning equation is:
Figure FDA0003280531450000032
in the formula: w: width of sub-basin, m; n: a Mannich coefficient; h isp: the ground water storage depth is mm; s0: the sub-basin slope.
10. The airport special rainfall, runoff and pipe network integrated drainage design method as claimed in claim 1, 4 or 6, wherein the local refinement analysis in the step 3) is specifically,
for the description of the water flow in the drainage pipe network (ditch) of the airport, solving according to a one-dimensional Saint-Venn equation set;
Figure FDA0003280531450000041
Figure FDA0003280531450000042
in the formula, x: a one-dimensional spatial variable; bs: water surface width, m; g: acceleration of gravity, m/s2;As: cross sectional area of water flow, m2;ib: a bottom slope; k: flow modulus, m2/s。
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