# Optimized Design of Sponge-Type Comprehensive Pipe Corridor Rainwater Chamber Based on NSGA-III Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Scheme Design

#### 2.2. Study Area

#### 2.3. Storm Water Management Model

#### 2.3.1. Model Description

#### 2.3.2. Establishment of the SWMM

#### 2.3.3. Design Rainfall

^{2}); $t$ is the rainfall duration (120 min); and $P$ is the design rainfall return periods (2 yr, 3 yr, 5 yr, 20 yr, and 50 yr). Figure 5 below shows the design rainfall process under different return periods, and Table 1 shows the rainfall intensity.

#### 2.3.4. SWMM Model Parameterization and Validation

^{2}); ${\psi}_{i}$ is the runoff coefficient of the i-th sub-catchment; and $F$ is the total area of all sub-catchments (hm

^{2}). The final parameters of the model and the comprehensive runoff coefficient under different rainfall return periods were obtained using this method. The study area is planned as an economic development zone with a high degree of development, and the average imperviousness established in the study area is 78.3%. According to the recommended values in the “Concise Drainage Design Manual” [30] compiled by the Beijing Municipal Design Research Institute (see Table 2 for the specific values), the corresponding integrated runoff coefficients of the study area range from 0.6 to 0.8. The integrated runoff coefficients of the model of the study area under different rainfall recurrence periods (2 yr, 3 yr, 5 yr, 20 yr, and 50 yr) and the comprehensive runoff coefficients of the model in the study area under different rainfall recurrence periods (2 yr, 3 yr, 5 yr, 20 yr, and 50 yr) were 0.649, 0.665, 0.685, 0.728, and 0.751, respectively, which were in a reasonable range and could be used as a follow-up study, and the specific parameters of the validated model are shown in Table 3.

#### 2.4. Design of Manual Subjective Design Schemes

#### 2.4.1. Comprehensive Pipe Corridor Rainwater Chamber Scheme

#### 2.4.2. Combination LID Measure Scheme

#### 2.4.3. Manual Optimization Scheme

#### 2.5. Optimization Model Scheme Based on NSGA-III Algorithm

#### 2.5.1. NSGA-III Optimization Algorithm

_{t}(N), after crossover and mutation to produce the offspring population Q

_{t}(N), combining the two populations to form R

_{t}(2N), and dividing them into multiple non-dominated layers (F

_{1}, F

_{2}, ……F

_{i}) by using non-dominated sorting, starting from the F

_{1}layer, the non-dominated sorting into S

_{t}, then F

_{2}…, until the size of S

_{t}is N, which serves as the parent population P

_{t+1}for the next iteration. The above process is repeated until the set number of genetic generations is reached.

#### 2.5.2. Objective Function

^{2}of the area of the comprehensive pipe corridor cross-section under the total length. Regarding the cost, the final cost can be determined by referring to the cost of the LID and comprehensive pipe corridor in the “Technical Guidelines for Sponge City Construction” [41] and the study of Hengyu Wang et al. [42], taking into account the local price of raw materials in the study area and other related costs, as shown in Table 7.

^{2}of the comprehensive pipe corridor cross-sectional area under the total length.

#### 2.5.3. Constraints

#### 2.5.4. Optimization Model Construction

- (1)
- Model SWMM and identify the different combinations of LID measures used in each sub-catchment;
- (2)
- Dimensional information for combination LID measures with different percentages of paving and different rainwater chamber section widths was entered into the model to create SWMM models with different ratios, and 100 groups of data were obtained;
- (3)
- Multiple linear regression was used to establish linear relationships between the percentage of combined LID measures laid, the width of the rainwater chamber section, the surface runoff coefficient, pipe overload time, nodal overflow, and the total investment cost;
- (4)
- The best design scheme is obtained by optimally solving the linear relationship between several by the NSGA-III algorithm to obtain the Pareto front;
- (5)
- Substitute the individual optimal solutions in the obtained solution set into the model for checking and verifying the validity of the optimization model and the applicability of the NSGA-III algorithm.

## 3. Results

#### 3.1. Comprehensive Pipe Corridor Rainwater Chamber Scheme

#### 3.2. Combination LID Measures

#### 3.3. Manual Optimization Scheme

#### 3.4. NSGA-III Optimization Model

#### 3.4.1. Optimal Variables

#### 3.4.2. Pareto Frontier of the Optimizing Model

#### 3.4.3. Optimization Model Convergence Evaluation

#### 3.4.4. Optimization Model Validation

## 4. Discussion

#### 4.1. Impact of Different Rainfall Return Periods on the Three Indicators

#### 4.2. Multi-Objective Tradeoffs

#### 4.3. Scheme Assessment

## 5. Conclusions

- (1)
- A four-objective NSGA-III optimization model is established, and two traditional drainage system state indicators, surface runoff coefficient and total investment cost, are selected as the optimization objectives to be solved, and optimization schemes are obtained;
- (2)
- The NSGA-III optimization model can realize the simultaneous optimization of surface runoff coefficient, pipe overload time, node overflow, and total investment cost, which can effectively reduce the three flooding evaluation indexes and control the total investment cost. The NSGA-III optimization algorithm has high reliability and effectiveness in this field;
- (3)
- The NSGA-III optimization model has a better mitigation effect than the integrated pipe corridor rainwater tank scheme and the combined LID measure scheme and has more choice space compared with the manual optimization scheme;
- (4)
- According to the Pareto front, surface runoff coefficient, pipe overload time, and nodal overflow volume are proportional to each other, while they are inversely proportional to the total investment cost, and designers must consider the balance and priority between them.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Effect of different rainwater chamber section sizes on the three indicators under different rainfall return periods.

**Figure 9.**Effect of different LID percentages on the three indicators under different rainfall return periods.

Rains Return Period (yr) | 2 | 3 | 5 | 20 | 50 |

Rainfall depth (mm) | 57.48 | 60.51 | 68.10 | 88.71 | 102.33 |

Degree of Land Development | Values |
---|---|

Most densely built-up central area (imperviousness rate > 70%) | 0.6~0.8 |

More densely built-up residential areas (50% < imperviousness rate < 70%) | 0.5~0.7 |

Sparsely built-up residential areas (30% < imperviousness rate < 50%) | 0.4~0.6 |

Sparsely populated areas (imperviousness rate < 30%) | 0.3~0.5 |

Item | Main Parameters | Value Range | Final Value |
---|---|---|---|

Sub-catchments | Manning coefficients in impervious areas | 0.011~0.014 | 0.013 |

Manning coefficients in pervious areas | 0.15 | 0.15 | |

Depression storage in impervious areas/mm | 1.27~2.54 | 2 | |

Depression storage in pervious areas/mm | 3~10 | 8 | |

Pipe | Pipeline Manning’s Coefficient | 0.012~0.015 | 0.012 |

Infiltration Data (HORTON) | Maximum infiltration rate (mm/h) | — | 75.4 |

Minimum infiltration rate (mm/h) | — | 3.66 | |

Infiltration decay constant (1/h) | — | 2 | |

Drainage time/d | — | 7 |

Land Use Type | Area (hm^{2}) | Percentage (%) |
---|---|---|

residential land | 299.00 | 26.0 |

Public administration and public service land | 113.85 | 9.9 |

Business services facilities land | 136.85 | 11.9 |

Industrial land | 162.15 | 14.1 |

Logistics and warehousing land | 148.35 | 12.9 |

Roads and Transportation Facility Land | 164.45 | 14.3 |

Serviced land | 21.85 | 1.9 |

Green space and plaza land | 103.50 | 9.0 |

Total | 1150.00 | 100 |

No. | Land Use Type | Combination |
---|---|---|

1 | residential land, Public administration and public service land and Business services facilities land | 50% green roof + 30% permeable pavement +10% vegetative swale + 10% bioretention pond |

2 | Industrial land | 40% green roof + 40% permeable pavement +10% vegetative swale + 10% bioretention pond |

3 | Logistics and warehousing land | 30% green roof + 50% permeable pavement +10% vegetative swale + 10% bioretention pond |

4 | Roads and Transportation Facility Land | 80% permeable pavement +10% vegetative swale + 10% bioretention pond |

5 | Green space and plaza land | 40% permeable pavement +30% vegetative swale + 30% bioretention pond |

LID Measures | Structural Layer | Design Parameters | Parameter Values (%) |
---|---|---|---|

Green roof | surface | berm height/mm | 80 |

surface roughness | 0.25 | ||

surface slope/% | 1 | ||

vegetation volume fraction | 0.4 | ||

soil | thicknesses/mm | 150 | |

porosity | 0.18 | ||

hydraulic conductivity/mm·h^{−1} | 18 | ||

storage | thicknesses/mm | 20 | |

porosity | 0.5 | ||

permeable pavement | surface | berm height/mm | 20 |

surface roughness | 0.11 | ||

surface slope/% | 1 | ||

pavement | thicknesses/mm | 120 | |

void ratio | 0.5 | ||

permeability/mm·h^{−1} | 300 | ||

storage | thicknesses/mm | 250 | |

void ratio | 0.43 | ||

bioretention pond | surface | berm height/mm | 300 |

surface roughness | 0.15 | ||

surface slope/% | 1 | ||

vegetation volume fraction | 0.4 | ||

soil | thicknesses/mm | 500 | |

porosity | 0.18 | ||

hydraulic conductivity/mm·h^{−1} | 18 | ||

storage | thicknesses/mm | 200 | |

void ratio | 0.75 | ||

vegetative swale | surface | berm height/mm | 150 |

surface roughness | 0.2 | ||

surface slope/% | 0.2 | ||

swale side slope | 3 |

Item | Items | Unit Cost (RMB/m^{2}) | Total Unit Cost after Calculation (RMB) |
---|---|---|---|

LID measures | Green roof | 179 | 16,723,411.52 |

permeable pavement | 104 | 9,716,395.52 | |

bioretention pond | 458 | 42,789,511.04 | |

vegetative swale | 87 | 8,128,138.56 | |

Comprehensive pipe corridor | Comprehensive pipe corridor | 2183 | 159,512,137.45 |

Indicators | 2 yr | 3 yr | 5 yr | 20 yr | 50 yr |
---|---|---|---|---|---|

Surface runoff coefficient | 0.707 | 0.726 | 0.748 | 0.799 | 0.824 |

Pipe overload time/h | 30.450 | 34.409 | 38.625 | 48.148 | 52.552 |

Nodal overflow/Mltr | 24.312 | 37.712 | 58.701 | 130.042 | 186.071 |

Combination | 20.0% + 0.756 m | 20.0% + 0.762 m | 30.0% + 0.775 m | |||
---|---|---|---|---|---|---|

SWMM | Optimization Model | SWMM | Optimization Model | SWMM | Optimization Model | |

Surface runoff coefficient | 0.508 | 0.508 | 0.508 | 0.508 | 0.449 | 0.449 |

Pipe overload time (h) | 8.730 | 8.997 | 8.606 | 8.968 | 7.245 | 7.112 |

Nodal overflow volume (Mltr) | 82.151 | 82.242 | 80.890 | 81.173 | 55.936 | 55.668 |

Average error | 1.03% | 1.46% | 0.78% |

Situation | Surface Runoff Coefficient | Pipe Overload Time (h) | Nodal Overflow Volume (Mltr) | Total Investment Cost (10^{8} RMB) |
---|---|---|---|---|

Initial scheme | 0.824 | 52.552 | 186.071 | — |

Comprehensive pipe corridor rainwater chamber scheme | 0.824 | 2.138~21.172 | 8.311~263.027 | 36.752~43.643 |

Combination LID measures scheme | 0.167~0.596 | 2.271~40.746 | 0~110.385 | 1.602~16.020 |

Manual optimization scheme | 0.449 | 2.497 | 10.996 | 44.620 |

NSGA-III optimization model scheme | 0.355~0.519 | 4.501~9.702 | 27.980~90.100 | 40.311~45.009 |

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## Share and Cite

**MDPI and ACS Style**

Ren, Y.; Zhang, H.; Wang, X.; Gu, Z.; Fu, L.; Cheng, Y.
Optimized Design of Sponge-Type Comprehensive Pipe Corridor Rainwater Chamber Based on NSGA-III Algorithm. *Water* **2023**, *15*, 3319.
https://doi.org/10.3390/w15183319

**AMA Style**

Ren Y, Zhang H, Wang X, Gu Z, Fu L, Cheng Y.
Optimized Design of Sponge-Type Comprehensive Pipe Corridor Rainwater Chamber Based on NSGA-III Algorithm. *Water*. 2023; 15(18):3319.
https://doi.org/10.3390/w15183319

**Chicago/Turabian Style**

Ren, Yazheng, Huiying Zhang, Xinhua Wang, Zhanfei Gu, Linie Fu, and Yang Cheng.
2023. "Optimized Design of Sponge-Type Comprehensive Pipe Corridor Rainwater Chamber Based on NSGA-III Algorithm" *Water* 15, no. 18: 3319.
https://doi.org/10.3390/w15183319