# Design of Drainage Downspouts Systems over a Road Embankment

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Design Hyetograph

#### 2.2. Numerical Tool: Iber

_{x}and q

_{y}denote the two components of the specific discharge, g is the gravitational acceleration, S

_{o}

_{,x}and S

_{o}

_{,y}are the two components of the bottom slope, and S

_{f}

_{,x}and S

_{f}

_{,y}are the two components of the friction slope, typically calculated using the Manning formula.

- Rainfall Field Definition: Iber allows users to define rainfall fields using data from rain gauges or raster files.
- Rainfall Loss Definition: Users can specify rainfall losses using various infiltration models, such as Green–Ampt, Horton, SCS, and constant infiltration, all of them constant or spatially distributed.
- Ad hoc Numerical Scheme: Iber incorporates a specialized numerical scheme known as the DHD scheme, purpose-built for hydrological applications.
- Digital Terrain Model Enhancement: Iber provides utilities to efficiently smooth Digital Terrain Models, even when they may have poor quality or unfavorable conditions.

#### 2.3. Design Criteria

- Design storm. In this case study, rainfall is established for a return period of T = 25 years, as indicated in the Spanish Road Drainage Regulation (5.2-IC).
- Flow depth is circulating over the side gutter, encroaching into the shoulder. This parameter relates to the driver’s safety to the extent that a vehicle driving on the shoulder could present stability problems due to aquaplaning [4,16,19,52]. This parameter depends on the dimensions of the prefabricated element that limits the flow, generally a barrier kerb of 10 cm high.
- Flow depth in the downspout drain inlet and in the downspout. This parameter is related to the maintenance of the road embankment to the extent that hypothetical drain overflows on the embankment could affect its stability. The authors, based on their experience, consider that a minimum guard of 3 cm should be considered, bearing in mind the potential existence of obstacles or sediments.
- Cross-section choice. A standard section must be selected with the indications of the Project Technical Specifications. The analysis of the possible standard sections is beyond the scope of this research; instead, a methodology where any cross-section can be considered is presented. Nevertheless, generally speaking, there are currently two possible cross sections, with or without a side gutter. For the purposes of the present paper, the latter type of cross-section has been selected (Figure 1).

## 3. Case Study

#### 3.1. Study Area

- Separation between embankment downspouts: 25 m, 20, and 15 m (three models)
- Longitudinal slope: 0.5% to 5% (six models)
- Gutter width: 30 cm and 20 cm (two models)
- Type of nozzle, called large and reduced (see dimensions in Figure 2) (two models)

#### 3.2. Climate Information

#### 3.3. Numerical Model and Domain Discretization

## 4. Results and Discussion

#### 4.1. Hydraulic Performance

#### 4.2. Nozzle Size

#### 4.3. Longitudinal Slope

#### 4.4. Gutter Width and Embankment Downspout Distancing

#### 4.5. Nozzle Type: Symmetrical and Asymmetrical

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Type of nozzles modeled in this research. Above: asymmetrical. Below: symmetrical. Left: large nozzles (LN). Right: reduced nozzles (RN). Blue arrows indicate the flow direction in the gutter and the downspout.

**Figure 7.**Maximum water depth in the nozzle for different longitudinal slopes for a 30 cm gutter and a large nozzle.

**Figure 8.**Maximum water depth (cm) for the 30 cm wide gutter for different slopes and types of nozzle (the black dotted line indicates the minimum guard that the sheet of water can reach according to the Spanish standard 5.2-IC).

**Figure 9.**Maximum water depth (cm) for the 20 cm wide gutter for different slopes and types of nozzles (the black dotted line indicates the minimum guard that the sheet of water can reach according to the Spanish standard 5.2-IC).

**Figure 10.**Longitudinal profile for a hydraulic model with 20 m downspout spacing, a 30 cm wide gutter, and large asymmetric and symmetric nozzles.

**Figure 11.**Water depth and velocity for a symmetrical nozzle with a downspout separation of 20 m, a longitudinal slope of 5%, and an gutter width of 30 cm. The yellow arrows represent the direction and magnitude of velocity vectors in each point.

**Figure 12.**Water depth and velocity for an asymmetrical nozzle with a downspout separation of 20 m, a longitudinal slope of 5%, and a gutter width of 30 cm. The yellow arrows represent the direction and magnitude of velocity vectors in each point.

Inner Shoulder | Inner Road Lane | Outer Road Lane | Outer Shoulder | Berm | Cross Slope (i_{t}) | Long. Slope (i_{l}) |
---|---|---|---|---|---|---|

1.0 m | 3.5 m | 3.5 m | 2.5 m | 1.5 m | 2% | 0–5% |

**Table 2.**Drainage area for each embankment downspout (B) (m

^{2}) for a separation of 25 m, depending on the longitudinal slope of the road (i

_{l}).

Slope (i_{l}) | B1 | B2 | B3 | B4 | B5 |
---|---|---|---|---|---|

0.5% | 262.75 | 262.75 | 262.75 | 262.75 | 40.17 |

1% | 262.75 | 262.75 | 262.75 | 262.52 | 25.25 |

2% | 262.75 | 262.75 | 262.75 | 246.31 | 11.52 |

3% | 262.75 | 262.75 | 262.75 | 220.92 | 6.97 |

4% | 262.75 | 262.75 | 262.75 | 193.22 | 4.73 |

5% | 262.75 | 262.75 | 262.75 | 164.61 | 3.41 |

**Table 3.**Drainage area for each embankment downspout (B) (m

^{2}) for a separation of 20 m, depending on the longitudinal slope of the road (i

_{l}).

Slope (i_{l}) | B1 | B2 | B3 | B4 | B5 |
---|---|---|---|---|---|

0.5% | 210.06 | 210.06 | 210.06 | 210.06 | 40.17 |

1% | 210.06 | 210.06 | 210.06 | 210.06 | 25.25 |

2% | 210.06 | 210.06 | 210.06 | 193.79 | 11.52 |

3% | 210.06 | 210.06 | 210.06 | 168.40 | 6.97 |

4% | 210.06 | 210.06 | 210.06 | 141.39 | 4.05 |

5% | 210.06 | 210.06 | 209.53 | 113.00 | 3.40 |

**Table 4.**Drainage area for each embankment downspout (B) (m

^{2}) for a separation of 15 m, depending on the longitudinal slope of the road (i

_{l}).

Slope (i_{l}) | B1 | B2 | B3 | B4 | B5 |
---|---|---|---|---|---|

0.5% | 157.55 | 157.55 | 157.55 | 157.55 | 40.17 |

1% | 157.55 | 157.55 | 157.55 | 157.49 | 25.25 |

2% | 157.55 | 157.55 | 157.55 | 141.28 | 11.52 |

3% | 157.55 | 157.55 | 157.55 | 168.40 | 6.97 |

4% | 157.55 | 157.55 | 156.86 | 88.75 | 4.73 |

5% | 157.55 | 157.55 | 146.72 | 69.75 | 3.40 |

Downspout Separation (m) | Longitude (m) | Width (m) | Surface Area (m^{2}) | Volume (m^{3}) |
---|---|---|---|---|

25 | 108 | 10.5 | 1134.3 | 171.2 |

20 | 88 | 10.5 | 924.27 | 140.04 |

15 | 68 | 10.5 | 714.21 | 109.06 |

**Table 6.**Percentage of evacuated volume of water with respect to the total volume for the 72 models analyzed for different downspout separations, gutter width, and nozzle type.

Downspout Separation | 25 m | 20 m | 15 m | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Gutter Width | 20 cm | 30 cm | 20 cm | 30 cm | 20 cm | 30 cm | |||||||

Nozzle Type | RN | LN | RN | LN | RN | LN | RN | LN | RN | LN | RN | LN | |

Longitudinal slope (i_{l}) | 0.5 | * 99 | * 99 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |

1 | * 99 | * 99 | * 98 | 100 | * 95 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | |

2 | * 96 | * 99 | * 96 | 100 | * 95 | 100 | * 97 | 100 | * 99 | 100 | 100 | 100 | |

3 | * 93 | * 99 | * 92 | 100 | * 92 | 100 | * 94 | 100 | * 96 | 100 | * 98 | 100 | |

4 | * 89 | * 98 | * 88 | 100 | * 88 | 100 | * 91 | 100 | * 94 | 100 | * 98 | 100 | |

5 | * 84 | * 97 | * 82 | * 99 | * 86 | 98 | * 86 | 100 | * 91 | 100 | * 97 | 100 |

**Table 7.**Maximum water depths (in cm) for the different drainage elements of the platform with a large nozzle and a 30 cm wide gutter.

25 m Downspout Separation | 20 m Downspout Separation | 15 m Downspout Separation | |||||||
---|---|---|---|---|---|---|---|---|---|

Slope | Gutter | Nozzle | Downspout | Gutter | Nozzle | Downspout | Gutter | Nozzle | Downspout |

0.5% | 7.5 | 8.2 | 6.6 | 6.5 | 7.5 | 6.1 | 5.4 | 7.0 | 5.0 |

1% | 6.9 | 7.5 | 6.2 | 6.0 | 7.0 | 6.0 | 5.2 | 6.0 | 5.0 |

2% | 6.0 | 7.0 | 6.0 | 5.6 | 6.7 | 5.6 | 5.0 | 6.0 | 5.0 |

3% | 5.7 | 7.3 | 5.8 | 5.3 | 6.0 | 5.2 | 4.9 | 6.0 | 5.0 |

4% | 5.3 | 7.1 | 5.7 | 4.8 | 5.9 | 5.0 | 4.6 | 5.0 | 4.0 |

5% | 5.0 | 6.9 | 5.5 | 4.6 | 5.8 | 4.8 | 4.0 | 5.0 | 4.0 |

**Table 8.**Maximum water depths (in cm) for the different drainage elements of the platform with a reduced nozzle and a 30 cm wide gutter.

25 m Downspout Separation | 20 m Downspout Separation | 15 m Downspout Separation | |||||||
---|---|---|---|---|---|---|---|---|---|

Slope | Gutter | Nozzle | Downspout | Gutter | Nozzle | Downspout | Gutter | Nozzle | Downspout |

0.5% | 7.9 | 7.1 | 3.8 | 7.0 | 6.1 | 3.3 | 5.3 | 4.8 | 2.6 |

1% | 7.7 | 6.6 | 3.7 | 6.7 | 5.7 | 3.1 | 5.1 | 4.5 | 2.5 |

2% | 7.5 | 7.4 | 3.8 | 6.5 | 6.1 | 3.0 | 5.0 | 4.5 | 2.6 |

3% | 7.1 | 8.7 | 3.6 | 6.2 | 7.0 | 3.0 | 5.0 | 5.9 | 2.5 |

4% | 6.8 | 9.7 | 3.4 | 5.8 | 7.8 | 3.0 | 4.7 | 6.4 | 2.3 |

5% | 6.6 | 10.0 | 3.3 | 5.7 | 8.9 | 3.0 | 4.4 | 8.1 | 2.6 |

**Table 9.**Maximum water depths (in cm) for the different drainage elements of the platform with a large nozzle and a 20 cm wide gutter.

25 m Downspout Separation | 20 m Downspout Separation | 15 m Downspout Separation | |||||||
---|---|---|---|---|---|---|---|---|---|

Slope | Gutter | Nozzle | Downspout | Gutter | Nozzle | Downspout | Gutter | Nozzle | Downspout |

0.5% | 8.9 | 7.2 | 6.3 | 7.2 | 6.6 | 5.2 | 6.5 | 6.1 | 4.3 |

1% | 7.8 | 6.4 | 5.5 | 6.8 | 6.3 | 4.8 | 6.0 | 5.4 | 4.6 |

2% | 6.9 | 6.1 | 5.3 | 6.0 | 6.1 | 4.5 | 4.9 | 4.9 | 4.1 |

3% | 6.3 | 6.0 | 5.3 | 5.2 | 6.0 | 4.4 | 4.3 | 4.4 | 4.1 |

4% | 6.0 | 5.8 | 5.1 | 4.9 | 5.8 | 4.3 | 4.0 | 4.2 | 3.8 |

5% | 5.8 | 6.2 | 4.9 | 4.7 | 5.6 | 4.2 | 3.9 | 4.1 | 3.8 |

**Table 10.**Maximum water depths (in cm) for the different drainage elements of the platform with a reduced nozzle and a 20 cm wide gutter.

25 m Downspout Separation | 20 m Downspout Separation | 15 m Downspout Separation | |||||||
---|---|---|---|---|---|---|---|---|---|

Slope | Gutter | Nozzle | Downspout | Gutter | Nozzle | Downspout | Gutter | Nozzle | Downspout |

0.5% | 9.5 | 6.2 | 3.3 | 7.9 | 4.8 | 2.6 | 6.8 | 5.4 | 3.1 |

1% | 9.3 | 6.2 | 3.6 | 7.8 | 5.2 | 3.0 | 6.5 | 4.5 | 2.4 |

2% | 8.1 | 7.1 | 3.4 | 7.0 | 6.6 | 2.8 | 6.1 | 4.5 | 2.5 |

3% | 7.6 | 8.0 | 3.3 | 6.6 | 7.0 | 3.0 | 5.4 | 5.3 | 2.3 |

4% | 7.3 | 8.8 | 3.2 | 6.4 | 7.3 | 2.7 | 5.1 | 5.9 | 2.2 |

5% | 7.2 | 9.5 | 3.1 | 6.3 | 7.9 | 2.6 | 5.2 | 7.4 | 2.8 |

20 m Downspout Distancing—30 cm Width Gutter | ||||||
---|---|---|---|---|---|---|

% of Evacuated Volume | Gutter Water Depth | Nozzle Water Depth | ||||

Slope | S | A | S | A | S | A |

0.5% | 100 | 100 | 6.5 | 6.5 | 7.0 | 6.1 |

1% | 100 | 100 | 6.0 | 6.3 | 7.3 | 6 |

2% | 99 | 100 | 5.0 | 5.6 | 7.2 | 5.6 |

3% | 93 | 100 | 5.2 | 5.3 | 7.5 | 5.2 |

4% | 81 | 100 | 5.8 | 4.8 | 7.6 | 5 |

5% | 66 | 100 | 6.2 | 4.6 | 8.1 | 4.8 |

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**MDPI and ACS Style**

Aranda, J.Á.; Sánchez-Juny, M.; Sanz-Ramos, M.; Beneyto, C.
Design of Drainage Downspouts Systems over a Road Embankment. *Water* **2023**, *15*, 3529.
https://doi.org/10.3390/w15203529

**AMA Style**

Aranda JÁ, Sánchez-Juny M, Sanz-Ramos M, Beneyto C.
Design of Drainage Downspouts Systems over a Road Embankment. *Water*. 2023; 15(20):3529.
https://doi.org/10.3390/w15203529

**Chicago/Turabian Style**

Aranda, José Ángel, Martí Sánchez-Juny, Marcos Sanz-Ramos, and Carles Beneyto.
2023. "Design of Drainage Downspouts Systems over a Road Embankment" *Water* 15, no. 20: 3529.
https://doi.org/10.3390/w15203529