# Quantification of the Effect of Bridge Pier Encasement on Headwater Elevation Using HEC-RAS

^{*}

## Abstract

**:**

^{b}was suggested for various channel slopes for the increased water surface elevation (Y) for each percentage decrease in channel area (X).

## 1. Introduction

## 2. Theoretical Background

_{1}and Z

_{2}are elevations of the conduit centerline (ft), V

_{1}and V

_{2}are mean velocities in the pipe, and $\gamma $ is the unit weight of fluids (lb/ft

^{3}). Similarly, g is the acceleration due to gravity, and h

_{e}is the energy head loss between downstream and upstream points.

#### 2.1. Bridge Pier Encasement

#### 2.2. Modeling Approach

- The energy method should be used in case the bridge deck is a small obstruction to the flow and the bridge opening is not behaving as a pressurized orifice.
- The pressure and weir method could be an appropriate choice when the bridge deck and the road embankment create a significant obstruction to the flow.

## 3. Material and Methodology

#### 3.1. HEC-RAS Model Inputs

#### 3.2. Model Establishment

## 4. Results

^{b}, could represent such a relationship for most slopes except for 1%. For the 1% channel slope, linear equation best fitted the data.

## 5. Summary and Conclusions

^{b}was developed for most channel slopes, where Y represent the rise in water surface elevation and X represents the percentage decrease in the channel area.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**The difference in water surface elevation at most upstream before and after pier encasement (both rise and no-rise condition seen) for 20 ft channel section for different flows.

**Figure 6.**The difference in water surface elevation at immediate upstream before and after pier encasement (both rise and no-rise condition seen) for 20 ft channel section for different flows.

**Figure 7.**The difference in water surface elevation at most upstream before and after pier encasement (both rise and no-rise condition seen) for 100 ft channel section for different flows.

**Figure 8.**The difference in water surface elevation at immediate upstream before and after pier encasement (both rise and no-rise condition seen) for 100 ft channel section for different flows.

**Figure 9.**The difference in water surface elevation at most upstream before and after pier encasement (only no-rise condition seen) for 180 ft channel section for different flows.

**Figure 10.**The difference in water surface elevation at immediate upstream before and after pier encasement (only no-rise condition seen) for 180 ft channel section for different flows.

**Figure 11.**The difference in water surface elevation with respect to percentage change in area due to encasement for flow (

**a**) 2400 cfs; (

**b**) 5000 cfs.

Serial No | Pier Shape | Drag Coefficient (CD) |
---|---|---|

1 | Circular pier | 1.20 |

2 | Elongated piers with semi-circular ends | 1.33 |

3 | Elliptical piers with 2:1 length to width | 0.60 |

4 | Square piers | 2.00 |

5 | Triangular nose with 30-degree angle | 1.00 |

6 | Triangular nose with 120-degree angle | 1.72 |

Run | Existing Size | Shape | Existing Type | Encasement | Type | Shape |
---|---|---|---|---|---|---|

1 | 12″ | Square | H-Pile | 24″ ID/28″ OD | PE | Round |

2 | 16″ OD | Round | Concrete Pile | 30″ ID/36″ OD | PE | Round |

Channel Bottom Width (ft) | Number of Piers | Number of Cross-Sections | Reach Length (ft) | Most Upstream from Center Line of Bridge (ft) | Immediate Upstream from Center Line of Bridge (ft) |
---|---|---|---|---|---|

20 | 2 | 10 | 250 | 125 | 13.88 |

40 | 2, 3 | 10 | 250 | 125 | 13.88 |

60 | 2, 3 | 10 | 300 | 150 | 16.66 |

80 | 2, 3 | 10 | 300 | 150 | 16.66 |

100 | 2, 3 | 11 | 400 | 180 | 30 |

120 | 2, 3 | 11 | 450 | 205 | 25 |

140 | 3 | 11 | 450 | 205 | 25 |

160 | 3 | 11 | 500 | 225 | 25 |

180 | 3 | 11 | 500 | 225 | 25 |

**Table 4.**Allowable state surcharge limits as of 2003 [8].

State | Surcharge (ft) |
---|---|

Illinois | 0.1 |

Indiana | 0.1 |

Michigan | 0.1 |

Minnesota | 0.5 |

Montana | 0.5 |

New Jersey | 0.2 |

Ohio | 0.5 |

Wisconsin | 0 |

All other states | 1 |

Serial No | Bottom Channel Width (ft) | Flow Range (cfs) | Number of Piers | Slope (%) | Most Upstream Cross-Section | Immediate Bridge Upstream Cross-Section |
---|---|---|---|---|---|---|

Flow (cfs) | Flow (cfs) | |||||

1 | 20 | 200–5600 | 2 | 0.3 | Flow ≤ 5600 | Flow ≤ 5600 |

0.5 | Flow ≤ 2400 | Flow ≤ 1800 | ||||

0.7 | Flow ≤ 1400 | Flow ≤ 800 | ||||

1 | Flow ≤ 1400 | Flow ≤ 800 | ||||

2 | 40 | 200–8400 | 2 | 0.3 | Flow ≤ 8400 | Flow ≤ 8400 |

0.5 | Flow ≤ 8400 | Flow ≤ 6800 | ||||

0.7 | Flow ≤ 7600 | Flow ≤ 4400 | ||||

1 | Flow ≤ 3800 | Flow ≤ 2600 | ||||

3 | 0.3 | Flow ≤ 8400 | Flow ≤ 8200 | |||

0.5 | Flow ≤ 3600 | Flow ≤ 2600 | ||||

0.7 | Flow ≤ 4000 | Flow ≤ 2400 | ||||

1 | Flow ≤ 2200 | Flow ≤ 1400 | ||||

3 | 60 | 200–11,400 | 2 | 0.3 | Flow ≤ 11,400 | Flow ≤ 11,400 |

0.5 | Flow ≤ 11,400 | Flow ≤ 11,400 | ||||

0.7 | Flow ≤ 8600 | Flow ≤ 5400 | ||||

1 | Flow ≤ 7800 | Flow ≤ 5400 | ||||

3 | 0.3 | Flow ≤ 11,400 | Flow ≤ 11,400 | |||

0.5 | Flow ≤ 8200 | Flow ≤ 6400 | ||||

0.7 | Flow ≤ 5200 | Flow ≤ 3200 | ||||

1 | Flow ≤ 5000 | Flow ≤ 3200 | ||||

4 | 80 | 200–13,400 | 2 | 0.3 | Flow ≤ 13,400 | Flow ≤ 13,400 |

0.5 | Flow ≤ 13,400 | Flow ≤ 13,400 | ||||

0.7 | Flow ≤ 12,400 | Flow ≤ 8200 | ||||

1 | Flow ≤ 9800 | Flow ≤ 8200 | ||||

3 | 0.3 | Flow ≤ 13,400 | Flow ≤ 13,400 | |||

0.5 | Flow ≤ 13,400 | Flow ≤ 9800 | ||||

0.7 | Flow ≤ 8200 | Flow ≤ 5400 | ||||

1 | Flow ≤ 7800 | Flow ≤ 5400 | ||||

5 | 100 | 200–15,000 | 2 | 0.3 | Flow ≤ 15,000 | Flow ≤ 15,000 |

0.5 | Flow ≤ 15,000 | Flow ≤ 15,000 | ||||

0.7 | Flow ≤ 15,000 | Flow ≤ 14,000 | ||||

1 | Flow ≤ 11,400 | Flow ≤ 10,600 | ||||

3 | 0.3 | Flow ≤ 15,000 | Flow ≤ 15,000 | |||

0.5 | Flow ≤ 15,000 | Flow ≤ 15,000 | ||||

0.7 | Flow ≤ 13,800 | Flow ≤ 8600 | ||||

1 | Flow ≤ 9800 | Flow ≤ 6000 | ||||

6 | 120 | 200–20,000 | 2 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 |

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

1 | Flow ≤ 13,200 | Flow ≤ 16,800 | ||||

3 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 | |||

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

1 | Flow ≤ 14,200 | Flow ≤ 8800 | ||||

7 | 140 | 200–20,000 | 3 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 |

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 19,000 | ||||

1 | Flow ≤ 17,000 | Flow ≤ 15,200 | ||||

8 | 160 | 200–20,000 | 3 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 |

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 17,600 | ||||

1 | Flow ≤ 18,200 | Flow ≤ 20,000 | ||||

9 | 180 | 200–20,000 | 3 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 |

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

1 | Flow ≤ 20,000 | Flow ≤ 20,000 |

Serial No | Bottom Channel Width (ft) | Flow Range (cfs) | Number of Piers | Slope (%) | Most Upstream Cross-Section | Immediate Bridge Upstream Cross-Section |
---|---|---|---|---|---|---|

Flow (cfs) | Flow (cfs) | |||||

1 | 20 | 200–5600 | 2 | 0.3 | Flow ≤ 5600 | Flow ≤ 5600 |

0.5 | Flow ≤ 2600 | Flow ≤ 1600 | ||||

0.7 | Flow ≤ 1800 | Flow ≤ 1000 | ||||

1 | Flow ≤ 1600 | Flow ≤ 1000 | ||||

2 | 40 | 200–8400 | 2 | 0.3 | Flow ≤ 8400 | Flow ≤ 8400 |

0.5 | Flow ≤ 7800 | Flow ≤ 6200 | ||||

0.7 | Flow ≤ 8400 | Flow ≤ 5000 | ||||

1 | Flow ≤ 4200 | Flow ≤ 3000 | ||||

3 | 0.3 | Flow ≤ 8400 | Flow ≤ 8400 | |||

0.5 | Flow ≤ 3800 | Flow ≤ 2800 | ||||

0.7 | Flow ≤ 4800 | Flow ≤ 2600 | ||||

1 | Flow ≤ 2600 | Flow ≤ 1800 | ||||

3 | 60 | 200–11,400 | 2 | 0.3 | Flow ≤ 11,400 | Flow ≤ 11,400 |

0.5 | Flow ≤ 11,400 | Flow ≤ 11,400 | ||||

0.7 | Flow ≤ 9400 | Flow ≤ 5800 | ||||

1 | Flow ≤ 7200 | Flow ≤ 4600 | ||||

3 | 0.3 | Flow ≤ 11,400 | Flow ≤ 11,400 | |||

0.5 | Flow ≤ 8400 | Flow ≤ 6400 | ||||

0.7 | Flow ≤ 6000 | Flow ≤ 4600 | ||||

1 | Flow ≤ 4800 | Flow ≤ 2800 | ||||

4 | 80 | 200–13,400 | 2 | 0.3 | Flow ≤ 13,400 | Flow ≤ 13,400 |

0.5 | Flow ≤ 13,400 | Flow ≤ 13400 | ||||

0.7 | Flow ≤ 13,400 | Flow ≤ 9000 | ||||

1 | Flow ≤ 8800 | Flow ≤ 7200 | ||||

3 | 0.3 | Flow ≤ 13,400 | Flow ≤ 13,400 | |||

0.5 | Flow ≤ 13,400 | Flow ≤ 13,400 | ||||

0.7 | Flow ≤ 8200 | Flow ≤ 5000 | ||||

1 | Flow ≤ 7600 | Flow ≤ 4800 | ||||

5 | 100 | 200–15,000 | 2 | 0.3 | Flow ≤ 15,000 | Flow ≤ 15,000 |

0.5 | Flow ≤ 15,000 | Flow ≤ 15,000 | ||||

0.7 | Flow ≤ 15,000 | Flow ≤ 13,800 | ||||

1 | Flow ≤ 10,400 | Flow ≤ 12,200 | ||||

3 | 0.3 | Flow ≤ 15,000 | Flow ≤ 15,000 | |||

0.5 | Flow ≤ 15,000 | Flow ≤ 15,000 | ||||

0.7 | Flow ≤ 14,800 | Flow ≤ 11,600 | ||||

1 | Flow ≤ 13,600 | Flow ≤ 9200 | ||||

6 | 120 | 200–20,000 | 2 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 |

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

1 | Flow ≤ 14,200 | Flow ≤ 19,000 | ||||

3 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 | |||

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20000 | Flow ≤ 20,000 | ||||

1 | Flow ≤ 14,800 | Flow ≤ 13,200 | ||||

7 | 140 | 200–20,000 | 3 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 |

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 17,200 | ||||

1 | Flow ≤ 15,200 | Flow ≤ 17,600 | ||||

8 | 160 | 200–20,000 | 3 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 |

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

1 | Flow ≤ 18,200 | Flow ≤ 20,000 | ||||

9 | 180 | 200–20,000 | 3 | 0.3 | Flow ≤ 20,000 | Flow ≤ 20,000 |

0.5 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

0.7 | Flow ≤ 20,000 | Flow ≤ 20,000 | ||||

1 | Flow ≤ 20,000 | Flow ≤ 20,000 |

**Table 7.**The generic equation proposed to estimate the increased water surface elevation with reduced area for two flow conditions (2400 cfs and 5000 cfs).

Flow = 2400 cfs | ||

Slopes | Proposed Equation | R^{2} |

0.30% | Y = 0.0009x^{2.802} | 0.909 |

0.50% | Y = 0.0011x^{2.8705} | 0.842 |

0.70% | Y = 0.0006x^{3.4191} | 0.845 |

1% | Y = 0.115–0.335 | 0.79 |

Flow = 5000 cfs | ||

Slopes | Proposed Equation | R^{2} |

0.30% | Y = 0.0037x^{2.236} | 0.909 |

0.50% | Y = 0.0025x^{2.831} | 0.894 |

0.70% | Y = 0.0044x^{2.746} | 0.801 |

1% | Y = 0.819x − 0.46 | 0.887 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Subedi, A.S.; Sharma, S.; Islam, A.; Lamichhane, N. Quantification of the Effect of Bridge Pier Encasement on Headwater Elevation Using HEC-RAS. *Hydrology* **2019**, *6*, 25.
https://doi.org/10.3390/hydrology6010025

**AMA Style**

Subedi AS, Sharma S, Islam A, Lamichhane N. Quantification of the Effect of Bridge Pier Encasement on Headwater Elevation Using HEC-RAS. *Hydrology*. 2019; 6(1):25.
https://doi.org/10.3390/hydrology6010025

**Chicago/Turabian Style**

Subedi, Abhijit Sharma, Suresh Sharma, Anwarul Islam, and Niraj Lamichhane. 2019. "Quantification of the Effect of Bridge Pier Encasement on Headwater Elevation Using HEC-RAS" *Hydrology* 6, no. 1: 25.
https://doi.org/10.3390/hydrology6010025