# Comparative Hydrodynamic Analysis by Using Two−Dimensional Models and Application to a New Bridge

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Hydrodinamic Model

_{x}, U

_{y}are the horizontal velocities averaged with depth, g is the acceleration of gravity, Z

_{s}is the elevation of the free surface, τ

_{s}is the stress on the free surface due to friction caused by the wind, τ

_{b}is the stress due to the friction of the bottom, ρ is the density of water, Ω is the angular velocity of rotation of the earth, λ is the latitude of the point considered, τ

^{e}

_{xx}, τ

^{e}

_{xy}, τ

^{e}

_{yy}are the horizontal effective tangential stresses, and M

_{s}, M

_{x}, M

_{y}are the source/sink terms of mass and of momentum, respectively. The source terms in the hydrodynamic equations include hydrostatic pressure, bottom slope, viscous and turbulent tangential stresses, bottom friction, surface wind friction, precipitation, and infiltration.

#### 2.2. Comparative Analysis

^{2}/s and represents the specific stream−flow through a 1 m wide vertical strip perpendicular to the velocity vector. This feature is a measure of the Flood Hazard Rating (FHR) [45,46,47] where zones showing values h > 1, v > 1, or h·v > 0.5 are normally considered dangerous flood zones.

#### 2.3. Description of the SHEE Software

## 3. Study Case for a New Bridge

^{3}/s, respectively. Figure 1 shows the valley with the implementation of the road infrastructure and a longitudinal section, along with the water level for different return periods. This bridge has a length of 109 m, and is divided into four spans: two 26 m central spans limited by the piers of the bridge, in which the main channel is located; and another two spans at the ends. Both measure about 24 m and are limited by the abutments of the bridge. The piers consist of three pairs, with a transverse separation of 4 m, with a foundation based on piles. They will have rounded edges, thus determining circular sections to improve the hydraulic behavior.

^{3}/s in the case of a 100-year return period), and remains constant from there for long enough so that there are no changes throughout the calculation domain. Thus, the simulations can be considered as a permanent flow corresponding to the peak flow.

## 4. Results and Discussion

#### 4.1. Study of Bridge Alternatives and Selection of the Most Suitable One

#### 4.2. Hydraulic Detail Study of the Suitable Alternative (Option 3)

^{2}/s in the main channel, and 2.5 m

^{2}/s in the rest of the floodway around the bridge section.

^{2}/s compared to the upstream area, which only reaches −0.5 m

^{2}/s.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Water depth coverage: (

**A**) initial state without bridge and (

**B**) final state with the bridge from option 3. In this Figure and the following one, for the sake of detail, only the most representative part of the calculation domain is represented.

**Figure 3.**Comparative analysis of the water depth for the three options studied: (

**A**) Option 1; (

**B**) Option 2, and (

**C**) Option 3. All of them show the variation in the water level produced by the execution of each option.

**Figure 4.**Velocity coverage: (

**A**) initial state without bridge and (

**B**) state with the option bridge 3. In (

**C**), the difference between the two previous velocity coverages is shown.

**Figure 5.**Coverage Flood Hazard Rating (FHR) (h·v) for (

**A**) initial state without bridge, and (

**B**) state with option’s 3 bridge, (

**C**) representation of the difference between the two previous coverages.

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**MDPI and ACS Style**

Mateo-Lázaro, J.; Castillo-Mateo, J.; García-Gil, A.; Sánchez-Navarro, J.Á.; Fuertes-Rodríguez, V.; Edo-Romero, V.
Comparative Hydrodynamic Analysis by Using Two−Dimensional Models and Application to a New Bridge. *Water* **2020**, *12*, 997.
https://doi.org/10.3390/w12040997

**AMA Style**

Mateo-Lázaro J, Castillo-Mateo J, García-Gil A, Sánchez-Navarro JÁ, Fuertes-Rodríguez V, Edo-Romero V.
Comparative Hydrodynamic Analysis by Using Two−Dimensional Models and Application to a New Bridge. *Water*. 2020; 12(4):997.
https://doi.org/10.3390/w12040997

**Chicago/Turabian Style**

Mateo-Lázaro, Jesús, Jorge Castillo-Mateo, Alejandro García-Gil, José Ángel Sánchez-Navarro, Víctor Fuertes-Rodríguez, and Vanesa Edo-Romero.
2020. "Comparative Hydrodynamic Analysis by Using Two−Dimensional Models and Application to a New Bridge" *Water* 12, no. 4: 997.
https://doi.org/10.3390/w12040997