# 2D and 3D Numerical Simulation of Dam-Break Flooding: A Case Study of the Tuzluca Dam, Turkey

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Dam Characteristics

^{2}. The settlements of Halimcan, Halikisla, Turabi, Surmeli, and Calpala on the Turkish border, and the settlements of Bagaran and Yervandashat on the Armenian border are potential at-risk settlements in the downstream region of the dam.

^{3}, is designed to generate hydroelectric power, with an installed capacity of 20 MW, while also providing irrigation benefits. Three villages will be submerged by the reservoir upon the construction of the dam. The cross-section of the dam body is shown in Figure 2, below.

#### 2.2. Geometric Data

#### 2.3. Estimation of Dam Breach Parameters

#### 2.4. Flow3D Numeric Model

#### 2.4.1. Two-Dimensional Shallow Water Equations

_{x}represents the area occupied by the fluid in the calculation cell in the x direction, V

_{f}represents the volume occupied by the fluid in the calculation cell, v represents the velocity of the fluid in the y direction, A

_{y}represents the area occupied by the fluid in the calculation cell in the y direction, and F represents the fluid depth.

#### 2.4.2. Three-Dimensional Reynolds-Averaged Navier-Stokes Equations

_{i}represents the velocity of the fluid in the i direction, A

_{i}represents the area occupied by the fluid in the calculation cell in the i direction, V

_{f}represents the volume occupied by the fluid in the calculation cell, p represents the pressure, G

_{i}represents the gravitational acceleration in the i direction, and f

_{i}represents the turbulence stresses in the i direction [49].

#### 2.5. Model Validation

## 3. Results and Discussion

^{3}/s, 67,323 m

^{3}/s, and 48,090 m

^{3}/s, respectively. The times taken to reach the peak discharge were observed as 3175 s, 1805 s, and 3529 s, respectively. The peak discharges for Scenarios 1, 2, and 3 in the 3D simulation were 51,227 m

^{3}/s, 69,446 m

^{3}/s, and 45,591 m

^{3}/s, respectively. The times taken to reach the peak discharge were observed as 3262 s, 2025 s, and 3578 s, respectively (Figure 17).

_{OL}= Par. f. a

_{OL}represents loss of life, Par represents people at risk, f represents the fatality rate, and a represents the flood severity coefficient.

_{1}+ bm

_{2}

_{i}and n

_{i}, used in calculating the m

_{1}and m

_{2}values, indicate the value of the factors affecting the loss of life; the expressions ${\theta}_{i}$ and t

_{i}represent the degree of influence of the factors in question.

_{1}, s

_{2}, s

_{3}, and s

_{4}values used in calculating the m

_{1}value are values depending on the population at risk, flood severity, warning time, and local people’s awareness about dam failures, respectively. The information regarding these values is given in Table 5. The values of θ

_{1}, θ

_{2}, θ

_{3}, and θ

_{4}show the degree of effect of the values of s

_{1}, s

_{2}, s

_{3}, and s

_{4}, respectively. The values in question were determined as θ

_{1}= θ

_{2}= 0.2 and θ

_{3}= θ

_{4}= 0.3 according to the Analytical Hierarchy Process (AHP), which is one of the multi-criteria decision-making methods widely used in the literature [65].

_{1}, n

_{2}, n

_{3}, n

_{4}, n

_{5}, n

_{6}, n

_{7}, n

_{8}, and n

_{9}values used in calculating the m

_{2}value represent, respectively, the young population rate, weather conditions, the time of dam failure, distance to the dam, evacuation and rescue capability, dam height, storage capacity, downstream slope, and building abrasion resistance. The information regarding these values is given in Table 6. Similarly, t

_{1,}t

_{2}, t

_{3}, t

_{4}, t

_{5}, t

_{6}, t

_{7}, t

_{8}, and t

_{9}indicate the degree of influence of the values n

_{1}, n

_{2}, n

_{3}, n

_{4}, n

_{5}, n

_{6}, n

_{7}, n

_{8}, and n

_{9}, respectively. According to the Analytical Hierarchy Process (AHP) method, these values were determined as t

_{1}= t

_{3}= t

_{4}= 0.2, t

_{2}= t

_{5}= 0.1, and t

_{6}= t

_{7}= t

_{8}= t

_{9}= 0.05 [65].

_{i}and n

_{i}values were determined by taking into account the 3D analysis results on the basis of the location and scenario. The results are presented in Table 7 and Table 8.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Section of Dam Body [40].

Method | B_{t} (m) | B_{ave} (m) | B_{b} (m) | T_{f} (h) | ||||
---|---|---|---|---|---|---|---|---|

O | P | O | P | O | P | O | P | |

MacDonald and Langridge-Monopolis [9] | 341 | 224 | 161 | 224 | 3 | |||

Bureu of Reclamation [46] | 135 | 1.5 | ||||||

Von Thun and Gillette [16] | 167 | 1 | ||||||

Froehlich [17] | 258 | 184 | 2.4 | |||||

Froehlich [6] | 218 | 156 | 2 | |||||

Xu and Zhang [18] | 380 | 222 | 287 | 168 | 217 | 87 | 2.4 | 2.3 |

_{t}: breach top width, B

_{ave}: breach average width, B

_{b}: breach bottom width, T

_{f}: failure time, O: overtopping, P: piping.

General | Finish time | 1. Scenario 7200 s |

2. Scenario 4700 s | ||

3. Scenario 6500 s | ||

Simulation units | SI | |

Flow Mode | Incompressible | |

Physics | Gravity z component | −9.81 m/sn^{2} |

Turbulence model | RNG k-ɛ | |

Fluids | Material | Water at 20 °C |

Density | 1000 kg/m^{3} | |

Meshing and Geometry | Size of cells | 10 m × 10 m; 20 m × 20 m |

Total number of real cells * | 606,248; 14,823,728 | |

Mesh type | Cartesian | |

Boundary conditions ** | X_{min} = Wall, Symmetry | |

X_{max} = Symmetry, Outflow | ||

Y_{min} * = Wall | ||

Y_{max} * = Wall | ||

Z_{min} = Wall | ||

Z_{max} = Outflow |

_{min}= Wall was applied, while in the other mesh blocks, the boundary condition X

_{min}= Symmetry was applied to ensure continuity. In the last mesh block, the boundary condition X

_{max}= Outflow was applied, while in the other mesh blocks, the boundary condition X

_{max}= Symmetry was applied.

Level Gauge | x (m) | y (m) |
---|---|---|

G1 | 5.575 | 0.25 |

G2 | 4.925 | 0.25 |

G3 | 3.935 | 0.25 |

Probe | RMSE (m) | |
---|---|---|

3D | 2D | |

G3 | 0.0047 | 0.0048 |

G2 | 0.0050 | 0.0051 |

G1 | 0.0048 | 0.0050 |

s_{i} | Population at Risk (Person) | Flood Severity | Warning Time (h) | Local People’s Awareness about Dam Failures |
---|---|---|---|---|

0.80–1.00 | >10^{5} | Extremely high | W_{t} < 0.25 | Extremely unclear |

0.60–0.80 | 10^{4}–10^{5} | High | 0.25 < W_{t} < 0.50 | Unclear |

0.40–0.60 | 10^{3}–10^{4} | Middle | 0.50 < W_{t} < 0.75 | Generally clear |

0.20–0.40 | 10^{2}–10^{3} | Low | 0.75 < W_{t} < 1.00 | Clear |

0.01–0.20 | 1–10^{2} | Extremely low | W_{t} > 1.00 | Extremely clear |

N_{i} | 0.80–1.00 | 0.60–0.80 | 0.40–0.60 | 0.20–0.40 | 0.01–0.20 |

Young population rate (%) | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 |

Weather conditions | Heavy storm | Rainstorm | Moderate rain | Sprinkle | Sunny days |

Time of dam failure | Holiday in the morning | Working day in the morning | Holiday at night | Working days at night | Daytime |

Distance to the dam (km) | 0–5 | 5–10 | 10–20 | 20–50 | >50 |

Evacuation and rescue capability | Very unsuccessful | Unsuccessful | General | Successful | Very successful |

Dam height (m) | >70 | 30–70 | 15–30 | 10–15 | <10 |

Reservoir capacity | Very Large | Large | Medium | Small | Very Small |

Downstream slope | Valley | Mountain | Hill | Plain | Beach |

Building abrasion resistance | Extremely weak | Weak | Middle | Strong | Extremely strong |

s_{i} | Halimcan | Sürmeli | ||||
---|---|---|---|---|---|---|

1. Scenario | 2. Scenario | 3. Scenario | 1. Scenario | 2. Scenario | 3. Scenario | |

s_{1} | 0.10 | 0.10 | 0.10 | 0.30 | 0.30 | 0.30 |

s_{2} | 0.60 | 0.80 | 0.50 | 0.60 | 0.80 | 0.50 |

s_{3} | 0.70 | 0.90 | 0.65 | 0.10 | 0.20 | 0.05 |

s_{4} | 0.70 | 0.70 | 0.70 | 0.70 | 0.70 | 0.70 |

n_{i} | Halimcan | Sürmeli |
---|---|---|

1., 2. and 3. Scenarios | 1., 2. and 3. Scenarios | |

n_{1} | 0.50 | 0.50 |

n_{2} | 0.40 | 0.40 |

n_{3} | 0.50 | 0.50 |

n_{4} | 0.90 | 0.50 |

n_{5} | 0.40 | 0.40 |

n_{6} | 0.65 | 0.65 |

n_{7} | 0.60 | 0.60 |

n_{8} | 0.80 | 0.90 |

n_{9} | 0.80 | 0.80 |

_{i}values are the same on a scenario-by-scenario basis as they include social and environmental factors.

Halimcan L _{OL} (Person) | Sürmeli L _{OL} (Person) | Total L_{OL} (Person) | |
---|---|---|---|

1. Scenario | 22 | 179 | 201 |

2. Scenario | 25 | 202 | 227 |

3. Scenario | 21 | 170 | 191 |

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**MDPI and ACS Style**

Akgun, C.; Nas, S.S.; Uslu, A.
2D and 3D Numerical Simulation of Dam-Break Flooding: A Case Study of the Tuzluca Dam, Turkey. *Water* **2023**, *15*, 3622.
https://doi.org/10.3390/w15203622

**AMA Style**

Akgun C, Nas SS, Uslu A.
2D and 3D Numerical Simulation of Dam-Break Flooding: A Case Study of the Tuzluca Dam, Turkey. *Water*. 2023; 15(20):3622.
https://doi.org/10.3390/w15203622

**Chicago/Turabian Style**

Akgun, Cagri, Salim Serkan Nas, and Akin Uslu.
2023. "2D and 3D Numerical Simulation of Dam-Break Flooding: A Case Study of the Tuzluca Dam, Turkey" *Water* 15, no. 20: 3622.
https://doi.org/10.3390/w15203622