# Modelling of Flood Inundation due to Levee Breaches: Sensitivity of Flood Inundation against Breach Process Parameters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Approach

#### 2.2. Telemac-2D

#### 2.3. The Breach Model Used in This Investigation

#### 2.4. The Levee Breach Case: The 1996 Awash River Levee Breach at Wonji

#### 2.4.1. The Study Area

#### 2.4.2. The 1996 Awash River Levee Breach at Wonji, Ethiopia

## 3. Model Set Up

#### 3.1. Computational Mesh

^{2}. This high mesh resolution ensures that the levee is represented in the model accurately. The river channel is discretised by more than ten mesh nodes over the cross-section and the size of the triangles is on average 21 m

^{2}. The flood plain is discretised with mesh element sizes of about 1.2 ha. In total the computational mesh has about 725,000 triangular mesh elements. Figure 4 shows excerpts of the computational mesh.

#### 3.2. Boundary and Initial Conditions

^{3}[42]. The water level at maximum capacity is 1539.04 m a.m.s.l. The dam operates like a weir and is overflown when the water level exceeds the maximum level. Thus, the downstream boundary condition of the model is a stage–discharge relationship. Since exact stage–discharge curve for the weir is unavailable, the stage–discharge relationship is derived using the overflow formula for broad-crested weirs given by Equation (1) [43,44].

_{d}, g and h

_{o}stand respectively for overflow discharge, width of the weir, discharge coefficient, acceleration due to gravity and upstream total head. The discharge coefficient considers losses due to friction, the effect of the upstream slope of the weir and the shape of the weir crest, among other factors. Experiments show that the discharge coefficient for a broad-crested weir can be very low [43]. An average discharge coefficient value of 0.55 is adopted. The upstream total head h

_{o}is approximated by the upstream water depth over the crest level. The width of the dam is 88 m. Therefore, the stage–discharge relationship at Awash II Dam is established by calculating the values of stage (depth over crest plus the crest level of the dam) for various Q values and is shown in Figure 5d.

#### 3.3. Model Calibration and Validation

^{2}/s.

## 4. Sensitivity Analysis of the Breach Model Parameters

#### 4.1. Breach Duration

#### 4.2. Breach Start Time (Breach Initiation)

#### 4.3. Final Breach Width

#### 4.4. Final Breach Level

#### 4.5. Breach Location

#### 4.6. Erosion Type

## 5. Discussion

## 6. Conclusions

- Flood inundation due to levee breach depends on the final dimensions of the levee breach and the breach location. The final breach dimensions affect the consequence of the levee breach as the amount of water that can flow into the hinterland is the function of the breach dimensions.
- The breach location affects the consequence of the levee breach even if the discharge through the breach is not significantly influenced.
- The process of the levee breaching (breach development) has marginal to no influence on the resulting flood inundation. This is shown, however, for floods lasting over several days. Consequences of levee breaches due to flash floods lasting for short period could be sensitive to the levee breaching processes.
- Accurate and reliable methods for determining the final breach dimensions and breach location are important for a more accurate flood inundation estimation.

## Author Contributions

## Funding

**Open Access Publishing*** of Hamburg University of Technology (TUHH).

## Acknowledgments

**Open Access Publishing***. The first author is grateful to The German Ministry of Education and Research (BMBF) for their financial support for his PhD research through the IPSWaT scholarship under contract number IPS 20/06P2.

## Conflicts of Interest

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**Figure 3.**Location of the study area—Wonji-Shoa Sugar Factory and its sugar cane plantation (background map courtesy of ESRI

^{®}, ArcGIS online service).

**Figure 5.**Awash River flow data: (

**a**) hydrograph of the August 1996 flood flow at KHD and Wonji gauging stations; (

**b**) hydrograph of the summer 1998 flood flow at KHD and Wonji gauging stations; (

**c**) hydrograph of the August 1999 flood flow at KHD and Wonji gauging stations; (

**d**) stage–discharge relationship of Awash River at Awash II derived using overflow equation for broad-crested weir.

**Figure 6.**Model calibration: measured discharge hydrograph of summer 1998 at Wonji gauging station (

**a**) compared with modelled discharge hydrographs for different Nikuradse’s roughness Ks-values, (

**b**) compared with modelled discharge hydrographs for different eddy viscosity values (Vis.).

**Figure 7.**Model validation: Modelled water depth at the office location corresponding to the breach information.

**Figure 8.**For the indicated levee breach durations (BD) and the historical levee breach location of the August 1996 levee breach flood event at Wonji: (

**a**) modelled water depth at an office location; (

**b**) modelled breach discharge. The office location and the historical breach location are shown in Figure 3.

**Figure 9.**For the indicated levee breach start times (BT) on 24.08.1996 and the historical levee breach location of the August 1996 levee breach flood event at Wonji, (

**a**) modelled water depth at an office location and (

**b**) modelled breach discharge. The office location and the historical breach location are shown in Figure 3.

**Figure 10.**For the indicated final levee breach widths (BW) and the historical levee breach location of the August 1996 levee breach flood event at Wonji, (

**a**) modelled water depth at an office location and (

**b**) modelled breach discharge. The office location and the historical breach location are shown in Figure 3.

**Figure 11.**For the indicated final breach levels (BL) (BL = 0 m (levee erodes to the ground level) and BL = 1.5 m (levee erodes to half its height, which is 3 m)) and the historical levee breach location of the August 1996 levee breach flood event at Wonji: (

**a**) modelled water depth at an office location; (

**b**) modelled breach discharge. The office location and the historical breach location are shown in Figure 3.

**Figure 13.**For levee-lowering options (Option 1: only vertical breach growth; Option 2: vertical and lateral breach growth) and the historical levee breach location of the August 1996 levee breach flood event at Wonji: (

**a**) modelled water depth at an office location; (

**b**) modelled breach discharge. The office location and the historical breach location are shown in Figure 3.

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**MDPI and ACS Style**

Tadesse, Y.B.; Fröhle, P. Modelling of Flood Inundation due to Levee Breaches: Sensitivity of Flood Inundation against Breach Process Parameters. *Water* **2020**, *12*, 3566.
https://doi.org/10.3390/w12123566

**AMA Style**

Tadesse YB, Fröhle P. Modelling of Flood Inundation due to Levee Breaches: Sensitivity of Flood Inundation against Breach Process Parameters. *Water*. 2020; 12(12):3566.
https://doi.org/10.3390/w12123566

**Chicago/Turabian Style**

Tadesse, Yohannis Birhanu, and Peter Fröhle. 2020. "Modelling of Flood Inundation due to Levee Breaches: Sensitivity of Flood Inundation against Breach Process Parameters" *Water* 12, no. 12: 3566.
https://doi.org/10.3390/w12123566