Analysis of numerical simulation results – Case Study 5

The analysis of the numerical simulation results was limited to the peak discharge and outflow volume. The results in Figure 6.10-3 illustrate the effect of the sediment transport equation on the shape and peak of the outflow hydrograph. The simulated peak discharges and outflow volumes from the breach opening for each of the four sediment transport equations is given in Table 6.10-3. The results in Table 6.10-3 show good agreement between the predicted peak discharges by Equation 5.2-6 and Smart and Jäeggi (1983) sediment transport equation. This is contrary to the observed trends for Case Studies 1 and 2 that showed significant disparities between the two equations. This could be due to the possibility that at a large prototype scale, the effects of the sediment transport equations become compensated.

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Table 6.10-3 Predicted peak discharge at the breach opening by each of the four sediment transport equations

Sediment Transport Equation Peak discharge (m3_{/s) Outflow volume (10}6 _m3₎

Equation 5.2-5 8130 2.271

Equation 5.2-6 7618 1.893

Smart & Jäeggi (1983) 7543 2.250

Camenen & Larson (2005) 3832 2.225

Figure 6.10-3 Simulated outflow hydrograph at the breach opening for a constant inflow of 100 m3_{/s – Case Study 5}

0 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 9 000 0 5 10 15 20 25 30 35 Disc h ar ge (m 3/s) Time (Min)

Simulated ouflow hydrographs at the breach opening using selected equations

Equation 5.2-5 simulated outflow Smart & Jaeggi (1983) simulated outflow Equation 5.2-6 simulated outflow Camenen & Larson (2005) simulated outflow

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In order to evaluate the realism of the results in Table 6.10-3, the results of the predicted peak discharge were compared with the estimated peak discharge using empirical equations from literature. Even though empirical equations are a conservative way of predicting dam-break characteristics, they are a better alternative in the absence of observed data. It could have been better to also compare the numerical model results with output results from other simpler methods of dam-break analysis such as the one-dimensional MIKE 11 numerical model, but this was not possible due to study time constraints. Empirical equations that provide envelope values were used instead. These empirical equations were: Hagen (1982) and Broich (1998). Hagen (1982) plotted the relationship between peak discharge (𝑄_𝑃) and the product of reservoir storage volume (S) and dam height (hd). Broich (1998) obtained a regression equation that gave the relationship between peak discharge (𝑄_𝑃) to the depth of water (hw) and volume of water (Vw) in the reservoir at the initial failure time. The two empirical equations were applied because they provide the upper limit envelope values for the peak discharge. The empirical equations are as follows:

𝑄_𝑃 = 0.54(ℎ_𝑑𝑆)0.5 _{Hagen (1982) 6.10-1}

𝑄_𝑃 = 72.611(𝑉_𝑤ℎ_𝑤4₎0.256 _{Broich (1998) 6.10-2}

Where

hd Dam height

hw Water depth in the reservoir initiating failure S Reservoir storage volume

Vw Volume of water (in 106 m3)

The peak discharge predictions using the two empirical equations based on the dam characteristics for Case Study 5 are given in Table 6.10-4.

Table 6.10-4 Peak discharge estimation using empirical equations

Equation Peak discharge (m3_/s)

Hagen (1982) 8752

Broich (1998) 6087

The peak discharges at the breach that were predicted by Equations 5.2-5 & 5.2-6 and Smart & Jäeggi (1983) sediment transport equation were found to be within the expected envelope values

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from empirical predictor equations 6.10-1 and 6.10-2. Based on the given envelope values, Camenen & Larson (2005) underestimated the peak discharge.

Peak discharges and outflow hydrographs were also determined for a location 1.85 km downstream of the breach. Figure 6.10-4 shows the simulated peak discharges and outflow volumes 1.85 km downstream from the breach opening and Table 6.10-5 shows the simulated peak discharges and outflow volumes for each of the four sediment transport equations. Equation 5.2-5 (which predicted the highest peak at the breach opening) exhibited the highest peak at a location 1.85 km from the breach opening. The results show that although the predicted downstream flood peak were attenuated, the predicted peak discharges at the breach opening determined the probable peak discharges at the specific locations downstream of the embankment.

Table 6.10-5 Predicted peak discharges by each of the four sediment transport equations at 1.85 km from the breach opening

Sediment Transport Equation Peak discharge (m3_{/s) Outflow volume (10}6 _m3₎

Equation 5.2-5 5282 2.190

Equation 5.2-6 3045 1.882

Smart & Jäeggi (1983) 3414 2.050

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Figure 6.10-4 Simulated outflow hydrographs at 1.85 km from the breach opening – Case Study 5

The effect of the sediment transport equation on the final bed profile at the breach is shown in Figure 6.10-5. It was found that even though the Camenen & Larson (2005) predicted the lowest peak discharge, the final bed profile was similar to the bed profile simulated by Equation 5.2-5 which simulated the highest peak discharge. The deepest bed profile was predicted by the Smart & Jäeggi (1983) sediment transport equation while the lowest profile was predicted by Equation 5.2-6. It is evident that the predicted final bed profile is not directly related to the greatest peak discharge. For instance, Smart & Jäeggi (1983) scoured a deeper final bed profile than Equation 5.2-5 despite having a lower peak discharge. This is due to the fact that the peak discharge is related to the breach invert and water level at peak and not necessarily the final bed profile.

0 1 000 2 000 3 000 4 000 5 000 6 000 0 5 10 15 20 25 30 35 Disc h ar ge (m 3/s) Time (Min)

Simulated ouflow hydrographs at 1.85 km from breach opening

Equation 5.2-5 simulated outflow Smart & Jaeggi (1983) simulated outflow Equation 5.2-6 simulated outflow Camenen & Larson (2005) simulated outflow

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Figure 6.10-5 Simulated final profiles using Equation 5.2-5, Equation 5.2-6, Smart & Jäeggi (1983) and Camenen & Larson (2005) sediment transport equations – Case Study 5

6.11 Summary

The application of Equations 5.2-5 and 5.2-6 was demonstrated in dam-break modelling using five case studies. The performance of Equations 5.2-5 and 5.2-6 was assessed through a comparative analysis of the measured and predicted model output parameters for the two calibrated equations with two other sediment transport equations from literature, namely; Smart & Jäeggi (1983) and Camenen & Larson (2005). The application focused on the ability of the sediment transport equations to predict the following model output parameters: longitudinal and transverse bed profiles at the breach opening, peak discharge, time to peak and outflow volume. The longitudinal bed profiles predicted by the four sediment transport equations for Case Study 1 showed different simulated temporal bed profiles for each equation. The measured temporal bed profiles in Case Study 1 were well reproduced by the newly calibrated sediment transport equations (Equations 5.2-5 and 5.2-6) and the Camenen & Larson (2005) sediment transport equation especially at the early breach depths of 0.05 m and 0.10 m.

In Case Study 2, the final breach dimension was well predicted by the newly calibrated sediment transport equations (Equations 5.2-5 and 5.2-6).

An assessment of the level of uncertainty due to the input of sediment transport equations showed that sediment transport equations have a particular range of best applicability with respect to slope data as evidenced by the failure by all four sediment transport equations to reproduce the peak discharge and times to peak in Case Studies 3 and 4.

0 10 20 30 40 50 60 0 50 100 150 200 250 300 350 400 450 500 E lev a tio n ( m ) Crest Width (m)

Final bed profile for selected sediment transport equations at the breach central transverse cross-section - Case Study 5

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The percentage slope of 60% in both Case Studies 3 and 4 was outside the calibration range for all the four sediment transport equations.

The agreement between simulated peak discharges in Case Study 5 and computed envelope peak discharge values using empirical formulations showed that the simulated model output results were generally reasonable.

It can be concluded that the newly calibrated equations (Equations 5.2-5 and 5.2-6) can be applied in the dam-break numerical simulation of peak discharge, flood volume and breach dimensions but could be limited in the prediction of time to peak or failure.

The Manning’s resistance coefficient (n) had a marked effect on the peak discharge of the outflow hydrographs. Generally, the trend in the four case studies where sensitivity analysis of resistance was assessed showed that, for a higher Manning’s resistance coefficient (n) in the numerical model, a lower peak discharge was observed while a high peak discharge was simulated for low Manning’s resistance coefficients (n). The results showed that the numerical model output parameters were influenced by the combined effect of the sediment transport equations and the Manning’s resistance coefficients (n).

Table 6.11-1 shows the final calibrated Manning’s resistance coefficient (n) and the corresponding recommended sediment transport equation(s) for each case study.

Table 6.11-1 Sensitivity analysis results

Case Study Percentage slope on downstream embankment Manning’s resistance coefficient (n) Recommended sediment transport equation (s) Remarks 1 33% (1V : 3H) 0.040 Equations 5.2-5 & 5.2-6 and Camenen & Larson (2005) - 2 33% (1V : 3H) 0.040 Equation 5.2-5 and 5.2-6 -

3 59% (1V : 1.7H) 0.044 None Percentage slope

outside calibration range – all sediment transport equations are not directly applicable

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4 59% (1V : 1.7H) 0.050 None Percentage slope

outside calibration range – all sediment transport equations are not directly applicable

5 33% (1V : 3H) 0.045 Equation 5.2-5,

Equation 5.2-6 and Smart and Jäeggi (1983)

Smart and Jäeggi (1983) was derived on slope data up to 20% but performed better in this case study

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