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Table 11 Extract of the reservoir routeing S
Head above spillway (m)
0.02 0.05 0.1 0.2 0.3 0.4
m3
2920 7300
14600 29200 43800 58400
Outflow Ο m3
/s
0.366 1.448 4.096
11.586 21.285 32.771
s2 / Δts1 1.622 4.055 8.111
16.222 24.333 32.444
/ Δt – 0.5 Ο1 1.439 3.331 6.063
10.429 13.690 16.058
s1
/ Δt – 0.5 Ο1 1.805 4.779
10.159 22.015 34.975 48.829
f to calculating discharges than a natural channel whose friction factor cannot be accurately determined although lies within a broad range of values.
For a given time period Δt (Dunne & Leopold, 1978, Husain, 2018) the inflow, outflow and storage are related:
IΔt = OΔt + Δs [2]
where IΔτ = change in inflow, OΔτ = change in outflow, Δs = change in storage during the time interval and Δt is the time interval in seconds. The inflow and outflow discharges are the average of the values at the start and end of each time step. The change in storage is also over the same time period. Equation 2 can be rewritten in more detail, with subscripts 1
and 2 + I2 ) = 0.5 ( O1 which refer to the start and
end of each time period. 0.5 (I1
+ O2 ) + ( s2 + s1 ) / Δt [3]
Equation 3 can be rearranged making the solution of the outflow discharge possible.
s2 / Δt + 0.5 O2 = (s1 / Δt – 0.5 O1 ) + 0.5(I1 + I2 )
The relationship between the inflow and outflow terms in equation 4 and the outflow discharge is shown in Table 11. The routeing procedure can now proceed but the outflow discharges over the spillway must be reduced by up to 2.7m3
[4]
crest of the spillway, and also the slight drawdown effect as shown at Bourton Mill (Clark, 2015a), a head of about 0.3m is realistic.
Discussion The flood of 31st July has been assessed as having
a rarity of about 1 in 30 years. Had the 1 in 100 year flood taken place Todd Brook dam would almost certainly have been breached. The safety check flood of 1 in 10,000 with an estimated peak discharge in excess of 100 cumecs would have caused considerable flooding even in the absence of dam-break. The previously reported 1 in 10,000 flood of 61 cumecs (Bennett pers comm) is clearly too low as is the PMF of 164 cumecs (Hughes, 2020) which is over 100 cumecs below the value reported here. This finding chimes in with the flood study of the upper Brue (Clark, 1997) and supported by Black & Veatch (2005) which found that the original design inflow PMF had a runoff rate half way between the normal maximum flood (NMF) and the extreme catastrophic flood (ECF) of Allard et al (1960). Since there have been at least seven well documented floods which have runoff rates close to the ECF, and given the nature of the Toddbrook catchment area the lower estimates can only be given little if any credibility. The main reasons for the higher estimates using the non-lnear flow model (Clark, 2012) are, first, a much higher estimate of PMP (Clark, 2002, Clark & Dent, 2021); second, higher percentage runoff rates than the FEH which were obtained by statistical analysis rather than direct field measurements. Third, a time to peak of the UH which is related to the value of Ksat of catchment soils since those soils which have a low permeability will produce a rapid and high percentage runoff. The greatest differences in estimates of PMF will be for catchments 15 km2 and below since the area reduction factors of the FEH do not change with rarity whereas the New Guide ARF’s are lowest for the PMP, increasing with decreasing rarity, but are highest for small areas where the difference between 1hr PMP (FEH) and Clark (2009), is greatest. Those who doubt the higher estimates of floods
/sec to take into account the
effect of the bywash channel. Soon after the flood the author visited the bywash channel and it was clear from the trash line and disturbance to above bank vegetation that the channel had overflowed. The peak outflow is estimated as 22.1m3 which 2.7m3
/sec of /sec passed down the bywash channel
/sec over the auxillary spillway equates with a head of 0.282m. Photographs taken of the spillway during the flood showed that the head was 0.3m +/- 0.02m. Bearing in mind that the photograph did not show the water level behind the
20 | August 2022 |
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with spillage into the reservoir. Figure 7 shows the routed hydrograph as well as the model based hydrograph just upstream of the reservoir. Balmforth (2020) suggested that the reservoir would have needed to have been up to 5m higher in order to avoid overtopping of the auxiliary spillway. This volume equates to a runoff depth of 43mm. The inflow hydrograph shown in this paper compares well with the estimate here of 37mm. The flow of 19.4m3
at Toddbrook should remember that pro rata, the 1768 flood at Bruton (Clark, 1999) has already exceeded the original design runoff rate for the PMF at Toddbrook. This lower rate of runoff when applied to Todd Brook at Whaley Bridge has been accepted by the Canal and River Trust, undertakers for the dam at Whaley Bridge. Careful reanalysis of the existing data and a proper recognition of historic flood data gathered elsewhere should now be undertaken. Finally, greater openness as regards dam safety assessments should be made with greater public involvement. This would help to improve trust between the different stake holders. Hiding the identity of Whaley Bridge as was done in the paper by Brown et al (2008) does not give the public a chance to change what they may do in the future. If Toddbrook dam failed completely the legacy of secrecy written by Dam Inspectors would have been made apparent, so that the near miss incident of 2019 should cause those involved both now and in the future to consider who they are serving when carrying out their duties. ●
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