River morphodynamics and sediment transportSedimentation in reservoir

Teschke, Ulf

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Conference Paper, Published VersionTeschke, UlfTrap efficiency of a forebay in a low mountain rangeVerfügbar unter/Available at: https://hdl.handle.net/20.500.11970/99759Vorgeschlagene Zitierweise/Suggested citation:Teschke, Ulf (2010): Trap efficiency of a forebay in a low mountain range. In: Dittrich,Andreas; Koll, Katinka; Aberle, Jochen; Geisenhainer, Peter (Hg.): River Flow 2010.Karlsruhe: Bundesanstalt für Wasserbau. S. 1119-1124.Standardnutzungsbedingungen/Terms of Use:Die Dokumente in HENRY stehen unter der Creative Commons Lizenz CC BY 4.0, sofern keine abweichendenNutzungsbedingungen getroffen wurden. Damit ist sowohl die kommerzielle Nutzung als auch das Teilen, dieWeiterbearbeitung und Speicherung erlaubt. Das Verwenden und das Bearbeiten stehen unter der Bedingung derNamensnennung. Im Einzelfall kann eine restriktivere Lizenz gelten; dann gelten abweichend von den obigenNutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.Documents in HENRY are made available under the Creative Commons License CC BY 4.0, if no other license isapplicable. Under CC BY 4.0 commercial use and sharing, remixing, transforming, and building upon the materialof the work is permitted. In some cases a different, more restrictive license may apply; if applicable the terms ofthe restrictive license will be binding.1 INTRODUCTION Solids enter the storage reservoir via the inflows in reservoirs and forebays. There, the solids settle more or less completely and, thus, contribute to a reduction of the storage capacity. This effect causes a decrease in the storage volume and, thus, reduces the trap efficiency of the reservoir since the retention time of the water in the storage res-ervoir is more and more reduced. Smaller sedimentary basins are built in front of large dams to prevent the latter from silting up. In these basins, the sediments introduced with the in-flow are supposed to settle. Since the sediments are also frequently polluted with harmful sub-stances, a trapping of the sediments in the forebay prevents the harmful substances from entering the barrage. In view of that fact, the trap efficiency of forebays is important for the latter’s dimensioning and maintenance. This article examines the trap efficiency of a forebay in the low mountain range of the Harz re-gion situated in the geographical centre of Ger-many. It deals with the question which effects the deposited sediment has on the forebay’s settling properties and at which point in time the forebay volume will have reduced itself to such a degree that the forebay will have to be evacuated in order to guarantee a certain extent of retention. It is to be examined, in particular, whether it will become necessary to evacuate the forebay as a result of the altered settling properties after it has been in operation for more than 70 years. Which effects will the sediments have on the set-tling properties of the forebay if they remain where they are during the next 70 years? 2 INVESTIGATION AREA The investigated forebay of a large drinking water reservoir is supposed to reduce or, if possible, prevent solids, in particular fine particles and nu-trients, from entering the barrage. Owing to this, a good raw water quality is to be guaranteed for the abstraction of drinking water from the barrage. Trap efficiency of a forebay in a low mountain range Ulf Teschke HafenCity University, Hebebrandstraße 1, 22297 Hamburg, Germany,  ABSTRACT: For storage reservoirs, a sustainable management of sediments is necessary that fulfils eco-nomic and ecological requirements. The process of silting reduces the storage volume and, thus, dimi-nishes the functional capability. Hence for barrages, the aim is to allow great amounts of sediments to pass through the dam or to prevent the sediment deposition by collecting the materials by means of sedi-mentation. It is essential to achieve high trap efficiency for a forebay. This function is especially of great importance for drinking water reservoirs in order to provide a good water quality. In the course of time, the trap efficiency decreases due to the deposition of sediment in the reservoir. For the economic life-time of a forebay, it is essential to know to what extend the decreased reservoir storage capacity influences the trap efficiency. The following work deals with an analysis of trap efficiency of the forebay of a reservoir in the low mountain range of the region Harz in Germany. For this purpose, Churchill’s Method is ap-plied. The changes in trap efficiency since the commissioning of the forebay are modelled. During the last 73 years, about 10% of the forebay volume has already silted up. On the basis of the model calibrated to the measured values, a forecast is made regarding the forebay’s settling properties during the next dec-ades. Keywords: Forebay, Trap efficiency, Sedimentation  River Flow 2010 - Dittrich, Koll, Aberle & Geisenhainer (eds) - © 2010 Bundesanstalt für Wasserbau ISBN 978-3-939230-00-71119The dam structure of the forebay consists of a dam body with a loam core. The dam is about 20 m higher than the original ground level and the crest is about 200 m long.  The main data of the forebay is as follows:  Length of the forebay     500 m Annual discharge       32.4·106 m³/a Catchment area        38.3 km2  Water volume V1 1931     699,600 m3 Water volume V2 2004     634,600 m3 Sediment volume since 1931  65,000 m3 Flooded area         128,500 m² Mean retention time      7.1 d  With regard to the forebay’s trap efficiency, it is known that a sediment volume of about 65,000 m³ has settled since the time of the forebay’s com-missioning. The sediment quantity was estimated on the basis of differential data from the original topographical survey in 1931 and the recording of the present condition by means of an aerial laser scan survey. High trap efficiency is essential for the forebay. Otherwise, problems with the drinking water puri-fication could arise in the subsequent barrage. 3 MODELLING TRAP EFFICIENCY The article by Verstraeten and Poesen (Ver-straeten, Poesen, 2000) gives a good review of the currently available empirical and theoretical mod-els for estimating the trap efficiency of water re-servoirs. From the existing models, amongst others ac-cording to Borland & Miller (Borland and Miller 1958) Brown (Brown, 1943), Brune (Brune, 1953), Churchill (Churchill, 1948) and Camp (Camp, 1945), the method according to Churchill was chosen for the issue on hand. 3.1 Churchill’s Method The model developed by Churchill in 1948 esti-mates the trap efficiency of a reservoir by means of a sedimentation index SEDI. With the Churchill Method, in contrast to other models, the y-axis of the plotted empirical curve is related to the per-centage rate of the sediments passing through the reservoir [%]100 TES A −=  (1) with TE standing for trap efficiency. The method is based on data measured by the Tennessee Valley Authority regarding the trap ef-ficiency of the dam system in the Tennessee Val-ley in the USA. In particular, the data related to the Hales Bar Dam and the Wilson Dam was ap-plied. The sediment examined in the Tennessee Valley is classified as fine and is, therefore, mainly transported in suspension. The curve determined empirically according to Churchill is given in Figure 1. The values for the sedimentation index SEDI are shown on the x-axis. In this context, the sedimentation index is described as the relation between the retention time t [s] and the mean flow velocity v [m/s]: vtSEDI =  (2) It is also possible to present the sedimentation in-dex in another way QVt = , AQv =  and LVA =  result in: ( )LQVLVQVQAVSEDI222/=⋅=⋅=  (3) with V = storage volume [m³] Q = inflow [m³/s], A = mean perfused cross-section of the forebay [m²] L = length of the reservoir (flow path) [m] and SEDI = sedimentation index [s²/m].   Figure 1. Trap efficiency (TE) related to sedimentation in-dex (Churchill, 1948) The Churchill curve for the local sediment in Fig-ure 1 is represented by the following equation [ ] 121600 2,0 −⋅⋅= −gSEDISA  (4) with SA = percentage of the sediment quantity in the discharge [%] and SEDI = sedimentation in-dex [s²/m]. The non-dimensional retardation factor R is di-fined as [ ]( )121600100 2,0 −⋅⋅−= −gSEDIR  (5) 1120with R = sediment retained [%], SEDI [s2/m] and g = gravitational acceleration [m/s2]. Since Churchill has carried out his investiga-tions in the area of the Tennessee Valley in which the dams are set up in a row, he had to make a fur-ther differentiation. Thus, he differentiates be-tween local and fine sediment. The local sediment comes from that part of the river’s course which does not feature any reservoir. In the first storage reservoir, the retention is going to be exception-ally high (lower Churchill curve) since the coarse material can quickly settle there. After that, only finer sediment is passed with less sedimentation velocity to the dams at the downstream face so that the percentage of sediments in the discharge increases (upper Churchill curve). In this context, only the lower curve according to (4) is of any importance. Owing to the sedimentation index and the tak-ing into consideration of the retention duration and the flow velocity in the reservoir, Churchill’s Method is able to describe the hydraulic condi-tions more precisely than other methods and, thus, is most suitable to estimate the trap efficiency in the present case. Studies conducted by Borland (Borland, 1971) were able to confirm that Churchill’s empirical approach would also deliver plausible results in case of reservoirs and sedimentary basins falling temporarily dry. In addition to this, the theory may easily be applied to smaller reservoirs as well. 3.2 Application of the Method In order to apply the empirical model according to Churchill, the sedimentation index has to be cal-culated. In the present case, it is recommendable to express the equation (5) in a different form  ⎟⎟⎠⎞⎜⎜⎝⎛ −⋅⋅−= 121600100 5 tgvR  (6) It can be recorded: the longer the retention time t in the forebay, the larger the factor R. That means, the longer the sediment particle can remain in the forebay, the higher the probability that the sedi-ments settle and the higher the retardation factor R. Moreover, the factor R is going to be smaller in case of an increasing flow velocity v within the forebay. That means, if the inflow increases in re-lation to the forebay volume V, the sediments will have less time to sediment. In order to be able to make a statement about the forebay’s trap efficiency in case of different discharges, the water inflow has to be linked with the respective bed load Qbl. For this purpose, measured data has to be used. Oftentimes, a linear relationship  QkcF ⋅=  (7a) is used as a basis, in this context, with cF total solid in kg/m³. It follows   2QkQbl ⋅=  (7b) where Qbl results in kg/s. For the present case, it is known that about 65,000 m³ of sediment has set-tled in the forebay between 1931 and 2004. A random sample taken during a flood showed a solid concentration of about 0,530 kg/m³ solid at an inflow of about Q = 33 m³/s for the inflow to the forebay. According to this pair of values, k would result in about 0,016 pursuant to equation (7). In order to convert the settled solids into a vol-ume, it is assumed that the grain density corre-sponds to a value of 2650 kg/m³ as is common in the region. The density of the materials settled at the forebay’s base is estimated with 1325 kg/m³. If approach (7) is combined with the daily in-flow to the forebay, the changes in the forebay volume may be calculated depending on the sedi-mentation rate. In this context, the relationship (7b) may be calibrated in such a way that it results exactly in the measured value of 65,000 m³ of sediment for the period between 1931 and 2004. If this approach is used, the following calculation formula applies to interval t1, ⎟⎟⎠⎞⎜⎜⎝⎛ −⋅⋅⋅−= 121600100 5 20211VgLQR  (8) tQkRFF Δ⋅⋅⋅= 111 %100      ρ11FFV =Δ  (9) and to interval tn+1 ( ) ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−Δ−⋅⋅⋅−= ∑ =++ 121600100 5 210211 ni innVVgLQR (10) tQkRFF nnn Δ⋅⋅⋅= +++ 111 %100       ρ11++ =Δ nn FFV  (11) with FF = the mass of sediment retained in the forebay during one time step Δt. As a whole, the following has to apply for the period between 1931 and 2004 for m time steps: 31000,65 mVmi=Δ∑ =  (12) Figure 2 shows the measured daily discharge of the river for the years 1931 to 2004. 1121Daily Discharge (1.11.1931 bis 31.10.2004)0510152025Mai.27Nov.30Mai.34Nov.37Mai.41Nov.44Mai.48Nov.51Mai.55Nov.58Mai.62Nov.65Mai.69Okt.72Apr.76Okt.79Apr.83Okt.86Apr.90Okt.93Apr.97Okt.00Apr.04Okt.07DateDischarge [m³/s] Figure 2. Daily measured discharge upstream of the forebay Since the hydrograph of the inflow in Figure 2 has a resolution of one day, the time step Δt = 1d was chosen. The solution of the system of equations (8), (9), (10), (11) and (12) is QQbl ⋅= 014.0  (13) with Qbl = discharge of bed load [kg/s] and Q = discharge of the river [m³/s]. Afterwards, the calculation for the period be-tween 2005 and 2077 is carried out on the basis of the same discharge hydrograph from 1931 to 2004 according to Figure 2. In this context, however, the volume of the forebay is reduced by 65,000 m³ (in comparison to 1931) resulting in a volume of 634,600 m³ which is applied as the storage vol-ume V for 2004. According to the result, a new sedimentation volume of 64,424 m³ will settle in the forebay dur-ing the next 73 years while the conditions and as-sumptions remain the same. Thus, the trap effi-ciency is diminished by 576 m³ or 8.86 % in the period from 2004-2077 as compared to the period from 1931-2004. According to relation (8), the retention R of the forebay in its original condition in 1931, in 2004 and in 2077 may be calculated and compared de-pending on the inflow Q.  The result of this calculation is presented in Figure 3. It can be noted for the years 1931, 2004 and 2077 that recognisable differences in the re-tention R of the forebay can only be found in case of larger discharges (Q > 20 m³/s). In case of a medium inflow or even smaller inflows in the forebay, however, no noticeable changes have to be expected for the retention capacity in the fu-ture.  Trap efficiency related to discharge for different volumes0204060801001200 10 20 30 40 50 60 70 80 90 100Discharge [m³/s]Sediment retained [%]1931 2004 2077 Figure 3. Computed trap efficiency for 1931, 2004, 2077 for the forebay 4 SUMMARY AND OUTLOOK By means of the mean daily discharge value of the past 73 years, it was possible to model the fore-bay’s trap efficiency for the period from its com-missioning to today. In this connection, the inflow /bed load ratio was calibrated in such a way that it resulted in a sediment volume of 65,000 m³ meas-ured up to today. Based on today’s condition of the forebay and the assumption that the forebay’s future inflow behaviour remains the same as in the past 73 years, the modelling with identical assumptions shows that the forebay’s trap efficiency will not change noticeably during the next 73 years in case of normal discharge. Only in case of higher dis-charges (Q > 20 m³/s), the retardation factor R is reduced by a few percent. All in all, it can be said that, in case of constant boundary conditions and with a high probability, the trap efficiency of the investigated forebay will not significantly change in the future. A further step to improve the forecast’s accu-racy would be a comparison with other methods as described in section (3). In order to make even more detailed state-ments, precise measurements of the bed load at the inflow and outflow of the forebay would be necessary. By means of these data, the established model could be tested. In this context, other meth-ods could be called upon for comparison as well. ACKNOWLEDGEMENTS The author would like to thank the Harzwasser-werke GmbH (Hildesheim, Germany) for their permission to publish the results of the present study. 1122REFERENCES Borland, W.M., Miller C.R. 1958. Distribution of sediment in large reservoirs. J. Hydraul. Div. ASCE HY2. Borland, W.M. 1971. Reservoir sedimentation. In Shen, H.W., editor, River Mechanics. Vol. II. Fort Collins, CO, Colorado State University. 29.1-29.38. Brown, C.B. 1943. Discussion of sedimentation in reser-voirs by J. Witzig. Proceedings of the American Society of Civil Engineers 69. 1493-1500. Brune, G.M. 1953. Trap efficiency of reservoirs. Transac-tions, American Geophysical Union, Vol. 34(3). 407-418. Camp, T.R. 1945. Sedimentation and the design of settling tanks. Proceedings of the American Society of Civil En-gineers 71. 445-486. Churchill, M.A. 1948. Analysis and use of reservoir sedi-mentation data. In: Gottschalk, L.C. (edt.): Proc. Federal Inter Agency Sedimentation Conference, Washington, 139–140. Verstraeten, G.; Poesen, J. 2000. Estimating trap efficiency of small reservoirs and ponds and implications for the assessment of sediment yield. In: Progress in Physical Geography 24(2), 219–251.    1123

Trap efficiency of a forebay in a low mountain range

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Trap efficiency of a forebay in a low mountain range

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