Colsterdale Spillway SYSTEM design

Water Engineering Research Ltd.Ashby RoadLoughboroughLeicestershire

16th November 2015

Managing DirectorA.N. Other and PartnersGrove RoadBirminghamWest Midlands

Spillway System Design

Dear Sir/Madam,

I am writing to you to supply you with the spillway system design for Colsterdale Reservoir, Yorkshire, as requested. The attached report gives details of the system location and dimensions, with accompanying calculations, for the design of a spillway, side channel, collecting channel, delivery channel and stilling basin. The design has been produced with a maximum design discharge of 118.3m3/s, suiting the provided maximum discharge of 120m3/s that was specified in the brief.

A summary drawing detailing key dimensions of the elements is attached as an Appendix to the report. A location map is also included; the location of the system was justified based on the ground profile of the site, with the aim of minimising the cut and fill required for installation. Channel optimisation was undertaken to minimise construction costs and the effect on the surrounding environment.

Design procedures and the design assumptions used have been detailed in the report so that any engineering decisions made can be followed and understood.The report specifies further details of the spillway system, however if any further information is required with regards to our design or any other matter, please do not hesitate to contact us.

Yours faithfully,

Rebecca Woodhouse(On behalf of Water Engineering Research Ltd)

Contents1.0Introduction12.0Executive Summary13.0Weir Design23.1Theory23.2Procedure23.3Spillway Design: 7m23.4Inflow/Outflow Hydrograph54.0Spillway Route75.0Collector and Delivery Channel Design85.1Theory85.2Channel Width85.3Water Surface Profile95.4Collector Channel Backwater Profile115.5Delivery Channel Backwater Profile115.6Collector and Delivery Channels Surface Profiles126.0Side Channel Design136.1Theory136.2Water Surface Profile of a Flat Rectangular Channel147.0Stilling Basin Design167.1Theory167.2Stilling Basin Length167.3Other specifications188.0References19

Appendix A 10m Wide Weir Results1Appendix B Inflow Hydrograph2Appendix C Reservoir Extents3Appendix D Site Map4Appendix E Backwater Profiles5Appendix F Side Channel Calculations6Appendix G Site Elevations7

List of FiguresFigure 1 - Simplified sketch of proposed spillway system1Figure 2 - Plot of N against Outflow for a 7m wide weir3Figure 3 - Inflow/outflow hydrograph for a weir width of 7m5Figure 4 - Proposed spillway system route7Figure 5 - Flow conditions at the connection between the collector and delivery channels9Figure 6 - Gradually varied flow10Figure 7 - Channel and water surface elevation13Figure 8 - Side channel layout13Figure 7 - Side Channel Surface Water Profile15Figure 8 - Stilling basin16Figure 9 - Graph showing Froude number against L/D2 for stilling basin design17Figure 10 - Stage-Discharge rating curve for River Burn17Figure 11 - Hydraulic jump profile18

List of TablesTable 1 - Values for Height above Crest, Outflow, Storage and N.3Table 2 - Values for average inflow, N, change in N and the outflow rate for a 7m wide weir4Table 3 - Inflow/outflow and volume relationship6Table 4 - Distance from transition point, water depth and elevation values12Table 5 - Example surface profile calculation: inputted values and Froude number14Table 6 - Example surface profile calculation: Newton Raphson Method15Table 7 - Summary of side channel water surface profile15

Colsterdale Spillway System DesignWater Engineering Research Ltd

1.0 IntroductionWater Engineering Research Ltd were commissioned by A.N. Other and Partners to undertake a spillway system design for a reservoir with an earth dam at Colsterdale, Yorkshire, connecting the dam to the River Burn downstream of the river. This includes producing an efficient design of a weir, side channel, collecting channel, delivery channel and stilling basin. The river downstream of the dam is the River Burn.The client provided a flood inflow hydrograph for a storm event at the proposed reservoir and informed Water Engineering Research Ltd that a maximum design discharge value of 120m3/s for the River Burn should be taken. The storage value for the weir has been given by the equation:

where h = water depth from the present water level.(Eq 1.1)

The level of the river downstream of the dam is to be taken as 171m AOD and the present water level in the dam is to be taken as 250m AOD.

2.0 Executive SummaryA simplified sketch of the spillway system can be seen in Figure 1. A weir of width 7m has been designed, giving a maximum outflow of 118.3m3/s. This flows into a 7m long side channel with a width of 6m. The 130m long collector channel has a slope of 0.0008, and leads into a delivery channel of length 555m and slope 0.133. To control the effects of a hydraulic jump at the end of the delivery channel, a stilling basin has been designed. This has a length of 16m. The whole design is to be constructed from concrete. Appendix F gives a summary of the key dimensions used and elevations for each element of the system.

Figure 1 - Simplified sketch of proposed spillway system

3.0 Weir Design3.1 TheoryDuring a flood event the water level will rise above the reservoir design water level. Additional water will overtop a weir crest and pass through the spillway to allow the water to safely travel downstream. The spillway system comprising of weir and spillway channel, is designed to ensure that water does not reach the crest of the dam which would likely cause significant problems and potential collapse. The system also ensures an appropriate discharge for the capacity available in the river downstream.3.2 ProcedureThe initial weir breadth was set at 10m however this gave a maximum outflow value of 141.9m3/s, above the specified value of 120m3/s. The calculations were repeated and it was found that a spillway width of 7m was the optimum dimension. The following calculations are based on the 7m spillway width however calculations for a 10m weir are attached in Appendix A.3.3 Spillway Design: 7mValues for time, t (s), and the corresponding inflow, I (m3/s), were extracted from the Flood Inflow Hydrograph (Appendix B). These were tabulated and Equation 3.1 was used to determine the outflow, O (m3/s) for depth values between 0 and 10m. Values of up to 10m were chosen as the top of the earth dam resides at 260m AOD (compared to a design normal water level of 250m AOD); therefore if the water was to rise above this 10m height difference, it would overtop the dam itself. Values for increments of 0.5m were taken to ensure that an accurate graph could be produced.

(Eq 3.1)

A Cd value of 0.62 was chosen for the design as suggested by Novak, Moffat, Nalluri & Narayanan. (2001).Storage for each height increment was calculated using Equation 1.1. N was then calculated using Equation 3.2 (with t given in seconds, i.e 1 hour = 3600 seconds).

(Eq 3.2)

The values for outflow, storage and N for height increments of 0.5m were tabulated as shown in Table 1.

Table 1 - Values for height above crest, outflow, storage and N.Height above crest, H(m)Ouflow, O(m3/s)Storage, S(m3)N (m3/s)

00.000

0.54.5499440141

112.81009160287

1.523.51529160437

236.22059440590

2.550.72600000748

366.63150840909

3.583.937119601073

4102.542833601241

4.5122.348650401413

5143.354570001587

5.5165.360592401766

6188.466717601947

6.5212.472945602132

7237.479276402321

7.5263.285710002512

8290.092246402707

8.5317.698885602906

9346.0105627603107

9.5375.3112472403312

10405.3119420003520

A graph of O against N (Figure 2) was then plotted and the trendline found, as shown by Equation 3.3. The trendline was assumed to pass through the origin as height, outflow, storage and therefore N, were all 0 at the start of the storm event.

Figure 2 - Plot of N against Outflow for a 7m wide weir

3.3(Eq 3.3)

Equations 3.4 and 3.5 were used to determine the average inflow and N values. The outflow, O, could be found using Equation 3.3. Inflow rate was taken at 1 hour increments, in keeping with the t used in previous calculations, from the inflow hydrograph provided.

3.4(Eq 3.4)

3.5(Eq 3.5)

These values were then tabulated, as shown in Table 2.

Table 2 - Values for average inflow, N, change in N and the outflow rate for a 7m wide weirTime (hours)Change in time, t (s)Inflow rate, I(m3/s)Average inflow rate, (m3/s)N (m3/s)N (m3/s)Outflow rate, O (m3/s)

000.0000.000

360033.000

163.0000.199

36001312.801

22015.8011.051

36003028.949

34044.7502.996

36005956.004

478100.7546.827

360010497.173

5130197.92713.690

3600156142.310

6182340.23724.236

3600203178.764

7224519.00138.315

3600234195.685

8244714.68754.789

3600246191.211

9248905.89871.959

3600242170.041

102361075.93988.119

3600228139.881

112201215.821102.041

360020097.959

121801313.780112.128

360016047.872

131401361.651117.159

360012810.841

141161372.492118.308

3600106-12.308

15961360.184117.004

360090-27.004

16841333.180114.159

360081-33.159

17781300.021110.695

360073-37.695

18681262.326106.795

360064-42.795

19601219.531102.418

360055-47.418

20501172.11397.630

360044-53.630

21381118.48492.293

360032-60.293

22261058.19186.393

3.4 Inflow/Outflow HydrographOnce outflow values were found, a hydrograph showing inflow and ouflow values could be plotted (Figure 3). This gives us the maximum outflow, Qpeak for the weir. The maximum outflow for a 7m weir was found to be 118.3m3/s (at 14 hours), and after several iterations of varying weir width, was discovered to be the optimum value for the 120m3/s limit. The point at which the inflow is equal to the outflow coincides with the reservoirs maximum storage.Figure 3 - Inflow/outflow hydrograph for a weir width of 7mUsing the average inflow and outflow rate during any given hour, the net change in volume can be calculated as shown in Table 3. This table shows a maximum change in volume of 4,730,000m3. From rough calculations of the area change between 250m AOD and 260m AOD and assuming area changes linearly with height over the 10m, the volume capacity of the reservoir is 11,780,000m3 before overtopping the dam. Hence it is predicted that the water level will reach a maximum of 254m for the given flood event. This gives a tolerance, ensuring that the dam will not be overtopped in the occurrence of a potentially larger flood event or reduction in outflow due to blockage. Example calculations for Table 3 values for the 2nd hour are shown below by Equations 3.6 3.10. Average inflow and outflow rates were taken from Table 2 (see numbers in italics). Appendix C shows a map of the area.

(Eq 3.6)

(Eq 3.7)

(Eq 3.8)

(Eq 3.9)

(Eq 3.10)

Table 3 - Inflow/outflow and volume relationshipHourInflow during the hour(m3)Total volume in (m3)Outflow during the hour(m3)Total volume out(m3)Change in volume(m3)

1st10,80010,80035835810,442

2nd46,80057,6002,2502,60954,991

3rd108,000165,6007,2859,893155,707

4th212,400378,00017,68127,574350,426

5th374,400752,40036,93164,505687,895

6th561,6001,314,00068,266132,7721,181,228

7th730,8002,044,800112,590245,3621,799,438

8th842,4002,887,200167,586412,9482,474,252

9th885,6003,772,800228,145641,0933,131,707

10th871,2004,644,000288,139929,2323,714,768

11th820,8005,464,800342,2871,271,5194,193,281

12th720,0006,184,800385,5041,657,0244,527,776

13th576,0006,760,800412,7182,069,7414,691,059

14th460,8007,221,600423,8412,493,5824,728,018

15th381,6007,603,200423,5612,917,1434,686,057

16th324,0007,927,200416,0943,333,2374,593,963

17th291,6008,218,800404,7373,737,9744,480,826

18th262,8008,481,600391,4824,129,4564,352,144

19th230,4008,712,000376,5834,506,0404,205,960

20th198,0008,910,000360,0864,866,1254,043,875

21st158,4009,068,400341,8615,207,9863,860,414

22nd115,2009,183,600321,6345,529,6203,653,980

4.0 Spillway RouteFigure 4 below shows the proposed route for the spillway system.

Figure 4 - Proposed spillway system routeOne of the primary reasons for choosing this route is that it allows for a relatively short delivery and collector channel to be used, therefore minimising the materials required for construction. It should be noted that the detail of the bend between the collector and delivery channels has not been designed. This will require reinforcing to account for the force of the water hitting the side of the channel at this point.To reduce the environmental effects on the site, the delivery channel is designed to closely follow the contour of the slope reducing the cut and fill required. This further reduces the cost of the system. Constructing the spillway system to the south of the dam ensures that the woodland to the north will not be lost. It also avoids the crags north of the dam. When considering the long term durability and sustainability of the project, it was decided that all of the elements will be constructed from concrete. The stilling basin must be constructed of concrete to resist scour and it is essential that all connections between elements are flush to ensure no cracking or leaking occurs, therefore making a fully concrete design the most sensible and efficient option.

5.0 Collector and Delivery Channel Design5.1 TheoryA channel is required to transport water from the side channel to river level. This has been broken down into a collector channel and delivery channel, with a mild slope and steep slope respectively. They have been designed to fit with the contours of the existing slope and the collector channel ensures that the water flow is limited.5.2 Channel WidthA channel width of 6m was chosen throughout the design. This value provides an economical design compared to a wider channel as it requires less materials. A narrower width would increase the water depth in the channel and would therefore require deeper side walls, increasing construction time, cost and material quantity. This would correspond to an increase in the length of the stilling basin required and would lead to a less environmentally friendly design.Several iterations were carried out at varying widths to determine normal height and therefore the optimum channel width for the system. The calculations led to the decision to provide a width of 6m.The critical depth, yc was calculated at the flow transition between the collector channel and the delivery channel, using Equation 5.1.

(Eq 5.1)

Where g = 9.81 m2/s.The evaluation of the critical depth is required for the solution of most rapidly varied and gradually varied flow problems. As can be seen from Equation 5.1, the critical depth is dependent on discharge so a critical depth line for a given discharge can be drawn on the water surface elevation drawing, as shown by the dashed line in Figure 5. An abrupt change in the geometry of the channel results in the flow suddenly changing its type. A highly supercritical flow, for example, flowing on a very steep slope and then flowing into mild or horizontal slope will transition into a subcritical flow through a hydraulic jump mechanism. In the design of the collector and delivery channels, the channel slope changes from mild to steep. This results in the transition from subcritical to supercritical flow, with critical depth occurring exactly at the point of transition. This is outlined by Figure 5.

Figure 5 - Flow conditions at the connection between the collector and delivery channels

5.3 Water Surface ProfileThe first step in defining the mild slope of the channel was to calculate the critical slope for the given discharge and channel width, which would enable the slope to be defined as mild. This is shown in Equation 5.2.(Eq 5.2)

Therefore, an acceptable slope for the collector channel is S0 = 0.0008. The horizontal length of the collector channel is 130m, as found from the map (see Appendix D).The slope for the delivery channel was then calculated. Using the map (Appendix D), a horizontal length of 555m is found. By taking the elevation of the transition point to be 245m AOD and taking away the change in height of the collector slope (0.0008*130), this gives a maximum level of 244.9m AOD for the delivery channel. Given that the river level is taken as 171m AOD (as per the brief), a fall of 73.9m (244.9-171) is present in the delivery channel. This gives a slope of S0= H/L = 73.9/555 = 0.133 for the steep slope.As previously explained, the collector channel has a mild slope and that the delivery channel has a steep slope. The critical depth was found to be 3.409m and the normal depths were found using trial and error with Mannings equation (see Equation 5.3). The normal depth is yn = 5.399m for the collector channel and yn = 0.853 for the delivery channel.

(Eq 5.3)

The position of the control point is the point of transition between the two flows as this is the point where the relationship between head and discharge is known. Additionally: - Left of this point the flow is subcritical and Frwave velocity and disturbances travel downstream. Therefore, the profiles are controlled from a point upstream (i.e. the transition point).It is also useful to derive the general equation of gradually varied flow, as shown below. From Bernoulli:(Eq 5.4)

Figure 6 - Gradually varied flowDifferentiating with respect to x gives Equation 5.5:

(Eq 5.5)

Where Sf is the friction slope;

Also hence

Now the direct step method is used to find the distances for corresponding depths for regular channels. For this purpose the equation is rewritten as (Chadwick et al.):(Eq 5.6)

5.4 Collector Channel Backwater ProfileThe following input data has been established for the collector channel:Q=118.3 m3/s, B=6m, n=0.012, S0=0.008, yn=5.399m, yc=3.409m.The n value for a concrete channel was chosen to be 0.012 in accordance with Chadwick, Morfett & Borthwick (2013).20 steps with a depth change of 0.1m were used to achieve the desired level of accuracy. The first calculation was carried out with the depth equal to yc and the last calculation was for y = 5m. As the length of the delivery channel is 130m, the corresponding value of depth at this location was found through the direct step method with additional trial and error adjustment in order to obtain the exact value. This was found to be a value of 4.048m, as can be seen in the table in Appendix E.It is worth noting that had the channel length at normal depth been required, a 2% increase would have been added to the normal depth value. It can be seen from the table that yn>y>yc, Sf>S0 and Fr2y>yn, S0>Sf and Fr2>1, hence the surface profile occupies region 2 for a steep slope. As yyn, S0 Sf and dy/dx0.5.6 Collector and Delivery Channels Surface ProfilesThe collector and delivery channels surface profiles were tabulated (see Table 4) and plotted as shown in Figure 7. This shows the elevation above ordnance datum for the channel and water surface for both channels. It can be seen that the water level approaches 171m AOD at around 540m from the transition point. This is due to the water reaching its normal depth near this value, resulting in no height change over the last 15m to the end of the channel.

Table 4 - Distance from transition point, water depth and elevation valuesDistance from transition point, x(m)Elevation, Z(m)Water depth, y(m)Water surface elevation, Z+y (m)

-129.862242.0004.048246.048

-108.485241.9834.000245.983

-71.467241.9533.900245.853

-43.325241.9313.800245.731

-22.955241.9143.700245.614

-9.444241.9043.600245.504

-2.024241.8983.500245.398

0.000241.8963.409245.305

0.043241.8903.300245.190

0.257241.8623.150245.012

0.683241.8053.000244.805

1.368241.7142.850244.564

2.374241.5802.700244.280

3.785241.3932.550243.943

5.710241.1372.400243.537

8.302240.7922.250243.042

11.777240.3302.100242.430

16.451239.7081.950241.658

22.803238.8631.800240.663

31.595237.6941.650239.344

44.126236.0271.500237.527

62.826233.5401.350234.890

92.944229.5341.200230.734

149.132222.0611.050223.111

307.203201.0380.900201.938

555.000168.0810.854168.935

Figure 7 - Channel and water surface elevation

6.0 Side Channel Design6.1 TheoryA side channel is normally incorporated into a spillway system design if it is not possible to have a direct over-fall spillway. For this reason, the proposed system requires a side channel due to the 90 degree change in direction between the weir and collector channel. A simple sketch of a side channel can be seen in Figure 8. For the proposed system, a horizontal rectangular channel has been designed to simplify constructability, saving time and cost.

Figure 8 - Side channel layout6.2 Water Surface Profile of a Flat Rectangular Channel In order to find the water surface profile in the side channel, the momentum equation between two given points within the channel was applied, as shown in Equation 6.1. After combining all relevant terms; momentum passing, weight of body of water between points, friction force and hydrostatic pressure at both points and simplifying by using substitutions and removing negligible terms, the surface profile of a rectangular can be found by Equation 6.2.

(Eq 6.1)

(Eq 6.2)

Where(Eq 6.3)

and(Eq 6.4)

Hence(Eq 6.5)

Where Q=Discharge, L=Spillway length, b=Spillway width, yo=Reference depth, y=Depth.For this design yo is the known depth at the discharge of the side channel as calculated in Section 5.4 to be 4.048m. The width of the side channel is 6m to ensure continuity with the collector and delivery channels, and has length 7m equal to the width of the weir, as shown in Section 3.3, feeding into the side channel.In order to obtain a full profile a range of water heights were obtained at distances ranging from 0-7m along the length of the channel. The chosen x value was substituted into the formula with all other known values. The Newton Raphson method was then used to compute the depth of water at that corresponding position. An example of this is shown in Table 5 for x=0m relative to yo at x=7m, the calculations used to compute this are shown in Appendix F.

Table 5 - Example surface profile calculation: inputted values and Froude numberWidth6m

Length7m

Q118.3m3/s

Yo (depth at exit)4.048m

Fo20.597415-

X0m

Table 6 - Example surface profile calculation: Newton Raphson Methody old (m)' Old Oldy new (m)

50.492521-0.691766.404536

6.4045362141.0988430.4083216.032944

6.0329444230.9239020.0328275.997414

5.997413570.9077220.0002885.997097

5.9970965930.9075782.28E-085.997097

5.9970965680.90757805.997097

This method was repeated at 1 meter intervals allowing a surface profile to be produced. The corresponding heights at each distance from the start of the side channel are shown in Table 5.

Table 7 - Summary of side channel water surface profileDistance (m)H (m)

06.00

15.97

25.91

35.78

45.60

55.33

64.91

74.05

This data has been used to create a graph so that the surface can be seen visually, as shown in Figure 6.

Figure 7 - Side Channel Surface Water Profile

7.0 Stilling Basin Design7.1 TheoryFlow discharged from the outlet of the delivery channel is often highly supercritical and if this flow is not controlled, it can lead to severe erosion at the toe of the dam. It is therefore necessary to dissipate the energy and return the water level to a normal depth appropriate for the river level and bed slope. A stilling basin is one way in which this can be done, and a general design can be seen in Figure 8.Figure 8 - Stilling basin

7.2 Stilling Basin LengthIn Section 5.5 it was found that for the delivery channel design the flow reaches normal depth within its length and hence remains at normal depth for the final section of the channel. This depth, D1=0.853m, can be used along with its associated velocity as calculated in Equation 7.1 in order to find the Froude number, as shown in Equation 7.2.

(Eq 7.1)

(Eq 7.2)

In order to obtain an initial estimate of length the US Bureau of Reclamation guide was used. With a Froude number of 8 and flow of 23.1m/s a type II stilling basin (for Fr>4.5, V>20m/s) has been designed, which should have a length of 4.35y3, where y3 is the tailwater depth. According to the stilling basin design specified (Shiono, 2015a) a ratio of length to tailwater depth, i.e. depth after the stilling basin, can be found using Figure 9. Given a Froude number of 8 the graph outputs L/D2 = 4.2, which is in line with our initial estimate.

Figure 9 - Graph showing Froude number against L/D2 for stilling basin designIn order to determine tailwater depth the stage-discharge rating curve was used, see Figure 10. Discharge is known to be 118.3 m3/s at the point, and elevation, at which the spillway re-joins the River Burn. From Figure 10, this means that the stage, or tailwater depth, is 3.8m.Using the above mentioned ratio the length of the stilling basin was found to be 15.96m as shown by Equation 7.3.

(Eq 7.3)

Figure 10 - Stage-Discharge rating curve for River Burn7.3 Other specificationsThe Froude number can also be used to determine the profile of the hydraulic jump from Figure 11. For the proposed design the angle of the hydraulic jump will be =9.The stilling basin will have a series of chutes and dentated sills in order to force the hydraulic jump within this region, as shown in Figure 8. At the upstream end the chutes will have the following dimensions: (Eq 7.4)

At the downstream end the sills are to be dimensioned as shown by Equations 7.5-7.7.

(Eq 7.5)

(Eq 7.6)

(Eq 7.7)

Figure 11 - Hydraulic jump profile

8.0 ConclusionIn order to come up with an integrated design solution for the flood risk posed on the dam, we had to go through the process of designing the individual parts of the whole configuration: namely weir, side channel, collector channel, delivery channel and stilling basin. The philosophy behind our solution was to take into account the specifics of the dam and its surroundings and aim to provide a design arrangement which is both economical and feasible. For this task we had to implement the knowledge and principle in hydraulics and water engineering acquired throughout our three years of our course. This meant, first, we either made an educated guess we considered to be optimal about the design parameters or in other cases we found those parameters by trial and error. Then we took those parameters and used them with formulae and computational models in order to test the validity of our solutions. For each step of the design, we have given an explanation of the hydraulic principles explaining the phenomena we were designing for. Constructability considerations have also been mentioned briefly throughout the report to and their solutions were given to justify some of the design choices we have taken. To conclude, we believe that the design and report we have produced is a concise effort which fully satisfies the needs and requirements of our client.

9.0 ReferencesShiono, K., 2015a. Spillway Design Coursework. Loughborough University.Shiono, K., 2015b. Spillways. Loughborough University.Shiono, K., 2015c. Gradually Varied Flow. Loughborough University.Chadwick, A.J., Morfett, J.C and Borthwick, M., 2013. Hydraulics in civil and environmental engineering. 5th edition. Boca Raton: CRC Press.Novak, P., Moffat, A.I.B., Nalluri, C. and Narayanan, R., 2001. Hydraulic Structures. 3rd edition. Spon Press.

Appendix A 10m Wide Weir Results

Appendix B Inflow Hydrograph

Appendix C Reservoir Extents

Appendix D Site Map

Appendix E Backwater Profiles

Appendix F Side Channel Calculations

Appendix G Site Elevations

20