F. Lempérière (HydroCoop), A. Ouamane (Biskra University) and J.-P. Vigny (HydroCoop)
For cost or safety reasons the fully gated spillways will probably be avoided for most future dams and free flow spillways will likely be the most used solution. There is thus a great future for labyrinth weirs, either as P.K. Weirs or by optimization of traditional labyrinths. Fuse devices may also be attractive.
For most dams built worldwide in last century, free flow spillways were used for small or medium catchment areas and gated spillways were used for large catchments corresponding to significant floods.
For design floods over some thousand m3/s, there was a majority of gated dams. The choice of gated spillways was favoured by the low specific flow Qs of traditional free flow Weirs:
Qs # 2,1 h1,5 Qs in m3/s/m and h the nappe depth in m.
Spillways of the future, and especially in Africa, could be different for 2 reasons:
– The management of gates raises many problems and the risk of total gates jamming which was overlooked in the past favours solutions discharging at least the yearly flood with all gates closed, i.e. essentially by a free flow weir.
– The progress in free flow weirs discharges has been very important either by new labyrinths (P.K. Weirs) or by various fuse devices.
For existing dams, P.K. Weirs may also be used for additional spillways or for increasing the discharge capacity or for raising the storage of ungated reservoirs.
1. P.K. Weirs and labyrinths
Traditional labyrinth weirs were developed since over 60 years with vertical walls, horizontal bottom, and triangular or trapezoidal lay-out which appeared logical. Most were limited to walls few m high with a nappe depth reduction limited to 1 m. This solution has the advantage of an easy construction of vertical walls but their structures become very expensive for high walls height. And the main reason of a very limited utilization of labyrinths was the fact that their usual structure could not be placed upon usual gravity structures of spillways.
1.1. P.K. Weirs studies
The basic target of studies made since 15 years was adapting the principle of labyrinth to this problem, i.e. in fact optimizing a structure with upstream and/or downstream overhangs. Many shapes were tested and it appeared that a rectangular lay-out was better adapted to such structure than trapezoidal ones; this justified the name of Piano Keys Weirs or P.K. Weirs. The other principle of these studies was to try to optimize not only the hydraulics but also their association with structural and construction problems. The target is not the best hydraulic coefficient; it is the lowest cost for a same reduction of nappe depth or for a same increase of discharge.
Many shapes are possible; some shapes have been selected as references such as a basic model A with same length of upstream and downstream hangovers. Some relevant data are given in appendix 1 of ICOLD Bulletin n°144 (Fig.1). Many other shapes are possible. But some data seem to apply generally:
Fig.1: Design suggestion for P.K. Weir type A
(The scale of cross sections is 1.5 the scale of plan view)
– The ratio L/W between the developed length of walls and the spillway length may be as high as 8 and as low as 3 but the optimum for new dams seems close to 4 or 5.
– The economical benefit as compared with a simple free flow spillway (Creager Weir) varies with the ratio k between the P.K. Weir discharge and the Creager discharge for a same nappe depth. A value of k between 2 and 4 seems advisable and a value above 5 seems usually unjustified economically.
– For an usual P.K. Weir such as model A, where Pm is the maximum walls height, the specific flow q (m3/s/m) for a nappe depth h (in m) is about q # 4 or 4,5 x h √Pm and the comparison with a Creager discharge is represented below (fig.2)
The nappe depth saving or the discharge increase remains about the same for a large variation of h and even for a nappe depth as important as the structure height.
For a new dam, P.K. Weirs are cost effective because increasing a free flow discharge by 1 m3/s requires only 0,5 m3 of reinforced concrete which may be made by the dam contractor.
The cost for adapting P.K. Weirs to an existing free flow spillway may be much higher because the existing structure will be modified and specific organisation and accesses will be necessary for works. The best design for relevant P.K. Weirs may not be the same as for a new dam.
Fig. 2: Hydraulic performance of reference designs
1.2. Adapting traditional labyrinths
Many studies and tests have analysed the impacts of various overhangs upon the hydraulic efficiency. But it appeared also from relevant analyses and tests that traditional labyrinths using vertical walls may be much improved:
– The shape of lay-out may be optimized: a rectangular or quite rectangular shape favours shorter structures with a structure basis length from upstream to downstream under fourfold the maximum nappe depth.
– The inlet may be wider than the outlet.
– With vertical walls, the thickness and cost of walls and bottom increases much more than the height and it may be much less expensive for large specific flows to use a structure as per (fig.3) where reinforce concrete is much reduced and the construction remains easy.
Fig.3: Proposed reference design for P.K. Weir model E – plan view (left) and cross sections (right)
Such optimized labyrinths may be preferred and overhangs avoided according to experience and costs data of contractors and the cross section under the P.K. Weir structure may be adapted accordingly.
1.3. Other new solutions: fuse devices
Beyond earth fuse plugs, mainly used for discharges over 1 000 m3/s, there are various possibilities of ordinary concrete fuse plugs which may tilt before overtopping or after overtopping.
A promising solution is detailed in appendix 3 of ICOLD Bulletin 144 (fig.4). The Concrete fuseplugs, if associated with an other spillway, may also be used with tilting before overtopping with a plug width such as 40% of the plug height i.e at a very low cost.
Tilting of such elements may be foreseen for a flood or 1/100 yearly probability or for a much lower probability such as 1/1 000 or even 1/10 000 on top of gravity dams.
Fig.4: Wedbila (Burkina Faso)
– Over the past 20 years, more than 50 large dams have been equipped with Fusegates, which are usually fuse elements with a labyrinth shape (fig.5). Their design is more complex than that of simple concrete fuseplugs or P.K. Weirs, but their performance is higher and is cost effective, for instance for improving existing free-flow spillways, or in addition to gated spillways for very large discharges (10 m-high fusegates combined with a freeboard of 5 m can discharge after tilting over 100 m3/s/m, which is about the same as large gated spillways).
Associating for large discharges P.K. Weirs with fusegates may also be a cost effective solution.
4. Spillways for future dams
4.1. Future dams with check flood under 5 000 m3/s
For such dams, (corresponding often roughly to catchment areas under 1000 km²) all or most of the discharge could be by free flow spillways using labyrinth shapes with a spillway length of about 10 m for 100 m3/s and 100 m for 5 000 m3/s (using partly fuse devices may also be an alternative). Gates should not be necessary but could be suitable in three cases:
– For reservoir management.
– As bottom gates for sluicing sediments at beginning of flood season or flushing them. This applies mainly to reservoirs storing a small part of the yearly river flow.
– As bottom gates for improving the mitigation of floods of yearly probability 10-1 or 10-2 for dams storing a large part of the yearly river flow.
The number of relevant bottom gates may be 1 or 2. The risk from wrong operation is limited.
For catchment areas under about 1 000 km², the check flood discharge should thus be quite 100% by free-flow spillways for most dams, 80% by free-flow spillways if mitigation of siltation or of floods is of interest and require gates.
4.2. Future dams with “check flood” over 5 000 m3/s
Such dams have usually in the past used totally gated spillways with at least 3 or 4 gates and an overall specific discharge (total discharge / spillway length) in the range of 80 to 150 m3/s/m.
For a free-flow spillway, the nappe depth necessary for a specific discharge of 100 m3/s is about 13 m for a traditional Creager Weir, 8 m for a Labyrinth Weir, 5 m for Fusegates.
The best solution will usually be to associate 2 spillways of about the same extreme discharge:
– A gated spillway with at least 2 gates.
– A free flow spillway with P.K. Weirs or with Labyrinth Fusegates (opening for floods over 10-3 probability). Such solution, for a cost similar to or lower than the cost of a fully gated spillway, has the key advantage of avoiding the huge risk from all gates jamming.
The choices presented here above should be adapted to the local physical and human conditions and should be considered as likely choices for many dams and not as fixed rules.
4.3. Future low dams in large rivers
The discharge of P.K. Weirs or optimized labyrinths is not modified if the downstream water level is as high as the top of the P.K. Weir structure; large discharges are possible with a gap of about 1 m between upstream and downstream levels.
Associating labyrinth weirs with gates may thus be a very cost effective solution for low dams in large rivers. It may be favoured by a longer dam and the construction schedule may be much easier than with a fully gated dam. The percentage of the extreme flood through gates could be reduced to 20 or 30%. A great advantage of this solution in Africa may be the possibility of building the P.K. Weirs during the dry season and to avoid or reduce costly cofferdams.
4.4. An example of P.K. Weirs utilization: Inga
The Inga scheme in RDC (Congo) will be by far the largest world energy site: it will supply as much as 30 nuclear plants or three fold Itaipu or 3 Gorges energy with a cost per MWh under 20$.
The average flow is 40 000 m3/s. The yearly flood is about 60 000 m3/s, the extreme flood in the range of 120 000 m3/s with as much uncertainty as for most dams. A design made in 1975 did foresee fully gated spillways.
The last design foresees to share over 120 000 m3/s between gates and a labyrinth free flow spillway. It is also possible as extra safety to use one of the 4 dams of the reservoir as one earth fuse plug of 30 000 m3/s.
It is possible to use a 1000 m long free flow spillway with P.K. Weirs with a discharge of 10 000 m3/s per m of nappe depth. It will be used permanently with a nappe depth under 2 m but may reach a discharge of 70 000 m3/s with a nappe depth of 7 m.
The P.K. Weirs spillway of Inga will discharge permanently 20 000 m3/s along decades and 5 000 m3/s later. It will be by far the largest waterfall worldwide. It seems possible to design it as a natural waterfall with some difference in shape or level between the 100 P.K. Weirs elements. Inga may then be also a very attractive touristic site.
P.K. Weirs Inga
F. Lempérière has been involved in the construction and/or design of 20 hydraulic structures on large rivers. He has been Vice-Chairman or Chairman of several ICOLD Committees on construction technology or cost savings. He has been involved in the P.K. Weirs studies since 15 years. He is Chairman of HydroCoop.
A. Ouamane is Professor of Hydraulics of Biskra University in Algeria and in charge of the Hydraulics University Laboratory. He has been deeply involved since over ten years in the researches and optimisation of P.K. Weirs.
J.-P. Vigny has been involved in the design or construction of large civil engineering schemes on rivers or at sea, including Cahora Bassa dam on the Zambezi, and the Mudhiq dam in Saudi Arabia. He is General Manager of HydroCoop. He has been deeply involved in the studies for P.K. Weirs and Concrete Fuseplugs.