ICOLD Bulletin on Cost saving in dams. Appendix 4.2

## 4.2. Labyrinth weirs

### 4.2.1. Existing labyrinths:

One drawback of free overflow spillways is their low specific discharge. A standard Creager type profile will have a unit flow per metre length of spillway close to 2.15 h^{1.5}, where h is the upstream head over the spillway crest in metres. Such spillways are therefore costly due directly to their length and/or indirectly due to the loss of storage or head corresponding to the upstream head depth required for the design flood.

For over 50 years, labyrinth weirs have been used to increase specific discharge at weirs. They are generally conceived and proportioned based on similar design criteria:

– Reinforced concrete vertical walls upon a flat base.

– Trapezoidal lay out.

Most are for spillways with design discharges of between 100 and 1 000 m^{3}/s with walls under 4 m high and with savings in term of required head above spillway crest level close to 1 m as compared to a standard Creager profile. At least three are much larger structures with walls up to 9 m high and discharges in the range of 10 000 m^{3}/s. The upstream head savings in these cases is close to 3 m.

The behaviour of these structures has been good but this solution has been used for only about 0.2% of all free overflow spillways. The vertical walls of such labyrinths may be built easily but they have three drawbacks:

– Vertical walls are not hydraulically favourable for large discharges.

– They may require significant reinforcement and base anchorage depending on their profile and on the hydraulic loading.

– While they have been used at some specific dam site with large flat areas close to the reservoir, the base plan area they require does not land itself to use on the crest of typical gravity dam sections.

### 4.2.2. New solution: P.K. Weirs

Since 2000, studies and model tests have been made in: Algeria, China, France, India, Switzerland and Vietnam for labyrinth designs which may be placed upon normal gravity dams cross sections. The designs produced tried to optimise both hydraulic efficiency as well as structural and economic requirements. Over 100 shapes were studied and many solutions proved possible, but the most favourable designs are based upon two principles:

– The lay out of walls has a rectangular shape similar to piano keys, justifying the proposed name of Piano Keys Weirs (or P.K. Weirs).

– Those walls orthogonal to the flow are inclined. This is favourable hydraulically especially for large discharges and also allows the base width of the structure to be reduced, thus favouring its utilization upon most spillways or gravity dams.

A design which appears cost efficient for most existing or new spillways is represented below. This model (model A) has an upstream and a downstream overhang of same length.

The proposed ratio N between the developed plan length of wall and overall spillway length is close to 5. An increase of this ratio does not usually seem cost effective.

Where this ratio of 5 is used, the proportions of other aspects of the PKWeir can be taken as follows, based on P_{m} (in metres) which is the maximum height of the labyrinth walls, see Fig.1.

The suggested upstream head over the weir crest, h, should be between 0.4 P_{m} and 2 P_{m .}

Within these limits, the discharge per metre of spillway q (in m^{3}/s) is close to

q = 4.3 h **√**P_{m} as compared to 2.15 h**√**h for a Creager weir.

The saving in term of required head above spillway crest level as compared to a Creager weir is close to 0.45 P_{m}.

As with Creager weirs, the estimated discharge may be reduced by 5 or 10%in the case of short weirs due to interference effects from the end abutments.

To improve the hydraulic efficiency when the design conditions do not limit the height of the P.K.Weir, it is generally more economic to increase P_{m} and to keep same proportions as suggested, rather than to increase the value of the N ratio. Suggested dimensions are of course only indications and are subject to adaptation according to local requirements.

P.K.Weirs can be made of reinforced concrete, either precast or in situ. In the case of low height walls, thickness may be governed by practical steel fixing requirements. Where P_{m } is less than 2m, it may be simpler to adopt complete steel fabrication, with stiffeners if necessary. Such a solution is certainly advisable where P_{m} is less than 1m.The cost per metre of spillway length is generally proportional to P_{m}.

### 4.2.3. Alternative shapes and models

It is possible for about the same cost and discharge, to slightly modify the weir shape as shown on Fig. 2. This favours the early discharge of floating debris, while a bottom outlet may be incorporated in the stepped downstream part of the spillway, see Fig.3.

Other models, also rectangular in plan shape and with walls inclined in the flow direction, have been successfully tested, but with different overhang arrangements. For instance model B has a longer upstream overhang and no downstream overhang, see Figs 4 to 6. This produced a slightly increased discharge for small values of h.

### 4.2.4. Utilization

Compared to Creager type weir profiles, P.K. Weirs may divide by a factor of about 3 the spillway lengths required at fill dams or by 2 the upstream head required at any weir.

For existing free overflow spillways they may be used to enhance freeboard and increase safety or to increase storage at low cost. They may be used as emergency spillways associated with an existing or new gated spillway, using the freeboard for discharging part of any exceptional floods. For instance a freeboard of 4 m could be used to discharge an additional 40 to 50 m^{3}/s per metre of spillway. As there is also much air entrainment in flows from P.K. Weir and other labyrinth structures, energy dissipation is enhanced and, for moderate discharges, any downstream erosion may be much reduced.

**Figure 1 – Design suggestion for PKWeir type A**

(scale of cross sections is 1.5 scale of plan view)

**Figure 2 – Alternative shapes for PK Weir type A**

**Figure 3 – Alternative shapes for PKWeir type A**

**with downstream steps **(Outlet cross section)

**Figure 4 – Design suggestion for PK Weir type B**

(scale of cross sections is 1.5 scale of plan view)

**Figure 5 – Alternative shapes for PK Weir type B**

**Figure 6 – Alternative shapes for PK Weir type B **

**with downstream steps **(Outlet cross section)