2.3 Models A and B
For models A and B:
 Increasing by 10 per cent the length or height for the same width of elernents increases the savings and cost by about 5 per cent.
Giving a better hydraulic shape to the vertical part of the inlet (Fig.4), as for the piers of a gated spillway, would increase the savings and flow increase by about 10 per cent for a small extra cost.
Modifying the low part of the outlet (Fig. 5) does not substantially reduce the flow. This may favour the construction conditions.
Fig. 2. The layout for Model B.
Fig. 3. Data for a wall height of 8 m
Floating trees or debris may reduce by about 10 per cent the flow when the nappe depth is in the range of 1 or 2 m (as for Creager weirs). For nappe depths of 2 m or more, the floating debris are washed away according to model tests.
The flow is considerably aerated through a PK. weir; the risk of downstream erosion or cavitation is thus greatly reduced. This is confirmed by model tests and existing labyrinth shaped spillways.
Model A: Data for H = 4 m
1. Nappe depth of P.K. weir(m) |
0.50 |
1 |
1.5 |
2 |
2.5 |
3 |
3.5 |
4 |
4.5 |
5 |
2. Specific flow of the P.K. weir (m3/s/m) |
3.5 |
8.2 |
12.5 |
15.6 |
19.2 |
22.4 |
25.5 |
28.7 |
32 |
35.5 |
3. Specific flow of a Creager weir (m3/s/m) |
0.8 |
2.2 |
3.9 |
6 |
8.8 |
11.4 |
14.5 |
17.7 |
21 |
24.5 |
4-Increase of specific flow 2-3 (m'/s/m) |
2.7 |
6 |
8.6 |
9.6 |
10.4 |
11 |
11 |
11 |
11 |
11 |
5. Ratio of specifiecflows 2/3 |
4.4 |
3.7 |
3.2 |
2.6 |
2.2 |
2 |
1.8 |
1.6 |
1.5 |
1.4 |
6. Nappe depth of a Creager weir for the specific flow 2(m) |
1.4 |
2.4 |
3.2 |
3.7 |
4.2 |
4.07 |
5.1 |
5.6 |
6 |
6.3 |
7. Depth saving 6-1 (m) |
0.9 |
1.4 |
1.7 |
1.7 |
1.7 |
1.7 |
1.6 |
1.6 |
1.5 |
1.3 |
Model B: Data for H = 8 m
1. Nappe depth of P.K.weir(m) |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
2. Specific flow of the P.K. weir (m3/s/m) |
11.5 |
27.4 |
39.9 |
50 |
59.4 |
68.5 |
77.6 |
88.5 |
98 |
108 |
3. Specific flow of a Creager weir (m'/s/m) |
2.2 |
6.2 |
Il |
17 |
25 |
32 |
41 |
50 |
59 |
69 |
4. Increase of specific flow 2-3 (m3/s/m) |
9.3 |
21.2 |
28.9 |
33 |
34.4 |
36.5 |
36.6 |
38.5 |
39 |
39 |
5. Ratio of specific flows 2/3 |
5.2 |
4.4 |
3.6 |
2.9 |
2.5 |
2.1 |
1.9 |
1.8 |
l.7 |
1.6 |
6. Nappe depth of a Creager weir for the specific flow 2(m) |
3.1 |
5.4 |
7 |
8 |
9 |
9.9 |
10.8 |
1l.7 |
12.6 |
13.4 |
7. Depth saving 6-1 (m) |
2.1 |
3.4 |
4 |
4 |
4 |
3.9 |
3.8 |
3.7 |
3.6 |
3.4 |
3. Structural data and costs
Studies have been done for structures in reinforced concrete. Prefabricated steel structures could also be used for specific flows of less than 20 m3/s/m, but would probably be more expensive.
The main stresses in reinforced concrete are in the vertical walls between the inlet and the outlet; these walls act as overhangs over the concrete blocks, and not as horizontal beams, and it is even possible, to avoid thermal stresses, to design a vertical joint at the highest part of this wall.
The triangular shape of the wall (Fig.6) considerably reduced the stresses as compared with a rectangular wall; the thickness of the upper part of the wall may be small (10 to 20 cm). The average thickness of the reinforced concrete structure may thus be 15 to 25 cm for specific flows of less than 20 m3/s/m and in the range of 50 cm for specific flow increases of 50 m3/s/m.
A P.K. weir as presented above, with a maximum wall height H, requires, per metre of spillway, a total area of reinforced concrete of 4.2H. As the nappe depth saving is 0.4 or 0.5H, the necessary volume of reinforced concrete for saving 1 m of depth along 1 m of existing spillway is about ten times the wall average thickness, that means it varies from 1.5 m3 for H = 2 up to 5 m3 for H = 8 m.
As the increase in specific flow is about 1.5 H 1.5 increasing the flow by 1 m3/s requires 0.35 m3 of reinforced concrete for H = 2; and 0.5 m to for H = 8 (to be compared with 2 m3 for the traditional labyrinth for the UTE dam).
When using P.K. weirs for improving existing freeflow spillways, a quantity of ordinary concrete equal to 70 per cent of the reinforced concrete quantity should be added to the quantities given above.
For new dams, the extra cost as compared with a Creager weir is limited to the cost of the reinforced concrete: 0.3 or 0.4 m3 per m3/s of the total spillway capacity.
Dozens of traditional labyrinth walls with a similar thickness have been in operation for a long time and have had no special maintenance problems. It is, advisable however, to use 350 or 400 kg of cement per m3 of reinforced concrete and about 200 kg of steel, to guarantee a long life for the structure.
Construction methods may vary with the height of the structure as well as the local economic situation and labour costs. They may be chosen with the contractor and the detailed design can be adjusted accordingly. For structures higher than 4 or 5 m, the P.K.weir overhang can easily be built in horizontal steps of about 2 m height. Structures 2 to 5 m high may be precast with unit weights of few tons (for instance Fig. 7).
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