The calculations for the great reservoirs in Radnorshire for the supply of the city of Birmingham are as follows (Min. Proc. Inst. C.E., vol. clxxx.). The ratio of the mean fall in the three driest years to the mean annual fall was taken as ·80 instead of ·77. There is some difference of opinion as to the best figure:—
| Mean annual fall determined from readings of various gauges | 65 | inches |
| Mean fall of three driest years | 52 | ” |
| Deduct loss from evaporation and absorption and losses during floods | 15 | ” |
| Available rainfall | 37 | ” |
This multiplied by 44,000 acres, the area of the catchment, gives 102 million gallons per day. Of this, 27,000,000 gallons is compensation water, leaving 75,000,000 gallons for Birmingham. Capacity of reservoirs, 17,250,000,000 gallons, or 169 days’ supply.
Fig. 59.
3. Earthen Dams.—Before an earthen dam is made, any soft soil on the site should be removed and the ground downstream of the site should be drained. A few trenches, running parallel to the axis of the dam, can be dug so as to give the dam a hold, though there is never any danger of its being moved horizontally by the thrust of the water. If the ground has a side-long slope it should be benched as shown in [fig. 59]. The front slope of an earthen dam is generally about 3 to 1, and the rear slope about 2 to 1. The top has a width of ⅓ to ½ the greatest depth of water held up, and is 5 to 10 feet above the highest water-level. The borrow pits from which the earth for the dam is got should not be near enough to it to in any way affect its stability.
Fig. 60.
In England, and generally in other countries, an earthen dam has a core-wall ([fig. 60]) which is carried down to an impervious stratum, and is keyed into it to a depth of a foot or more in the case of hard rock and several feet in the case of clay. On this core-wall the impermeability of the dam chiefly depends. The core-wall may be of clay puddle, concrete, or masonry. In England it is generally of clay puddle. The core-wall sometimes extends down to a depth of 100 or 200 feet. Its top is horizontal and about level with the highest water-level. It is desirable not to make the foundation stepped, but to let it follow the profile of the impervious stratum. The wall is keyed at its ends into the sides of the valley or gorge. A core-wall of concrete or masonry is, in a high dam, necessarily a comparatively thin structure, and it may be subjected to great strains by unequal pressures of the earth which surrounds it. It is therefore to some extent liable to crack. A core-wall of concrete used for the water-works of Boston, U.S.A., is 100 feet high, 8 feet thick at the base, and 4 feet thick at the top. A clay-puddle wall, being plastic and moist, at least during the period immediately succeeding the construction of the work, is not very liable to crack. The top width of a puddle wall may be 4 to 10 feet, and the batter of the sides from 1 in 20 to 1 in 8. The clay used for the wall above the ground-level should contain about 33 per cent. of sand and stones. This diminishes its shrinkage if it dries. It should not be given too much water in mixing. It should be thoroughly mixed and worked up and trodden down.
The clay puddle and the earth of the dam should be carried up uniformly. The allowance for settlement may be 1/30 to 1/50. The earth should be deposited in thin layers, moistened and rammed, and all clods broken. In India and some other countries, instead of the earth being rammed, cattle or sheep are driven over it repeatedly. This makes earthwork of most excellent quality, and the settlement, if any, is very small.