WATER-SUPPLY 407 the water on the portions of dam, at different distances from the top, with the horizontal base lines of these portions (figs. 5 and 8). The direction and amount of the resultant are readily obtained graphically by the parallelogram of forces, the point of application being at the intersection of the vertical from the centre of gravity with the horizontal line one-third up from the base ; for, by drawing the horizontal and vertical lines proportionate in length to the water-pressure and weight of the dam respectively, the diagonal represents the resultant of these forces both in magnitude and direction. When the inner face of the dam is battered, the weight of water resting on this face must be added to the weight of the dam when the reservoir is full. The resultant pressures neces sarily increase with the depth ; and the maximum pres sure is at or near the base of the inner face when the reservoir is empty, and of the outer face when the reservoir is full. The top has only to be made wide enough to resist the shock of the waves and floating ice in the reservoir ; but the base, having to bear the weight of the dam together with the water-pressure, requires widening out adequately for the safe limit of pressure on the masonry not to be exceeded ; and, as the water-pressure with the full reservoir deflects the resultant towards the outer face, this face is given a considerable batter (fig. 5). All dams have to be raised high enough not to be over topped by the highest waves in a storm, depending on the size and exposure of the reservoir. Sections of three of the largest masonry dams erected within the last twenty-five years, namely, Furens, Gileppe, and Villar (figs. 5, 6, and 7), as well as the Vyrnwy rubble concrete dam, now in course of construction (fig. 8), drawn to the same scale, illustrate the forms adopted for these dams. The Furens and Villar dams follow closely the theoretical requirements ; whilst the Gileppe and Vyrnwy dams, with their excess of thickness, impose an un necessary weight on the base, and absorb extra material, without any adequate compensating advantage. Provision, however, was made in the section of the Gileppe dam to admit of its being raised at some future time, and for a roadway along the top, which in some measure accounts for its excess of width ; and the Gileppe and Vyrnwy dams are the first examples of such structures in Belgium and Great Britain. The Furens dam (fig. 5), constructed in 1859-66, across the Gouifre d Enfer, for forming a reservoir with a capacity of 56^ million cubic feet, has a maximum height of 183 feet, and a length along the top of 337 feet; and the maximum pressure on the masonry is 61 tons per square foot on the inner face, a few feet above the base, with the reservoir empty; whereas, with the reservoir full, the maximum pressure on the outer face is under 6 tons. No allowance was made for the arched form of the dam, in plan, towards the re servoir, which reduces the pressure, due to the head of water, at the lower part where the valley is very contracted, and would have admit ted of the omis sion of the pro jecting outer portion for the bottom 60 feet. A very low limit of pres sure, in addi tion to the ex cess of strength 100 Scale to Figs. 5. 6, 7, and 8. -f- 1000 so n tn FIG. 5. Furens Reservoir Dam, near St Etienne. just referred to, was adopted, owing to the unprecedented height and type of the Furens dam. By raising, however, the limit to 6-6 tons per square foot, it was possible to reduce the section of the Ban dam, 138 feet in height at the water-line, making it 110-1 2t wide at the base, as compared with 116J feet for the Furens cam at the same depth; whilst with the same limit applied to a dam of the full height of the Furens dam, the reduction in width at the base would be from 161 feet to 154 feet. 1 Any further raising of the limit of pressure, which might be safely effected, would be of little advantage for dams down to a depth of about 100 feet, as the reduction in width is restricted by the condition of the middle third ; but beyond that depth the width is regulated by the pressure. The Gileppe dam (fig. 6), built in 1869-75, having a maximum height of 154 feet, and a length along the top of 771 feet, retains a reservoir with a capacity of 423f million cubic feet. The average pressure on the base is 8 "2 tons per square foot ; so that, even W/m allowing for the Wm m^ specific gravity of the masonry being about one-seventh greater at Gileppe than at Furens, the maximum pressure on the Gileppe dam FIG. 6. Gileppe Reservoir Dam, near Verviers. is considerably greater than on the Fnrens dam, in spite of its greater base and the smaller head of water (compare figs. 5 and 6), owing to the excess of material employed in its construction. The Villar dam (fig. 7), built across the river Lozoya in 1870-78, convex towards the reservoir as at Furens and Gileppe, has a maximum height of 168| feet, and a length along the top of 546 feet ; and it forms a reservoir having a capacity of 70 1 million cubic feet. It differs -t- W//////ML ver y i ittle in hei s ]it and typ 6 from Hf^ the Furens dam ; but the form given to the batter of the outer face is cal culated to render the pressures more uniform towards the base. The Vyrnwy dam (fig. 8), now (1888) in course of construction, across the Vyrnwy in Montgo meryshire, for form ing a reservoir, 1100 acres in area, to supply 40 million gallons per day to Liverpool, is to sus tain a maximum head of water of only 70J feet; but, as it has to be car ried down about 60 feet below the sur face, in the centre of the valley, to reach solid rock, its maximum height is about 140 feet, and its length along the top is 1350 feet. The maximum pressure on the inner face with the reservoir empty has been estimated at 8 7 tons per square foot, and with the reservoir full at 67 tons on the outer face. These pressures are considerably in ex cess of the maxima pressures on the Furens dam, though the head of water to be supported is much less, and the width at the base is greater in propor tion to the depth. The pressures at the base in the Vyrnwy and Gileppe dams show that a super abundant mass of material
- : ik in a masonry dam, whilst
%i involving a larger outlay, "vS&in A, ,,-. / ^ isi.s. . FIG. ~. illur Reservoir Dam, near Madrid. imposes a greater pres- sure upon the masonry, whereas the stability is ample in the Furcng type . 124. FIG. 8. Vyrnwy Reservoir Dam. and the oozing of water through the dam should be provided against by the quality of the materials and workmanship, rather than by an extra thickness of masonry.
1 Annales des Ponts ct Chausstes, 4th ser., vol. xii. pi. 127.