4. Masonry Dams.—For heights much exceeding 110 or 120 feet a masonry dam may be cheaper than an earthen dam; and in case a flood occurs while work is in progress the masonry might suffer little injury, while earthwork might be swept away completely. Masonry dams are usually built of random rubble masonry with faces of dressed stone. Such masonry weighs about 140 lbs. per cubic foot, and is ordinarily quite safe when subjected to pressures of 20 tons per square foot, but in a masonry dam a high factor of safety is necessary, and 15 tons per square foot may be allowed. In a wall of such masonry with both faces vertical, the pressure, owing to the weight of the wall, will reach the above limit when the wall has attained a height of about 220 feet.
In a masonry dam, although the masonry is always of the best quality, it is a rule to calculate the dimensions so as to give no tension on any part of the masonry. Any crack or opening of a joint, occurring perhaps before the masonry had hardened, would let in water, and its pressure would tend to gradually extend the crack and eventually to overturn the portion above the crack.
Fig. 62 shows the upper part of a masonry dam. The lines with arrows show the vertical force due to the weight of the masonry above A B, the horizontal force due to the water-pressure on it—acting at two-thirds of the depth,—and the resultant of these two. In order that there may be no tension on the masonry, the resultant must always fall within the middle third of the thickness of the dam. In order to prevent its falling outside the middle third, the downstream face must be splayed out, and the splay will go on increasing somewhat. Suppose, now, that the reservoir is laid dry. It will be found that in the case of a dam more than 100 feet high the pressure due to the weight of the wall alone will fall outside the middle third—to the upstream side of it, of course—of the thickness of the wall, and a slight splay must be given to the upstream side. The vertical pressure of the water on this splayed part must be taken into consideration. The limit of pressure, 15 tons per square foot, may eventually be reached owing to the height of the dam, and additional splay may have to be given for this. When the outside splay becomes considerable a further allowance is made for it, because the stress at the edge of a horizontal section is tangential to the face. In order that the tangential stress may not exceed 15 tons per square foot, the vertical stress at the outer edge of a horizontal section of the dam must not exceed about 12 tons. By following the above rules the section of the dam can be calculated, beginning from the top and working downwards. The resulting profile of the dam is somewhat as shown in [fig. 63]. If a masonry dam is designed on the principles given above—that is, so as to be safe as regards crushing and overturning—it will be safe as regards shearing or sliding horizontally, but a test calculation can easily be made for this.
Fig. 62.
Fig. 63.
Calculations of the above kind do not, of course, enable all the stresses in a solid mass of masonry to be found. Great stresses are caused by expansion and contraction owing to changes in temperature. Others are caused by the connections of the dam with the rock on which it rests and with the sides of the gorge. The method of calculation described above indicates a suitable form for the profile of a dam. The large factor of safety adopted allows for other stresses. The sections of the oldest dams, made in Spain, were somewhat as shown in [fig. 64], and contained about twice as much material as was necessary. The object of the calculations is to save this needless expenditure.
Masonry dams designed on the above principles have been constructed for heights ranging up to nearly 300 feet, measured from the foundation to the top. The foundation is always on hard rock free from fissures. Generally a foundation trench is cut. The ends of the dam are carried into the rock on the sides of the gorge. They should not, however, if the sides of the gorge are steep, be built in with mortar, but be allowed to expand and contract vertically, a water-tight joint being made by means of asphalt (Ency. Brit., Tenth Edition, vol. 33, “Water Supply”). This obviously reduces the straining. A dam should be built in cool weather, so that any stresses to which it will eventually be subjected owing to changes in temperature will be chiefly compressive. The upstream face should be as water-tight as possible. There should not, however, be too sudden a change in the character of the masonry from the face work to the inside work. If there are any springs, they must be carefully connected to pipes and carried outside the dam. No water must be permitted to get under or inside the dam, either from springs in the sides of the gorge or from the water in the reservoir. Many existing dams leak slightly where they join the sides of the valley, and most have developed some vertical cracks normal to the face.
