Outlines of the Design

Foreign Dams. The preceding six dams are the largest in America, and are considerably larger than any other in the world. For a list of forty-six masonry dams higher than 100 feet, fifteen of which are in the United States, see Wegmann's Design and Con struction of Dams, page 400. The profiles of many of the high ma sonry dams, particularly the older ones, are exceedingly extravagant.

If the wall is to be one side of a rectangular reservoir, all the vertical sections will be alike; and therefore the heel, the toe, and the crest will all be straight. If the wall is to be a dam across a narrow valley, the height of the masonry, and con sequently its thickness at the bottom, will be greater at the center than at the sides. In this case the several vertical cross sections may be placed (1) so that the crest will be straight, or (2) so that the heel will be straight in plan, or (3) so that the toe will be straight in plan. Since the up-stream face of the theoretical profile is nearly vertical, there will be very little difference in the form of the dam whether the several cross sections are placed in the first or the Second position as above. If the crest is straight, the heel, in plan, will be nearly so; if the crest is straight, the toe, in plan, will be the arc of a circle such that the middle ordinate to a chord equal to the span (length of the crest) will be equal to the maximum thickness of the dam; and if the toe is made straight, the crest will become a circle of the 'same radius. This shows that strictly speaking it is impossible to have a straight gravity dam across a valley, since either the crest or toe must be curved. The question then arises as to the relative merits of these two forms.

Straight Crest vs. Straight Toe. 1.

The amount.of masonry in the two forms is the same, since the vertical sections at all points are alike in both.* 2. The stability of the two forms, considered only as gravity dams, is the same, since the cross sections at like distances from the center are the same. 3. The form with a curved crest and straight toe will have a slight advantage due to its pcssible action as an arch.

However, it is not necessary to discuss further the relative advantages of these two types, since it will presently be shown that both the toe and the crest of a gravity dam should be curved.

Gravity vs. Arch Dams.

A dam of the pure gravity type Is one in which the sole reliance for stability is the weight of the masonry. A dam of the pure arch type is one relying solely upon the arched form for stability. With the arched dam, the pressure of the

water is transmitted laterally through the horizontal sections to the abutments (side hills). The thickness of the masonry is so small that the resultant of the horizontal pressure of the water and the weight of the masonry passes outside of the toe; and hence, con sidered only as a gravity dam, is in a state of unstable equilibrium. If such a dam fails, it will probably be by the crushing of the masonry at the ends of the horizontal arches. In the present state of our knowledge concerning the elastic yielding of masonry, we can not determine, with any considerable degree of accuracy, the distribution of the pressure over the cross section of the arch.

If it were not for the incompleteness of our knowledge of the laws governing the stability of masonry arches, the arch dam would doubtless be the best type form, since it requires less masonry for any particular case than the pure gravity form. The best infor mation we have in regard to the stability of masonry arches is derived from experience. The largest vertical voussoir arch in the world has a span of 295 feet, and the longest vertical concrete arch has a span of 280 feet, while most masonry dams have spans several times as long.

The experience with large arches is so limited (see Table 90, page 648, and Table 99, page 703), as to render it unwise to make the stability of a dam depend wholly upon its action as an arch, except under the most favorable conditions as to rigid side-hills and also under the most unfavorable conditions as to cost of masonry.

971. Examples of Arch Dams. Apparently there are only three dams of the pure arch type in the world—the Zola, the Bear Valley, and the Upper Otay. A fourth dam—the Sweetwater—closely approaches the arch type. Fig. 104, page 484, shows the profiles of these four dams, and also the position of the resultant pressure on the foundation. The position of the resultant shows that no one of the pure arch-type dams is as stable as a gravity dam; and the stability of the Sweetwater Dam is at least doubtful when considered only as a gravity dam. The stability of the Bear Valley and of the Sweetwater Dam has been tested practically. Water stood for several days within a "few inches" of the flow line of the Bear Valley Dam; and for several days water 22 inches deep flowed over the crest of the Sweetwater Dam, which was 5.5 feet more than it was designed to carry. In neither case was any damage done by the unexpectedly high water.