Outlines of the Design

The Bear Valley Dam was built in 1884 in the Bernardino Moun tains in California to store water for irrigation. The arch type was adopted because of the excessive cost of transporting cement from the railroad to the site ($10.00 per barrel). The crest of the dam is about 300 ft. long, and is curved up-stream with a radius of 335 ft.

The Upper Otay Dam is situated about 20 miles southeast of San Diego, California. The length of the dam on top is 350 ft., the radius being 359 ft. The up-stream face is vertical. The dam was completed several years ago, but the catchment area is so limited that the reservoir has never been full, nor will it likely ever be filled.

The Zola Dam, named after the designer—the father of the noted novelist,—was built in 1843 to form a reservoir for supplying water to the city of Aix, France. The length on top is 205 ft., and the radius at the crown is 158 ft.

The Sweetwater Dam was constructed about 12 miles southeast of San Diego, California, in 1887-88, to store water for irrigation and municipal supply. At first the dam had a height of 60 ft. and the profile shown in Fig. 104 by the dotted line. The length on top is 380 ft.. and the radius of the top of the up-stream face 222 ft.

Curved Gravity Dams.

Although it is not generally wise to make the stability of a dam depend entirely upon its action as an arch, a gravity dam should be built in the form of an arch, i.e., with both crest and toe curved, and thus secure some of the advantages of the arch type. The vertical cross section should be so propor tioned as to resist the water pressure by the weight of the masonry alone, and then any arch-like action will give an additional margin for safety. If the section is proportioned to resist by its weight alone, arch action can take place only by the elastic yielding of the masonry under the water pressure; but it is known that masonry will yield somewhat, and that therefore there will be some arch action in a curved gravity dam. Since but little is known about the elas ticity of stone, brick, and mortar (see f 21), and almost nothing at all about the elasticity of actual masonry, it is impossible to deter mine accurately the amount of arch action, i.e., the amount of pres sure that is transmitted laterally to the abutments (side-hills).*

In addition to the increased stability of a curved gravity dam due to arch action, the curved form has another advantage. The pressure of the water on the back of the arch ii everywhere perpendicular to the up-stream face, and can be decomposed into two components—one perpendicular to the chord (the span) of the arch, and the other parallel to the chord of the arc. The first com ponent is resisted by the gravity and arch stability of the dam, and the second throws the entire up-stream face into compression. The aggregate of this lateral pressure is equal to the water pressure on the projection of the up-stream face on a vertical plane perpendicular to the span of the dam. This pressure has a tendency to close all vertical cracks and to consolidate the masonry transversely—which effect is very desirable, as the vertical joints are always less per fectly filled than the horizontal ones. This pressure also prepares the dam to act as an arch earlier than it would otherwise do, and hence makes available a larger amount of stability due to arch action.

The compression due to these lateral components is entirely independent of the arch action of the dam, since the arch action would take place if the pressure on the dam were everywhere per pendicular to the chord of the arc. Further, it in no way weakens the dam, since considered as a gravity dam the effect of the thrust of the water is to relieve the pressure on the back face, and considered as an arch the maximum pressure occurs at the sides of the down stream face.

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e c t ion The curved dam is a little longer than a straight one, and hence would cost a little more. The difference in length between a chord and its are is given, to a close degree of approximation, by the formula in which a — the length of the arc, c = the length of the chord, and r = the radius. This shows that the increase in length due to the arched form is comparatively slight. For example, if the chord is equal to the radius, the arc is only , or 4 per cent, longer than the chord. Furthermore, the additional cost is less, proportionally, than the additional quantity of masonry; for example, 10 per cent additional masonry will add less than 10 per cent to the cost.