APPENDIX D.

TYPE AND DESIGN OF DAM.

1. Whether the type should be the overfall, or a higher dry-top dam with spillway past one or both ends, is a question which for the site in mind has not a decisive answer. Though the overfall type would be some 10 feet lower, yet the pressures, both horizontal and upthrust, in times of maximum floods would be nearly as great, requiring about as much masonry. It is a matter of topography whether the excavations to be made in quarrying stone for the dam would of themselves afford sufficient passageway for floods past the ends of the dam. At the upper site such quarrying, if confined to the east side, would provide 300 feet of spillway at an elevation of 180 feet.

2. The usually stated objections to an overfall high dam are two. One is that there may not be room for a power plant out of reach of the waters or its spray except by going some distance downstream, which would require that the penstock be long and costly. But it must be remembered that so seldom and for such short periods would floods more than fill the San Carlos Reservoir, that resulting inconvenience, if that were all, could be easily borne, and that a power house could be built to withstand much punishment even of water temporarily passing over its roof. A modern idea is to economize by molding power rooms within the body of the dam; but with a dam so high nothing should be allowed in its design which would weaken the structure-possible earthquakes as well as static forces considered. The other objection is the vibration which has resulted with some overfall dams, threatening their permanency. It is believed that such vibration is induced by the falling waters entraining alr causing a partial vacuum next the dam into which the outside air periodically breaks through the descending sheet only to be entrained again, causing pulsations, and that to wholly avoid vibration it is only necessary to so form the face of the dam that maximum floods would, in vacuo, bear upon it all the way down with some pressure but without shock and be guided into the horizontal direction by a vertical curve at the toe of the dam, for it would seem that water alone, free from waves and flowing from a reservoir which regulates its amount, is as constant a force as gravity itself. It is sometimes asked what becomes of the great energy of the descending water if not expended destructively in eroding bed and banks and in creating vibration, to which is answered that with the aid of standing waves ahead it is converted into heat, raising the temperature such fraction of a degree as the fall is part of 778 feet.

3. Yet if cost with separate spillway be not much in excess that type would be chosen to better follow usual practice.

4. The design of the dam is curved in plan, with a radius of 500 feet, for the length of the dam is not so great but that the arch action would add safety to the gravity section were that required, and the arch form is the current practice for dams so short.

5. The form of cross-section to be a "gravity section" so called results from comparatively simple calculations into which enter the weights of materials and intensities of pressures. The only room for judgment is as to amount and distribution of upthrust to be provided against and amount of water to be passed in maximum floods. 6. The resultant of all forces under all the varying conditions should not fall outside the middle third of base if tension in masonry is to be avoided. This is strictly true only if yielding by compression is proportional to load. It is often written that to have the resultant fall within the middle third of base insures a factor of safety of 2 against overturning, but this is not true except in special cases. The resultant may fall on the one third point and yet the factor of safety be even less than 1; but it is still safe enough, for gravity is so true that 10 foot-pounds never overcame 11 foot-pounds, though the margin of safety was but 10 per cent.

7. As stated above, the principal unknown quantity is the possible upthrust. The writer would in the present case assume a full upthrust under the heel diminishing uniformly to zero at the toe.

FLOOD FLOW AND SPILLWAY.

12. Water Supply Paper No. 33, on page 35, states that the greatest flood at the Buttes up to that time was that of February 22, 1891, which was calculated to be 102,566 cubic feet per second. On page 72 of same paper, 83,620 cubic feet per second was considered the maximum flood discharge of the Gila at San Carlos. Since the date of paper 33 (1899), one greater flood is known to have occurred that of 1905. Mr. A. C. Sieboth, of Florence, states that high-water marks made by this flood between Florence and the Buttes indicated a flow of 190,000 cubic feet per second. During the present investigation, lodged drift wood has been found at San Carlos several hundred feet upstream from the proposed dam site, at an elevation of 26 feet above. low water in the river alongside; which indicates a flow of possibly as much as 150,000 cubic feet per second at that point.

13. The floods of the Gila are characterized by rapid rise and short duration, with flow seldom reaching 50,000 cubic feet per second, which, considering the moderating effect of the reservoir with area so extensive, would be accommodated by a small spillway.

14. The spillway proposed is at elevation 180, or 10 feet below the crest of dam, and its length is 300 feet. The discharge with water 10 feet above it, would be about 3 by 10% by 300 33,000 cubic feet per second.

15. The area of reservoir within the 180 or 190 foot contours will probably always be as great as 10,000 acres; for, though it is not proposed to desilt more than about 7,000 acres, the highest levels will have water so seldom that the amount of silting in them will be negligible, except at the extreme upper end of the reservoir where such level is within reach of the river and its delta building work.

16. Considering how flashy the floods, and that 10,000 acres even without an outlet would require a continuous flow of 50,000 cubic

feet per second for 24 hours to raise it 10 feet, there remains no doubt of the sufficiency of the proposed spillway for all ordinary floods.

17. It is interesting to determine the behavior of such reservoir and such spillway under some hypothetical greater flood. Hence, assume that the outlet through the dam will discharge the ordinary flow of the river, and that when the reservoir is full, or by the time it becomes full, a flood inflow shall amount to 50,000 cubic feet per second in excess of the ordinary flow, and shall increase hourly 5,000 cubic feet per second for 10 hours, making a maximum of 100,000 cubic feet per second, and then decrease hourly 5,000 cubic feet per second for 20 hours, or down to normal flow. The resulting hourly heights would be as tabulated below:

It appears from the above table that the spillway would just care for the hypothetical flood therein assumed, and that in the twentythird hour the water would be at its highest. Also that it would be at elevation 9.05 feet at the close of the flood. Water would continue to pass at a decreasing rate over the spillway for 76.6 hours after the flood inflow had ceased.

18. If water were 20 feet over the 300 feet of spillway and 10 feet over 506.73 feet of dam, the discharge would be 93,915 cubic feet per second over spillway and 56,085 cubic feet per second over dam, making 150,000 cubic feet per second discharge, besides whatever amount would be discharging through the outlet conduits. That so great a flood should come on a full reservoir and continue so long that the reservoir would cease to moderate the flow, is less to be expected than a destructive earthquake. Nevertheless that height

of water, namely, 10 feet above the dam, or to elevation 200, has been assumed in designing the dam; and the structure would continue to be stable with the water higher still.

CROSS SECTION OF DAM.

19. The elements which enter into the problem are as follows: Water, assumed to weigh 624 pounds per cubic foot, extending h feet above the dam, pressing on upstream face from bedrock to crest; Water under dam lifting with full head at the heel, diminishing uniformly to zero under the toe;

No additional downstream pressure from sand or silt;

No upstream pressure except that of wind assumed to be W pounds per square foot.

Dam masonry assumed at 150 pounds per cubic foot.

Resultant in no case to fall outside the middle third of base, but under extreme conditions to fall on the one-third points.

Because the cross section of the gorge is substantially V-shaped, and because the dam is to be adapted to possible overfall, the batter lines will be made straight, and not in concave curves, which otherwise would be justified.

20. The dam, though of gravity section, making it safe if it were straight, is curved in plan, with radius of 500 feet to upstream line of top. The curved form is supposed to adjust itself better to temperature changes. It also, by arch action, reinforces the stability resulting from the gravity section. Even without arch action, the curved dam, if to any degree monolithic or has its parts interlocked, would be, like a worm fence, harder to overturn. Since in straight dams calculations are made on a section a unit long, it has been urged that in similar calculations on curved dams the planes limiting the unit section should not be parallel but radial, and that such convergence of planes makes relatively more area on the back to receive water pressure and less area and material at the toe to withstand the thrust, thus reducing the efficiency of the gravity section. But this is faulty reasoning. It can be as well imagined that the planes a unit apart are all parallel to the median plane, which would make the middle unit section, if standing alone, of the same stability it would have if the dam were straight; and make all other sections. stronger because of the obliqueness. For example: Examine a unit section situated d° on either side of the center. Its back, which receives normal water pressure, is more than a unit, being u sec do, but the pressure upon it, pu sec d°, is resolvable into two components, one being Pu Sec d° cos d°-Pu, directed downstream, and having more masonry and longer base to resist it than in a straight dam; and the other component being Pu Sec do sin d°-Pu tan d°, directed normally toward the median plane, having no downstream overturning moment, but a side pressure with resulting friction and viselike hold through which the stability of the central sections, already as great as in a straight dam, is augmented by a fraction of the excess stability of the outer sections, making the whole more efficient as a gravity section than the same section would be in a straight dam, and this without invoking any arch action pushing on the abutments at all.