be required under natural cooling. There is also the advantage of uniform temperature conditions throughout the section, instead of the large temperature gradient from the exposed surface to the interior, during the cooling period.

With artificial cooling it is also possible, and in many instances desirable, to subcool the concrete. With the joints grouted in the subcooled condition, the subsequent temperature rise to the stable temperature can only expand the concrete and place the joints under compression.

Another advantage is that if artificial cooling is used in conjunction with a cement having a low rate of heat development, the maximum temperature may be materially reduced. Any reduction in the maximum temperature reduces the range of the subsequent temperature drop, thereby decreasing the volume change and tendency to crack. The temperature rise in Boulder Dam averaged about 9°, 22 percent less when low-heat cement was used with artificial cooling than when standard cement was used. Standard cement was used for a short while before low-heat cement was available. This advantage, however, would not have been obtained from the use of low-heat cement alone.

Investigation of Cooling Methods. The mass of Boulder Dam is so large and the construction program was so rapid that, except for the loss of some heat from the upper surface of the concrete, the interior of the dam was subject to virtual adiabatic conditions. Investigations were conducted to determine the most efficient and most economical method of cooling. These included the use of slots and shafts with refrigerated air circulated in the openings, cooling the aggregate and materials comprising the concrete combined with prolonged sprinkling, and the use of variously sized and spaced embedded pipe for circulating a cooling medium.

After the plans for cooling Boulder Dam had been issued but before work was started, cooling by running water through vertical holes was tried in certain blocks of Ariel Dam with encouraging results. The trial at Ariel Dam was made without the benefit of mathematical investigation but demonstrated the feasibility and practicability of the method. Mathematical Investigations. Problems in the flow of heat have been studied for many years and the existence of the mathematical theory of heat conduction may be said to date from the publication in 1822 of a treatise by the French. mathematician Fourier, entitled "Theorie Analytique de la Chaleur." Since then a number of forms of the equations for the solution of particular types of problems have been derived and may be found in texts dealing with the subject. It is only quite recently, however, that mathematical forms have been applied to the solution of the particular problems relating to the flow of heat in concrete dams; problems which include such considerations as heat generation due to hydration of the cement, thermal characteristics of the concrete, and effects of exposure conditions peculiar to these structures.

Solutions of certain of the problems investigated have been published (see ref. 1, 2, and 3 of bibliography). These solutions cover the problems of cooling from the surface of a lift, cooling of a flat slab, cooling of a prism of rectangular cross section, cooling of a rectangular parallelepiped, cooling of slabs exposed to variable temperatures, and cooling of hollow cylinders.

In all solutions the use of the diffusion constant, or diffusivity, of the concrete is required. The value of the diffusivity K cp

where K is the conduc

(h2) is given by the relation h2= tivity, c is the specific heat, and p is the density of the concrete. An important step preliminary to the mathematical investigation is the determination of the thermal properties of the concrete.

The diffusion constant may be determined by observing the flow of heat through a test specimen and computing the average diffusion constant; or by determining the conductivity, specific heat, and density, separately, and computing the diffusion constant from these values. The latter method permits the determination of the variation of the thermal properties and diffusion constant with temperature. Variation of the thermal properties with temperature of test specimens, representing concrete from various dams, have TABLE 1.-Thermal properties at 50°, 70°, and 90° F. of concrete representing various dams and of concrete containing coarse aggregate of various mineral content

been published (see ref. 4). In the idealized mathematical problems, however, a constant value of the diffusivity, the average value throughout the range in temperature, is used and the single value obtained by the direct method is satisfactory. Values of the diffusion constant of concrete may be estimated very closely if the percentages of the various ingredients, water, cement, and mineral composition of fine and coarse aggregates, are known. Empirical factors of the effect of these ingredients on the thermal properties of concrete have been obtained from laboratory investigations.

Values of the thermal properties at 50°, 70°, and 90° F. of concrete representing various dams and of comparable mass concrete containing coarse aggregates of various mineral compositions, but with quartz sand, as determined in the laboratories of the Bureau, are given in table 1. It is interesting to note that the range of values given is much larger than is usually attributed to concrete. It would require 2.5 times as long, under the same conditions, to cool the concrete of Bull Run Dam as to cool Seminoe Dam.

With the formulas and curves representing the solutions of the aforementioned problems and with the diffusion constants determined or assumed, studies are made yielding complete estimated temperature histories of proposed dams from the time of placing to the ultimate stable temperature under many different exposure conditions. The curves also serve as a basis for determination of the necessity for artificial cooling.

In the interior of a large dam where the construction surface is kept practically level, as at Boulder Dam, heat is lost only from the surface of the lift during the time of exposure. Subtracting the heat lost from the heat gained, due to hydration of the cement, yields a measure of the mean temperature rise. This simple computation does not consider the transfer of heat into the lift below and gives no indication of the temperature distribution throughout the mass in the early period following placement. After the surface of a lift is covered and the temperatures become equalized, such a computation yields very closely the actual temperature conditions of the mass. Figure 1 shows curves computed in this manner as a comparison of the mean temperatures in the interior of large masses of concretes made with standard and low-heat cements.

The solid lines show the comparison for an exposure of 3 days between lifts and the dashed lines for an exposure of 10 days. The exposed surface is assumed to be maintained at the initial temperature. It is apparent that artificial cooling is necessary if the temperature of the concrete is to be reduced to the stable temperature in a reasonably short length of time. Also, if the maximum temperature is to be reduced materially through the use of low-heat cement, it is necessary that artificial cooling be started as soon as possible after the concrete is placed.

Since curves of this type depict only the average temperatures, they do not accurately represent the conditions in a

smaller dam. For smaller structures, the temperature distributions should be investigated in determining the temperature stresses and formation of cracks. This can best be shown by a series of curves, each representing the momentary distribution at a certain time. Figure 3 shows average temperature curves for a dam 50 feet thick under the same exposure conditions as figure 1.

Here again the solid lines show the comparison for an exposure of 3 days at the surface of the lift and the dashed lines for an exposure of 10 days. Study of the curves reveals that the maximum temperature advantage of slow heat-developing cement is obtained when the rate of cooling can be made, either artificially or naturally, to exceed the rate of heat development in the early age. Concrete made of cement having a high rate of heat development in the early age, such as high-early strength cement, will attain a rather high temperature before the rate of cooling equals the rate of heat generation; so that even with artificial cooling comparatively high maximum temperatures are attained, except in extremely thin sections.

The figures show only the temperature rise above the initial temperature. When the concrete is placed under extreme conditions, as in the middle of the summer, the initial temperature may be far above the final stable temperature. In certain parts of Boulder Dam the total temperature drop was as high as 90°. It is apparent that the placing temperatures may have a more important bearing on the temperature drop and consequent contraction of the concrete than any change that may be effected by varying the heat generating characteristics of the concrete.

Experimental Investigations.-At the time plans were made for cooling Boulder Dam, cooling of the concrete by circulating cold water through embedded pipes was an untried procedure. Before installing the system in Boulder Dam, therefore, a large scale experiment was conducted in Owyhee Dam during the summer of 1931 to determine the feasibility of the method.

One-inch pipes were embedded 4 feet 8 inches apart throughout a region approximately 28 feet square in

-Grout stops limiting grouting lifts

FIGURE 2.-Estimated final stable temperature of Boulder Dam.

vertical cross section and about 120 feet long, the width of the dam at the level of the section.

Twenty-two resistance thermometers were located throughout the test section to give accurate information of the temperature changes and of the temperature distribution surrounding a single pipe during the test as well as the thermal state of the concrete before and after the test. The drop in temperature of the central part of the test section was from 118.0° to 80.2° F. during the 18 days that river water was pumped through the embedded pipe. The deviation from the previously computed values throughout the whole temperature range did not exceed 1.7° and was within 1° over the greater part of the range. Equally close agreement was obtained between the computed and observed values of the temperature distribution surrounding a single pipe.

COOLING BOULDER DAM

Accounts of the cooling system installed in Boulder Dam and the results obtained have been published in references 5 to 13, inclusive, the main features of which are herein repeated. The cooling of the dam was accomplished by circulating water through metal tubing buried in the concrete. The 1-inch outside diameter, 14-gage tubing was laid on the surface of each 5-foot lift and was spaced 5 feet 9 inches horizontally, as shown in figure 4.

FIGURE 3.-Simplified average temperature-rise history of concrete dam of moderate size.

The cooling process was carried on in two stages: (1) circulation of air-cooled water through the embedded pipe system and (2) circulation of refrigerated water through the same pipe system. A cooling slot 8 feet wide extended through the center of the dam to facilitate the connection of the embedded pipes to the headers. The cooling water was conducted from the pumps, located in the refrigeration plant about 800 feet downstream from the dam, through 14-inch cork-insulated pipes to the downstream face of the dam at the cooling slot. The main headers continued up the face of the dam, as shown in figure 5, and were connected to the 6-inch headers in the cooling slot which, in turn, were connected to the embedded coils through rubber hose and standard fittings.

The fitting assembly was designed to permit testing each coil for quantity of flow and temperature of the water without interference with the flow through the headers. The embedded pipes were arranged in coils running in a circumferential direction from the cooling slot to the canyon wall and return. The coils varied in length from 220 to 1,340 feet with an average length of 513 feet for the 5,880 coils.

The cooling pipes (see fig. 4) were laid on the top of each 5-foot lift after the concrete had hardened and were anchored by wire loops buried in the concrete while it was still plastic. All sections of the pipe, both within the block and at the contraction joints, have plain ends and are connected by expansion-type couplings.

Operation of the System. From study of various schemes it was determined that the most economical one for Boulder Dam was the two-stage operation that reduced the temperatures through part of the range with air-cooled water and completed the reduction with refrigerated water. Lack of a continuous suitable supply from the river for the primary stage of cooling necessitated the re-use of the water. The water was pumped through a supply line to the dam and was circulated through the embedded coils, removing some of the heat from the concrete while rising from 4° to 18° in temperature. The warmed water was carried through a return line to the top of the cooling tower located on the downstream cofferdam, where it was cooled in falling over

the tower and then flowed to the pumps to start another cycle.

The refrigerated water was circulated in a closed system. The water, which was cooled in an ammonia refrigerating plant, was pumped through the supply lines and headers,

on through the embedded coils and return headers, and back to the water coolers in the refrigeration plant for extraction of the heat taken up, after which it was recirculated. The temperature difference of the supply and return water at the plant varied from 7° to 18°, and at the dam it varied

A total of 416 resistance thermometers were embedded in the concrete throughout 2 vertical sections of the dam, 1 on either side of the cooling slot. The temperature of the concrete surrounding each cooling coil was determined before cooling was started by inserting a special resistance thermometer into the pipes some 25 to 30 feet from the face of the cooling slot. The temperature was determined again, before the connections were removed, after circulation through the coil had been discontinued for 48 hours to permit equalization of the temperature. An estimate of the concrete temperature could also be obtained by a simple calculation, using charts prepared from observed temperatures of the inlet and outlet water. Temperatures of the water were obtained directly by inserting a thermometer in samples drawn into thermos flasks through small pet cocks provided at the inlet and outlet of each coil.

Cost of Cooling. The cost of cooling Boulder Dam cannot be itemized readily because of a change in accounts and method of payment for construction and operation of the cooling plant before and after March 1, 1934. The cost to the Government of all materials, labor, and contracts relating to all work chargeable to cooling is as follows: All embedded pipes and fittings, material, and labor of installing about 590 miles of 1-inch outside diameter tubing . . .

. . $201, 711. 40

FIGURE 4. Spacing and arrangement of cooling pipe in top of 5-foot lift, Boulder Dam.

from 5° to 16°. About 18 percent of the refrigeration was lost through the supply and return headers notwithstanding the insulation.

The system was designed for a flow through each cooling coil of not less than 3 gallons per minute, but data in table 2 indicate that the average actual flow was more than 4 gallons per minute.

The refrigeration plant was rated at 825-ton capacity. One ton of refrigeration is the amount of heat required to melt 1 ton of ice in 24 hours, or a rate of 200 B. t. u.'s per minute. This plant capacity, plus the effect of the cooling tower, combined to produce an average of 1,815 tons of refrigeration during September 1934. The total amount of heat removed from the concrete was about 159 billion B. t. u.'s, of which 74 billion were removed with air-cooled water and 85 billion with refrigerated water. Data on the cooling system and its operation are given in table 2.

Temperature Control. As cooling progressed, temperatures of the concrete were obtained periodically to check the progress and to determine when cooling should be stopped.

743, 195. 28

A total of 3,287,664 cubic yards of concrete was cooled, including 3,181,664 cubic yards in the dam and 106,000 cubic yards in the tunnel plugs. The average cost of cooling was $0.226 per cubic yard.

COOLING OTHER DAMS

Owyhee Dam. During the construction of Owyhee Dam it was determined that by the time it was proposed to grout the contraction joints, the temperature of the lower sections would still be far in excess of the mean annual air temperature. It was then proposed to remove this excess temperature before grouting by pumping river water through the embedded grout pipe system.

Cooling was started in the lower 200 feet of the dam in October 1932 but had to be discontinued for 3 months during the winter season of 1932-33 because of the accumulation of ice on the downstream face of the dam and because of freezing of the pipes. From March through July 1933 cooling was resumed, to be discontinued another 3 months because of ineffectiveness due to the rising river water temperatures and lowered concrete temperatures approaching each other. Cooling was resumed again in November 1933 and continued throughout the comparatively mild winter until March 1934 when the temperature of the con