is usually very close to the initial concrete temperature. For a given mix of constant thermal characteristics the temperature rise in winter and summer is about the same for the same length of exposure. Certain cements have a higher heat of hydration with low initial temperatures than with high initial temperatures, but the difference between the temperature rise in winter and summer is not material. When the surface of a 5-foot lift is exposed continuously to air temperature, a maximum point in the average temperature-rise curve occurs about 3 days following placement. Curves showing the average temperature-rise history of the concrete in the interior of a very large dam are shown in figure 1. For concrete of average thermal properties and mass mix the temperature rise to the 3-day maximum is about 40° for standard portland cement and 23° for lowheat portland cement.

In the interior of a large dam the loss of heat from the surface of the lift is about the only loss occurring during construction. As soon as the lift is covered, practically no further loss occurs, and the temperature rises again, due to the continuing hydration of the cement. If an exposure of only 3 days is obtained, the temperature of the concrete some 6 to 12 months later will be about 47° above the initial temperature, regardless of the type of cement used. If the top of the lift is exposed for 10 days the temperature of the concrete from 6 to 12 months later will be about 32° above the initial temperature, as shown by the dashed lines in figure 1. In this case the maximum average temperature for standard cement will occur about 3 days after placement. With low-heat cement, however, the heat generated after 10 days will raise the temperature above the peak occurring at the age of 3 days.

From these considerations it is evident that the concrete in the interior of a very large dam will attain maximum average temperatures ranging from about 70° to 140° F., depending on the various factors mentioned.

In smaller dams and in the thinner sections and near the surfaces of very large dams, the temperature changes are affected by the exposure of the faces. Generally the temperature of the interior is much higher than the surface temperature; so that heat is lost to the surface. When the construction period extends through the winter season and the surface is exposed to extremely cold weather, cracks often develop from the surface inward, due to the resistance to shrinkage of the comparatively warm interior. Thus the concrete temperature of a large dam normally varies during construction from the maximums mentioned to the coldest temperature to which the dam will be subjected, the variation commonly exceeding 100°. Temperature gradients of this order, from the interior to the exposed surfaces, may be established. Therefore, the strains occurring during construction, due to temperature changes, are usually greater than any occurring later, due to loading of the structure.

Final Stable Temperature. Any dam must eventually as

sume a temperature dependent on the mean annual air and water temperatures to which the structure is exposed. The temperature difference from the maximum to the final stable temperature is made up of two parts, (1) the difference between the placing temperature and the final stable temperature, and (2) the temperature rise due to the hydration of cement. Temperatures near the surface of the dam will fluctuate with the seasonal changes in air and water temperatures. The eventual temperature state need not necessarily be a constant temperature throughout the structure. Figure 2 shows the temperature gradients for the estimated final stable temperature of Boulder Dam.

The top of Boulder Dam and downstream face above the power-house section and tail water will be exposed continuously to the air whose mean annual temperature is 72° F. Water will cover the upstream face to within a short distance of the top. The ultimate temperature of the still water below elevation 895, which is at the bottom of the lower gates of the intake towers, is expected to be close to the temperature of maximum density of water. Water at this temperature is fed into the reservoir during part of the year and will seek the bottom. Water at other temperatures, being lighter, will remain above the still water. The lower upstream face of the dam will thus be at a constant temperature of about 40° F. and the top and downstream face will approach the mean annual air temperature of 72° F. The temperature gradient between these extremes, assumed to be a straight-line gradient, will probably be the final stable temperature of the concrete.

The normal temperature state of a dam following the construction period will usually be continually lowered, with the attendant continual shrinkage, to the final stable temperature. The time required to attain temperature equilibrium, naturally, depends upon the mass and thermal properties of the concrete. In Boulder Dam, the most massive concrete dam built, more than a century would be required for Nature to develop this state of temperature equilibrium.

DEVELOPMENT OF ARTIFICIAL COOLING

The necessity of controlling the normal and natural temperature state more definitely than had ever been done before was evident in the design of Boulder Dam, if that structure were to be constructed free from troublesome shrinkage cracks. Artificial cooling, in combination with division of the mass by joints into small sections which offered little restraint to temperature shrinkage, was successfully employed.

Advantage of Cooling. The most obvious advantage of artificial cooling is that the concrete can be cooled through the entire range, from the maximum to the stable temperature, during construction and before the contraction joints are grouted, instead of over the period of many years that would

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 (h2) is given by the relation h2= where K is the conduc

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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