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elements. In the case of unusually important dams, such as Boulder, effects of the nonlinear distribution of stress are determined by subsequent trial load analyses which bring the horizontal and vertical slopes and deformations in the interior of the arches and cantilevers into agreement in all parts of the dam. Effects of nonlinear distribution of stress have been found important at locations near the foundation and abutments. However, they seem to be negligible in the upper central portions of the dam; that is, in the portions extending from the crown section horizontally to about the quarter points in the case of the arch elements, and from the top of the dam down about half way to the foundation rock in the case of the cantilever elements.
With the exception of the Poisson's ratio adjustments, all the supplemental effects included in the trial load method of analyzing curved concrete dams since the first
use of the method have been found worthy of consideration, the importance of the effects usually varying with the size and height of the structure. Poisson's ratio adjustments were not found to have important influences on maximum stresses even in the case of Boulder Dam.
Effects of including radial shear in calculating arch deflections were found to be particularly important in the case of thick arches, as would naturally be expected, the importance increasing rapidly as the ratio of the thickness of the arch to the radius of curvature increases. Not infrequently, the radial shear deflections in the lower arches of a massive curved concrete dam are found to equal or exceed the moment and thrust deflections at practically all locations along the arch ring.
The importance of making proper allowances for the radial sides of the cantilever elements increases with the size of the dam and the sharpness of curvature. The downstream base width of a cantilever with radial sides, 1 foot apart at the upstream face, was only 0.496-foot
at the crown section of Gibson Dam, and only 0.490-foot at the crown section of Owyhee Dam. Proper allowances for radial sides tend to increase the flexibility of the cantilever elements, this throwing more load on the arch elements. Consequently, the net result of such allowances is a new load distribution with slightly increased radial deflections and slightly higher maximum stresses in both arch and cantilever elements.
Allowances for foundation and abutment deformations naturally tend to increase the calculated deflections of the structure. The maximum downstream movement of the foundation rock calculated for the base of the crown cantilever of Owyhee Dam amounted to about 10 percent of the maximum radial deflection at the top of the dam. The corresponding movement of the foundation rock at the base of the crown cantilever of Boulder Dam amounted to about 30 percent of the maximum radial deflection. The general result of including foundation and abutment movements in the trial load calculations seems to be some
what lower arch and cantilever stresses along the foundation and abutment locations without material stress changes in the central and upper portions of the structure.
The general result of considering tangential shear in trial load analyses is a decrease in radial deflections near the crown section, an increase in radial deflections near the abutments, and a slight increase in arch stresses at the abutments without appreciable stress changes at the crown. The importance of tangential shear effects varies primarily with the ratio of the length of the dam to the height. Such effects are not important in an arch dam built in a narrow canyon, as in the case of Shoshone Dam, where the length of the top arch is less than the height of the structure. However, they are important in a relatively long arch dam like Gibson, where the top length is about 4% times the height of the structure.
The general effect of considering twist action is a decrease in radial deflections at practically all locations, a decrease in maximum arch stress, a decrease in cantilever stress at
the downstream face of the dam, and an increase in cantiliver stress at the upstream face of the dam. Twist effects are important in most high dams of the curved gravity type, such as Owyhee and Boulder. They are also important in arch dams of more usual size and in straight gravity dams built at sites where the canyon walls are relatively steep and comparatively close together. In the latter case the transfer of load horizontally to the abutments by twist action may cause failure by sliding at the end sections of the dam, unless special precautions are taken to prevent the occurrence of twist.
Effects of temperature changes in the interior of the dam are included in the trial load analyses by adding the temperature deflections of the arch elements to the waterload deflections before adjusting the arch and cantiliver movements. No temperature corrections are necessary in the case of the cantilever elements since temperature
changes in the vertical sections do not cause appreciable horizontal movements. Increases in the temperature of the arch elements cause upstream movements which work against the water load, while decreases in temperature cause downstream movements which work with the water load. Consequently, the maximum probable decrease in temperature, below the temperature existing at the time of grouting the construction joints, is the change which must be included in the arch analysis. Of course, proper allowances must be made for any setting heat which may not have been generated or dissipated at the time of grouting the joints.
Temperature changes in the arch elements vary with the thickness of the arch and the temperature changes at the faces of the dam. For the purpose of the trial load analyses the temperature changes in the interior of the structure are assumed to be uniform from abutment to abutment and from the upstream to the downstream face of the dam at each elevation analyzed. In the case of unusually important structures, such as Boulder Dam, effects of nonuniform temperature changes in the arch elements may be made by special analyses after the trial load studies are completed.
RESULTS OF A TRIAL LOAD ANALYSIS
The accompanying illustrations, Figures 1 to 6, inclusive, show the results of a trial load analysis of the Seminoe Dam a 261-foot constant radius arch dam now under contract for construction on the North Platte River about 37 miles northeast of Parco, Wyo. Although the dimensions of the dam may be modified, and the analysis revised, when the foundation and abutment excavation is completed, the drawings are useful in showing the load distributions, deflections, and stresses obtained in a typical trial load study. The analysis shown was made on the assumption that the construction joints will be grouted when the concrete temperatures are 5° F. below mean annual values and that horizontal earthquake vibrations may occur when the reservoir is filled to elevation 6,361. All the more recent amplifications of the trial load method were included in the analysis, except that no readjustments were made for supplemental Poisson's ratio effects and no trial load analyses were made to determine the true nonlinear distribution of stress in the arch and cantilever elements.
Figure 1 shows a general plan of the dam, a developed profile looking upstream, and a vertical cross section at the crown location. Figure 2 shows the arch, cantilever, and principal stresses at the upstream and downstream faces of the dam; also the maximum shearing stresses along the contact planes between the concrete and the rock. Figure 3 shows the distribution of the radial, tangential, and twist loads at the cantilever sections used in the analysis, earthquake load increments due to concrete inertia and increased water pressures being shown on the radial distribution curves. Adjustments of radial, tangential, and twist deflections are shown at the right of the load distribution diagrams. Figures 4, 5, and 6 show the load distribution and deflection curves at the arch elements, for the radial, tangential, and twist adjustments, respectively.
The data on figure 2 show that no tension stresses occur at the upstream face of the dam in the case of the cantilever elements; that no tension stresses greater than 100 pounds per square inch occur below elevation 6,361 at the upstream face of the dam in the case of the arch elements; and that the maximum principal stress along the abutments occurs at the downstream face at elevation 6,250 and amounts to 485 pounds per square inch compression. The maximum shearing stress along the abutments occurs at elevation 6,150 and amounts to 134 pounds per square inch. The load distribution and deflection diagrams on figure 3 show that a little' more than half the radial water load is carried by arch action; that appreciable proportions of the radial water load are carried by cantilever action at all vertical
sections; and that very close agreements of arch and cantilever deflections were obtained in tangential and rotational directions as well as in the radial direction.
TRIAL LOAD DAMS
Thus far, the Bureau of Reclamation has designed seven arch dams on the basis of trial load analyses; namely, the Boulder, Owyhee, Parker, Seminoe, Gibson, Deadwood, and Cat Creek Dams. The Cat Creek Dam was designed for the Bureau of Yards and Docks, United States Navy Department. All of these have been built and placed in operation except the Parker and Seminoe Dams which are now under construction. The Bureau of Reclamation has also made preliminary trial load designs for several contemplated arch dams where construction has not yet become feasible or where other types of dams have been found more desirable; also trial load analyses for several additional existing arch dams, including the Gerber, Stevenson Creek, Hetch Hetchy, Mormon Flat, Horse Mesa, and Stewart Mountain Dams. Existing arch dams designed on the basis of trial load analyses and built by agencies other than the Bureau of Reclamation include the Ariel, Calles, and Eleven Mile Canyon Dams. Dimensions and descriptive data regarding the most of the above-mentioned dams may be found in articles published in the Reclamation Era or in the various engineering journals. Descriptive data regarding the Boulder, Owyhee, and Deadwood Dams are given in special articles on those dams included in this book.
The following bibliography includes the principal articles on the trial load method and its application in the design of curved concrete dams, which have been published in engineering literature up to the present time. Some of the articles prepared by the writer have been freely drawn upon in the preparation of the foregoing material. Analysis of Arch Dams by the Trial Load Method, by
C. H. Howell and A. C. Jaquith, Trans. Am. Soc. C. E.,
vol. 93, 1929, pp. 1191-1316. Arch Dam Analysis by Trial Loads Simplified, by H. M.
Westergaard, Eng. News-Rec. Jan. 22, 1931, pp. 141-143. Technical Design Studies for Hoover Dam, by Ivan E.
Houk, West. Constr. News, Apr. 10, 1932, pp. 187-193. Technical Design of High Masonry Dams, by Ivan E.
Houk, The Engineer, Aug. 4 and 11, 1933, pp. 105-106
Trial Load Method of Masonry Dam Analysis, by Ivan E.
Houk, West. Constr. News, November 1933, pp. 455—460. Actual Deflections and Temperatures in a Trial Load Arch
Dam, by A. T. Larned and W. S. Merrill, Trans. Am.
Soc. C. E., vol. 99, 1934, pp. 897-961. Trial Load Analyses of Curved Concrete Dams, by Ivan
E. Houk, The Engineer, July 5 and 12, 1935, pp. 3-5
TEMPERATURE CONTROL OF MASS CONCRETE
IN LARGE DAMS
BY CLARENCE RAWHOUSER, ASSOCIATE ENGINEER, BUREAU OF RECLAMATION
THE PURPOSE of controlling the temperature of the concrete in a dam is to regulate the volume change and thereby prevent or govern the formation of shrinkage cracks in the structure. The principal cause of volume change is the temperature variation during and subsequent to construction. Moisture change is an important factor in thin structures and road slabs, but not in massive dams. With recent developments in materials, methods, and equipment, the trend in the construction of dams is toward larger concrete structures, built at a faster rate, with the result that the mass attains high temperatures and is subjected to subsequent large volume changes.
Remedial measures to prevent or repair the damage of cracking have been applied from the time the formation of cracks was first studied. Transverse contraction joints have been included in the design of all recent important dams. The contraction joints are usually filled with grout, a mixture of cement and water, before the full water load is permitted to come on the structure. Other remedial measures have been used at times. For instance, open joints or slots have been left between the blocks until after they have cooled and shrunk, when the slots were filled. In some instances the construction surface has been built in steps, to permit as much heat as possible to be radiated from the concrete during construction. Special cements, which generate less heat and at a slower rate than normal portland cement, have been developed and used in some dams. The placing of concrete has, in instances, been confined to the most favorable time of the year. The depth of the lift or layer of concrete has been limited, and the top of each lift exposed for a determined minimum period to reduce the temperature rise.
For very large dams under rapid construction schedules, the above measures are inadequate. To them has recently been added a practical method of artificially cooling the concrete, which, in combination with other expedients, affords a means of controlling the temperatures and completing the temperature change within the construction period. Temperature control of large concrete dams is thus resolved into the selection of the most favorable and feasible conditions involving materials, rate and time of construction, depth of lift, spacing of contraction joints, exposure of surfaces, and application of artificial cooling.
THE NORMAL TEMPERATURE STATE
The temperature state of the dam during construction is dependent on the ambient temperature and the temperature control. The temperature of the concrete at the time of placement depends chiefly on the temperature and specific heat of the various ingredients. It is usually very close to the mean monthly air temperature. The temperatures of the aggregate in the stock pile and of the mixing water do not ordinarily follow the daily air temperature fluctuations. If the temperatures of the concrete ingredients fluctuate greatly, the initial concrete temperatures will do likewise. At Boulder Dam, where the mean annual air temperature is 72° F., the initial temperature of the concrete varied from 48° F. in midwinter to 92° F. in midsummer.
In a cold climate, the usual procedure is to discontinue placing concrete during the winter when the air temperatures are definitely below freezing. Bureau specifications require that the placing temperatures shall be not less than 40° F., and that all concrete placed in freezing weather shall be protected from freezing. Discontinuing placement subjects the top surface of each block to severe exposure conditions, which is conducive to the formation of cracks.
Hydration Effects. The temperature rise caused by the hydration of cement depends upon the heat-generating characteristics of the cement, richness of mix, thermal properties of the concrete, and exposure conditions. A maximum temperature is attained when the rate of cooling equals and exceeds the rate of heat generation. Various methods are available and have been used to minimize temperature rises as much as possible consistent with economic placement of concrete. The depth of lift has been limited to 5 feet in all dams constructed by the Bureau. A major advantage of so doing is that a considerable proportion of the total heat generated is dissipated from the surface during the time that the top of the lift is exposed. A minimum time of exposure between lifts is provided in Bureau specifications by limiting the rate of placing so that not more than 5 feet shall be placed in 72 hours. The amount of heat dissipated from the surface of the lift depends on the exposure temperature and on the thermal characteristics of the concrete. The average exposure temperature