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able to design and build a practical model of Boulder Dam, the eventual objective of the early investigations.
It was quite fitting therefore, that the first model should be constructed of the Stevenson Creek Test Dam, on which the model measurements could be checked against similar measurements on the actual dam as well as computed mathematically for both. The model was constructed to a one-twelfth scale, giving a model 5 feet high, 2 inches thick at the top, 7% inches thick at the bottom and 11 feet 8 inches long at the crest. Concrete, mixed from the same aggregate as the real dam, was used to build the model. The model was loaded with a film of mercury, contained in a rubber bag which fit the upstream face and was held in place by a steel plate securely braced against the walls of the testing pit. Dial gages attached to a rigid concrete reference post were used to measure radial deflections on the downstream face. Measurements of changes of chord length and strains at the downstream face were also made. These measurements checked very closely with the measurements taken on the real dam and also with the deflections calculated by the trial load method of arch dam analysis.
The following conclusions were reached from these tests:
1. A properly constructed small scale model can be relied upon to produce strains and deformations similar to its prototype.
2. Mercury is a satisfactory loading medium where the effects of hydrostatic pressure only are being investigated.
3. The trial-load method gives accurate results for the thin-arch dam.
The next step in the program was to build an arch-dam model where a considerable portion of the load was carried by gravity action. Such a test would supply the necessary data to check the trial-load method for this type of structure. Accordingly a model of the Gibson Dam was constructed. This dam was considerably different from the Stevenson Creek Dam since it was built in a relatively wide valley whereas the Stevenson Creek Dam was located in a narrow V-shaped canyon. The Gibson model was 2 feet IOJ2 inches high, 2% inches thick at the top, and \5% inches thick at the bottom, with a crest length of 13 feet 6 inches.
This model was constructed of concrete and loaded with mercury in the same manner as in the Stevenson Creek model tests. The procedure of the tests was also practically the same as the Stevenson Creek tests, except that a temperature test was run on the Gibson model. The temperature of the model was first raised by running hot water over the faces. When a fairly uniform high temperature had been reached, it was allowed to cool, after which the temperature was lowered further by running ice water over the faces. Continuous observations of radial deflection and temperature were taken throughout the temperature cycle.
The behavior of this model was entirely satisfactory and the agreement with the calculated deflections obtained from the trial-load analysis was excellent. In the analysis of
the Gibson model, a number of refinements had been made to take into account the effects of tangential shear and twist. The fact that good agreement was obtained was very gratifying.
FIRST MODEL OF BOULDER DAM
It was evident from the deflection measurements on the Gibson model that a concrete model of Boulder Dam, with its greatly increased cross section, would be entirely too stiff to obtain measurable deflections. Boulder Dam, having a heavy cross section and a relatively short span compared to its height, would therefore require a model to be constructed of a much more flexible material than concrete. After a careful study of many possible materials, it was concluded that the most satisfactory material was produced from a mixture of commercial plaster and diatomaceous earth (Celite) combined with the proper amount of water. Other possible materials were celluloid and rubber.
After this preliminary investigation indicated that the plaster-celite mixture had desirable properties, an extensive study was made, using various brands of commercial plasters with different proportions of celite and water.
The results of this study are summarized as follows:
1. Average proportions.—One part celite, 2 parts plaster, 3% parts water, all by weight. The exact proportions must
be determined by trial for each project, since considerable variation occurs in different shipments of the same brands of plaster.
2. Workability.—When freshly mixed, the material has a consistency of pancake batter, and flows into forms easily. When dry, it can readily be cut to shape with hand tools. Freshly mixed material will bond perfectly with dry material if the latter is first waterproofed with two coats of shellac and one coat of varnish. The material is not elastic until thoroughly dry, and because of the slow rate of drying it must be cast in layers not more than 3 inches thick.
3. Elastic properties.—(a) Modulus of elasticity from 90,000 to 150,000 pounds per square inch. The value for different supplies of material vary considerably, but for a given supply the modulus can be held to very close limits.
(b) Average Poisson's ratio of 0.20.
(c) Average maximum compressive strength, 200 pounds per square inch.
(d) Average maximum tensile strength, 30 pounds per square inch.
(e) Average working stress, 80 pounds per square inch.
(f) Average specific gravity, 42 pounds per cubic foot.
(g) Average time of set, 15 to 30 minutes.
The foregoing discussion of the properties of plaster-celite material, while developed for the first Boulder Dam model, also applies to subsequent plaster-celite models constructed in the Boulder laboratory.
The plaster-celite model of Boulder Dam was constructed to a scale of 1 inch equals 20 feet, and was loaded with mercury in a similar manner to the Stevenson Creek and Gibson models. The model, when completed, was 32 inches high and rested on foundations and abutments 12 inches deep, constructed of the same material as the model. Since the effect of live load only was to be investigated, the weight of the model was not considered in these tests. Direct measurement of gravity forces on a model of this type would be difficult and the results very uncertain, whereas they may be readily obtained analytically with a fair degree of accuracy.
Figure 1 shows the completed model before assembling the mercury loading apparatus and dial gages. Thermocouples were placed in the model for recording temperatures. Their locations are shown by the coils of wire on the downstream face of the model. Radial, tangential and twist deflections were measured for full load, partial loads, and overload conditions, with and without canyon wall loads. Strain measurements were made on the entire downstream face in horizontal, vertical, and diagonal directions, using dial gages sensitive to 0.0001 inch on gage lengths of 5 inches or less. These strain measurements furnished data for the calculation of the principal stresses at the downstream face. The model was made from one of the earlier designs for Boulder Dam in which the horizontal arches were made up of circular elements. The strain measurements indicated high stresses in the top arches near the abutments and showed the desirability of fillets on the downstream face. These were incorporated in the final design.
Figure 2 shows the agreement between observed and calculated deflections. These results gave further evidence of the applicability of the trial load method of analysis. Further refinements in the method had been made after the completion of the Gibson model tests; so that the results of this investigation gave a valuable check on additional refinements.
After completion of load tests, a temperature test was run. Because the plaster-celite material had to be kept dry it was necessary to use some temperature changing medium other than water. Solidified carbon dioxide (dry ice) was used to cool the model. The entire model was enclosed in a jacket, and the carbon dioxide vapor circulated through it. Openings were provided in the jacket through which rods, attached to the model, extended. Dial gages registered the movement of the rods without interference from the jacket. When the temperature was lowered as much as possible, the model was allowed to return to room temperature, after which it was heated by air circulating over electric heating elements. Continuous readings of radial deflections and temperature were taken throughout the temperature cycle. The model was very sensitive to changes in temperature, although it took considerable time for the temperature of the interior of the model to change. It was found that for an average temperature drop of 20° F., the deflection of the top of the model was double that observed for a mercury load.
RUBBER MODEL OF BOULDER DAM
It had originally been planned to build a second model of celluloid. However, a rubber and litharge compound had been developed for use in building model dams and it was decided to use this material. The model was designed on a scale of 1 inch equals 15 feet and was built
up of 1-inch-thick layers, joined together with vulcanizing cement. Figure 3 shows the completed model.
The rubber and litharge compound had the same specific gravity as concrete and was sufficiently soft to allow fairly large deflections with a water load. This model, therefore, had the same ratio of specific gravities as its prototype. Using a water load it was possible to measure strains on the upstream face with gages designed to work under water. This procedure was not possible with a model loaded with mercury.
The procedure of the tests on the rubber model was quite similar to previous tests except for changes in technique imposed by the use of the softer material. The measurements included radial, tangential, vertical, and twist deflections, and strains on the upstream and downstream faces, for partial and full-load conditions. A tem
Figure 4.—Principal stresses, plaster-celite model, Norris Dam.
perature test was run, using the reservoir water as the cooling and heating medium.
After the completion of the tests on the model, it was removed, one layer at a time, using benzol as a solvent for the cement. Continuous strain measurements were made on the upstream and downstream faces as the model was dismantled, giving in a reversed order, the dead load strains. When the model dam was completely removed, a study was made of the deformation of the canyon walls due to water pressure only for comparison with the deformations produced by water pressure combined with the arch thrust.
A very thorough study of the elastic properties of the rubber-litharge compound showed that it was an anisotropic material. The model had an average modulus of elasticity of 400 pounds per square inch horizontally and 350 pounds per square inch vertically with an average Poisson's ratio of 0.50. With this value of Poisson's ratio there was no volume change in the material. This caused unusually large vertical deformations in the model and introduced many peculiarities in its behavior. There would be little similarity, with this value of Poisson's ratio between the
Figure 5.—Vertical stresses, plaster-celite model, Norris Dam.
observed strains in the model and at corresponding points in the actual dam. However, much valuable information was obtained from the deflection measurements. The model was analyzed by the trial-load method, using the experimentally determined moduli of elasticity and Poisson's ratio, and a good agreement was obtained. This was one of the most severe tests to which the analytical methods had been subjected. The results of the rubber model tests were not, in general, considered as satisfactory as those obtained from the plaster-celite models.
MODELS OF GRAVITY DAMS
While the rubber model of Boulder Dam was being tested, a cross-section model of the Grand Coulee Dam spillway section was constructed. The work on this model was an attempt to apply the general method devised by Wilson and Gore i to testing a plaster-celite section, since apparatus much superior to theirs was available for the measurement of strains and deflections. The model was cast as a hori
i Stresses in Dams: An Experimental Investigation by Means of India Rubber M0del9. Vol. 172. Minutes of the proceedings of the British Institute of Civil Engineers.
zontal slab 3 inches thick. When the slab was dry it was set up in a vertical plane in an H-shaped concrete frame, and the model was cut out to its correct size. The model scale was 1 inch equaling 20 feet, giving a model 21 % inches high, resting on a foundation slab 18 inches deep and 6 feet long. The reservoir pressure was produced by mercury contained in a rubber bag which exactly fit the upstream face of the model and the top of the foundation. It was desired to include dead-load effects in this investigation, and in order to do this it was necessary to increase the apparent specific gravity of the model to 13.6 times the weight of concrete to preserve the proper relation between hydrostatic and gravity forces. This increase in specific gravity was obtained by external loads applied to pins extending through the model. The face of the model section was divided into convenient divisions, either squares or trapezoids, and the pins were set into the model at the center of gravity of the divisions. By applying a weight to the pins equivalent to the volume of the division times its new specific gravity the necessary dead load in its proper distribution was obtained. While each pin produced a concentrated stress at the point where its load was transferred to the model section, the load rapidly distributed itself so that the effect along the foundation was very close to that obtained by a material with an actual high specific gravity.
The tests on this model included measurements of the deflection of the dam and foundation in horizontal and vertical directions, and measurements of strains at the base of the dam and at points in the interior of the dam for dead load, and dead and live loads combined. Deflections were measured with dial gages sensitive to 0.0001 inch and strains were measured with an optical strain gage, sensitive to 0.000002 inch on a 2-inch gage length.
On this project were developed the mathematical stressstrain relationships for the calculation of principal stresses and shears from strain measurements on gage lines arranged in a rosette about a point. The performance of this model indicated that much better results could be obtained with a larger model, with greater depth and extent of foundation. With the 2-inch strain gage length, there was not enough room for as many strain gage measurements as was desired and stress concentrations over small areas could not be measured. A larger model would have greater unit strains which could be measured more accurately and would also proved for a greater number of gage settings.
MODEL OF NORRIS DAM
The methods developed on the Grand Coulee model having demonstrated their merit, a much larger model of the abutment section of the Norris Dam, designed for the Tennessee Valley Authority, was constructed. The model scale selected was 1 inch equals 5 feet, giving a model 52 inches high resting on a foundation 45% inches deep and
Figure 6.—Model of crown section of Boulder Dam, showing full mercury load arrangement.
10 feet 11 inches long. The section had a uniform thickness of 3 inches and was supported in a reinforced concrete frame which was sufficiently rigid to allow practically no deformation when the loads were applied to the model. The mechanical details of applying loads to the model were similar to the Grand Coulee tests except that mercury was used to produce tailwater pressure.
Dial gages were used to measure deflections and optical strain gages were used to measure strains. Three tensimeters, using either 1- or }i-inch gage lengths, were obtained for this test. These gages were used to investigate stress concentrations around the corners where the dam joined the foundation. They showed that high stresses occurred at the corners accompanied by some plastic yield.
Figure 4 shows the principal stresses calculated from the strain measurements. Figure 5 shows the vertical stress curves for the base of the dam and at two higher elevations. The foundation deformation caused considerable curvature of the vertical stress diagrams in the lower elevations. At the upper elevations they are more nearly linear. The results of this model test are in good agreement with similar tests performed on photo-elastic models and with the latest mathematical theories of nonlinear stress distribution. The behavior of the model was very satisfactory, since it was of ample size to provide for a large number of gage points, and had fairly high unit stresses.
A gallery was cut through this model section to the same scale as the model and an attempt was made to measure the stress concentrations around it. It was found that the gallery, which was about 1}£ inches high, was too small in comparison to the gage lengths used to give very satisfactory results. Consequently a special model investigation was made of gallery stresses.