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normal to the plane of sliding, and pulling the lower half of the container from under the upper half. The maximum resistance to sliding of soil on soil is the ultimate shearing strength for that one normal load. This process is repeated for other normal loads until sufficient data are obtained for determining the cohesion and the angle of internal friction. The testing machine used has a specimen container that is one foot square, and the load capacity of the machine is approximately 30,000 pounds for both horizontal shearing load and for compression or normal loading. Strain meters are so connected to the specimen that both the consolidation and deflection under shearing load may be measured accurately to one-thousandth of an inch.

The specific gravity is needed for computing the amount of voids in soil specimens. The method of determination needs no explanation except that it is important to remove all entrapped air from the specimen. This may be accomplished by reducing the pressure on the specimen, by boiling, or by a combination of the two, the last probably being better than either pressure reduction or boiling.

The soluble-solids test is the determination of the amount of material that will go into solution in water. The test as usually made is not quantitatively correct as the degree of solubility of the salts or mineral is not taken into account. The test merely indicates that there are large or small amounts of solids that are readily soluble in water. If a questionable condition is indicated a process of continued leaching is used to more accurately determine the percent of soluble solids.

EXPERIMENTAL WORK

In addition to the above-mentioned routine tests, experimentation has been started to determine the rate of hydrostatic pressure travel through soils. Soil specimens are compacted in a cylinder with a hydrostatic pressure cell at one end, this end being sealed watertight. At the other end water pressure is applied and the pressure measured until full hydrostatic pressure is obtained at the sealed end. Then the hydrostatic pressure is released at the end opposite the cell and the pressure on the cell is observed, thus de

termining the rate at which the specimen drains. It is believed tests of this nature will give data which may be used in the computation of hydrostatic pressure in embankments after reservoir draw-down.

Another phase of hydrostatic pressure for which experimentation has been started is the hydrostatic pressure created by the consolidation of soil specimens. It is known that all soil specimens artifically compacted contain soil, water, and air. If these specimens are consolidated, either the air or water must escape or the air will be compressed, thus creating pressure as indicated by Boyle's law on the compression of gases. The amount of pressure thus produced will be dependent upon the rate of escape of the air or water from the specimen as the consolidation occurs. The plan for measuring this pressure is to place a hydrostatic pressure cell in the middle of compacted specimens and observe the hydrostatic pressure created by consolidating the specimen and also observe how rapidly this pressure is dissipated. It is believed that tests of this nature will show clearly the advantages gained by artificial compaction and may indicate the artificial compaction necessary for different load conditions. This may also indicate the limiting moisture content for different load conditions or for different embankment heights.

The laboratory has also done considerable work with different amounts of compaction and with different types of compaction. For impact or hammer compaction the number of blows per layer has been varied over a wide range, the weight of the hammer has been varied, and the length of stroke has been varied. For pressure compaction the number of load applications, compacting load, size of compacting foot, and amount of rock in compacted specimens has been varied. The laboratory staff realizes that there is a large field for experimentation in soil mechanics; also that many improvements probably are yet to be made in the test apparatus and procedure now in use. As much time is given this phase of the work as routine tests will allow. The accompanying photographs show the principal equipment and machines now being used in the earth materials laboratory investigations.

TRIAL LOAD METHOD OF ANALYZING

ARCH DAMS

BY IVAN E. HOUK, SENIOR ENGINEER, BUREAU OF RECLAMATION

THE DEVELOPMENT of the trial load method of analyzing arch dams was begun in the Denver office of the Bureau of Reclamation in 1923. Prior to that time most concrete dams had been designed on the assumption that the entire water load would be carried vertically to the foundations by gravity action in the case of both straight and curved gravity dams; and horizontally to the abutments by arch action in the case of arch dams. The use of the trial load method now enables the designing engineer to analyze the load distribution, deflections, and stresses in curved concrete dams of all sizes and shapes, whether of the massive arched gravity type or the relatively thin, monolithic arch type. Furthermore, an adaptation of the method enables him to analyze beam and twist action in straight gravity dams located at sites where steep canyon walls may render such effects important.

In the case of a few arch dams designed prior to 1923, also a few designed by other agencies than the Bureau of Reclamation since that time, stress analyses were made on the assumption that the water load would be divided between the arch and cantilever elements in such a way as to produce equal arch and cantilever deflections in a radial direction at the crown cantilever. However, in such cases the division of load was assumed to be constant from abutment to abutment at each horizontal element analyzed; and no vertical elements were analyzed except at the crown section. This method might, logically, be called the "arch and crown cantilever" method.

The trial load method is, essentially, an amplification of the arch and crown cantilever method. The trial load method, as now used in the Denver office of the Bureau of Reclamation, assumes that the water load is divided between the arch and cantilever elements; that the division may or may not be constant from abutment to abutment at each horizontal element analyzed; and that the true division of load is the one which will cause equal arch and cantilever deflections at all points in all arches and cantilevers, instead of at the crown cantilever only. Furthermore, the trial load method assumes that the distribution of load must be such as to cause equal arch and cantilever deflections in all directions; that is, in tangential and rotational directions as well as in radial directions. Since the required agreement of arch and cantilever deflections

can only be obtained by assuming different distributions of load and calculating resulting arch and cantilever movements until the specified criterion is fulfilled, the procedure is logically called the "trial load" method.

Having determined the true distribution of load between the horizontal and vertical elements of the dam, the resulting arch, cantilever, and principal stresses may be calculated. Arch and cantilever stresses are usually calculated at the upstream and downstream faces of the dam. Arch stresses are usually calculated at the crown and abutment locations, but may also be calculated at other sections along the arch rings. Cantilever stresses are usually calculated at the elevations of the arches and at the foundation ends of the elements. Magnitudes and directions of principal stresses are usually calculated along the lines of contact between the faces of the dam and the rock profiles. Principal stresses are usually found to act in approximately horizontal directions at the abutment ends of the top arch, in approximately vertical planes at the base of the crown cantilever, and in gradually changing directions at intervening locations between the bottom of the canyon and the ends of the top arch. These calculated arch, cantilever, and principal stresses are considered to be the true stresses caused by the assumed condition of reservoir loading.

DEVELOPMENT OF THE METHOD

In the first use of the trial load-method the foundation and abutment rock was considered rigid, and both arches and cantilevers were assumed to have constant unit thicknesses. The arch elements were considered to be horizontal layers having a uniform vertical thickness of 1 foot, and the cantilever elements to be vertical slices having a uniform horizontal thickness of 1 foot. In the earlier analyses the calculations included effects of bending and thrust in the case of the arch elements; and bending, thrust, and shear in the case of the cantilever elements. The next step in the development of the method was the introduction of radial shear effects in the arch computations. Since then the method has been gradually amplified until now the formulas consider effects of radial sides of cantilever elements, twist action, tangential shear, and movements of foundation and abutment rock, as well as the more usually considered effects of thrust, shear, and flexure in the concrete elements. The influence of Poisson's ratio is introduced into the present methods of analysis, indirectly, through the use of the shearing modulus of elasticity in calculating shear, twist, and tangential movements. In the case of unusually important dams, further effects of Poisson's ratio are analyzed by special readjustments made after the preliminary trial load calculations are completed.

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The formulas used in computing the movements of the horizontal and vertical elements are the usual arch and cantilever beam equations derived on the basis of the elastic theory. Since the trial load method brings the arch and cantilever movements into agreement in all parts of the structure, the procedure automatically makes proper allowances for irregularities in the rock profile and lack of symmetry on the two sides of the canyon.

BASIS OF TRIAL LOAD METHOD

The trial load method of analyzing curved concrete dams as now used by the engineers of the Bureau of Recla

mation is based on the following general assumptions:

1. The rock formations which make up the foundation and abutments at the site are homogeneous and uniformly elastic in all directions, and are strong enough to carry the applied loads with stresses well below the elastic limit.

2. The concrete in the dam is homogeneous and uniformly elastic in all directions and is strong enough to carry the applied loads with stresses well below the elastic limit.

3. The dam is thoroughly keyed into the foundation and abutment rock throughout its contact with the canyon profile; so that the arches may be considered as fixed with relation to the abutments, and the cantilevers as fixed with relation to the foundation.

4. The vertical construction joints in the dam are grouted, or the open joints filled, before the water load is applied so that the structure may be considered to act as a monolith and arch action to begin as soon as the reservoir begins to fill.

5. The horizontal water load is carried by two systems of

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structural elements; namely, a system of horizontal arch elements and a system of vertical cantilever elements.

6. The horizontal elements have a constant vertical thickness of one foot from abutment to abutment and from the upstream to the downstream face of the dam.

7. The vertical elements are bounded by vertical radial planes a horizontal distance of 1 foot apart at the upstream face in cases where the upstream face is vertical, or a horizontal distance of 1 foot apart at a vertical circumferential plane passing through the upstream edge of the top arch in cases where the upstream face is built on a batter.

8. Both horizontal and vertical elements may be considered free to move under reservoir loads, without restraint from adjacent elements, and then brought into geometric continuity with adjacent elements by the application of selfbalancing tangential shear and twist loads or couples, one set of loads or couples being applied to the arch elements and the balancing set of loads or couples being applied to the cantilever elements.

9. The total horizontal water load is divided between the two systems of elements in such a way as to satisfy the conditions of equilibrium and produce equal arch and cantilever deflections in all directions in all parts of the loaded structure.

10. The total vertical loads, including the weight of the water on the faces of the dam as well as the weight of the concrete, are assigned to the cantilever elements and are assumed to be transmitted to the foundation without any transfer of load laterally to adjacent cantilevers by means of vertical arching.

11. Effects of flow can be adequately allowed for by using somewhat smaller values of the modulus of elasticity than would otherwise be adopted.

TRIAL LOAD CALCULATIONS

During the early work on the development of the trial load method, arch and cantilever deflections were calcu

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lated in the radial direction only. Then the tangential shear deformations were analyzed, and next the twist deformations. During some of the earlier analyses, tangential shear and twist effects were evaluated by successive trial load adjustments and readjustments after the arch and cantilever movements had been brought into radial agreement. However, tangential shear and twist adjustments are now being made simultaneously with the radial adjustments.

In the early use of the trial load method the arches were divided into voussoirs, and the cantilevers into vertical increments, and the total loads, moments, shears, slopes, and deflections, calculated by summation methods. Vertical increments and summation methods, much amplified, are still used in analyzing cantilever elements. However, mathematical formulas, based on circular curves at the upstream and downstream edges of the horizontal elements, are now being used in analyzing arch elements. If the extrados and intrados curves are not concentric, so that

the arch thickness varies from the crown to the abutment, the half arch is divided into four segments, a uniform thickness assumed for each segment, and the analysis made by the use of special formulas derived for the shorter sections. If appreciable tensile stresses are indicated in the arch elements, so that the investigation of cracked arches is considered advisable, analyses may be made by the original summation method. During the last 4 years, analyses of uncracked arches have been greatly facilitated by the compilation and use of tables of arch constants. Analyses of both arch and cantilever elements have also been greatly facilitated by calculating effects of unit loads of rectangular and triangular shape, covering different parts of the loaded surface; so that the effects of practically any shape of arch or cantilever load desired can be obtained by combining the effects of unit loads already calculated.

Concrete stresses are computed on the assumption of a straight line distribution of stress from the upstream to the downstream face of the dam in both arch and cantilever

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