Professor Unwin 1 has shown that the maximum unit compression at the face of the dam occurs on a section normal to the face, and that the maximum value of this compression at the outer edge of a hor izontal section through the dam is = , in which is the value cos= 0 of unit vertical compression and 0 is the angle made by the batter of the face of the dam with the vertical.
A method of finding the maximum diagonal compression and its direction at any point of a horizontal section of the profile of a clam is given by Professor which agrees practically with Unwin's results for the stress at the edge.
Compression upon Inclined distribution of pressure upon an inclined section is sometimes investigated and the maximum unit stress at the outer face of the dam found to be greater than that for a horizontal sect ion. In Fig. 7-1 using the same profile employed in Fig. 72, the pressure upon the inclined section k-n is that due to the water pressure (II) upon the inner face 0- K of the (lain combined with the weight of masonry (ii') above the section k-n. The unit compression at n is obtained in the same manner as for the Horizontal section. This stress for this profile is gre.rtcr than for the same point when obtained by using the horizontal section through n, and about the same as that at the outer edge of the base section k-k.
Lateral Distribution of Stress.—In the trapezoidal distribution of stress, which considers the stresses to vary uniformly from the inner to the outer edge of the section, it is assumed that the whole width of the dam acts together as a single homogeneous body. It; is not probable that this is the case in a wide section. The riddle portion of the section carries more and the edges less stress than the assumed distri bution shows, and for this reason many designers have considered that the ordinary method, with low allowable stress upon the outer edge, as proposed by Ran kine, to be sufficiently exact. The ordinary method, taking successive horizontal sections, provides an easy way of determining an approximate profile. Careful study should, however, be given to the possible diagonal stresses in a high dam, and if such stresses exceed the allowable unit compression, the profile should be widened so as sufficiently to reduce them.
139. Horizontal Tension.—Experiments have been made by Sir J. W. Ottley and Mr. A. W. Brightmore r upon models of dams made
of plasticine (a kind of modeling clay), and by Messrs. J. W. Wilson and W. Gore 2 on models made of india rubber.
The distribution of stresses through the profile was determined in each case by observing the horizontal and vertical displacement of points in the section. These experiments seemed to confirm, in general, the ordinary theory of the trapezoidal distribution of stresses, and to justify the methods of design in common use.
At the base of the dam, where the profile section joins the founda Lion, it was found that a different distribution of stress occurs, ten sion being developed at the inner edge of the base by the immovability of the foundation. Thus, in Fig. 75 the shear on A-B, due to the horizontal water pressure causes horizontal or diagonal tension (T) in the foundation at the inner edge (A) of the base. In the plasticise models diagonal cracks (A-C) occurred at this point in the foundation.
Various methods have been suggested for meeting or reducing this tension by modifying the shape of the profile at the base or reinforc ing the foundation. This does not seem necessary for darns as usually constructed. A high masonry dam is usually on solid rock foundation, and the strength of the rock is such that no break in the foundation is to be anticipated from this cause. In most clams the foundation is in rock at considerable depth below the bed of the stream, and the lower part of the dam is enclosed on both sides by gravel or other soil which usually may he considered to strengthen the dam, although the full depth of water pressure should be assumed to act upon it. If, however, this filling is soft material, which flows when saturated, it may increase the pressure against the dam and may be considered as a fluid heavier than water.
140. UpIift.—If a dam be so constructed that water under pres sure may penetrate into the interior of the clam or under its base, the effect of such pressure must be considered in its design. There is considerable difference of opinion among engineers concerning the necessity of providing for uplift in designing the profiles for dams. Some allow for it in all cases; while others claim that properly con structed masonry or concrete will be so nearly water-tight that the effect of uplift may be neglected.