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# Gravity Dams 135

## section, pressure, dam, water, edge, ab and base

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GRAVITY DAMS 135. Stability of Dams.—A gravity dam, like a retaining wall, depends upon the weight of the mass of masonry to resist the thrust of the water against it. As the dam carries water pressure instead of earth pressure, the loads to which the darn is subjected are defi nitely known, and the thrusts are everywhere normal to the surfaces of contact.

Let A BCD, Fig. 71, represent a slice, 1 foot thick, of a gravity dam sustaining a head of water as shown.

h= height of water above section AB; pressure of water against the dam; V=vertical pressure of water on back of dam; TV= weight of data above section AB; pressure upon section A B; k= horizontal distance from inner edge of base to line of action of T'; of base A B; d= distance from outer edge of base to line of action of TV; x= distance from outer edge of base to point of application of resultant R.

The conditions of stability for the clam are the same as for the retaining wall: It must not slide or shear on a horizontal section.

It must not overturn about outer edge of section.

The masonry must not be crushed by pressure upon the section.

Stability against Sliding.—Taking the weight of water as 62.5 the horizontal thrust against the dam above AB is This is the shear upon the section AB. If AB is a joint in the dam, or the base of the dam, H must be resisted by the friction of the masonry upon the masonry below, or upon the foundation under the dam, and the value of H/(TTr+ T') must not exceed the coefficient of friction for the material. If A B is a section in a concrete clam, H is resisted by the shearing strength of the concrete as well as by the friction.

Continuous joints are not usually employed in construction of masonry dams, and the interlocking of stones eliminates the tendency to slide without shearing blocks of stone. The possibility of sliding need usually only be considered at the foundation.

Stability against Overturning.—The overturning moment about the outer edge of the section at A, due to pressure of water, is Assuming that pressures upon AB are distributed with uniform variation from A to B, x should be greater than b/3 in order that no tension may be developed in the section, as in the gravity retain ing wall.

Stability against Crashing.—The total pressure normal to the section AB is distributed over the section with center of pres sure distant x from A. The maximum normal unit pressure is therefore (see Section 52) This is approximately the crushing stress in the masonry at the outer edge of the section, or the maximum pressure upon the founda tion if AB is the base of the dam.

When the reservoir is empty and the water pressure is removed, the pressure upon the section AB will he 1h', with center of pressure distant d from the outer edge. The unit pressure at the outer edge of the section will be and at the inner edge, In dams of unsymmetrical cross-sections it is necessary to con sider the pressures coming upon the bases of sections when the water pressures are removed, as when the reservoir is empty. In this case, the weight of dam will be the only load, and the centers of pressure due to this weight must always come within the middle third of the base, and the crushing stress be within proper limits, so that removal of the water pressure may produce no harmful effects upon the darn.

136. Graphical Analysis of Profiles of Dams.—For low dams carrying small heads of water, trapezoidal cross-sections may he employed, and designs made in the same way as for retaining walls using water pressure instead of earth pressure upon the back face of the dam. As the depth increases such a section becomes increasingly uneconomical and the form of cross-section should be modified so as to make the thickness only that required to carry the load above, and the profile such as to distribute the material to the hest advan tage.

Fig. 72 shows a method of graphical analysis applied to the sec tion of a gravity dam. ookk represents a section of a dam 100 feet high. Take a slice of the dam 1 foot thick and of the section shown and divide this by horizontal planes, a-a, etc., into a number of horizontal layers (in this case, each 10 feet thick).

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