CIVIL ENGINEERING FORMULAS

350 CHAPTER TWELVE

The resistance of a gravity dam to sliding is primarily dependent upon the
development of sufficient shearing strength. The factor of safety due to com-
bined shearing and sliding resistance may be expressed by the formula.

(12.183)

In practice, this resistance is attained in part by stepping the foundation and
by measures taken to ensure bond between concrete and rock and successive
pours of concrete.

Structural Analysis. In final designs for high gravity dams, consideration
should be given to combined beam and cantilever action, the effect of rock
movements and the effects of twist and beam action along sloping abutments in
addition to the conventional stability and stress analyses.
Ordinarily the following steps will suffice:

1.Compute the righting and overturning moments on selected horizontal planes,
taking into consideration all of the forces which may act on the section.

2.Compute the vertical normal stresses xon each selected plane of analysis by
the formulas

xmax (at downstream face) (12.184)

xmin (at upstream face) (12.185)

Vertical normal stresses may be assumed to have straight-line variation

between the toe and the heel. Usually these stresses are computed on the

assumption that no uplift pressure is acting on the base.

3.Compute the principal and shearing stresses at the downstream face. The first
principal stress in which the angle between the down-
stream face and the vertical. The horizontal shearing stress at the toe is

4.Estimate the probable distribution of uplift pressure on the foundation, and
determine its effects upon the stability of the section.

5.Considering the effects of uplift on the sliding factor, compute the shear-
friction factor of safety and the factor of safety against overturning.

Arch Dam

Anarch damis a curved dam that carries a major part of its water load horizon-
tally to the abutments by arch action, the part so carried being primarily depen-
dent on the amount of curvature. Massive masonry dams, slightly curved, are

!xxtan.

 1 xcos^2



V

144 b

1 

6 e

b



V

144 b

1 

6 e

b

Q

[( VU)f](bq)

H