GRAVITY DAM ANALYSIS 149
flare also serves to reduce any tensile stress which may generate at the
downstream face under the reservoir empty condition.
The optimum height for the flare can be set by the elevation where
the line of action of the crest mass, shaded on Fig. 3.8, intersects the
upstream middle third line, as shown. The flare width required can be cal-
culated by equating the summation of the self-weight moments about the
revised upstream third point to zero.
3.2.7 Gravity profile selectionThe primary load régime for a gravity dam of given height is essentially
fixed. Little scope exists to modify the ‘standard’ triangular profile signific-
antly, and a vertical upstream face is invariably associated with a mean
downstream slope equating to a ratio for base thickness to height to spill-
weir level of the order of 0.75:1.00. Design of a small dam may therefore
be based on adopting such a geometry, checking its adequacy, and effect-
ing any minor modification necessary.
In the case of larger dams a unique profile should be determined to
match the specific conditions applicable. Two approaches are possible: the
multistage and the single stage.
The multistage approach defines a profile where the face slopes are
altered at suitable intervals, as in the example of Fig. 3.9. Design com-
mences from crest level, and descends through profile stages corresponding
to predetermined elevations. Each stage is proportioned so as to maintain
stress levels within acceptable limits, e.g. no tension under any condition of
loading. The resulting profile allows marginal economies in concrete, but
may be more expensive to construct than the single-stage equivalent. Multi-
stage profiles are now seldom employed, even on large dams.
Fig. 3.9 Multistage gravity dam profile