GRAVITY DAM ANALYSIS 135
3.2.2 Overturning stabilityA simplistic factor of safety with respect to overturning, FO, can be
expressed in terms of the moments operating about the downstream toe of
any horizontal plane. FOis then defined as the ratio of the summation of
all restoring (i.e. positive) moments, ∑Mve, to the summation of all over-
turning moments, ∑M ve: thus
FO∑Mve/∑M ve. (3.19)It may be noted that ∑M veis inclusive of the moment generated by uplift
load. Seismic loads are excluded from overturning calculations on account
of their transient and oscillatory nature. Values of FOin excess of 1.25 may
generally be regarded as acceptable, but FO 1.5 is desirable (Kennard,
Owens and Reader, 1996).
Overturning of a complete and intact gravity profile of significant
size is, strictly, an unrealistic instability mode. The overturning moments,
e.g. from water load etc., control internal stress levels, and the overturning
mode is therefore closely linked to possible overstress, i.e. to criterion 3.
As the nominal margin of safety against overturning is reduced the com-
pressive stresses generated at the downstream toe will rapidly escalate and
tensile stress at the upstream heel will initiate local cracking which may
propagate (Section 3.2.5), leading to a reduction in sliding resistance.
Determination of a value for FOis not universal practice owing to the
link between overturning moments and stress level. Adequate stability in
relation to overturning may be assured by specifying limiting stress levels
for the concrete, e.g. ‘no tension’.
Fig. 3.4 Sign convention diagram: forces, moments and shears