GRAVITY DAM ANALYSIS 133
obligation remains with the designer to exercise discretion in defining load
combinations which properly reflect the circumstances of the dam under
consideration, e.g. anticipated flood characteristics, temperature régimes,
operating rules, etc.
3.1.3 Forces, moments and structural equilibriumThe reactive forces developed in the foundation and/or abutments of the
dam in response to applied loads must also be accounted for to satisfy the
conditions for static equilibrium. Combination of the applied vertical and
horizontal static loads equates to the inclined resultant force, R(Fig. 3.1).
This is balanced by an equivalent and opposite reactive resultant R,
derived from vertical reactions and the reactive horizontal resistance of
the foundation. The conditions essential to structural equilibrium and so
to stability can therefore be summarized as
∑H∑V 0 (3.18a)and
∑M0. (3.18b)In equations (3.18a) and (3.18b), ∑Hand∑Vrespectively denote the sum-
mation of all active andreactive horizontal and vertical forces, and ∑M
represents the summation of the moments of those forces with respect to
any point.
The condition represented by ∑H∑V0 determines that no trans-
lational movement is possible. The further condition that ∑M0 pro-
scribes any rotational movement, e.g. overturning. With respect to the
latter condition some qualification is necessary in relation to the stress dis-
tribution as determined by the applied moments.
3.2 Gravity dam analysis
3.2.1 Criteria and principlesThe essential criteria governing the structural competence of a gravity
dam follow from consideration of equations (3.18a) and (3.18b). Assessed
in relation to all probable conditions of loading, including the reservoir
empty condition, the profile must demonstrate an acceptable margin of
safety with regard to