Contents preface (VII) introduction 1—37

16.5. ELEMENTARY PROFILE OF A GRAVITY DAM
The stability conditions required to be met for a gravity dam, subjected only to its self-weight W, force due to water pressure P, and uplift force U can be satisfied by a simple right-angled triangular section (Fig. 16.7) with its apex at the reservoir water level, and which is adequately wide at the base where the water pressure is maximum. Such a section is said to be an elementary profile of a gravity dam. For the empty-reservoir condition the only force acting on the dam is its self-weight whose line of action will meet the base at b/3 from the heel of the dam and thus satisfy the stability requirement of no tension. The base width of the elementary profile is determined for satisfying no tension and no sliding criteria as given below, and the higher of the two base widths is chosen for the elementary profile.
For the elementary profile shown in Fig. 16.7, if one considers that the resultant R of all the three forces W_c (= 0.5 s ρgbh), W₁ (= 0.5 ρgh²), and U (= 0.5 ρghbc′) (here, s = specific gravity of concrete and c′ is a correction factor for uplift force) passes through the downstream middle-third point, one gets
(0.5 s ρgbh) ₃^b − (0.5 ρgh² ) ^h₃ − (0.5 ρghbc′ ) ₃^b = 0 or b² (s – c′) = h²

GRAVITY DAMS	547

h
W₁

^WC

R

h/3

b/3 b/3 b/3

U
b