Forces acting on gravity dam

A gravity dam stays in place by its own weight. The forces acting on it are grouped into stabilising forces (self weight, tailwater) and destabilising forces (water pressure, uplift, silt, waves, earthquake).

          crest
   ~~~~~ +---+  <- wave pressure Pw
   |     |   |\
 Pi ->   |   | \  <- wind
   |     | W |  \    W = self weight
 P1 ->   |   |   \   (+ EQ: aW horizontal)
   |     |   | W2 \
 Ps ->   |   |     \  ~~~~ tailwater
 (silt)  |   |      \  <- P2
         +---+-------+ toe
  heel   ^  ^  ^  ^  ^
         U (uplift)

1. Self weight (W)

Main resisting force. $W = \gamma_c \times$ cross-sectional area (per metre length), acting through the centroid. The section is split into rectangles and triangles.

2. Water pressure

• Upstream: $P_1 = \frac{1}{2}\gamma_w h_1^2$, horizontal, at $h_1/3$ above the base. If the upstream face is sloping, the weight of water above the slope acts vertically downward.
• Tailwater: $P_2 = \frac{1}{2}\gamma_w h_2^2$ acting upstream, and the weight of water on the downstream slope.

3. Uplift pressure (U)

Seepage water under the base and in the joints acts upward and reduces the effective weight. It varies linearly from $C\gamma_w h_1$ at the heel to $\gamma_w h_2$ at the toe; drains reduce it.

4. Silt (sediment) pressure

$P_s = \frac{1}{2}\gamma_{sub}h_s^2 K_a$, where $K_a = (1-\sin\phi)/(1+\sin\phi)$, acting at $h_s/3$ from the base.

5. Wave pressure

Wind waves strike the top of the dam. $P_w = 2\gamma_w h_w^2$ acting at $3h_w/8$ above the reservoir level; wave height from Molitor's formula.

6. Earthquake forces

• Horizontal inertia force on the dam $\alpha_h W$ (and vertical $\alpha_v W$).
• Hydrodynamic pressure of the reservoir water (Westergaard/Zanger method), acting at about $4h/(3\pi)$ above the base.

7. Ice and wind pressure

Ice thrust (cold regions) about 250 kN/m² on the ice thickness; wind pressure is small and usually neglected.