When vertical acceleration is acting downward foundation try to move downward away from dam body. This reduces effective weight and stability of dam. It is worst case for design.

Hydrodynamic pressure and horizontal inertia force are caused by horizontal acceleration of an earthquake wave acting towards reservoir. As foundation and dam accelerate towards reservoir re is an increase in water pressure which is resisted by water, extra pressure is hydrodynamic pressure.

The net effective weight of dam is given as W [1 ? K_v] and vertical acceleration a_v = K_v.g = 0.1.g i.e 10%
where W is total weight of dam and K_v is fraction of gravity adopted for vertical acceleration.
This is considered as worst case for design as foundation tries to move downward away from dam body when re is downward vertical acceleration. This reduces effective weight and stability of dam.

Hydrodynamic pressure is extra pressure exerted when horizontal acceleration of an earthquake wave is acting towards reservoir. As foundation and dam accelerate towards reservoir re is an increase in water pressure which is nothing but hydrostatic pressure acting at a height of 3H/4? above base. Mamatically, this value is given by Von-Karman equation.

The major resisting force is weight of dam body and its foundation. A unit length of dam is considered in 2D analysis of a gravity dam. The resultant of all downward forces will represent total weight of dam acting on it.

When F > 32 km, wave height is given by h_w = 0.032 (V.F)^1/2
h_w = 0.032 (172 x 52)^1/2 = 3.02 m
The force caused by waves is given by equation ? P_w = 19.62 h_w² KN/m run of dam
P_w = 19.62 x 3.02² = 179.69 KN.

When F < 32 km, wave height is given by ? H_w = 0.032(V.F)^1/2 + 0.763 ? 0.271 F^1/4
H_w = 0.032(92 x 18)^1/2 + 0.763 ? 0.271 (18)^1/4 = 1.5 m
Free board is generally provided equal to 1.5 H_w = 1.5 x 1.5 = 2.25 m.

Vertical acceleration can be resolved in two parts i.e. upward vertical accelerations and downward vertical accelerations. The effective weight of dam increases when re is an upward vertical acceleration as it brings foundation closer to dam. In downward acceleration, effective weight reduces and is considered as worst design case.

An average value of acceleration equal to 0.1 to 0.15 g is sufficient for high dams in seismic zones and for areas not subjected to extreme earthquake a_h = 0.1 g and a_v = 0.05 g may be used. These forces are neglected in areas of no earthquake or very less earthquake.

According to Von-Karman, hydrodynamic force is given by ?
P_e = 0.555. K_h. ?_w H² where, ?_w is unit weight of water, H is depth of water and K_h is a fraction of gravity adapted for horizontal acceleration which acts at height of 4H/3? above base. In addition to this, an inertia force is also produced by horizontal acceleration into body of dam.