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.

The maximum possible height of low gravity dam is H = f / ?_w (S_c + 1) where f = allowable stress of dam material = 4.2 MPa, S_c = 2.57, and ?_w = 9.81 KN/m².
H = [4.2 / (9.81 x 3.57)] x 1000 = 119.92 m.

Bligh has given an empirical formula for finding out thickness of dam at top.
A = 0.522 H^1/2 = 0.522 x 84^1/2 = 5.05 m.
As per Creager, economical top width has been found to be equal to 14% of dam height without considering earthquake forces.

The transverse joints in dam body are generally not grouted in U-shaped valleys but are keyed toger in V-shaped valleys. In V-shaped valleys, entire length of dam acts monolithically as a single body. The assumption that dam is considered to made up of a number of cantilevers of unit width each may involve errors here.

Transverse joints are vertical joints that divide dam length into a number of vertical cantilevers each of which is independent of or. It runs through entire height and extends through full width of dam section. Hence, it justifies two-dimensional analysis of gravity dams.

Small openings made in dam only produce local effects as per St. Venant?s principle. They do not affect general distribution of stresses. This is one of most important assumptions made in two-dimensional analysis of gravity dams.

The critical height or limiting height of a dam having elementary profile is ?
H_max = f / (S_c + 1) ?_w where f = allowable stress of dam material, S_c = Specific gravity of concrete and ?_w = unit weight of water.
This limiting height draws a dividing line between a low gravity dam and a high gravity dam.

When re is no tailwater, principal stress in such a case is P_v secQ² where P_v is intensity of vertical pressure. This value of principal stress should not be allowed to exceed maximum allowable compressive stress of dam material.

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.

In a gravity dam, grout curtain is provided near toe to reduce exit gradient. A drainage gallery with its drainage pipe system provided in gravity dam reduces uplift pressure at all levels below upstream water level. Vertical cut-off walls are most effective to reduce seepage flow and uplift force.