THE FORCES THAT ARE ACTING ON THE DAM ARE
Weight of the dam acting vertically. This is equal to (Hb/2) x w x p (where w is the weight of water per unit) acting at a distance of b/3 from the upstream vertical face.
Horizontal water pressure:
This is equal to wH2/2 acting at a height of H/3 above the base of the dam.
Net Moment = Hb/2 x wp x 2b/3 x wH2/2 x H/3
The vertical component of the resultant is HB/2 x wp
If the resultant cuts the base at the outer mid third point, the lever arm of the resultant force about the Toe has to be ' b'/3
Thus the equation giving the relationship is
[ Hb/2 wp x 2b/3 - wH2/H x H/3 ] / [ Hb/2 x wp ]
This is reduced to
2Hb2 wp - Hp2 wp - wH3 = 0
i.e., Hb2 wp = wH3
b2 p = H2
The base width of the elementary profile of a dam storage to a height H, is a right angled triangle of base width
it is on the assumption, that there are no uplift pressures base of the dam from the foundation. If uplift is taken count, the value of p will be (p â€'1), thus giving a base