1. Water pressure.

2. Uplift pressure.

3. Pressure due to earthquake.

4. Slit pressure.

5. Wave pressure.

6. Ice pressure.

7. Weight of Dam.

- Water pressure (P).

• P is the major external force acting on dam.

• It can be estimated by hydrostatic pressure diagram.

• When the upstream face is vertical, the intensity is zero at top of the water surface and rwH at base, where rw is the unit wt of water and H is depth of water.

• Resultant force due to this external force is ½ rwH @ H/3 from base.

• When upstream face is partly vertical and partly ? the resulting force can be resolved into horizontal comp and vertical comp (Pv)

Horizontal component = ½ rw $H^2$ @ H/3 from base vertical component = wt of water stored in column ABCD.

- Uplift pressure: It is the second major external force acting upward due to seeping water. The uplift forces occur as internal pressures in pores, cracks and seams within the body of the dam, at the contact surface between the dam and its foundation and within the foundation. The pressure intensities at the heel and toe of the dam are taken equal to the hydrostatic pressures at the heel and toe joined by a straight line in between (Fig. 18.4). Drainage galleries are sometimes provided in the dam body to release uplift pressure. Accordingly, the uplift pressure distribution in the body of the dam is assumed to have an intensity which at the line of the formed drain/drainage holes exceeds the tail water head by one third the differential between reservoir levels and tail water level. The pressure gradient is then extended linearly to heads corresponding to reservoir level and retail water level (Fig. 18.5). The pressure is assumed to act over 100 percent of the area. The uplift criteria in case of dams founded on compact and unfissured rock is as specified above.

Under worst loading conditions, i.e. drains inoperative, the uplift is considered to vary linearly from maximum flood water pressure at heel to tail pressure (or zero if no tail water is present) at the toe of dam.

- Ice pressure:

• Ice which may be formed on water surface of the reservoir in cold countries may sometimes melt and expand.

• Dam face has then to resist the thrust exerted by expanding ice.

• Force acts linearly along the length of dam and at reserve ir level.

• The magnitude of this force varies from 25D to 1500 KN/m depending upon temperature variations.

• On a average, a value of 500 $KN/m^2$ may be allowed.

- Weight of Dam:

• Weight of body and its foundation is the major resisting force.

• In two dimensional analysis, a unit length of the dam is considered.

• The c/s can then be divided into rectangles and triangles.

• The wt of each along their c.gs can be determined.

- Earth and slit pressures: Earth pressures have a minor effect on a stability of the dam and are ignored. Slit gets deposited against the upstream face of the dam. Dam is thus subjected to slit pressure in addition to the water pressure. Slit is treated as saturated cohensionless soil having full uplift and whose value of internal friction is not materially changed on account of submergence. Slit pressure and water pressure exist together in a submerged fill and slit pressure on the dam is reduced in the proportion that the weight of the fill is reduced by submergence. The horizontal slit pressure

$P_s = W_s \ \frac{h^2}{2} ( \frac{1 – sin \ \beta}{1 + sin \ \beta})$ is assumed to be equivaler to that of a fluid weighing 1360 $kg/m^3$. Vertical slit and water pressure is determined as if slit and water together have a density of 1925 $kg/m^3$. $\beta$ is the angle of internal friction taken as 30° for sand, gravel, clay and slit, $W_s$ is unit of slit or earth submerged in water, and h is the height of slit submerged in water above the base of dam.

- Wind pressure: Wind loads on dams are ignored.

- Ice pressure: Ice pressure is not encountered in the design of dams in India. Ice is formed on the water surface of the reservoir expands and contracts with change in temperature. The dam face is subjected to force due to expansion of ice. Ice pressure is taken as 25000 $kg/m^2$ applied to the face of dam over the anticipated area of contact of ice with the face of the dam as per IS:6512-1984.

- Wave pressure: Upper portions of the dam are subjected to impact of waves. Wind pressure depends on the height of wave. The wave pressure diagram is approximated by triangle 1-2-3 in Fig. 17.7. The total force $P_w$ is given by the area of triangle or $P_w = 2000 \ hw^2$. The centre of application is at a height of 0.375 hw above the still water level. T Saville method recommended by IS : 6512 – 1984 for the computation of wave height is discussed in section 17.4.

[1] Maximum unit pressure, $P_w = 2400 \ h_w \ kg/m^2$ acting at 0.125 $h_w$ above the still water level.

[2] Total wave force, $P_w = 2400 \ H_w \times ½ \times 5/3 \ H_w = 2000 \ H^2_w$ acting at 0.375 $h_w$ above the still water level assuming pressure distribution is triangular and height equal to $5/3 \ H_w$

[3] When a maximum wind velocity is known, the same is used for FRL condition and 2/3 times for MEL condition.