STABLITY ANALYSIS OF GRAVITY DAM

Gravity dam shall be designed based on Indian Standards IS: 6512-1984

Active pressure coefficients for static condition

Passive pressure coefficients for static condition

In case of seismic condition, as per IS1893:1984 Clause 8.1.1, the active pressure coefficient shall be calculated as.

Where,

\(\alpha\) = Angle which the earth face of the wall makes with the vertical

\(i\) = Slope of earthfill

\(\delta\) = Angle of friction between the wall and earth fill

\(\alpha_h\) = Horizontal seismic coefficient

\(\alpha_v=\frac{2}{3}\alpha_h\) = vertical seismic coefficient

CALCULATION OF LOADS

1. DEAD LOAD (\(F_1\))

2. RESERVOIR AND TAILWATER LOADS (\(F_2\))

Reservoir pressure \(=F_{2R}\)

Tailwater pressure \(=F_{2T}\)

3. UPLIFT PRESSURE (\(F_3\))

Case A: Uplift pressure when drains are inappropriate, or no drain has been provided.

Case B: When drain are provided or approprite.

It is assumed that uplift pressures are not affected by earthquake.

Case A: When drains are inappropriate, or no drains have been provided. \(F_3=\frac{B}{2}\gamma_w(H+h)\)	Case B: When drain are provided or approprite. \(F_{31}=\frac{b_1}{2}\gamma_w(H+h+\frac{H-h}{3})\) \(F_{32}=\frac{B-b_1}{2}\gamma_w(h+h+\frac{H-h}{3})\)

4.EARTHQUAKE FORCES (\(F_4\))

Seismic load has been calculated based on IS 1893: 2002 or NBC 105: 2022.

Horizontal Seismic force (static method)

Vertical Seismic force (static method)

5. EARTH AND SILT PRESSURE (\(F_5\))

In case of no seismic load combination

In case of seismic load combination

Similarly passive pressure shall be calculated by;

In case of no seismic load combination

In case of seismic load combination

Where, \(C\) = Passive pressure contribution

6. ICE PRESSURE (\(F_6\))

This force can be neglected.

7. WIND PRESSURE (\(F_7\))

This force can be neglected.

8. WAVE PRESSURE (\(F_8\))

Where, \(h_w\)=height of wave and can be found by following chart

Maximum unit pressure occurs at \(0.125h_w\) above still water level is given by the equation

Total wave force can be calculated by

The Centre of application is \(0.375h_w\) above the sill water level.

9. THERMAL LOAD (\(F_9\))

COMBINATION OF LOADS

As per IS 6512: 1984, the combination of load shall be carried out as follows.