Correct Answer - Option 2 : The dam is stable against overturning

**Explanation**

Given Data:

Critical Angle(\(α\))= 450

Concept:

Shear stress(\(τ\)o) at a horizontal plane near the toe is given by

⇒ τo = γw × H × (S_{c} - C) × tan α

Where

γw = Unit weight of water, H = height of the dam,

Sc= Specific Gravity,

C = Constant, α = Angle, B = Base width

Now

\(\tan α = {B \over H}\)

We know,

\(\tan α = \frac{B}{H}\)

Here,

α = 45°, Hence, B = H.

__a) For safety against overturning:__

\(\frac{B}{H} \ge \frac{1}{{\sqrt {\left( {G - C} \right)} }}\)

Here, G – specific gravity and C – factor for uplift pressure

Since G > 1 (Always)

So, B/H > 1 (Always)

Hence,

**The structure is stable against overturning.**

b)__ For safety against sliding or lateral force __

\(\frac{B}{H} \ge \frac{1}{{\mu \left( {G - C} \right)}}\)

Here,

μ – Coefficient of friction (< 1 always)

B/H < 1

Hence,

The structure is not stable against lateral forces.

- Safety of dam against uplift pressure or seeping pressure depends upon exit gradient and weight of the dam. We can’t comment about the stability depending on the critical angle alone.
- The stability of a dam against heave pressure depends on the environmental conditions (i.e. the prevailing conditions of the frost heaving are present or not).

Note: Safety of dam against seeping pressure & heave pressure can't be determined using only critical angle.