Question

 It was found that the critical angle of a dam against seepage pressure with respect to normal was 45 degrees. According to Khosla creep theory, what can you say about the structure?
1. The dam is stable against seepage pressure
2. The dam is stable against overturning
3. The dam is stable against lateral pressure
4. The dam is stable against heave pressure

Answer 1

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.

1. 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.
2. 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.