A retaining wall is constructed in a clayey soil. The height of the backfill is found to be 9m, the unit weight of the sand is 2t/m3 and the angle of internal friction is 30˚. Find out the earth pressure per meter length on the retaining wall with a smooth vertical back.a)1tb)2tc)27td)81tCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given data:
Height of backfill (h) = 9 m
Unit weight of sand (γ) = 2 t/m^3
Angle of internal friction (φ) = 30°

The earth pressure on a retaining wall with a smooth vertical back can be calculated using Coulomb's active earth pressure theory, which states that the active earth pressure at any depth (h) is given by:

P = K * γ * h^2

where P is the earth pressure per unit length of the wall, γ is the unit weight of the soil, and K is the coefficient of earth pressure.

To find the coefficient of earth pressure (K), we can use the formula:

K = (1 - sinφ) / (1 + sinφ)

where φ is the angle of internal friction.

Calculations:
Given that the angle of internal friction (φ) = 30°, we can find the coefficient of earth pressure (K):

K = (1 - sin(30°)) / (1 + sin(30°))
= (1 - 0.5) / (1 + 0.5)
= 0.5 / 1.5
= 1/3

Now, we can substitute the values of K, γ, and h into the equation for earth pressure:

P = (1/3) * 2 * 9^2
= (1/3) * 2 * 81
= 54 t

Therefore, the earth pressure per meter length on the retaining wall with a smooth vertical back is 54 t.

Hence, the correct answer is option (c) 27 t.

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