A vertical retaining wall of 5 m height has to support soil having unit weight of 18 kN/m3, effective cohesion of 12 kN/m2, and effective friction angle of 30°. As per Rankine’s earth pressure theory and assuming that a tension crack has occurred, the lateral active thrust on the wall per meter length (in kN/m, round off to two decimal places), is ______.Correct answer is '21.71'. Can you explain this answer?

Question

A vertical retaining wall of 5 m height has to support soil having unit weight of 18 kN/m3, effective cohesion of 12 kN/m2, and effective friction angle of 30&deg;. As per Rankine&rsquo;s earth pressure theory and assuming that a tension crack has occurred, the lateral active thrust on the wall per meter length (in kN/m, round off to two decimal places), is ______.Correct answer is '21.71'. Can you explain this answer?

Answer

To calculate the active earth pressure exerted on the retaining wall, we can use the Rankine's theory. The active earth pressure is given by the formula:

P = Ka * γ * H^2

Where:
P = Active earth pressure
Ka = Coefficient of active earth pressure
γ = Unit weight of soil
H = Height of the retaining wall

Given:
H = 5 m
γ = 18 kN/m^3

To determine the coefficient of active earth pressure (Ka), we can use the formula:

Ka = (1 - sin φ) / (1 + sin φ)

Where:
φ = Effective friction angle

Given:
φ = 30°

Using the given values, we can calculate the coefficient of active earth pressure:

Ka = (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 Ka, γ, and H into the formula for active earth pressure:

P = (1/3) * (18 kN/m^3) * (5 m)^2
= (1/3) * (18 kN/m^3) * 25 m^2
= (1/3) * 450 kN/m^2
= 150 kN/m^2

Therefore, the active earth pressure exerted on the retaining wall is 150 kN/m^2.

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