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What is active earth pressure at the bottom of a vertical cut, 4.0 m deep in soil with ϕ’ = 30° and c’ = 20 kN/m2 and γ = 25 kN/m3?
- a)10.24 kN/m2
- b)14.5 kN/m2
- c)16 kN/m2
- d)18.5 kN/m2
Correct answer is option 'A'. Can you explain this answer?
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The active earth pressure at the bottom of a vertical cut in soil depends on several factors, including the soil properties, the angle of internal friction, the cohesion of the soil, and the depth of the cut. Without knowing these factors, it is impossible to provide an accurate answer to this question.
However, if we assume that the soil is a typical clay with an angle of internal friction of 30 degrees and a cohesion of 10 kPa, we can estimate the active earth pressure at the bottom of a 4.0 m deep vertical cut using the Rankine earth pressure theory.
According to the Rankine theory, the active earth pressure coefficient (Ka) for a vertical cut in clay is given by:
Ka = (1 - sin φ) / (1 + sin φ)
where φ is the angle of internal friction of the soil.
For a soil with an angle of internal friction of 30 degrees, we have:
Ka = (1 - sin 30) / (1 + sin 30) = 0.17
The active earth pressure at the bottom of the cut is then given by:
Pa = Ka * γ * H^2
where γ is the unit weight of the soil and H is the depth of the cut.
Assuming a unit weight of 18 kN/m3 for the soil, we have:
Pa = 0.17 * 18 * 4^2 = 4.9 kPa
Therefore, the estimated active earth pressure at the bottom of a 4.0 m deep vertical cut in clay with an angle of internal friction of 30 degrees and a cohesion of 10 kPa is approximately 4.9 kPa. However, it is important to note that this is just an estimate and the actual value may vary depending on the specific properties of the soil.
However, if we assume that the soil is a typical clay with an angle of internal friction of 30 degrees and a cohesion of 10 kPa, we can estimate the active earth pressure at the bottom of a 4.0 m deep vertical cut using the Rankine earth pressure theory.
According to the Rankine theory, the active earth pressure coefficient (Ka) for a vertical cut in clay is given by:
Ka = (1 - sin φ) / (1 + sin φ)
where φ is the angle of internal friction of the soil.
For a soil with an angle of internal friction of 30 degrees, we have:
Ka = (1 - sin 30) / (1 + sin 30) = 0.17
The active earth pressure at the bottom of the cut is then given by:
Pa = Ka * γ * H^2
where γ is the unit weight of the soil and H is the depth of the cut.
Assuming a unit weight of 18 kN/m3 for the soil, we have:
Pa = 0.17 * 18 * 4^2 = 4.9 kPa
Therefore, the estimated active earth pressure at the bottom of a 4.0 m deep vertical cut in clay with an angle of internal friction of 30 degrees and a cohesion of 10 kPa is approximately 4.9 kPa. However, it is important to note that this is just an estimate and the actual value may vary depending on the specific properties of the soil.
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