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The cohesion (c), angle of internal friction (Φ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m3, respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is ________________.
Correct answer is '4.90'. Can you explain this answer?
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The cohesion (c), angle of internal friction (Φ) and unit weight (γ) ...
Given data:
Cohesion (c) = 15 kPa
Angle of internal friction (Φ) = 20°
Unit weight (γ) = 17.5 kN/m3
Calculating the maximum depth of unsupported excavation:
The maximum depth of unsupported excavation in the soil can be determined using the Rankine's earth pressure theory. According to this theory, the lateral earth pressure acting on a retaining wall is given by the following equation:
P = Ka * γ * H + 2 * c * √(Ka) + γ * H * tan²(Φ)
Where:
P = Lateral earth pressure
Ka = Rankine's active earth pressure coefficient
γ = Unit weight of the soil
H = Depth of excavation
c = Cohesion of the soil
Φ = Angle of internal friction of the soil
Determining the Rankine's active earth pressure coefficient (Ka):
The Rankine's active earth pressure coefficient (Ka) can be calculated using the following equation:
Ka = (1 - sin(Φ)) / (1 + sin(Φ))
Substituting the given value of Φ into the equation:
Ka = (1 - sin(20°)) / (1 + sin(20°))
≈ 0.375
Substituting the values into the lateral earth pressure equation:
P = 0.375 * 17.5 * H + 2 * 15 * √(0.375) + 17.5 * H * tan²(20°)
Simplifying the equation:
P = 6.5625H + 26.658 + 17.5H * 0.36397
P = 6.5625H + 26.658 + 6.397H
P = 12.9595H + 26.658
Determining the maximum depth of unsupported excavation:
The maximum depth of unsupported excavation occurs when the lateral earth pressure is equal to zero. Therefore, setting P = 0:
12.9595H + 26.658 = 0
Solving for H:
H = -26.658 / 12.9595
H ≈ -2.06
Since the depth cannot be negative, the maximum depth of unsupported excavation in the soil is approximately 2.06 meters.
However, this negative value indicates that the soil cannot support any excavation. Therefore, there might be an error in the given data or calculation. Please double-check the values and equations to ensure accuracy.
Cohesion (c) = 15 kPa
Angle of internal friction (Φ) = 20°
Unit weight (γ) = 17.5 kN/m3
Calculating the maximum depth of unsupported excavation:
The maximum depth of unsupported excavation in the soil can be determined using the Rankine's earth pressure theory. According to this theory, the lateral earth pressure acting on a retaining wall is given by the following equation:
P = Ka * γ * H + 2 * c * √(Ka) + γ * H * tan²(Φ)
Where:
P = Lateral earth pressure
Ka = Rankine's active earth pressure coefficient
γ = Unit weight of the soil
H = Depth of excavation
c = Cohesion of the soil
Φ = Angle of internal friction of the soil
Determining the Rankine's active earth pressure coefficient (Ka):
The Rankine's active earth pressure coefficient (Ka) can be calculated using the following equation:
Ka = (1 - sin(Φ)) / (1 + sin(Φ))
Substituting the given value of Φ into the equation:
Ka = (1 - sin(20°)) / (1 + sin(20°))
≈ 0.375
Substituting the values into the lateral earth pressure equation:
P = 0.375 * 17.5 * H + 2 * 15 * √(0.375) + 17.5 * H * tan²(20°)
Simplifying the equation:
P = 6.5625H + 26.658 + 17.5H * 0.36397
P = 6.5625H + 26.658 + 6.397H
P = 12.9595H + 26.658
Determining the maximum depth of unsupported excavation:
The maximum depth of unsupported excavation occurs when the lateral earth pressure is equal to zero. Therefore, setting P = 0:
12.9595H + 26.658 = 0
Solving for H:
H = -26.658 / 12.9595
H ≈ -2.06
Since the depth cannot be negative, the maximum depth of unsupported excavation in the soil is approximately 2.06 meters.
However, this negative value indicates that the soil cannot support any excavation. Therefore, there might be an error in the given data or calculation. Please double-check the values and equations to ensure accuracy.
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Community Answer
The cohesion (c), angle of internal friction (Φ) and unit weight (γ) ...
Cohesion (c) = 15 kPa = 15 kN/m2
Angle of internal friction (Φ) = 20°
Unit weight of soil (γ) = 17.5 kN/m3
Maximum depth of unsupported excavation = 2 × critical depth =
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The cohesion (c), angle of internal friction (Φ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m3, respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is ________________.Correct answer is '4.90'. Can you explain this answer?
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The cohesion (c), angle of internal friction (Φ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m3, respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is ________________.Correct answer is '4.90'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The cohesion (c), angle of internal friction (Φ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m3, respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is ________________.Correct answer is '4.90'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The cohesion (c), angle of internal friction (Φ) and unit weight (γ) of a soil are 15 kPa, 20° and 17.5 kN/m3, respectively. The maximum depth of unsupported excavation in the soil (in m, rounded off to two decimal places) is ________________.Correct answer is '4.90'. Can you explain this answer?.
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