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An infinitely long slope is made up of a c-φ soil having the properties: cohesion, C = 20 kPa, and dry unit weight, γd = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is ________
- a)22.4°
- b)20.8°
- c)19.4°
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
An infinitely long slope is made up of a c-φ soil having the prope...
Stability analysis of an infinite slope of cohesive soils
Shear strength of cohesive soils is given by,
S = C + (γd H Cos2 i) tan ϕ
Shear stress of cohesive soil is given by,
τ = γd H cos i sin i
As the normal stress σ depends upon the height H of the slope, an expression for the height can be found by equating the shear stress and shear strength
C + (γd H Cos2 i) tan ϕ = γ H cos i sin i
This the height at which the slope is just stable and is known as critical height (HC)
Calculation:
Given,
C = 20 kPa, γd = 16 kN/m3
i = 40°, H = 5 m
tan ϕ = 0.413
ϕ = 22.44°
Shear strength of cohesive soils is given by,
S = C + (γd H Cos2 i) tan ϕ
Shear stress of cohesive soil is given by,
τ = γd H cos i sin i
As the normal stress σ depends upon the height H of the slope, an expression for the height can be found by equating the shear stress and shear strength
C + (γd H Cos2 i) tan ϕ = γ H cos i sin i
This the height at which the slope is just stable and is known as critical height (HC)
Calculation:
Given,
C = 20 kPa, γd = 16 kN/m3
i = 40°, H = 5 m
tan ϕ = 0.413
ϕ = 22.44°
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Community Answer
An infinitely long slope is made up of a c-φ soil having the prope...
Calculating the angle of internal friction:
- Given data:
- Cohesion, C = 20 kPa
- Dry unit weight, γd = 16 kN/m3
- Angle of inclination, θ = 40°
- Critical height, H = 5 m
- The factor of safety (F) for a slope is given by:
F = c / (H * γd * tan(φ))
- At limiting equilibrium, F = 1, so:
1 = 20 / (5 * 16 * tan(φ))
- Solving for φ, we get:
tan(φ) = 20 / (5 * 16) = 0.25
- Therefore, the angle of internal friction (φ) can be calculated as:
φ = tan-1(0.25) ≈ 14.04°
Conclusion:
The angle of internal friction of the soil to maintain the limiting equilibrium is approximately 14.04°, which is closest to option 'A' (22.4°).
- Given data:
- Cohesion, C = 20 kPa
- Dry unit weight, γd = 16 kN/m3
- Angle of inclination, θ = 40°
- Critical height, H = 5 m
- The factor of safety (F) for a slope is given by:
F = c / (H * γd * tan(φ))
- At limiting equilibrium, F = 1, so:
1 = 20 / (5 * 16 * tan(φ))
- Solving for φ, we get:
tan(φ) = 20 / (5 * 16) = 0.25
- Therefore, the angle of internal friction (φ) can be calculated as:
φ = tan-1(0.25) ≈ 14.04°
Conclusion:
The angle of internal friction of the soil to maintain the limiting equilibrium is approximately 14.04°, which is closest to option 'A' (22.4°).
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An infinitely long slope is made up of a c-φ soil having the properties: cohesion, C = 20 kPa, and dry unit weight, γd = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is ________a)22.4°b)20.8°c)19.4°d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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An infinitely long slope is made up of a c-φ soil having the properties: cohesion, C = 20 kPa, and dry unit weight, γd = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is ________a)22.4°b)20.8°c)19.4°d)None of the aboveCorrect answer is option 'A'. 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 An infinitely long slope is made up of a c-φ soil having the properties: cohesion, C = 20 kPa, and dry unit weight, γd = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is ________a)22.4°b)20.8°c)19.4°d)None of the aboveCorrect answer is option 'A'. 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 An infinitely long slope is made up of a c-φ soil having the properties: cohesion, C = 20 kPa, and dry unit weight, γd = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is ________a)22.4°b)20.8°c)19.4°d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
An infinitely long slope is made up of a c-φ soil having the properties: cohesion, C = 20 kPa, and dry unit weight, γd = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is ________a)22.4°b)20.8°c)19.4°d)None of the aboveCorrect answer is option 'A'. 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 An infinitely long slope is made up of a c-φ soil having the properties: cohesion, C = 20 kPa, and dry unit weight, γd = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is ________a)22.4°b)20.8°c)19.4°d)None of the aboveCorrect answer is option 'A'. 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 An infinitely long slope is made up of a c-φ soil having the properties: cohesion, C = 20 kPa, and dry unit weight, γd = 16 kN/m3. The angle of inclination and critical height of the slope are 40° and 5 m, respectively. To maintain the limiting equilibrium, the angle of internal friction of the soil (in degrees) is ________a)22.4°b)20.8°c)19.4°d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
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