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A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2, φ = 22.50 and ρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..m
- a)8.45 m
- b)7.25 m
- c)3.47 m
- d)2.36 m
Correct answer is option 'B'. Can you explain this answer?
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A slope is to be constructed at an angle of 300 with the horizontal. T...
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A slope is to be constructed at an angle of 300 with the horizontal. T...
Φ = 20°, γ = 18 kN/m3
To determine the stability of the slope, we can use the method of slices. The slope can be divided into several slices, each having a width of 1 meter and a height equal to the slope angle. The weight of each slice can be calculated by multiplying its volume (width x height x depth) by the unit weight of the soil (γ).
The critical slip surface of each slice can be assumed to be a straight line passing through its base and making an angle of 300 + φ/2 with the horizontal. The driving force acting on the slice is the weight of the slice and the resisting force is the shear strength of the soil acting along the critical slip surface.
The shear strength of the soil can be calculated using the Mohr-Coulomb theory as:
τ = c' + σ' tan φ
where τ is the shear strength, c' is the effective cohesion (taking into account the factor of safety), σ' is the effective normal stress (equal to the weight of the slice divided by the base area), and φ is the angle of internal friction.
Assuming a trial slip surface for each slice, we can calculate the factor of safety (FS) as:
FS = (resisting force / driving force) = (sum of τ x base length / sum of γ x base length)
If the calculated factor of safety is less than 1.5, we need to adjust the trial slip surface and recalculate the factor of safety until a satisfactory value is obtained.
The stability analysis can be summarized as follows:
Slice 1 (from top to bottom):
- Volume = 1 x 1 x 0.5 = 0.5 m3
- Weight = 0.5 x 18 = 9 kN
- Base area = 1 x tan 300 = 0.577 m2
- Effective normal stress = 9 / 0.577 = 15.6 kN/m2
- Effective cohesion = 10 / 1.5 = 6.67 kN/m2
- Shear strength = 6.67 + 15.6 x tan 20 = 10.9 kN/m2
- Trial slip surface = straight line passing through base at 300 + 10° = 310°
- Resisting force = 10.9 x 1 = 10.9 kN
- Driving force = 9 kN
- Factor of safety = 10.9 / 9 = 1.21 (less than 1.5)
Slice 2:
- Volume = 1 x 1 x 0.5 = 0.5 m3
- Weight = 0.5 x 18 = 9 kN
- Base area = 1 x tan 310 = 0.541 m2
- Effective normal stress = 9 / 0.541 = 16.6 kN/m2
- Effective cohesion = 10 / 1.5 = 6.67 kN/m2
- Shear strength = 6.67 + 16.6 x tan 20 = 11.0 kN/m2
- Trial slip surface = straight line passing through base at 310 + 10° = 320°
- Resisting force = 11.0 x 1
To determine the stability of the slope, we can use the method of slices. The slope can be divided into several slices, each having a width of 1 meter and a height equal to the slope angle. The weight of each slice can be calculated by multiplying its volume (width x height x depth) by the unit weight of the soil (γ).
The critical slip surface of each slice can be assumed to be a straight line passing through its base and making an angle of 300 + φ/2 with the horizontal. The driving force acting on the slice is the weight of the slice and the resisting force is the shear strength of the soil acting along the critical slip surface.
The shear strength of the soil can be calculated using the Mohr-Coulomb theory as:
τ = c' + σ' tan φ
where τ is the shear strength, c' is the effective cohesion (taking into account the factor of safety), σ' is the effective normal stress (equal to the weight of the slice divided by the base area), and φ is the angle of internal friction.
Assuming a trial slip surface for each slice, we can calculate the factor of safety (FS) as:
FS = (resisting force / driving force) = (sum of τ x base length / sum of γ x base length)
If the calculated factor of safety is less than 1.5, we need to adjust the trial slip surface and recalculate the factor of safety until a satisfactory value is obtained.
The stability analysis can be summarized as follows:
Slice 1 (from top to bottom):
- Volume = 1 x 1 x 0.5 = 0.5 m3
- Weight = 0.5 x 18 = 9 kN
- Base area = 1 x tan 300 = 0.577 m2
- Effective normal stress = 9 / 0.577 = 15.6 kN/m2
- Effective cohesion = 10 / 1.5 = 6.67 kN/m2
- Shear strength = 6.67 + 15.6 x tan 20 = 10.9 kN/m2
- Trial slip surface = straight line passing through base at 300 + 10° = 310°
- Resisting force = 10.9 x 1 = 10.9 kN
- Driving force = 9 kN
- Factor of safety = 10.9 / 9 = 1.21 (less than 1.5)
Slice 2:
- Volume = 1 x 1 x 0.5 = 0.5 m3
- Weight = 0.5 x 18 = 9 kN
- Base area = 1 x tan 310 = 0.541 m2
- Effective normal stress = 9 / 0.541 = 16.6 kN/m2
- Effective cohesion = 10 / 1.5 = 6.67 kN/m2
- Shear strength = 6.67 + 16.6 x tan 20 = 11.0 kN/m2
- Trial slip surface = straight line passing through base at 310 + 10° = 320°
- Resisting force = 11.0 x 1
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A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. Can you explain this answer?
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A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. 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 A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. 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 A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. Can you explain this answer?.
A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. 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 A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. 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 A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. Can you explain this answer?.
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A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A slope is to be constructed at an angle of 300 with the horizontal. The required factor of safety with respect to both cohesion and angle of internal friction is 1.5 and the soil has following properties.C = 10 kN/m2,φ = 22.50 andρ = 20 kN/m3 ,Taylor’s stability numbers for mobilized friction angles of 22.50 and 150 are 0.016 and 0.046 respectively. Safe height of slope is…………..ma)8.45 mb)7.25 mc)3.47 md)2.36 mCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
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