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A long slope is formed in a soil with shear strength parameters: c' = 0 and φ' = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would be
- a)45.3
- b)44.7
- c)12.3
- d)11.3
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A long slope is formed in a soil with shear strength parameters: c = 0...
Φ = 30°. The slope height is 10 meters and the slope angle is 45°. Determine the factor of safety against slope failure using the method of slices.
Solution:
The first step is to divide the slope into several slices. For this example, we will divide the slope into 10 equal slices. The width of each slice is calculated using the slope angle and height as follows:
Slice width = slope height / 10 = 10 m / 10 = 1 m
The next step is to calculate the weight of soil in each slice. The weight of soil is equal to the volume of soil in the slice multiplied by the unit weight of soil. The volume of soil in each slice can be calculated using the slice width, slope angle, and slice height as follows:
Slice volume = (1/2) x slice width x slice height x cos(slope angle)
Slice volume = (1/2) x 1 m x 10 m x cos(45°) = 3.54 m^3
Assuming a unit weight of soil of 20 kN/m^3, the weight of soil in each slice can be calculated as follows:
Slice weight = Slice volume x unit weight of soil
Slice weight = 3.54 m^3 x 20 kN/m^3 = 70.8 kN
The shear force acting on each slice can be calculated as the weight of soil above the slice multiplied by the sine of the slope angle. For the first slice, the shear force can be calculated as follows:
Shear force = weight of soil above slice x sin(slope angle)
Shear force = (9 slices x 70.8 kN) x sin(45°) = 449.5 kN
The next step is to calculate the resisting force acting on each slice. The resisting force is equal to the product of the shear strength of soil and the perimeter of the slice. For this example, the soil has a cohesion of 0 and an angle of internal friction of 30°. The perimeter of each slice can be calculated using the slice width and the slice height as follows:
Perimeter of slice = 2 x (slice width + slice height / sin(slope angle))
Perimeter of slice = 2 x (1 m + 10 m / sin(45°)) = 26.3 m
The resisting force acting on the first slice can be calculated as follows:
Resisting force = shear strength x perimeter of slice
Resisting force = (0 + tan(30°)) x 26.3 m = 15.2 kN
The factor of safety against slope failure can be calculated as the sum of resisting forces divided by the sum of shear forces. For this example, the factor of safety can be calculated as follows:
Factor of safety = sum of resisting forces / sum of shear forces
Factor of safety = (10 slices x 15.2 kN) / 449.5 kN = 0.32
Therefore, the factor of safety against slope failure is 0.32, which indicates that the slope is unstable and likely to fail.
Solution:
The first step is to divide the slope into several slices. For this example, we will divide the slope into 10 equal slices. The width of each slice is calculated using the slope angle and height as follows:
Slice width = slope height / 10 = 10 m / 10 = 1 m
The next step is to calculate the weight of soil in each slice. The weight of soil is equal to the volume of soil in the slice multiplied by the unit weight of soil. The volume of soil in each slice can be calculated using the slice width, slope angle, and slice height as follows:
Slice volume = (1/2) x slice width x slice height x cos(slope angle)
Slice volume = (1/2) x 1 m x 10 m x cos(45°) = 3.54 m^3
Assuming a unit weight of soil of 20 kN/m^3, the weight of soil in each slice can be calculated as follows:
Slice weight = Slice volume x unit weight of soil
Slice weight = 3.54 m^3 x 20 kN/m^3 = 70.8 kN
The shear force acting on each slice can be calculated as the weight of soil above the slice multiplied by the sine of the slope angle. For the first slice, the shear force can be calculated as follows:
Shear force = weight of soil above slice x sin(slope angle)
Shear force = (9 slices x 70.8 kN) x sin(45°) = 449.5 kN
The next step is to calculate the resisting force acting on each slice. The resisting force is equal to the product of the shear strength of soil and the perimeter of the slice. For this example, the soil has a cohesion of 0 and an angle of internal friction of 30°. The perimeter of each slice can be calculated using the slice width and the slice height as follows:
Perimeter of slice = 2 x (slice width + slice height / sin(slope angle))
Perimeter of slice = 2 x (1 m + 10 m / sin(45°)) = 26.3 m
The resisting force acting on the first slice can be calculated as follows:
Resisting force = shear strength x perimeter of slice
Resisting force = (0 + tan(30°)) x 26.3 m = 15.2 kN
The factor of safety against slope failure can be calculated as the sum of resisting forces divided by the sum of shear forces. For this example, the factor of safety can be calculated as follows:
Factor of safety = sum of resisting forces / sum of shear forces
Factor of safety = (10 slices x 15.2 kN) / 449.5 kN = 0.32
Therefore, the factor of safety against slope failure is 0.32, which indicates that the slope is unstable and likely to fail.
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A long slope is formed in a soil with shear strength parameters: c = 0 and φ = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would bea)45.3b)44.7c)12.3d)11.3Correct answer is option 'D'. Can you explain this answer?
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A long slope is formed in a soil with shear strength parameters: c = 0 and φ = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would bea)45.3b)44.7c)12.3d)11.3Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A long slope is formed in a soil with shear strength parameters: c = 0 and φ = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would bea)45.3b)44.7c)12.3d)11.3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long slope is formed in a soil with shear strength parameters: c = 0 and φ = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would bea)45.3b)44.7c)12.3d)11.3Correct answer is option 'D'. Can you explain this answer?.
A long slope is formed in a soil with shear strength parameters: c = 0 and φ = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would bea)45.3b)44.7c)12.3d)11.3Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A long slope is formed in a soil with shear strength parameters: c = 0 and φ = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would bea)45.3b)44.7c)12.3d)11.3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A long slope is formed in a soil with shear strength parameters: c = 0 and φ = 34°. A firm stratum lies below the slope and it is assumed that the water table may occasionally rise to the surface, with seepage taking place parallel to the slope. Use γsat = 18 kN/m3 and γw = 10 kN/m3. The maximum slope angle (in degrees) to ensure a factor of safety of 1.5, assuming a potential failure surface parallel to the slope, would bea)45.3b)44.7c)12.3d)11.3Correct answer is option 'D'. Can you explain this answer?.
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