GATE CE 2025 Set 2 — Question 55
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Geotechnical Engineering → Stability of Slopes → Factor of Safety
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Question
The bank of a canal has the profile shown in the figure. The material is a homogeneous clay with a bulk unit weight of kN/m, undrained cohesion of kPa and it is fully saturated (). For the trial slip circle shown, the area ABCDEA is m and the centroid is at P. A tension crack (DE) of m deep was also observed. Assume unit weight of water is kN/m and consider m run of the bank for the analysis.Considering the canal is empty and tension crack is completely filled with water, the factor of safety against slope failure of the bank is ______ (round off to two decimal places).
Correct answer
1 to 1.1
Solution
Given:
Bulk unit weight, kN/m
Undrained cohesion, kPa
Area, m
Radius of slip circle, m
Angle of arc,
Centroid distance from vertical through O, m
Tension crack depth, m
Unit weight of water, kN/m
Lever arm (approximate based on geometry)Total Driving Moment,
Bulk unit weight, kN/m
Undrained cohesion, kPa
Area, m
Radius of slip circle, m
Angle of arc,
Centroid distance from vertical through O, m
Tension crack depth, m
Unit weight of water, kN/m
1.Resisting Moment ():
2.Driving Moment ():
Driving moment due to weight of soil ():Driving moment due to water pressure in tension crack ():From the figure, the vertical distance from O to the top of the bank is m. The water pressure acts at from the bottom of the crack.Lever arm (approximate based on geometry)Total Driving Moment,
3.Factor of Safety (FOS):
Rounding off to two decimal places, .Continue learning with Success Tracker
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