GATE CE 2020 Set 1 — Question 33
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Geotechnical Engineering → Stability of Slopes → Factor of Safety
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Question
A fully submerged infinite sandy slope has an inclination of with the horizontal. The saturated unit weight and effective angle of internal friction of sand are and , respectively. The unit weight of water is . Assume that the seepage is parallel to the slope. Against shear failure of the slope, the factor of safety (round off to two decimal places) is _______.
Correct answer
0.59 to 0.61
Solution
Step 1: Identify given parameters. Slope angle , effective friction angle , saturated unit weight , unit weight of water .
Step 2: Calculate submerged unit weight .
Step 3: For an infinite slope with seepage parallel to the slope, the factor of safety () is given by .
Step 4: Substitute values: .
Step 5: Rounding to two decimal places, .
Step 2: Calculate submerged unit weight .
Step 3: For an infinite slope with seepage parallel to the slope, the factor of safety () is given by .
Step 4: Substitute values: .
Step 5: Rounding to two decimal places, .
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