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Question

For the construction of a highway a cut is to be made as shown in the figure.
The soil exhibits c' = 20kPa, ϕ=18, and the undrained shear strength = 80 kPa. The unit weight of water is 9.81 kN/m3. The unit weights of the soil above and below the ground water table are 18 and 20kN/m3, respectively. If the shear stress at a point A is 50 kPa, the factors of safety against the shear failure at this point, considering the undrained and drained conditions respectively, would be

A
1.6 and 0.9
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B
0.9 and 1.6
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C
0.6 and 1.2
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D
1.2 and 0.6
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Solution

The correct option is A 1.6 and 0.9
Case-I : Undrained condition

F.O.S=resistingshearstrengthActingshearstress

=8050=1.6

Case-II: Drained condition

F.o.S=¯¯¯σ tanϕ+cActingshearstress

=[2×18+4(209.81)]×tan18+2050

= 0.9

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