A fully submerged infinite sandy slope has an inclination of 30^{\circ} with the horizontal. The saturated unit weight and effective angle of internal friction of sand are 18 {kN} \/ {m}^{3} and 38^{\circ}, respectively. The unit weight of water is 10 {kN} \/ {m}^{3}. 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

GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 15 of 65

Marks: +1, -0

A fully submerged infinite sandy slope has an inclination of

30^{∘}

with the horizontal. The saturated unit weight and effective angle of internal friction of sand are

18 {kN} \/ {m}^{3}

and

38^{∘}

, respectively. The unit weight of water is

10 {kN} \/ {m}^{3}

. 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

Solution:

FOS=\;{γ_{\;\text "sub "\;}}/{γ_{\;\text "sat "\;}} \;{\tan φ}/{\tan β}

FOS

=\;{(18-10)}/{18} × \;{\tan 38^{∘}}/{\tan 30^{∘}}=0.6014

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