GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 59 of 65

Marks: +1, -0

A granular soil has a saturated unit weight of

20 {kN} {/} {m}^{3}

and an effective angle of shearing resistance of

30^{∘}

. The unit weight of water is

9.81 {kN}{/}{m}^{3}

. A slope is to be made on this soil deposit in which the seepage occurs parallel to the slope up to the free surface. Under this seepage condition for a factor of safety of

1.5

, the safe slope angle (in degree, round off to 1 decimal place) would be

Your Answer:

Validate

Solution:

γ_{\;\text "sat "\;}=20 {KN} {/} {m}^{2}

φ=30^{∘}

γ_{ {w}}=9.81 {KN}{/} {m}^{2}

{FOS}=1.5

We know that

FOS=\;{γ_{ {\sub}}}/{γ_{sat}} × \;{\tan φ}/{\tan {i}}

[i = safe slope angle]

1.5=\;{20-9.81}/{20} × \;{\tan 30}/{\tan {i}}

⇒ {i}=11.0953

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