GATE 2019 CE (CE1) – Question 63
A granular soil has saturated unit weight 20 kN/m³ and effective friction angle 30°. Water unit weight is 9.81 kN/m³. Seepage occurs parallel to an infinite slope up to its free surface. For safety factor 1.5, find safe slope angle (degrees), to one decimal place.
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Correct answer: 10.8 to 11.3
Explanation
For cohesionless infinite slope with parallel seepage, $F=(\gamma^\prime/\gamma_{\rm sat})\tan\phi/\tan\beta$. Hence $$\tan\beta=\frac{20-9.81}{20}\frac{\tan30^\circ}{1.5}=0.196105.$$ Thus **β = 11.1°**. Submerged weight controls friction, while total saturated weight drives sliding.