GATE 2024 CE (CE1) – Question 54
An infinite slope is made up of cohesionless soil with seepage parallel to and up to the sloping surface. The angle of slope is 30° with respect to horizontal ground surface. The unit weights of the saturated soil and water are 20 kN/m$^3$ and 10 kN/m$^3$, respectively.
The minimum angle of shearing resistance of the soil (in degrees) for the critically stable condition of the slope is _____________ (rounded off to the nearest integer).
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Correct answer: 49
Explanation
For a cohesionless infinite slope with seepage parallel to the surface, the factor of safety is $F = \frac{\gamma'}{\gamma_{sat}}\cdot\frac{\tan\phi}{\tan\beta}$ with $\gamma' = 20 - 10 = 10$ kN/m³. For critical stability $F = 1$, so $\tan\phi = \frac{\gamma_{sat}}{\gamma'}\tan\beta = 2\tan 30° = 1.1547$ and $\phi = 49.1° \approx 49°$.