GATE 2026 CE (CE1) – Question 56
An infinite slope with slope angle $\beta = 22°$ consists of soil with the following properties:
Unit weight $\gamma = 15.72$ kN/m$^3$
Cohesion $c' = 12$ kPa
Angle of internal friction $\phi' = 15°$
The critical height of the slope (in m) is ______ (*rounded off to two decimal places*).
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Correct answer: 6.50 to 6.56
Explanation
For an infinite slope with no seepage, the critical height is $H_c = \frac{c'}{\gamma\cos^2\beta(\tan\beta - \tan\phi')}$. With $\cos^2 22° = 0.8597$, $\tan 22° = 0.4040$ and $\tan 15° = 0.2679$, we get $H_c = \frac{12}{15.72 \times 0.8597 \times 0.1361} = 6.53$ m (the exact value is 6.525).