Question Bank • QB_SWCE_SM_006 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Stability of slopes

Question Statement:

An infinite dry cohesionless sand slope ($c = 0$) has an internal friction angle $\phi = 35^\circ$. If the slope inclination angle with the horizontal is $\beta = 25^\circ$, the factor of safety ($FS = \frac{\tan \phi}{\tan \beta}$) against shearing failure is ________ (round off to 2 decimal places).

Answer Key:

1.50

Step-by-Step Solution & Explanation

For an infinite slope in dry cohesionless soil: $FS = \frac{\tan \phi}{\tan \beta}$ Given: • $\phi = 35^\circ \implies \tan 35^\circ \approx 0.7002$ • $\beta = 25^\circ \implies \tan 25^\circ \approx 0.4663$ $FS = \frac{0.7002}{0.4663} \approx 1.5016 \approx 1.50$
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