Question Bank • QB_SWCE_SM_003 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Shear strength

Question Statement:

A direct shear test conducted on a dry cohesionless sand specimen ($c = 0$) at failure yielded an effective normal stress $\sigma = 150\text{ kPa}$ and a shear stress $\tau = 100\text{ kPa}$. The angle of internal friction $\phi$ of the sand in degrees is ________ (round off to 1 decimal place).

Answer Key:

33.7

Step-by-Step Solution & Explanation

From the Mohr-Coulomb failure criterion for cohesionless soil ($c = 0$): $\tau = \sigma \tan \phi$ $\tan \phi = \frac{\tau}{\sigma} = \frac{100}{150} = \frac{2}{3} \approx 0.6667$ $\phi = \arctan(0.6667) \approx 33.69^\circ \approx 33.7^\circ$
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