Question

A cohesionless soil having an angle of shearing resistance of \( \phi \) is standing at a slope of angle \( i \). The factor of safety of the slope is

• A. \( \frac{\tan i}{\tan \phi} \)
• B. \( \frac{\tan \phi}{\tan i} \)
• C. \( \tan \phi - \tan i \)
• D. \( \tan i - \tan \phi \)

Hint:

For cohesionless soils, the factor of safety depends on the slope angle and the internal friction angle. Always use the ratio \( \frac{\tan \phi}{\tan i} \) to calculate FS.

Answer 1

The Correct Option is B

The factor of safety (FS) for a slope with cohesionless soil is given by the ratio of the shear resistance to the shear stress. Using the formula for factor of safety in cohesionless soils, we get: \[ FS = \frac{\tan \phi}{\tan i} \] where \( \phi \) is the angle of internal friction and \( i \) is the slope angle. Hence, the correct answer is option (2).