Question

A hillslope with an angle of 40° consists of soil having an internal friction angle of 30°. The factor of safety of the hillslope is __________. (Round off to two decimal places)

Answer 1

Correct Answer: 0.65

Given:
Hillslope angle: \(\theta = 40^\circ\)
Soil internal friction angle: \(\phi = 30^\circ\) 

Step 1 — Use the simplified slope stability (infinite slope) formula:
For cohesionless soil, the factor of safety (F) is approximated by: \[ F = \frac{\tan\phi}{\tan\theta} \] 
Step 2 — Plug in the values:
\[ F = \frac{\tan 30^\circ}{\tan 40^\circ} \] \[ \tan 30^\circ \approx 0.577,\quad \tan 40^\circ \approx 0.839 \] \[ F = \frac{0.577}{0.839} \approx 0.687 \] Step 3 — Round off to two decimals:
\[ \boxed{0.69} \]