Question

If an infinite slope of clay at a depth 5 m has cohesion of 10 kPa and unit weight of 20 kN/m\(^3\), then the stability number corresponding to a critical condition will be ............

• A. 0.02
• B. 0.20
• C. 0.01
• D. 0.10

Hint:

Stability number helps in evaluating slope safety. Lower values indicate higher safety, while critical conditions often relate to specific \( N_s \) limits.

Answer 1

The Correct Option is D

The stability number (N\(_s\)) is a dimensionless number used in slope stability analysis, defined for an infinite slope with cohesive soil as: \[ N_s = \frac{c}{\gamma H} \] where:
- \( c \) = cohesion of the soil = 10 kPa
- \( \gamma \) = unit weight of the soil = 20 kN/m\(^3\)
- \( H \) = depth of the slope = 5 m
Substituting the values into the formula: \[ N_s = \frac{10}{20 \times 5} = \frac{10}{100} = 0.10 \] Therefore, the stability number for the critical condition is \( \boxed{0.10} \).