Question

An embankment has a slope of 30° which was constructed with soil having C = 30 kN/m², ϕ = 20° and γ = 15 kN/m³. The height of the embankment is 20 m. Using Taylor’s stability no 1/40, the factor of safety with respect to cohesion is
1. 0.25
2. 2
3. 4
4. 1.5

Answer 1

Correct Answer - Option 3 : 4

Concept:

Taylor Stability Number (S_n) = \(\frac{c}{{{F} × γ × H}}\)

Where C = cohesion, F = Factor of safety, γ = unit weight of soil, H = height of embankment

Calculation:

Given:

S_n = 1/40

c = 30 KN/m²

γ = 15 KN/m²

H = 20 m

Sn = \(\frac{c}{{{F} × γ × H}}\)

\(\frac{{30}}{{F × 15 × 20}} = \frac{1}{{40}}\)

F = \(\frac{40\ \times \ 30}{15\ \times \ 20}\)

F = 4

Then, Factor of safety with respect to cohesion = 4.