What is the maximum depth to which a trench of vertical sides can be excavated in a clay stratum with c = 50 kN/m², γ = 16 kN/m³, β = 90°, φ = 0°, Fc = 1 and N = 0·261?
- A12 mCorrect
- B14 m
- C16 m
- D18 m
Solution
Concept
Taylor stability number for a vertical cut in clay
Formula
H = c / (N γ Fc)
Step-by-step solution
1. Stability number N = c / (γ H Fc) = 0.261. 2. H = c / (N γ Fc) = 50 / (0.261 × 16 × 1) = 11.97 m ≈ 12 m.
Explanation
For a vertical cut in φ = 0 soil, Taylor's stability number is 0.261. Setting the factor of safety to 1 gives the maximum unsupported depth.
Why the other options are wrong
14, 16 and 18 m would require smaller values of N.
Shortcut
H = c/(0.261 γ).
Common mistake
Using Hc = 4c/γ (= 12.5 m, a different method).
Correct answer: A) 12 m