A long braced excavation in soft clay is 4 m wide and 8 m deep. The saturated unit weight of the clay is 20 kN/m³ and the undrained shear strength adjacent to the bottom of the excavation is given by cu = 40 kN/m² (φu = 0). What is the factor of safety against base failure of the excavation ? (Take Nc = 7·1)
- A1·5
- B3·25
- C1·25
- D1·8Correct
Solution
Concept
Stability against base heave (Bjerrum and Eide / Terzaghi)
Formula
FS = cu Nc / (γ H)
Step-by-step solution
1. FS = 40 × 7.1 / (20 × 8) = 284 / 160 = 1.775 ≈ 1.8.
Explanation
Base failure (heave) in soft clay occurs when the weight of soil adjacent to the excavation exceeds the bearing capacity of the clay at the base. The factor of safety compares cu Nc with the overburden pressure γH.
Why the other options are wrong
1.5, 1.25 and 3.25 do not equal cu Nc / γH = 1.775.
Shortcut
FS = cu Nc / (γ H).
Common mistake
Using the width of the cut in the formula.
Correct answer: D) 1·8