In an in-situ vane test on a saturated clay, a torque of 35 Nm is required to shear the soil. The vane is 50 mm wide by 100 mm long. What is the undrained strength of the clay ?
- A56 kN/m²
- B76 kN/m²Correct
- C150 kN/m²
- D50 kN/m²
Solution
Concept
Undrained shear strength from the vane test
Formula
T = π cu (D² H / 2 + D³ / 6)
Step-by-step solution
1. D = 0.05 m, H = 0.10 m. 2. D²H/2 + D³/6 = 0.000125 + 0.0000208 = 1.458 × 10⁻⁴ m³. 3. cu = T / [π × 1.458×10⁻⁴] = 35 / 4.58×10⁻⁴ = 76 400 N/m² ≈ 76 kN/m².
Explanation
The torque resists shear on the cylindrical surface and on the top and bottom discs of the sheared cylinder. The vane test gives the undrained strength of soft clays.
Why the other options are wrong
Only 76 kN/m² satisfies T = π cu (D²H/2 + D³/6) for T = 35 N·m. The other values give a different torque.
Shortcut
cu = 2T / [π D² (H + D/3)].
Common mistake
Ignoring the end discs of the vane (using only the cylindrical surface gives about 89 kN/m²).
Correct answer: B) 76 kN/m²