For a shallow foundation resting on a sand layer having effective friction angle of 30°, the sides of the triangular zone immediately under the footing makes what angle with the base of the foundation as per Terzaghi’s bearing capacity theory?
- A30°Correct
- B60°
- C45°
- DNone of these
Solution
Concept
Terzaghi's Bearing Capacity Theory
Formula
α = ϕ
Step-by-step solution
1. Identify the given effective friction angle: ϕ = 30° 2. Apply Terzaghi's formula for the angle with the base: α = ϕ 3. Substitute the given value: α = 30°
Explanation
According to Terzaghi's bearing capacity theory, the triangular elastic zone formed directly underneath the footing has sides that make an angle equal to the soil's internal friction angle (ϕ) with the base of the foundation. Since the soil's friction angle is given as 30°, the angle made by the sides of this triangular zone with the base is also 30°.
Shortcut
For Terzaghi's bearing capacity theory, remember: Base Angle = Friction Angle (α = ϕ). The angle made with the base directly equals the soil's friction angle, so if ϕ = 30°, the angle is 30°.
Common mistake
Many students confuse Terzaghi's assumption (where the base angle equals ϕ = 30°) with the passive wedge angle or general failure wedge formula (45° + ϕ/2 = 60°) and incorrectly select Option B (60°).
Correct answer: A) 30°