According Boussinesq’s theory, the vertical stress at a point in a semi-infinite soil mass depends upon
- APoint load, coordinates of the point and modulus of elasticity of soil
- BPoint load, coordinates of the point, modulus of elasticity of soil and its Poisson’s ratio
- CPoint load and coordinates of the pointCorrect
- DPoint load, coordinates of the point, modulus of elasticity of soil and its density
Solution
Concept
Boussinesq stress formula
Formula
σz = (3P / 2π z²) · [1 + (r/z)²]−5/2
Step-by-step solution
1. The expression for σz contains only P and the coordinates (r, z). 2. The elastic constants E and ν do not appear in the vertical stress expression.
Explanation
Boussinesq's vertical stress due to a point load does not depend on E or Poisson's ratio. It depends only on the load and the position of the point.
Shortcut
σz = P × influence factor (depends on r/z only).
Common mistake
Including E or ν.
Correct answer: C) Point load and coordinates of the point