Question

If the r/z ratio is unity, then the vertical pressure on a horizontal plane is given by _________

(a) \(σ_z=\frac{0.56Q}{z^3} \)

(b) \(σ_z=\frac{0.0844Q}{z^2} \)

(c) \(σ_z=\frac{0.2733Q}{z^2} \)

(d) \(σ_z=\frac{0.4775Q}{z^2} \)

I had been asked this question in an interview for internship.

I would like to ask this question from Stress Distribution in section Stress Distribution of Geotechnical Engineering I

Answer 1

The correct answer is (b) \(σ_z=\frac{0.0844Q}{z^2} \)

For explanation I would say: Boussinesq’s vertical stress σz is given by,

\(σ_z=\frac{3Q}{2πz^2} \left[\frac{1}{1+(\frac{r}{z})^2}\right]^{\frac{5}{2}} \)

Substituting \(\frac{r}{z}=1,\)

We get,

\(σ_z=\frac{0.0844Q}{z^2}. \)