Question

If the r/z ratio is 2, then the vertical pressure on a horizontal plane is given by _________

(a) \(σ_z=\frac{0.0085Q}{z^2} \)

(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 have been asked this question in my homework.

The doubt is from Stress Distribution topic in chapter Stress Distribution of Geotechnical Engineering I

Answer 1

The correct option is (a) \(σ_z=\frac{0.0085Q}{z^2} \)

Explanation: 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 \(\frac{r}{z}=2,\)

We get,

\(σ_z=\frac{0.0085Q}{z^2}. \)