Question

If the r/z ratio is 0.5, then the vertical pressure on a horizontal plane is given by _________

(a) \(σ_z=\frac{0.56Q}{z^3} \)

(b) \(σ_z=\frac{0.4775Q}{z^3} \)

(c) \(σ_z=\frac{0.2733Q}{z^2} \)

(d) \(σ_z=\frac{0.4775Q}{z^2} \)

I got this question in quiz.

I'd like to ask this question from Stress Distribution topic in section Stress Distribution of Geotechnical Engineering I

Answer 1

Correct option is (c) \(σ_z=\frac{0.2733Q}{z^2} \)

The explanation: Boussinesq’s vertical stress σz is given by,

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

Substituting r/z=0.5,

We get,

\(σ_z=\frac{0.2733Q}{z^2}. \)