Question

The vertical stress is proportional to __________

(a) \(\frac{z^2}{K_B} \)

(b) \(\frac{K_B}{z^2} \)

(c) \(\frac{K_B}{z^3} \)

(d) \(\frac{z^3}{K_B} \)

I got this question in quiz.

This is a very interesting question from Stress Distribution topic in section Stress Distribution of Geotechnical Engineering I

Answer 1

Correct choice is (b) \(\frac{K_B}{z^2} \)

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

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

Representing \(K_B \,as\, \frac{3}{2π} \left[\frac{1}{1+(\frac{r}{z})^2}\right]^{\frac{5}{2}} \)

∴ we get,

\(σ_z=K_B  \frac{Q}{z^2}, \)

∴ \(σ_z∝\frac{K_B}{z^2} \).