Question

The vertical pressure distribution on any horizontal plane at a depth z below the ground due to concentrated load is ___________

(a) \(σ_z=K_B  \frac{Q}{z} \)

(b) \(σ_z=K_B  \frac{Q}{z^2} \)

(c) \(σ_z=K_B  \frac{z}{Q} \)

(d) \(σ_z=K_B  \frac{Q}{z^3} \)

The question was asked in an international level competition.

My enquiry is from Stress Distribution topic in portion Stress Distribution of Geotechnical Engineering I

Answer 1

Right answer is (b) \(σ_z=K_B  \frac{Q}{z^2} \)

Easiest 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,

\(σ_z=K_B  \frac{Q}{z^2}. \)