Question

The Boussinesq’s vertical pressure σz due to line load at a point situated vertically below the line load is given by ________

(a) \(σ_z=\frac{2q’}{πz}\)

(b) \(σ_z=\frac{3q’}{πz}\)

(c) \(σ_z=\frac{2q’}{πz}\frac{1}{[1+(z)^2 ]^2} \)

(d) \(σ_z=\frac{2q’}{z}\)

The question was posed to me in a national level competition.

The question is from Stress Distribution in section Stress Distribution of Geotechnical Engineering I

Answer 1

Correct answer is (a) \(σ_z=\frac{2q’}{πz}\)

The explanation: The Boussinesq’s vertical pressure σz due to line load is given by,

\(σ_z=\frac{2q’}{πz}\frac{1}{[1+(\frac{x}{z})^2 ]^2} \) at a point situated vertically below the line load implies x=0

∴ \(σ_z=\frac{2q’}{πz}\frac{1}{[1+(\frac{0}{z})^2 ]^2} \)

∴ \(σ_z=\frac{2q’}{πz}.\)