Question

The Boussinesq’s vertical pressure σz due to line load is given by ________

(a) \(σ_z=\frac{5q’}{πz}\frac{1}{[1+\frac{x}{z}^2 ]^2} \)

(b) \(σ_z=\frac{3q’}{πz}\frac{1}{[1+(\frac{x}{z})^2 ]^2} \)

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

(d) \(σ_z=\frac{2q’}{z}\frac{1}{[1+⌊\frac{x}{z}⌋^2 ]^2} \)

I have been asked this question in exam.

This interesting question is from Stress Distribution in portion Stress Distribution of Geotechnical Engineering I

Answer 1

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

The best I can explain: The Boussinesq’s vertical pressure σz due to line load is given by,

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

Where q’=line load intensity per unit length

X=horizontal distance from line load

Z= depth of point.