Question

A uniformly distributed line load of 500kN/m is acting on the ground surface. Based on Boussinesq's theory, the ratio of vertical stress at a depth 2 m to that at 4 m right below the line of loading is

• A. 0.25
• B. 0.5
• C. 2.0
• D. 4.0

Answer 1

The correct option is C 2.0

Due to uniformly distributed line load vertical stress

$=\frac{2q}{\pi z}{\left[\frac{1}{1+{\left(\frac{x}{z}\right)}^2}\right]}^2$

Vertically below line load x = 0

${\sigma }_z=\frac{2q}{\pi z}$

$\frac{{\sigma }_1}{{\sigma }_2}=\frac{z_2}{z_1}$

$=\frac{4}{2}=2$