Question

A concentrated load of 500kN is applied on an elastic half space. The ratio of the increase in vertical normal stress at depth of 2m and 4m along the point of the loading, as per Boussinesq's theory, would be .

• A. 4

Answer 1

The correct option is A 4
Boussinesq's theory = $\frac{3Q}{2\pi z^2}{\left(\frac{1}{1+{\left(\frac{r}{z}\right)}^2}\right)}^{5/2}$

r = 0

$Q_1=\frac{3Q}{2\pi z^2}$

$Q_1\alpha \frac{1}{z^2}$

$\frac{Q_1}{Q_2}={\left(\frac{4}{2}\right)}^2=4$