Question

${\sigma }_z$ is the vertical stress at a depth equal to Z in the soil mass due to a surface point load Q. The vertical stress at depth equal to 2Z will be

• A. $0.25{\sigma }_z$
• B. $0.50{\sigma }_z$
• C. $1.0{\sigma }_z$
• D. $2.0{\sigma }_z$

Answer 1

The correct option is A $0.25{\sigma }_z$

Under the point load, the vertical stress is given by
${\sigma }_z=\frac{0.4775Q}{z^2}$
(From Boussinesq's equation at r/z =0)
$\therefore {\sigma }_{2z}=\frac{0.4775Q}{4z^2}=0.25{\sigma }_z$
The depth at which ${\sigma }_z=0.1$ per unit area is $z=\sqrt{4.775}=2.185units$ under the load.
Thus isobar extends up to 2.185 units of depth under the load to dissipate 90% of stresses.