Question

The soil profile at a site up to a depth of 10 m is shown in the figure ( not drawn to the scale ). The soil is preloaded with a uniform surcharge (q) of 70 kN/$m^2$ at the ground level. The water table is at a depth of 3 m below ground level. The soil unit weight of the respective layers is shown in the figure. Consider unit weight of water as 9.81 kN/$m^3$ and assume that the surcharge (q) is applied instantaneously.

Immediately after preloading, the effective stresses (in kPa) at points P and Q, respectively are

• A. 36 and 90
• B. 36 and 126
• C. 124 and 204
• D. 54 and 95

Answer 1

The correct option is D 54 and 95

Effective stress at point 'P'

$\overline{{\sigma }_P}=3\times 18=54kPa$

Effective stress at point 'Q'

${\overline{\sigma }}_Q=18\times 3+4\times 20-4\times 9.81$

= 94.76 kPa

Immediately after load application, effective stress does not change because load does not get transferred to the soil grains.

Here effective stress immediately after load application will remain the same as that before the load application

Hence, $\overline{\sigma }{}_p=54kPa$

$\overline{\sigma }{}_Q=94.76kPa=95kPa$