Question

A water tank is to be constructed on the soil deposit shown in the figure below. A circular footing of diameter 3 m and depth of embankment 1 m has been designed to support the tank. The total vertical load to be taken by the footing is 1500 kN. Assume the unit weight of water as 10$kN/m^3$ and the load dispersion pattern as 2V:1H. The expected settlement of the tank due to primary consolidation of the clay layer in _____ mm.

• A. 53.236

Answer 1

The correct option is A 53.236

Given:
${\gamma }_{sat}=18kN/m^3$

$C_c=0.3$
$e_o=0.7$
$C_v=0.004c{m}^3/s$

$\Delta H=\frac{C_c{H}_0}{1+e_0}lo{g}_{10}\left(\frac{{\overline{\sigma }}_0+\overline{\Delta \sigma }}{{\overline{\sigma }}_0}\right)$

$H_0$ = thickness of clay layer = 10 m.

${\overline{\sigma }}_0$ = effective stress before application of load at the centre of clay layer.

${\overline{\sigma }}_0$ = (15 $\times$ 2) + (18 - 10) $\times$ 6 + (18 - 10) $\times$ 5

$=118kN/m^2$

$\overline{\Delta \sigma }$ = increase in effective stress due to the structural weight at the centre of clay layer.

$\overline{\Delta \sigma }=\frac{1500}{\frac{\pi }{4}\times (3+12{)}^2}=8.488kN/m^2$

$\Rightarrow \Delta H=\frac{0.3\times 10}{1+0.7}lo{g}_{10}\left(\frac{118+8.488}{118}\right)$

= 0.053236 m

= 53.236 mm