Question

For the $(3\times 3)$ pile group shown in the figure, the settlement of pile group in a normally consolidated clay stratum having properties as shown in the figure, will be

• A. $13.20\text{mm}$
• B. $12.775\text{mm}$
• C. $7.345\text{mm}$
• D. None of these

Answer 1

The correct option is D None of these

$\text{Assuming equivalent raft at a distance of}\frac{L}{3}=\frac{5}{3}$
from the bottom of the pile and from that raft load is supposed to disperse at $2H:1V$

Thickness of compressible layer
$=7-5+\frac{5}{3}=3.667\text{m}$
Average stress at the centre of compressible layer,
${\overline{\sigma }}_0={\gamma }_{\text{sub}}\times 5.17$
$=(20-10)\times 5.17$
$=51.7{\text{kN/m}}^2$
Increased width of equivalent raft at a depth of $5.17\text{m}$
$=1.2+\frac{(\frac{5}{3}+2)}{2}=3.03\text{m}$
Increase in pressure due to load on pile,
$\Delta \sigma =\frac{500}{3.03\times 3.03}=54.34{\text{kN/m}}^2$
$\Delta H=\frac{C_c{H}_0}{1+e_0}log\left(\frac{{\overline{\sigma }}_0+\Delta \sigma }{{\overline{\sigma }}_0}\right)$
$=\frac{0.027\times \frac{11}{3}}{1+1.05}\text{log}\left(\frac{51.7+54.34}{51.7}\right)$
$=15.07\text{mm}$