Question $7$:

$($Value: $24$ marks$)$

Bored cast$-$in$-$place concrete piles of $300$ mm diameter are proposed to be designed as a pile group to carry a load of $1800$ kN in a $12$ m deep soil deposit of clay having the following properties:

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$begin$\{$tabular$\}\{$c$\}$

Depth $\backslash \backslash$

$\backslash ((\backslash$mathrm$\{$m$\})\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Unit weight of soil $\backslash \backslash$

$\backslash (\backslash$left$(\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash$right$)\backslash )$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$c$\}$

Undrained shear strength $\backslash \backslash$

$\backslash (\backslash$left$(\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash$right$)\backslash )$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $0$ & $18$ & $34\backslash \backslash$

$\backslash$hline $2$ & $18\mathrm{.}5$ & $44\backslash \backslash$

$\backslash$hline $4$ & $19$ & $55\backslash \backslash$

$\backslash$hline $6$ & $19\mathrm{.}5$ & $66\backslash \backslash$

$\backslash$hline $8$ & $20$ & $80\backslash \backslash$

$\backslash$hline $10$ & $20$ & $90\backslash \backslash$

$\backslash$hline $12$ & $20$ & $100\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

If the piles are $10$ m long, estimate the number of piles required in the pile group and suggest how they should be arranged. Also, determine the pile group efficiency. If the liquid limit of the clay is $\backslash (40\backslash \%\backslash ),$ what will be the approximate settlement in the clay layer due to this loading. Note: Make any suitable assumptions in solving this problem.