$10.$ The following data was obtained from a plate load test carried out on a $60$ cm square plate at a depth of $2$ m below ground surface on a sandy soil which extends up to a large depth. Determine the settlement of a foundation $\backslash (3\mathrm{.}0\backslash$mathrm$\{$~m$\}\backslash$times $3\mathrm{.}0\backslash$mathrm$\{$~m$\}\backslash )$ carrying a load of $110$ tonne and located at a depth of $3$ m below the ground surface. Water table is located at large depth below the ground surface.

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

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

Load $\backslash \backslash$

intensity $\backslash \backslash$

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

$\backslash$end$\{$tabular$\}$ & $5$ & $10$ & $15$ & $20$ & $25$ & $30$ & $35$ & $40\backslash \backslash$

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

Settlement $\backslash \backslash$

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

$\backslash$end$\{$tabular$\}$ & $2\mathrm{.}0$ & $4\mathrm{.}0$ & $7\mathrm{.}5$ & $11\mathrm{.}0$ & $16\mathrm{.}3$ & $23\mathrm{.}5$ & $34\mathrm{.}0$ & $45\mathrm{.}0\backslash \backslash$

$\backslash$hline

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