calculate field calibrated cv$-$h Problem $2$:

Based on your calculations from Problem $1,$ you observe that it will take an unacceptably long time for settlement to occur before you can start construction. In order to speed the process, you decide to place $10$ ft of fill on your site, which includes a surcharge load, and to install vertical drains. The drains have an effective diameter $\backslash (\backslash$mathrm$\{$d$\}\_\{\backslash$mathrm$\{$w$\}\}=4\backslash )$ in$.$

$1.$ Calculate ultimate settlement for the case with $10$ ft of fill.

$2.$ What drain spacing is required to achieve $\backslash (90\backslash \%\backslash )$ consolidation by the end of $1$ year? You will have to assume a value for $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$mathrm$\{$v$\}-\backslash$mathrm$\{$n$\}\}\backslash )$ based on $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$mathrm$\{$v$\}\}\backslash ).$

Six months after the placement of your surcharge you measure $1\mathrm{.}6$ feet of settlement that has occurred, and consolidation is $\backslash (85\backslash \%\backslash )$ complete.

$3.$ Use this data to calculate field calibrated $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$mathrm$\{$v$\}-\backslash$mathrm$\{$h$\}\}\backslash ).$

$4.$ Use same data to update your estimate of ultimate settlement.

$5.$ Assume that the surcharge is removed at $\backslash ($ t$=1$ y r $\backslash ).$ Confirm $($using the calibrated $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$mathrm$\{$v$\}-\backslash$mathrm$\{$n$\}\}\backslash ))$ that after $1$ year the primary consolidation will be practically complete. What is the effective OCR following the surcharge removal?

$6.$ Estimate the new $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$alpha $\backslash$varepsilon$\}\backslash )$ following surcharge removal. Use the updated $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$alpha $\backslash$varepsilon$\}\backslash )$ to calculate the amount of settlement between year $1$ and $51.$