$9\mathrm{.}11$ The settlement analysis for a proposed structure indicates that the underlying clay layer will settle $7\mathrm{.}5$ cm in $3$ yr $,$ and that ultimately the total settlement will be about $32$ cm $.$ However, this analysis is based on the clay layer being doubly drained. It is suspected that there may be no drainage at the bottom of the layer. Answer the following questions based on single drainage only, assuming $c_v=1\mathrm{.}5{10}^{-4}c\frac{m^2}{sec}$ for both single and double drainage.

$($a$)$ How will the total settlement change from the double to the single drainage case?

$($b$)$ How long will it take for $7\mathrm{.}5$ cm of settlement to occur if there is only single drainage?