Problem $2/$ Probleem $2$

The soil profile on a site is made up of $2$ m of sand and $21$ m of homogeneous clay. The consolidation coefficient is $\backslash ($ c$\_\{$v$\}=1\mathrm{.}75\backslash$mathrm$\{$~m$\}^\{2\}/\backslash$mathrm$\{$yr$\}\backslash ),$ and the water table is at the top of the clay. The clay rests on rock that is totally impermeable to water. Construction of a large fill will cause $185$ mm settlement in the top $14$ m of clay and $45$ mm in the bottom $7$ m $.$ Assume that the load from the fill is applied instantaneously.

a$)$ Calculate the settlement of the clay after $15$ years.

b$)$ How long will it take for $100$ mm of settlement $($total for both clay layers$)$ to occur?

c$)$ If a thin sand layer is located at $16$ m depth $(14$ m from the top of the clay$),$ calculate the settlement of the clay after $15$ years.

d$)$ How long will it now take for $100$ mm of settlement $($total for both clay layers$)$ to occur?