A foundation is to be installed on site whose $8\mathrm{.}0$ m thick clay layer has a coefficient of consolidation of $20\mathrm{.}71$ mm$2/$hr$.$ The clay layer is sandwiched by a sand layer on top and gravel at the bottom. If there is a requirement that the settlement due to consolidation in the clay layer in the $50$ years design life of the structure must be limited to $68$ mm$,$ how much should be the theoretical total $($i$.$e$.100\%)$ expected consolidation of the clay?