A $10\:m$ thick clay layer is resting over a $3\:m$ thick sand layer and is submerged. A fill of $2\:m$ thick sand with unit weight of $20\:kN/m^3$ is placed above the clay layer to accelerate the rate of consolidation of the clay layer. Coefficient of consolidation of clay is and coefficient of volume compressibility of clay is $9\times10^{-2}\:m^2/year$ and coefficient of volume compressibility of clay is $2.2\times10^{-4}m^2/kN$. Assume Taylor’s relation between time factor and average degree consolidation.
The settlement (in $mm$, round off to two decimal places) of the clay layer, $10$ years after the construction of the fill, is ______.