A $20$ m thick clay layer is sandwiched between a silty sand layer and a gravelly sand layer. The layer experiences $30$ mm settlement in $2$ years.
Given:
$T_v = \begin{cases} \dfrac{\pi}{4} \bigg( \dfrac{U}{100} \bigg)^2 & \text{ for } U \leq 60 \% \\ 1.781 – 0.933 \log_{10} (100-U) & \text{ for } U > 60 \% \end{cases}$
where $T_v$ is the time factor and $U$ is the degree of consolidation in $\%$.
If the coefficient of consolidation of the layer is $0.003 \: cm^2/s$, the deposit will experience a total of $50$ mm settlement in the next _____ years.