A $10m$ thick clay layer overlies a $2m$ layer of sand, below which is a rigid rock layer is located,

as shown in the figure given below. Water table is measured to be at the ground surface. To reduce

consolidation$-$induced soil settlements, a $5m$ high and a very wide preload $(-20k\frac{N}{m^2})$ is to be

applied. The lower $0\mathrm{.}5m$ of the preload is composed of a permeable clean sand layer. Answer the

following questions:

i$)$ Estimate the amount of consolidation settlement expected under one dimensionally applied

structural stress of $50$kPa, without the application of preload.

ii$)$ When, the earliest, the $5m$ high preload $($embankment$)$ be removed to ensure very small

consolidation settlements after the construction of the structure.