Given: $1$D compression curve below. Specimen height is $25\mathrm{.}4mm,w=32\mathrm{.}55\%,{}_d=1\mathrm{.}45\frac{g}{c}{m}^3.$ Sample is from a depth of $11\mathrm{.}5m.$

a$)$ Determine the preconsolidation pressure, the modified compression index, the modified recompression index.

b$)$ At the site where the sample was taken, the soil profile consists of about $6\mathrm{.}5m$ of sand and rubble fill and then $9\mathrm{.}1m$ of clay. The water table is about $1\mathrm{.}8m$ below the ground surface. Average densities of the sand and rubble fill are above the water table and below the water table. Estimate the consolidation settlement if the average stress increase in the compressible layer is $($a$)50$kPa, $($b$)100$kPa, and $($c$)250$kPa.