A foundation is to be built on a soil layer that is underlain by a compressible clay layer that is $20$ feet

thick. The clay's void ratio, $e=0\mathrm{.}98,$ the compression index, $c_C=0\mathrm{.}26,$ swell index, $c_S=0\mathrm{.}06,$ the pre$-$

consolidation pressure, ${}_c^{\text{'}}=300\frac{\text{\#}}{f}{t}^2$ and ${}_o^{\text{'}}=277\frac{\text{\#}}{f}{t}^2.$ Primary consolidation is estimated to be

complete in $15$ years. What is the secondary compression settlement expected to occur from $15$ to $50$

years after construction if $c_{}=0\mathrm{.}016?$

$1\mathrm{.}0$ in$.$

$1\mathrm{.}5$ in$.$

$2\mathrm{.}0$ in$.$

$2\mathrm{.}5in.$