A foundation is to be built on a soil layer that is underlain by a compressible clay layer that is $8$ feet

thick. The clay's void ratio, $e=0\mathrm{.}69,$ the compression index, $c_c=0\mathrm{.}22,$ swell index, $c_s=0\mathrm{.}08,$ the pre$-$

consolidation pressure, ${}_c^{\text{'}}=345\frac{\text{\#}}{f}{t}^2$ and ${}_o^{\text{'}}=269\frac{\text{\#}}{f}{t}^2.$ Primary consolidation is estimated to be

complete in $10$ years. What is the secondary compression settlement expected to occur $50$ years after

primary consolidation is complete if $c=0\mathrm{.}015?$

$\frac{1}{4}$ in$.$

$\frac{1}{2}$ in$.$

$\frac{3}{4}$ in$.$

$1$ in$.$