$3.$ A foundation for a bridge abutment will apply a gross bearing pressure to the top of the sand layer as shown below. The stress influence factor calculated using elastic solutions below the foundation centerline is shown to the right. A consolidation test was performed on an undisturbed sample taken from the midpoint of the clay layer and the results are also shown below. $($a$)$ Evaluate the stress history of the clay assuming one sublayer $($i$.$e$.$ at the layer midpoint$).($b$)$ Estimate the ultimate consolidation settlement assuming one sublayer. Assume $\backslash (\backslash$mathrm$\{$G$\}\_\{\backslash$mathrm$\{$s$\}\}=2\mathrm{.}7\backslash ).$

The ultimate consolidation settlement is $4$ inches. Please show all steps to get to the answer of $4$ inches for a thumbs up$.$