Figure $2$ shows a cross$-$section through a former sand and gravel quarry that is now used as a landfill for the co$-$disposal of municipal and industrial wastes. The site is covered daily with low$-$permeability clay and leachate develops within the waste. Although the site has an impermeable base, horizontal movement of leachate through the sand and gravel aquifer has been induced by groundwater abstraction from a borehole located at a distance of $100m$ from the site. The borehole completely penetrates the aquifer. The aquifer comprises three layers, each with homogeneous and isotropic hydraulic properties. Table $1$ details the aquifer characteristics of the three layers. Analysis of the leachate reveals that the chlorinated solvent trichloroethene $($TCE$)$ is present as a dissolved phase. Assuming steady$-$state groundwater flow conditions and a partition coefficient between organic carbon and water, $K_{oc},$ for TCE of $150c\frac{m^3}{g},$ find the following:

$[30$ points$]$

$($a$)$ A distribution coefficient, $K_d,$ and retardation factor, $R,$ for each of the three aquifer layers.

$($b$)$ The breakthrough time for TCE in each layer at the abstraction borehole.

$($c$)$ The resulting concentration breakthrough curve for TCE arriving at the borehole.