Consider a deep pit solid waste disposal facility constructed in $18m$ thick horizontal saturated clay layer as shown in Fig$\mathrm{.}2.$ Underneath the clay layer, there is a sand aquifer with constant thickness $(10m).$ In the waste leachate, two chemicals, Lead $(Pb)$ and Chloride $(Cl)$ are dissolved in relatively high concentration. Two monitoring wells are installed at the upstream side $($Well$\_1)$ and downstream side $($Well$\_2).$ Using the hydrogeological conditions and the additions given below, answer the following questions. $(40)$

$-$Datum line to define the elevation head: Ground surface $z=0m$

Leachate level in the pit: Ground surface

$-$Hydraulic conductivity of clay: $K={10}^{-9}\frac{m}{s},$

$-$Porosity of clay: $n=0\mathrm{.}5$; density of soil grain: ${}_s=2\mathrm{.}6\frac{g}{c}{m}^3,$

$-$Effective diffusion coefficient of clay: $D_m=2{10}^{-9}\frac{m^2}{s},$

water depths of Well$\_1$ and Well$\_2$: $6m$ and $10$m$,$

$-$In the sand layer horizontal flow can be approximated from Well$\_1$ to Well $2.$

One dimensional vertical flow can be assumed in the $3m$ thick clay beneath the pit.

$(1)$ How much are the void ratio $($e$)$ and moisture content $(w)$ of the clay?

$(2)$ How much is the transmissivity of sand layer?

$(3)$ How much are the elevation head $(h_c)$ and pressure head $(h_p)$ at points A and B respectively?

$(4)$ How much are the hydraulic gradient and interstitial velocity in the sand layer?

$(5)$ How much is the interstitial velocity of the downward flow in the clay under the pit center?

$(6)$ Calculate the time $($years$)$ for a pollutant to reach the bottom of clay liner in the case with no dispersion condition, assuming zero concentration as the initial condition in the clay.

$(7)$ Explain why the mechanical dispersion can be negligible in the process of contaminant transport in the clay.

$(8)$ By monitoring at well $2,$ which chemical will be first detected, Chloride $(Cl$ or Lead $(Pb)?$ Also explain the reason of the answer.

$(9)$ Finding the risk of ground water contamination in this site, propose the measures against the risk