$($a$)$ A $13$ m long anchored sheet pile retaining wall is to be used to support a $7$ m deep excavation, for a site in Central Cork, as shown in Figure $1$ below. The soil conditions are the same in the front of and behind the wall. Note that $\backslash (\backslash$rho$=\backslash )$ density and $\backslash (\backslash$mathrm$\{$k$\}=\backslash )$ coefficient of permeability. Determine:

$($i$)$ the likely seepage into the excavation,

$($ii$)$ the exit hydraulic gradient at Point X $,$

$($iii$)$ the critical hydraulic gradient,

$($iv$)$ the pressure at Point A on the passive side of the wall.

Ground level

Figure $1$