Q$6(25\%)($a:$7\%,$ b:$7\%,$ c:$6\%,$ d:$5\%)$

For the Marmaray metro line in Istanbul, $$sk$$dar station $("$cut and cover" type$)$ construction, a $278-$mlong, $32-$m$-$wide, $30-$m$-$deep excavation below sea level was constructed. The groundwater level is $2$ m below the ground surface. A $1\mathrm{.}5-m-$thick diaphragm wall $($impervious wall$)$ is constructed along the sides of the rectangular$-$shaped excavation area $($Figure $1).$

Figure $1.$ Aerial View and a Cross Section of the Marmaray Uskudar Station Excavation

As shown in Figure $1,$ the diaphragm wall penetrates into the rock layers $($sandstone$,$ mudstone$),$ and an impervious "bottom plug" $($in Turkish $"$t$$ka$")$ was constructed by "jet grouting" method, to prevent seepage into the excavation site and to provide bottom stability against liquefaction hazard in alluvial silty sands at the site.

We change the geometry and soil profile for CE$363$ HW purposes. The geometry is drawn to scale and a flownet is drawn as shown in Figure $2,$ using $5$ flow channels $(2\mathrm{.}5$ flow channels from each of the left and right side$)$ and $8$ equipotential drops. Saturated unit weight of soil is $19k\frac{N}{m^3}.$

Due Date: November $24,23$:$59$ No late submissions allowed!

a$)$ The water level in the excavation will be kept at the ground surface, by using pumps. So$,$ we need to know how much water $($in $m^3)$ is expected to flow into the excavation in $1$ day. Calculate that, if the coefficient of permeability of the sandy soils is $2\mathrm{.}3{10}^{-3}c\frac{m}{sec}.$

b$)$ Indicate your datum on the figure and calculate the total head of points A and B $.$

c$)$ Calculate pore water pressure at point B $.$

d$)$ Assume that $1-$dimensional water flow is taking place near the ground surface in the excavated area. Check if "quick condition $($boiling$)"$ may occur or not, at the ground surface in the excavated area. In this check, you may consider $1$ square of the flownet near the ground surface, or the embedded length of the wall, both solutions are acceptable.