Question $3$:

A flow net has been constructed and is illustrated below for a cross$-$section through a sheet pile wall excavation in a uniform, isotropic and homogenous clayey sand deposit $($SC$).$ The median grain size is $D_{15}=0\mathrm{.}1mm,$ the permeability is $0\mathrm{.}004c\frac{m}{sec},$ the void ratio is $0\mathrm{.}8,$ and the saturated unit weight is $19k\frac{N}{m^3},$ the dry unit weight is $15\mathrm{.}5k\frac{N}{m^3}.$ Dimensions: $L1=1\mathrm{.}5m$ and $L2=3\mathrm{.}5m$; scale any other needed dimensions to the lengths provided. If the seepage conditions are well described by the flow net solution, answer the following questions:

$($a$)$ Calculate the quantity of flow in liters $\frac{?}{?}$ minute $\frac{?}{m}$

$($b$)$ Estimate the time $($in minutes$)$ for a water molecule to travel from point A to point B in the deposit.

$($c$)$ Imagine a piezometer is installed to Point C; determine the level to which the water in the piezometer will eventually stabilize.

$($d$)$ Estimate the effective vertical and total horizontal stress at point $C,$ assuming the coefficient of earth pressure is $0\mathrm{.}45.$

$($e$)$ What is the most critical location for failure due to sand boiling$/$piping$.$ What is the Factor of Safety against this mode of failure?