Given:

$-$ the sheet$-$pile soil system shown in Figure $2,$ where $L_1=1\mathrm{.}5m$ and $L_2=3m$

for the sand:

$-{}^{\text{'}}=33$

$-=16\mathrm{.}5k\frac{N}{m^3}$

$-{}_{\text{s}\text{a}\text{t}}=19\mathrm{.}0k\frac{N}{m^3}$

for the clay:

$-c=50k\frac{N}{m^2}=0,$ and y$\_$sat$=20$ kn$/$m$^3.$

Determine the required depth of embedment of the sheet pile, allowing for a $50\%$ increase from the theoretical estimate. $($Figure $2$ is attached$)$