A circular, concrete pile with a diameter D$=1\mathrm{.}0$m is to be constructed within a medium density sand. Geotechnical investigation revealed that the sand has a friction angle equal to $30,$ a void

ratio e$=0\mathrm{.}61$ and a specific gravity Gs$=2\mathrm{.}65.$ Moreover, it was revealed that a water table exists at a depth of $3$m from the surface of the ground. Calculate the required length of the pile for a working load at the top of the pile equal to Q$=800$kN$.$ Assume a reasonable safety factor value

and concrete unit weight yc$=24\mathrm{.}0$