Q$\mathrm{.}1(25$ marks$)$

A closed end precast concrete pile with a diameter $(D_p)$ of $0\mathrm{.}5m$ is driven into a uniform sand deposit. The sand has a saturated unit weight, ${}_{\text{s}\text{a}\text{t}\text{,}},$ of $17k\frac{N}{m^3}$ and a drained friction angle ${}^{\text{'}}$ of $35.$ Groundwater table is at the ground surface.

Determine $q_p$ for the pile when the toe is driven to $4m(L_1),$ and $5m(L_2)$ below ground surface.