$9\mathrm{.}4$ A driven closed$-$ended pile, circular in cross section, is shown in Figure P$9\mathrm{.}4.$ Calculate the following.

a$.$ The ultimate point load using Meyerhof's procedure.

b$.$ The ultimate point load using Vesic's procedure. Take $I_{rr}=50.$

c$.$ An approximate ultimate point load on the basis of parts $($a$)$ and $($b$).$

d$.$ The ultimate frictional resistance $Q_s.[$Use Eqs. $(9\mathrm{.}40)$ through $(9\mathrm{.}42),$ and take $K=1\mathrm{.}4$ and $[$:${}^{\text{'}}=0\mathrm{.}6{}^{\text{'}}.$