please solve the problem $2.$ Deep Foundations $(\backslash (\backslash$mathbf$\{30\}\backslash )$ marks$)$

As part of a residential development, it is required to design several pile foundations. The proposed piling system involves $18$ m long steel H$-$piles of flange width $310$ mm and depth of $307$ mm $,$ web and flange thickness of $15\mathrm{.}5$ mm $,$ driven into a clayey soil profile. The top $8$ m of the site soil is normally consolidated clay with a unit weight of $\backslash (16\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ and undrained cohesion equal to $60$ kPa ; underlain by a $18$ m thick lightly overconsolidated clay layer with a unit weight equal to $\backslash (18\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ and undrained shear strength equal to $110$ kPa ; this is underlain by a very dense sand layer that extends to the end of the available borehole.

a$)$ Determine the design axial capacity of this pile considering a factor of safety of $2\mathrm{.}5.(10$ marks$)$

b$)$ Design a square group of these piles to support a structural load of $2$ MN $.(10$ marks $)$

c$)$ Considering that the normally consolidated clay has compressibility index, $\backslash (\backslash$mathrm$\{$Cc$\}=0\mathrm{.}35\backslash )$ and void ratio, $\backslash (\backslash$mathrm$\{$e$\}\_\{0\}=0\mathrm{.}95\backslash ),$ and the overconsolidated clay has $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$mathrm$\{$c$\}\}=0\mathrm{.}15\backslash )$ and $\backslash (\backslash$mathrm$\{$e$\}\_\{0\}=0\mathrm{.}6\backslash ),$ calculate the consolidation settlement using the equivalent raft method. $(10$ marks$)$