$12\mathrm{.}1$ A $1500kN$ load was applied on two $20m$ long and $500mm$ diameter piles that were instrumented for measuring the load variation with depth.

a$.$ The variation of frictional resistance per unit area, $f_{(z)},$ with depth for the first pile is shown in Figure P$12\mathrm{.}1$a$.$

$($a$)$

Using Eq$.(12\mathrm{.}9),$ draw the variation of pile load $Q_{(z)}$ with depth.

b$.$ The variation of pile load $Q_{(z)}$ with depth for the second pile is shown in Figure P$12\mathrm{.}1$b$.$ Using Eq$.(12\mathrm{.}9),$ draw the variation of frictional resistance per unit area, $f_{(z)},$ with depth.