a$)$ A building with a basement is to be constructed in saturated loose silt. The foundation consists of a raft $8$ m width which will rest on the top of the same soil at depth of $5$ m$.$ If the saturated unit weight $=18$ kN$/$m$3,$ For a fully compensated foundation, Estimate the maximum applied pressure.

b$)$ A circular tank to be placed on the surface of saturated clayey silt deposit $($undrained shear strength $=25$ kPa$).$ Assuming undrained local shear failure, use Terzaghi bearing capacity equation and factor of safety of $2\mathrm{.}5.$ Estimate the maximum height of water to fill the tank $($in m$).$

c$)$ A planned flexible loaded area is to be $3$ m x $4\mathrm{.}5$ m and carries a uniformly distributed load of $180$ kN$/$m$2.$ on a bed of saturated normally consolidated clay extended to a great depth. Estimate the elastic settlement below the loaded area. Assume Df $=1\mathrm{.}0$ m$,$ PI$=25\%$ and Undrained strength $=50$ kN$/$m$2.$

d$)$ A steel H$-$pile is driven by a hammer. The maximum rated hammer energy is $54$ kN$.$m the hammer efficiency is $0\mathrm{.}8.$ The number of blows for the last $($one inch $25\mathrm{.}4$ mm$)$ penetration is $10.$ Estimate the pile capacity using a factor of safety of $5.$