$($b$)$ Two vertical point loads, $10000kN$ and $7500kN,$ act on the surface of a soil mass at a distance of $5m$ apart. Between $2m$ and $4m$ below the ground surface, there is a stratum of clay. The clay has a coefficient of compressibility, $mv,$ of $0\mathrm{.}02\frac{m^2}{M}N$ for the range of effective stresses under consideration. Calculate the ultimate consolidation settlement that will be produced in the clay stratum beneath the $10000kN$ load.

$[17$ marks$]$ The increase in vertical stress, $v,$ beneath a point load, $Q,$ at a point within a soil mass can be expressed as:

${}_v=\frac{3Q{z}^3}{2R^5}$

where the point in the soil is at vertical depth, $z,$ beneath the horizontal soil surface and is at diagonal distance, $R,$ from the point load, $Q,$ acting vertically at the soil surface.