$($c$)$ Consider the shaded load area shown in Figure Q$4$c$.$ Using the Fadum's chart and$/$or relevant elastic solutions, estimate the vertical stress increment $({}_z)15m$ below Point A if the surface load is $250k\frac{N}{m^2}.$

$(5$ marks$)$

$($d$)$ The load area shown in Figure Q$4$c can be subdivided into three blocks. Estimate the vertical stress increment $({}_z)15m$ below Point A if the surface loads at Block I, Block II and Block III are revised to $150$kPa,$300$kPa and $450$kPa, respectively.

$(3$ marks$)$

Note:

${}_z$ at depth $z$ under the centre of a circular loaded area with radius $R$ is given by:

${}_z=q{I}_c=q[1-\{\frac{1}{1+(\frac{R}{z}{)}^2}{\}}^{\frac{3}{2}}]$

${}_z$ at depth $z$ under the corner of rectangular loaded area, with dimensions $BL$ is given by:

${}_z=q{I}_r$;$,I_r=\frac{1}{4}[\frac{2mn\sqrt[\phantom{2}]{m^2+n^2+1}}{m^2+n^2+m^2{n}^2+1}(\frac{m^2+n^2+2}{m^2+n^2+1})+ta{n}^{-1}(\frac{2mn\sqrt[\phantom{2}]{m^2+n^2+1}}{m^2+n^2-m^2{n}^2+1})]$

where $m=\frac{B}{z}$;$n=\frac{L}{z}.$