$($a$)$ For the configuration shown on Figure $4,$ calculate total and effective vertical stresses for Point X for a time before the structure is built.

$($b$)$ Calculate the change in stress $\backslash (\backslash$left$(\backslash$Delta $\backslash$sigma$\_\{$z$\}\backslash$right$)\backslash )$ at this same point due to the proposed new structure $(\backslash (8\backslash$mathrm$\{$~m$\}\backslash$times $7\backslash$mathrm$\{$~m$\}\backslash )$ in plan and applying a stress of $100$ kPa at ground level$).$ Use the Newmark chart attached to Appendix B of this paper for the calculation.

$($c$)$ Calculate the new vertical effective stress at Point X $,$ corresponding to a time after the structure is constructed $($i$)$ in the short term $/$ immediately after construction and $($ii$)$ in the long term.