$1.$ A building is to be constructed on the soil profile shown in figure $1.$ Construction will begin by excavating $15-$meter$-$deep into the ground. Then a circular raft $(\backslash ($ B$=35\backslash$mathrm$\{$~m$\}\backslash ))$ will be laid at $15$ meter below ground. From there, construction of the building will continue until finished. The load on the foundation as a result of construction is approximated to be linear as shown in figure $2.$ Soil profile characteristics are shown in table $1.$

Your tasks are:

a$.$ Calculate and draw the variation of in situ stresses with depth until bedrock $($total and effective in situ stresses$).$

b$.$ Calculate and draw the variation of added stress $($vertical and horizontal$)$ at $\backslash (100\backslash \%\backslash )$ of the applied load.

c$.$ Specify and calculate the expected stress paths $($effective $\backslash$& total stress path$)$ at points A$,$ B$,$ and C$.$ assume excavation is immediate and all construction load $(\backslash (220\backslash$mathrm$\{$KN$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ))$ will be applied post excavation immediately. Take into consideration changes in pore water pressure.

d$.$ Suggest tri$-$axial testing scheme $($lateral extension, vertical compression, lateral compression$)$ for each point $\backslash ($ A$,$ B $\backslash ),$ and $\backslash ($ C $\backslash ).$

e$.$ Calculate the factor of safety against failure at point A at $20\backslash \%$ of loading assuming undrained conditions.

f$.$ Calculate the factor of safety against failure at point $\backslash ($ A $\backslash )$ at $\backslash (100\backslash \%\backslash )$ loading assuming drained conditions.

g$.$ Derive an equation that describe failure $($using effective parameters$)$ as a function of the applied stress at point A$.$ Figure $1$: Soil profile adopted for design and excavation details. Figure $2$: Pressure applied on foundation as a result of constructed building