A $2\mathrm{.}0$ m wide $($B$)$ continuous foundation is placed at a depth $($Df$)$ of $1\mathrm{.}2$ m in a very thick homogeneous sand deposit $($constant cone tip resistance, qc $=8\mathrm{.}8$ MN$/$m$2$ and gamma $=17\mathrm{.}4$ kN$/$m$3).$ The stress increase $($q$)$ at the bottom of the

foundation due to the structural load is $245$ kN$/$m$2.$

a$)$ Perform necessary calculations and plot the variations of $($a$)$ strain influence factor $($Iz$)$ vs$.$ depth and $($b$)$ Modulus $($Es$)$ vs$.$ depth $($you may use an engineering paper for plotting$)$ for computing the settlement of the foundation using the strain influence factors method $($Schmertmann et al$.).$ You must select a suitable scale to reduce plotting and measurement errors.

b$)$ Calculate the settlement of the foundation $25$ years after construction using the strain influence factor method $($Schmertmann et al$.)$