Q$1)(10\%)$

A column that carries a load of $9500kN$ is supported on a $8-m$ by $8-m$ square footing will be

placed at the ground surface. The groundwater table is at $5m$ below the ground surface. The

subsoil is a sandy soil with a unit weight of $19k\frac{N}{m^3}$ and $21k\frac{N}{m^3},$ above and below the

groundwater table, respectively. Using EXCEL:

a$)$ Prepare a plot of the initial, in$-$situ effective vertical stress $($i$.$e$.$ the stress present before

the footing was built$)$ versus depth starting from the ground surface to a depth of $16m$

below the ground surface $($in your plot use vertical axis downward as the depth z$).$

b$)$ On the same plot you prepared for part $($a$)$: Also plot the final effective vertical stress

$($after construction$)$ with depth:

i$.$ Using Boussinesq's method: Firstly, you should calculate the increase in vertical

stress, ${}_v,$ under the center of the footing, with depth; and add these values to the

initial effective vertical stresses to find the final effective vertical stress. Show

your ${}_v$ values with depth, in a table.

ii$.$ Using $2V$:$1H$ approximation method: Firstly, you should calculate the increase in

vertical stress with depth, add these values to the initial effective vertical stresses

to find the final effective vertical stress. Show your ${}_v$ values with depth, in the

same table as in part b$($i$).$