$2.[70$ points$]$ You are a staff engineer for a local geotechnical engineering firm. As part of the geotechnical exploration for a project, several subsurface tests have been conducted. You are given the results of one traditional soil boring with Standard Penetration Testing $($SPT$).$ The results of this boring, labeled as B$-2,$ are presented on page $3$ of this assignment. Based on testing of collected soil samples, the encountered soils have the unit weights listed in Table $1($Note that two ML layers have a same unit weight, so are the two CH layers; and the soil layers listed in the Table aren't meant to represent the actual layer sequence or order$).$

Table $1.$ Summary of Soil Unit Weights from Boring B$-2.$

NOTE: Assume the asphalt and base course layers are remowed and replaced with material identical to that underneath them.

$2$a$.$ Determine the total, pore pressure, and effective stresses in the soils from the ground surface to the bottom of the borehole $($i$.$e$.,$ a depth of $75$ ft $).$ Provide a plot of these stresses with depth. $[30$ points$]$

$2$ b $.$ The figure below presents the general cross$-$section of two planned footings at your project site. $[40$ points$]$

The project structural engineer has given you design loads of $90$ kips for the columns and $7$ kips per linear foot for the wall loads, respectively. Refer to Boring B$-2$ for the soil profile profile at both footing locations.

$-$ Determine the change in vertical effective stresses $($i$.$e$.,$ induced vertical stresses$)$ at the locations under the center of the footings using Boussinesq, in $0\mathrm{.}5$ B increments to a depth of $5$ times the footing width $($i$.$e$.,$ at depths of $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~B$\},\backslash$mathrm$\{$~B$\},1\mathrm{.}5\backslash$mathrm$\{$~B$\},2\backslash$mathrm$\{$~B$\},\backslash$ldots$,5\backslash$mathrm$\{$~B$\}\backslash )).($Hint: Column footing corresponds to uniform rectangular loading while the wall load corresponds to uniform strip loading: I is convenient to use a table to carry out your calculations$)$