Q$2)$ For the soil layer that is $15m$ thick with a water table at a depth of $4m$ as shown in the figure,

the insitu unit weight of the sand is $17k\frac{g}{m^3}$ above the water table and $20k\frac{g}{m^3}$ below while the

saturated unit weight of the upper clay layer is $21k\frac{g}{m^3}$ and the lower clay layer is $23k\frac{g}{m^3}.$ A

surface surcharge pressure of $90$kPa is applied at $t=0.$

Set up a table of calculation for ${}_v,u$ and ${}_v^{\text{'}}$ as in class notes and determine with explanation of

logic and equation$($s$)$ used for the following:

a$)$ the in situ vertical total stress, pore water pressure and effective stress profiles before the

applied surface pressure $-)$

b$)$ the same stress quantities immediately after the applied pressure $(t=0+)$ at together with

their possible changes ${}_v,u$ and ${}_v^{\text{'}}$ from the insitu values.

Explain Plot the profiles of ${}_v,u$ and ${}_v^{\text{'}}$ from $($a$)$ and $($b$)$ over the $15m$ depth.