PROBLEM $2(80$ points$)$

A future structural load of $60$ kPa will be applied on the site as shown below. An undisturbed sample with a void ratio of $1\mathrm{.}1$ is collected from the middle of the clay layer and subjected to a $1$D consolidation testing. It was found that $6$ minutes is required to reach $\backslash (80\backslash \%\backslash )$ average consolidation. Results showed that the clay has a compression index of $0\mathrm{.}28,$ a recompression index of $0\mathrm{.}06,$ and pre$-$consolidation pressure of $180$ kPa $.$ The glacial till is permeable.

$1.$ Draw the distribution of effective stress. $(10$ points$)$

$2.$ Determine the total pore water pressure $18$ m below the ground surface before and immediately after the application of the structural load. $(15$ points$)$

$3.$ Determine the consolidation settlement of the clay layer. $(15$ points$)$

$4.$ What will be the settlement $5$ years after the load is applied? $(15$ points$)$

$5.$ Determine the effective stress $18$ m below the ground surface $5$ years after the load is applied. $(15$ points$)$

$6.$ Many many years after the construction of the structure, what would be the vertical stress on a soil element $18$ m below the ground surface? $(10$ points$)$