PARTA

Consider a $4-$layer soil profile with the following characteristics $($top to bottom$)$: $($i$)$ A $4-$ft sand layer with a unit weight of $118pcf$; $($ii$)$ A $7-$ft sand layer with a unit weight of $123pcf$; $($iii$)$ A $11ft$ clay layer with a unit weight of $116$pef; and $($iv$)$ A $3-$ft gravel layer with a unit weight of $127$pef. The ground water table is at a depth of $4ft.$

$(1)$ Draw the distribution of total stress, pore water pressure and effective stress with depth.

$(2)$ What is the effective stress in the middle of the clay layer?

$(3)$ If the ground water table rises to the ground surface, what will be the change in effective stress calculated in part $2?$ Show all calculations.

PART B

You dropped a truck load of rocks on the top of a saturated clay layer. It applied a stress of $2000$ kPa on the clay. Answer the following with respect to the clay layer:

$($a$)$ At time $T$~~$0,$ what are the changes in total stress, pore water pressure and effective stress in the clay? Justify your responses mathematically.

$($b$)$ At time $T$~~$,$ what are the changes in total stress, pore water pressure and effective stress in the middle of the clay? Justify your responses mathematically.

PART C

You are performing a "big$-$scale" permeability experiment. The soil has a diameter of $2m,$ and a ength of $4m.$ The permeability for this soil is $0\mathrm{.}005c\frac{m}{sec}.$

$($a$)$ Find the total head, pressure head and elevation head at the entrance, exit and at point A the specimen.

$($b$)$ What is the hydraulic gradient?

$($c$)$ Determine the amount of water that will travel through the specimen in $1$ day.