Question $2$

$[8]$

A layer of clay $4m$ thick lies between two layers of sand each $4m$ thick. The water table is $2m$ below ground level. The lower layer of sand $($the one below the clay$)$ is under artesian pressure, the piezometric surface being $4m$ above ground water level. The saturated unit weight of the clay is $20k\frac{N}{m^3}$ and that of the sand is $19k\frac{N}{m^3}.$ The unit weight of the sand above the water table is $16,5k\frac{N}{m^3}.$

Calculate the effective vertical pressure at the top and bottom of the clay layer.

Question $3$

$[8]$

The following information was recorded after conducting a test on a clay soil sample in a triaxial:

Initial height of the specimen $=76mm$

Initial diameter $=38mm$

Loading gauge reading at failure $=45$ divisions

Strain gauge reading at failure $=5\mathrm{.}5mm$

Proving ring constant $=4\mathrm{.}5\frac{N}{?}$ division

Angle of the failure plane $=52$

The test was conducted with cell pressure $=50k\frac{N}{m^2}$

Pore pressure at failure $=26k\frac{N}{m^2}$

Calculate the major $($principal$)$ stress in relation to effective pressure.

Question $4$

$[20]$

A $6\mathrm{.}6m$ thick clay layer underlain by very stiff clay $($impermeable$)$ is normally consolidated. An oedometer test was conducted for the sample of the same soil. When the pressure was increased from $85k\frac{N}{m^2}$ to $200k\frac{N}{m^2},$ the voids ratio decreased from $1\mathrm{.}20$ to $0\mathrm{.}98.$

The following results were also obtained after conducting a falling head test $($on the same soil sample$)$ in order to determine the coefficient of permeability of the clay:

Length of specimen $=100mm$

Area of specimen $=1000m{m}^2$

Area of standpipe $=20m{m}^2$

At time $=0,$ the head difference is $500mm$

At time $=180$ minutes, the head difference is $300mm.$

a$)$ How long $($in days$)$ will it take for the clay layer to reach $80\%$ consolidation?

b$)$ What is the settlement at that time $($that is$,$ at $80\%$ consolidation$)?$