A $5-$m$-$thick sand $($saturated unit weight is $19k\frac{N}{m^3})$ layer overlies a clay layer; and clay layer $($of

$10m$ thickness with a saturated unit weight of $20k\frac{N}{m^3})$ overlies a sandstone formation. The

ground water table is at the ground surface. Piezometric mesaurements show that there is

artesian pressure in the sandstone amounting to a water level of $2m$ above the ground surface.

a$)$ Assuming $1-$D upward flow is taking place, and ignoring the head loss in sand $($i$.$e$.$ assuming

$i=0$ in sand$),$ determine the hydraulic gradient in the clay.

b$)$ Assuming $1-$D upward flow is taking place, and ignoring the head loss in sand $($i$.$e$.$ assuming

$i=0$ in sand$),$

$($i$)$ indicate your datum and determine the elevation head, pressure head and total head

at the mid$-$depth of clay.

$($ii$)$ Calculate the effective vertical stress at the mid$-$depth of clay.

c$)$ Determine the depth of excavation from the ground surface, at which we will see heaving of

the bottom of the excavation. Water level inside the excavation will be kept at the base level

of excavation.