PROBLEM $2$: $[26$ POINTS$]$

A soil profile consisting of a sandy layer $(6$ m $)$ overlaying a clayey layer $(5$ m $)$ is shown below. The water table is $2$ m below the ground surface. You are given the unit weights of the sand layer, and the consolidation properties along with the unit weight of the clay layer. A surcharge loading is applied, and we are interested in calculating the settlement of the clay layer as such.

Determine the initial effective stress at the center of the clay layer $($at the location of the sample$).$

Calculate the induced stress at the center of the clay layer using the $2$:$1$ method.

Determine if the clay layer is normally consolidated or over$-$consolidated.

Calculate the settlement due to the loading at the top.

The allowable settlement is $3$ inches. Is the settlement acceptable or not?

$(1$ inch is $2\mathrm{.}54$ cm $)$