PROBLEM $4$: $[25$ POINTS$]$

A proposed structure is to be built over $15$ ft of sandy soils overlaying a $10$ ft of clayey layer. The engineer is worried about the settlement of the clayey layer as the maximum allowable settlement is $2$ inches for this project. All dimensions shown on the figure are in ft $.$ The structure has a square cross$-$sectional area at the base. The estimated total pressure from the structure is $2,000psf.$

Soil Properties: $($Note that the soil properties for the clay layer are determined from a sample obtained from the center of the layer$).$

Sand: ${}_t=110pcf,{}_{\text{s}\text{a}\text{t}}=120pcf$

Clay: ${}_t=110pcf,{}_{\text{s}\text{a}\text{t}}=120pcf,e_0=0\mathrm{.}85,c_c=0\mathrm{.}25,c_s=0\mathrm{.}03,{}_p^{\text{'}}=2,000psf$

a$.$ Calculate the initial effective stress at a point in the center of the clay layer $[5$ Points$]$

b$.$ Calculate the induced, effective stress due to the structure at the center of the clay layer $($use the $2$:$1$ method!$)[5$ Points$]$

c$.$ Determine if the clay is normally consolidated or over consolidated $[3$ Points$]$

d$.$ Calculate the expected settlement due to the new loading $77$ Points$]$

e$.$ Does the settlement meet the specifications of the project? $[5$ Points$]$