Problem $2$: For a construction site in Fresno, an engineer designed a square footing with $B=3ft$ and $D_f=2ft,$ and is expected to carry $10$ kips of load. Estimate the settlement of the foundation using Schmertmann method. Given: ${}_{\text{c}\text{o}\text{n}\text{c}\text{r}\text{e}\text{t}\text{e}}=150pcf.$ The first layer of soil extends from ground level to $8ft$ and has the unit weight, ${}_{\text{s}\text{o}\text{i}\text{l}}=115pcf,$ The second layer of soil extends from $8ft$ to $12ft$ and has the unit weight, ${}_{\text{s}\text{o}\text{i}\text{l}}=120pcf.$ Assume time $=2yrs$ after the construction.

$(25$ points$)$