Problem $1(16$ points$)$

A square column carries a dead load of $4$ kip $,$ and a live load of $1$ kin $.$ It is supported on a $4$ ft by $4ft,2ft$ deep square footing. The foundation rests in homogenous clean sand with $c^{\text{'}}=0psf$ and ${}^{\text{'}}309$ and the groundwater table is at a depth of $1\mathrm{.}5$ ft below the ground surface. The unit weight above the groundwater table is $110l\frac{b}{f}{t}^t$; the saturated unit weight below the groundwater table is $120l\frac{b}{f}{t}^3$ The SPT results were obtained using a USA safety hammer with a standard sampler. The boring diameter was $6$ in and the depth of boring was $3$ ft $.$ Number of blow counts: $5,4,6$

a$)$ Determine the factor of safety for the bearing capacity. Use Terzaghi's equation. $($Draw a sketch for the foundation$)(5$ points$)$

b$)$ Using the Schmertmann method, compute the settlement of this footing $9$ months after construction in inches. Neglect the weight of the footing. $(11$ points$)$