Problem $1.$ As shown in Figure below, a shallow rectangular footing $(\frac{B}{L}=0\mathrm{.}5)$ is intended to be

designed to support a column. The load on the column, including the column weight, is $Q=230$

kip. The foundation rests in homogeneous sand. Subsurface exploration and laboratory testing

found that the soil's effective friction angle is $35.$ The groundwater table is $3\mathrm{.}5ft$ below the ground

surface. The bulk unit weight above the groundwater table is $105l\frac{b}{f}{t}^3$; the saturated unit weight

below the groundwater table is $118l\frac{b}{f}{t}^3.$ Determine the foundation embedment and design the

dimensions of the footing $-$ the thickness of the foundation is considered to be $2\mathrm{.}5ft$ based on

analysis. The factor of safety for bearing capacity is $3\mathrm{.}0.$ Use general bearing capacity theory.

Assume general shear failure. and $\{$:${}_{\text{c}\text{o}\text{n}\text{c}\text{r}\text{e}\text{t}\text{e}}=150l\frac{b}{f}{t}^3)$