A centered, vertical column load of $229$ kips is applied to a $4\mathrm{.}75$ ft square concrete footing. The footing is $2\mathrm{.}25$ ft thick and its top is at the ground surface. The soil is uniform and has the following properties: $c^{\text{'}}=0$;$=115pcf$; and ${}^{\text{'}}=$ uncertain. The groundwater table is $20$ ft deep. Use Vesic's bearing capacity formula. If the target factor of safety is $2\mathrm{.}0,$ what minimum ${}^{\text{'}}($integer values only$)$ is required? Consider, as part of your solution, developing a plot of factor of safety against a bearing capacity failure vs$.{}^{\text{'}}.[$Course Objective #$2]$