A rectangular foundation $3\mathrm{.}4$m$\backslash$times $2\mathrm{.}5$m transmits a total load of $4\mathrm{.}2$ MN to a deep, uniform deposit of stiff,

overconsolidated clay with an OCR$=3\mathrm{.}9.$ the soil properties are shown in figure. A CU test was conducted

on a soil sample taken at a depth $4\mathrm{.}8$ m below the center of the foundation. The results obtained are $($s$\_($u$))\_($p$)=$

$35$kPa,$\backslash$phi $\_($p$)^(\text{'})=27\backslash$deg $,$ and $\backslash$phi $\_($cs$)^(\text{'})=23^(0).$ Assume that the increase in the horizontal direction is $(1)/(12)$ of the

increase in the vertical direction. Determine if the soil will reach the failure state for short$-$term and long$-$term

loading conditions. If the soil does not reach the failure state, what are the factors of safety for short$-$term

and long$-$term loading conditions?