$(10\%)$ For cohesive surface layer $($total stress analysis$)-$Assume that based on a liquefaction analysis, there will be a zone of liquefaction that extends from a depth of $3$ to $8\mathrm{.}5$ m below ground surface. Assume the surface soil $($upper $3$ m $)$ consists of an unliquefiable cohesive soil. It is proposed to construct a sewage disposal plant. The structural engineer would like to use shallow strip footings to support exterior walls and interior spread footings to support isolated columns. It is proposed that the bottom of the footings will be at a depth of $0\mathrm{.}5$ m below ground surface. The structural engineer has also indicated that the maximum total loads $($including the weight of the footing and the dynamic loads$)$ are $50k\frac{N}{m}$ for the strip footings and $500$ kN for the spread footings. It is desirable to use $1-$m wide strip footings and square spread footings that are $2$ m wide. For the $3-m$ thick unliquefiable cohesive soil layer, assume that the undrained shear strength su of the soil is equal to $50$ kPa $.$ Calculate the factor of safety of the footings