III$)$ Calculation $(80$ pts $,$ please list all your calculations in all questions$)$

$(10\%)$ For a site, the design earthquake has the following parameters: Recurrence interval $=540$ years, Richter's magnitude $=7\mathrm{.}2,$ Cyclic stress ratio $=0\mathrm{.}23,$ The surface soil layer is a $30-ft$ deep bed of fine sand with the following characteristics: Unit weight $=124l\frac{b}{f}{t}^3,$ Angle of internal friction $=34,$ Relative density $=850$

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$*$

Tie roirowing results are produced by a laboratory test on a similar soil sample:

Relative density $=95\%,$ shear stress to cause liquefaction $=1,200l\frac{b}{f}{t}^2$

The factor of safety for liquefaction, at a depth of $30$ ft $,$ is most nearly: