Problem $4.(50$ pt $).$ You have purchased some land and are ready to build the house of your dreams. A geotechnical study revealed that the soil is a homogeneous silty sand with: Unit

weight $=110pcf,c^{\text{'}}=400psf,{}^{\text{'}}=23,c_u=550psf.$ Ground water table was encountered at $15$ ft of depth. For parts $"a^{\text{'}\text{'}}-c^{\text{'}\text{'}},$ consider long term conditions.

a$)(12$pt$)$ One of the columns is supported by a square footing of $B=3ft,$ and $Df=4ft$; what is the allowable load for that column for a factor of safety of $3?$

b$)(13$pt$)$ If the allowable load calculated in task $1$ was applied with one$-$way eccentricity of $0\mathrm{.}3$ ft $,$ what is the new factor of safety for that spread footing?

c$)(15$ pt