A square foundation is $4m4m$ in plan. The soil supporting the foundation has a friction angle of $35$ and cohesion of $20k\frac{N}{m^2}.$ The unit weight of soil is $18k\frac{N}{m^3}.$

I. Determine the allowable gross load on the foundation with a factor of safety of $3.$ Assume that the depth of the foundation is $1\mathrm{.}5$ m and that general shear failure occurs in the soil.

$2.$ Assume that the shear$-$strength parameters of the soil are the same. A square foundation measuring BxB will be subjected to an allowable gross load of $1000$ kN with FS of $3$ and depth of foundation of $1\mathrm{.}0$ m and that local shear failure occurs in the soil. Determine the size of the foundation.