Design a shallow foundation $($its shape, dimension and placement$)$ in the soil site shown below.

The sand above the water table has a unit weight of $17k\frac{N}{m^3}$ and below the water table its saturated unit weight is $19k\frac{N}{m^3},$ its angle of friction is ${}^{\text{'}}=25.$ The clay layer has a saturated unit weight of $20k\frac{N}{m^3},$ its cohesion is $20k\frac{N}{m^2}$ and angle of friction is $30.$ The Poisson's ratio and modulus of elasticity for the sand are $0\mathrm{.}25$ and $20M\frac{N}{m^2},$ respectively; for the clay, they are $0\mathrm{.}3$ and $30M\frac{N}{m^2}.$

The clay is an overly consolidated clay with a compression index $C_c=0\mathrm{.}26$ and its recompression index can be estimated as $C_r=0\mathrm{.}2C_c,$ its pre$-$consolidation stress is $160$ kPa and its original void ratio is $1\mathrm{.}2.$

The foundation is supposed to support a dead load of $500$ kN and a live load of $400$ kN $.$

Use the Load Resistance Factor Design $($LRFD$)$ method for strength requirement, based on AASHTO's LRFD recommendations.

The service requirement is that the allowable settlement should not exceed $50$ mm $.$

Note: of course, anyone can simply "overdesign" an excessively large foundation to surpass design requirement by a large margin without regards to the economic cost, however in reality we cannot afford to grossly overdesign foundations. In this project, while we are not intentionally seeking an optimal design to save the cost, we should always keep in mind the implications of an excessively large foundation and be reasonable with our choices.