Design an isolated shallow foundation for a column with an applied load of $500$ kips. The results of the site investigation indicate that the supporting clayey soil's cohesion and angle of internal friction are $800$ psf and $30\backslash$deg $,$ respectively. Groundwater is $3$ ft below the ground surface, and the total depth of the layer is $25$ ft$.$ Below this layer, there is a stiff bedrock. The total unit weights above and below the water table are. $115$ pcf and $120$ pcf$,$ respectively. The initial in situ void ratio of the clay layer is $0\mathrm{.}5,$ and the compression and recompression indices are $0\mathrm{.}40$ and $0\mathrm{.}10,$ respectively. The maximum past pressure is $400$ psf above the initial effective vertical stress at any given depth. The modulus of elasticity of the soil is $10$ ksi.