It is proposed to build a 8 story building with a footprint of 15 m × 20 m, resting on a mat foundation of the same dimensions, in a saturated clay where c_u = 50 kN/m², γ = 19.0 kN/m³. Assume approximately 15 kN/m² per floor for the live and dead loads.

a. At what depth would you place the mat to make this a fully compensated foundation?

b. What should be the factor of safety if the mat is placed at 3.0 m depth?