A footing 3m X 3m carries a pressure of 500 kN/ m2 at a depth of 1m in a sand substrate. The saturated unit weight of the sand is 20 kN/ m3 and the unit weight above the water table is 18 kN/ m3. The design shear strength parameters are c’ = 0 and ?’ = 40°. Determine the factor of safety with respect to shear failure for the following cases:
(a) the water table is 5m below ground level,
(b) the water table is 1m below ground level,
(c) the water table is at ground level and there is seepage vertically upwards under a hydraulic gradient of 0.2.