A square footing of 4 m side is placed at 1 m depth in a sand deposit. The dry unit weight (g) of sand is 15 kN/m3. This footing has an ultimate bearing capacity of 600 kPa

Q. A square footing of 4 m side is placed at 1 m depth in a sand deposit. The dry unit weight (g) of sand is 15 kN/m³. This footing has an ultimate bearing capacity of 600 kPa. Consider the depth factors: dq = dg = 1.0 and the bearing capacity factor: Ng = 18.75. This footing is placed at a depth of 2 m in the same soil deposit. For a factor of safety of 3.0 as per Terzaghi’s theory, the safe bearing capacity (in kPa) of this footing would be 

Solution:

Skide of square footing = 4 m
depth of footing = 1m
Unit weight of soil = 15 KN/m3
Ultimate bearing capacity = 600 KPa
Depth factors, dq = dγ = 1
Nγ = 18.75
According to terzaghi, the ultimate bearing capacity of square footing is given as at depth of footing = 1 m
qu = 1.3 CNc + qNqdq + 0.4BγNγdγ
For sand, C = 0, q = γDf = 15 × 1 = 15 KN/m2
600 = 0 + 15 × Nq × 1 + 0.4 × 4 × 15 × 18.75 × 1
⇒ Nq = 10
Now at depth of footing at 2 m
qu=1.3CNc +qNq + 0.4BγNγ dγ
qu = 0 + (2 × 15)10 × 1 + 0.4 × 4 ×15 × 18.75 × 1
qu = 750 KPa
∵ We know that
qnu = qu – γDf
qnu = 750 -15 × 2
qnu = 720 KPa
and safe bearing capacity qsafe

q_safe = q_nu/FOS + γD_f

= 720/3 + 15 × 2

= 270 KPa