Discussion
A building is to be founded on a clay stratum. The water table is practically at ground surface level. Laboratory test shows that the unit weight of the soil is r = 20 kN/m3 and classify the soil as a firm clay. The uniaxial compressive strength is qu = 150 kN/m2. Supposing that the footing will be square, 2 m wide and the foundation depth will be 2 m below the ground surface. Calculate the ultimate bearing capacity :
Answer: D
The ultimate bearing capacity comes to 502.6 kPa.
A clay loaded quickly behaves undrained (\(\phi = 0\)), with cohesion half the unconfined compressive strength:
\[ c_{u} = \frac{q_{u}}{2} = \frac{150}{2} = 75\ \text{kPa} \]
For \(\phi = 0\) the bearing capacity factor is \(N_{c} = 5.14\) and the shape factor of a square footing is \(s_{c} = 1 + 0.2\,B/L = 1.2\). The overburden at the founding level is the total stress \(\gamma D_{f}\), because in an undrained analysis the pore pressure does not enter, even though the water table is at the surface:
\[ \begin{aligned} q_{ult} &= c_{u}N_{c}s_{c} + \gamma D_{f} \\ &= 75(5.14)(1.2) + 20(2) \\ &= 462.6 + 40 = 502.6\ \text{kPa} \end{aligned} \]
The other options (304.8, 403.9 and 700.9 kPa) cannot be reproduced from these data with a standard method.
This is the answer under the general bearing capacity equation without a depth factor. Skempton's chart value for a square footing at \(D_{f}/B = 1\) (\(N_{c} \approx 7.2\)) gives a larger figure of about 580 kPa, which is not among the options, so the question evidently intends the equation above.
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