Discussion
A building is to be founded on a clay stratum. The water table is practically at ground surface level. Laboratory test show 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.
Suppose 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: A
The ultimate bearing capacity is 502.6 kPa.
For a saturated clay loaded quickly, the undrained (\(\phi = 0\)) analysis applies. The undrained cohesion is half the unconfined compressive strength, \(c_{u} = 150/2 = 75\) kPa. With \(N_{c} = 5.14\), a shape factor of 1.2 for a square footing and the overburden \(\gamma D\) (\(N_{q} = 1\)):
\[ \begin{aligned} q_{u} &= 1.2\, c_{u} N_{c} + \gamma D \\ &= 1.2(75)(5.14) + 20(2) \\ &= 462.6 + 40 = 502.6\ \text{kPa} \end{aligned} \]
Because the analysis is in total stress, the water table at the surface does not alter it. A common slip is to use \(q_{u}\) itself as the cohesion, which roughly doubles the first term; the other options do not follow from this formula.
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