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.
502.6 kPa
502.6 kPa option is correct.
Under saturated conditions with qu given, the clay is analysed in undrained (\(\phi\) = 0) terms. Undrained shear strength cu = qu/2 = 75 kN/m². Meyerhof's bearing-capacity formula for \(\phi\) = 0 uses \(N_c\) = 5.14, Nq = 1, Nγ = 0 with shape factor \(s_c\) = 1 + 0.2·(B/L) = 1.2 for a square footing.
\(q_{ult}=c_{u}N_{c}s_{c}+\gamma D_{f}N_{q}\)
Step 1 — cohesion term: \(c_{u}N_{c}s_{c}=75\times5.14\times1.2=462.6\ \text{kPa}\).
Step 2 — surcharge term: \(\gamma D_{f}N_{q}=20\times2\times1=40\ \text{kPa}\).
Step 3 — add: \(q_{ult}=462.6+40=502.6\ \text{kPa}\).
The other options arise from misusing Terzaghi factors, forgetting the shape factor, or omitting the surcharge, and therefore fail to reproduce Meyerhof's standard undrained square-footing result.
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