Discussion
The foundation footing for a viaduct are to be sunk into sand and gravel alluvium. According to the borehole data the water table is at considerable depth, below the foundation area of influence. The unit weight of the ground is r = 20 kN/m3 and the effective angle of internal friction, as deduced from penetrometer test is φ' = 35°.
Find the effective ultimate bearing capacity for the footing of the viaduct, 4 m wide and 8 m long on the ground plan, if they are sunk 2 m below ground level.
Answer: B
The key gives 3313 kPa.
Above the water table the sand is dry, so the overburden at the base of the footing is q = 20 × 2 = 40 kPa. For φ' = 35° the bearing capacity factors are Nq ≈ 33.3 and Nγ ≈ 48. For a 4 m by 8 m rectangle (B/L = 0.5) the shape factors are about 1 + 0.5 tan 35° = 1.35 for the overburden term and 1 - 0.4 × 0.5 = 0.8 for the self-weight term:
\[ \begin{aligned} q_{u} &= q N_{q} s_{q} + 0.5\gamma B N_{\gamma} s_{\gamma} \\ &= 40(33.3)(1.35) + 0.5(20)(4)(48)(0.8) \\ &\approx 1798 + 1536 \approx 3330\ \text{kPa} \end{aligned} \]
That agrees with the keyed 3313 kPa to within the rounding of the factors, which vary slightly between textbooks. 1105 kPa is roughly a third of the true value, and 5002 and 8017 kPa are far too high for a footing only 2 m deep.
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