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A raft foundation of 6 m × 9 m is placed at a depth of 3 m in a cohesive soil having c = 120 kN/m2. The net ultimate bearing capacity of the soil using Terzaghi's theory will be.
1. 820 kN/m2
2. 1020 kN/m2
3. 1220 kN/m2
4. 1420 kN/m2

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Correct Answer - Option 1 : 820 kN/m2

Concept:

As per Terzaghi's theory, ultimate bearing capacity of strip footing is given by the equation

qu = cNc + γDfNq + 0.5BγNγ 

Modified equation of ultimate bearing capacity becomes for rectangular or raft footing:

\({q_u} = \left( {1 + 0.3\frac{B}{L}} \right)c{N_c} + γ {D_f}{N_q} + \frac{1}{2}\left( {1 - 0.2\frac{B}{L}} \right)γ B{N_γ }\)

Net ultimate bearing is given by, qnu = qu - γDf

Calculation:

Given soil is cohesive, so for cohesive soil, ϕ = 0°

For ϕ = 0°, Nc = 5.7, Nq = 1 and Nγ = 0

B = 6 m, L = 9 m, Df = 3 m and c = 120 kN/m2

Ultimate bearing capacity is given by,

\({q_u} = \left( {1 + 0.3\frac{B}{L}} \right) \times c \times 5.7 + \gamma {D_f} \times 1 + \frac{1}{2}\left( {1 - 0.2\frac{B}{L}} \right)\gamma B \times 0\)

\({q_u} = \left( {1 + 0.3\frac{B}{L}} \right) \times c \times 5.7 + \gamma {D_f}\)

Net ultimate bearing capacity is given by

qnu = qu - γDf 

\({q_{nu}} = \left( {1 + 0.3\frac{B}{L}} \right) \times c \times 5.7\)

\({q_{nu}} = \left( {1 + 0.3 \times \frac{6}{9}} \right) \times 120 \times 5.7\) = 820.8 kN/m2

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