Correct Answer - Option 1 : 820 kN/m
2
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