Question

A 6 m \(\times\) 6 m square footing constructed in clay is subjected to a vertical load of 2500 kN at its centre. The base of the footing is 2 m below the ground surface, as shown in the figure. The footing is made of 2 m thick concrete. The ground water table is at a great depth. Considering Terzaghi's bearing capacity theory, the factor of safety of footing against the bearing capacity failure is ....... (rounded off to 2 decimal places).
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Hint:

When calculating the factor of safety, remember to account for both the vertical load and the shear stress parameters. Terzaghi’s bearing capacity theory is often used for this type of problem.

Answer 1

Correct Answer: 4.62

\[ Q = 2500 \, {kN}, \quad c' = 50 \, {kN/m}^2, \quad \phi' = 0^\circ, \quad \gamma = 19 \, {kN/m}^3 \] Unit weight of concrete: \( \gamma_{{c}} = 24 \, {kN/m}^3 \)
\[ Q_{{safe}} = \frac{Q_u - \sigma}{FOS} + \sigma \] For square footing: \[ Q_u = 1.3 c' N_c + \gamma D_f N_q + 0.4 \gamma B N_{\gamma} \] Substituting the values: \[ Q_u = 1.3 \times 50 \times 5.7 + 19 \times 2 \times 1 + 0.4 \times 19 \times 6 \times 1 = 370.5 + 38 = 408.5 \, {kN}. \] Now, for the safe load: \[ Q_{{safe}} = \frac{408.5}{FOS} + 38 \quad {where} \quad FOS = 4.66 \] Thus: \[ FOS = 4.66 \quad {(rounded to 2 decimal places)}. \] Correct Answer: 4.66 (rounded to two decimal places).