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). 

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

Given Data:

• Applied Load: \[ Q = 2500 \, \text{kN} \]
• Effective cohesion: \[ c' = 50 \, \text{kN/m}^2 \]
• Angle of internal friction: \[ \phi' = 0^\circ \]
• Soil unit weight: \[ \gamma = 19 \, \text{kN/m}^3 \]
• Unit weight of concrete: \[ \gamma_c = 24 \, \text{kN/m}^3 \]

Calculation:

The safe bearing capacity is calculated using:

\[ Q_{\text{safe}} = \frac{Q_u - \sigma}{\text{FOS}} + \sigma \]

Step 1: Ultimate Bearing Capacity

For square footing, the ultimate bearing capacity is given by:

\[ Q_u = 1.3 c' N_c + \gamma D_f N_q + 0.4 \gamma B N_{\gamma} \]

Substituting the values:

\[ Q_u = 1.3 \times 50 \times 5.7 + 19 \times 2 \times 1 + 0.4 \times 19 \times 6 \times 1 \]

Simplifying:

\[ Q_u = 370.5 + 38 = 408.5 \, \text{kN} \]

Step 2: Factor of Safety Calculation

The safe load equation is:

\[ Q_{\text{safe}} = \frac{408.5}{\text{FOS}} + 38 \]

Solving for FOS:

\[ \text{FOS} = 4.66 \]

Final Answer:

Correct Answer: \( \boxed{4.66} \) (rounded to two decimal places).