Question

Consider the following statements:

(1) Bearing capacity of Cohesionless soil increases with an increase in the width of the foundation.

(2) Bearing capacity of purely cohesive soil independent of the width of the foundation.

(3) Bearing capacity of a footing on pure clay does not significantly get affected by the presence of the water table.

Out of these statements:

1. only 1 and 2 are correct
2. only 1 and 3 are correct
3. only 2 and 3 are correct
4. 1, 2, and 3 are correct

Answer 1

Correct Answer - Option 4 : 1, 2, and 3 are correct

Explanation:

Ultimate bearing capacity of strip footing is given by;

\({q_u} = C{N_c} + γ {D_f}{N_q} + 0.5Bγ {N_γ }\)

Effect of width and water table on bearing capacity:

Case1: For Cohesionless soil ( sand, C=0)

Ultimate bearing capacity for cohesionless soil is given by;

\({q_u} = γ {D_f}{N_q} + 0.5Bγ {N_γ }\)

If the water table rises to ground level

\({q_u} = γ '{D_f}{N_q} + 0.5Bγ '{N_γ }\)

or 

\({q_u} = \frac{1}{2}{γ _{sat}}{D_f}{N_q} + 0.5B\left( {\frac{1}{2}{γ _{sat}}} \right){N_γ }\)

Conclusion:

• In case of sand ultimate bearing capacity is proportional to width of the foundation means if Bearing capacity of Cohesionless soil increases with an increase in the width of the foundation
• If water table rises to ground level in sand ultimate bearing capacity approximately reduces to 50%.

Case 2: For cohesive soil (clay):

For pure clay, angle of internal friction, ϕ = 0° 

For ϕ = 0°, N_c = 5.7, N_q = 1 and N_γ = 0

Ultimate bearing capacity is given by;

\({q_u} = C{N_c} + γ {D_f}{N_q} + 0.5Bγ {N_γ }\)

⇒ \({q_u} = 5.7C + γ {D_f}\)

If water table rises to ground level

q_u = 5.7 C + γ'D_f

qnu = 5.7 C + γ'D_f - γ'D_f = 5.7 C

Conclusion:

• In case of clay ultimate bearing capacity is independent of the width of footing.
• Net ultimate bearing capacity is nearly unaffected due to rise of the water table.