Question

The percent reduction in the bearing capacity of a strip footing resting on sand under flooding condition (water level at the base of the footing) when compared to the situation where the water level is at a depth much greater than the width of footing, is approximately

• A.
  0
• B.
  25
• C.
  50
• D.
  100

Answer 1

The correct option is C

50
Terzaghi's bearing capacity equation
$$q_u=C{N}_c+q{N}_q+\frac{1}{2}B\gamma N_{\gamma }$$
For cohensionless soil, $$C=0$$ Footing resting on sand surface so, $$D_f=0$$
When water level is at base of footing
$$q_{u_1}=\frac{1}{2}B{\gamma }_{sub}{N}_{\gamma }$$
When water level is at much greater depth
$$q_{u_2}=\frac{1}{2}B{\gamma }_t{N}_{\gamma }$$
Percentage reduction in bearing capacity
$$=\frac{q_{u_2}-q_{u_1}}{q_{u_1}}\times 100$$
$$=\frac{{\gamma }_t-{\gamma }_{sub}}{{\gamma }_t}\times 100$$
As
$${\gamma }_{sub}\simeq 0.5{\gamma }_t$$
So, percentage reduction = 50%.