Question

A rectangular footing of plan dimensions $3m\times 4m$ rests at a depth of 1.8 m from the the surface of a sand deposit. The water table is at a depth of 8 m below the base of the footing. For dense sand, bulk unit weight is $19kN/m^3$ and bearing capacity factors are $N_q=28$ and $N_{\gamma }=21$. The net ultimate bearing capacity of the footing based on Terzaghi's bearing capacity equation is

• A. $1466.3kN/m^2$
• B. $1432.1kN/m^2$
• C. $1351.8kN/m^2$
• D. $1508.9kN/m^2$

Answer 1

The correct option is B $1432.1kN/m^2$

As per Terzaghi's bearing capacity equation for rectangular footing
$q_u=(1+0.3\frac{B}{L})c{N}_c+\gamma D_f{N}_q+\frac{1}{2}\gamma B{N}_{\gamma }(1-0.2\frac{B}{L})$
For sand c = 0
$q_u=19\times 1.8\times 28+\frac{1}{2}\times 19\times 3\times 21(1-0.2\times \frac{3}{4})$
$=957.6+508.725$
$=1466.325kN/m^2$
$\therefore$ The net ultimate bearing capcity is
$q_{nu}=q_u-\gamma D_f$
$=1466.325-19\times 1.8$
$=1432.125kN/m^2$