Question

A large scale bearing capacity test on a footing of size 1.05 m $\times$ 1.05 m at a depth of 1.5 m yielded an ultimate value of 141 kN. Unconfined compression tests on the soft saturated clay yielded strength of 0.33 N/$m{m}^2$. If the unit weight of the soil is 1.6 g/cc, how much does the test value differ from that obtained using Terzaghi's bearing capacity equation?

• A. 6.804

Answer 1

The correct option is A 6.804
The footing is a square footing of size 1.05 m $\times$ 1.05 m
Terzaghi's bearing capacity of square footing is -
$q_u=1.3c{N}_c+q{N}_q+0.4\gamma B{N}_{\gamma }$
For a soft saturated clay,
$N_c=5.7;N_q=1;N_{\gamma }=0$
$\Rightarrow q_u=1.3\times 5.7\times c+q\times 1=7.41c+q$

$Now,c=\frac{q_u}{2}$

$\Rightarrow c=\frac{0.03}{2}N/m{m}^2$

$=0.015N/m{m}^2$
$=15kN/m^2$

From (1):

$q_u=(7.41\times c)+\gamma D$
$=111.15+(1.6\times 9.81\times 1.5)$
$\Rightarrow$ $q_u$ = 134.694 kN/$m^2$

Test result yielded ultimate value as 141 kN
$\Rightarrow q_u$ ${}_{test}=\frac{141}{1.05\times 1.05}=127.89kN/m^2$

Difference in test value and Terzaghi bearing capacity equation is = 134.694 - 127.84 = 6.804 kN/$m^2$