Question

Two identical concrete piles having the plan dimensions $50\text{cm}\times 50\text{cm}$ are driven into a homogeneous sandy layer as shown in the figures. Consider the bearing capacity factor $N_q$ for $\varphi ={30}^{\circ }$ as 24.

If $Q_{P_1}$ and $Q_{P_2}$ represent the ultimate point bearing resistances of the piles under dry and submerged conditions, respectively, which one of the following statements is correct ?

• A. $Q_{P_1}>Q_{P_2}$ by about $100\%$
• B. $Q_{P_1}<Q_{P_2}$ by about $100\%$
• C. $Q_{P_1}>Q_{P_2}$ by about $5\%$
• D. $Q_{P_1}<Q_{P_2}$ by about $5\%$

Answer 1

The correct option is A $Q_{P_1}>Q_{P_2}$ by about $100\%$

$Q_{P_1}=q{N}_q+0.4B\gamma N_{\gamma }$
$=18\times 20\times N_q+0.4\times 0.5\times 18\times N_{\gamma }$
$=18(20N_q+0.2N_{\gamma })$
$Q_{P_2}=q{N}_q+0.4B_{\gamma }{N}_{\gamma }$
$=(19-10)\times 20\times N_q+0.4\times 0.5\times (19-10)N_{\gamma }$
$=9(20N_q+0.2N_{\gamma })$
(Assuming ${\gamma }_w=10{\text{kN/m}}^3$)
$\frac{Q_{P_1}}{Q_{P_2}}=2$
Hence, $Q_{P_1}>Q_{P_2}$ by about $100\%$