Question

A friction pile of diameter 500 mm is embedded into a homogenous sand stratum having angle of internal friction $\varphi ={25}^o$, dry unit weight ${\gamma }_d=17kN/m^3$ and coefficient of earth pressure as 2.5. The design capacity of pile is 1000 kN. The length of pile required for the above design load with a factor of safety 2.5 ?.
(Critical length of pile is 30% of length of pile)

• A. 17.75 m
• B. 9.05 m
• C. 26 m
• D. 2.5 m

Answer 1

The correct option is A 17.75 m


$\therefore Asfrictionpile$

$Q_u=Q_s=f_s{A}_s$

$Q_u=K{\sigma }_a^{\prime }tan\delta \pi dL$

$\therefore Q_s=\frac{Q_u}{F}$

$A{}^{\prime }{\delta }^{\prime }isnotgiven\Rightarrow \delta =\varphi$

${\gamma }_d=17kN/m^3$

$\varphi ={25}^o$

K = 2.5

d = 0.5 m

F = 2.5

$D_c=0.3L$

$Q_s=1000$ kN

$\therefore \delta =\varphi$

$\therefore {\sigma }_a^{\prime }=\frac{\frac{{\gamma }_d.D_c}{2}\times D_c+{\gamma }_d{D}_c\times (L-D_c)}{L}$

$\therefore {\sigma }_a^{\prime }\times L=\frac{17}{2}\times (0.3L{)}^2+17\times 0.3L\times 0.7L$

${\sigma }_a^{\prime }\times L=0.765L^2+3.57L^2$

${\sigma }_a^{\prime }\times L=4.335L^2$

${\sigma }_a^{\prime }=\frac{K.{\sigma }_a^{\prime }tan\delta \pi dL}{F}$

$1000=\frac{2.5\times 4.335L^2\times tan{25}^o\times \pi \times 0.5}{2.5}$

$\therefore$ L = 17.75 m