A concrete pile of size 0.4 x 0.4 m is driven to a depth of 12 m into medium dense sand. The water table is close to the ground surface. Static cone penetration tests were carried out at this site by using an electric cone penetrometer. The values of qc and fc as obtained from the test have been

Question

A concrete pile of size 0.4 x 0.4 m is driven to a depth of 12 m into medium dense sand. The water table is close to the ground surface. Static cone penetration tests were carried out at this site by using an electric cone penetrometer. The values of qc and fc as obtained from the test have been plotted against depth and shown in Fig. Ex. 15.20. Determine the safe load on this pile with [latex]F_{s}=2.5[/latex] by Schmertmann's method (Section 15.21).

Accepted Answer

First determine the representative cone penetration value [latex]q_{p}[/latex] by using Eq. (15.54)

[latex]q_{p}=\frac{\left(q_{c 1}+q_{c 2} ight) / 2+q_{c 3}}{2}[/latex] (15.54)

[latex]q_{p}=\frac{\left(q_{c 1}+q_{c 2} ight)+q_{c 3}}{2}[/latex]

Now from Fig. Ex. 15.20 and Eq (15.56a)

[latex]q_{c 1}=\frac{d_{3}\left(q_{o}+q_{b} ight) / 2+d_{2}\left(q_{b}+q_{c} ight) / 2+d_{1}\left(q_{d}+q_{c} ight) / 2}{4 d}[/latex] (15.56a)

[latex]\begin{aligned}q_{c 1} &=\frac{d_{3}\left(q_{o}+q_{b} ight) / 2+d_{2}\left(q_{b}+q_{d} ight) / 2+d_{1}\left(q_{d}+q_{c} ight) / 2}{4 d} \&=\frac{0.7(76+85) / 2+0.3(85+71) / 2+0.6(71+80) / 2}{4 imes 0.4} \&=78 kg / cm ^{2}\end{aligned}[/latex]

[latex]q_{c 2}=q_{d}=[/latex] the minimum value below the tip of pile within 4d depth [latex]=71 kg / cm ^{2}[/latex].

FromEq. (15.56b)

[latex]q_{c 3}=\frac{d_{4} q_{e}+d_{5}\left(q_{e}+q_{f} ight) / 2+d_{6} q_{f}+d_{7}\left(q_{g}+q_{h} ight) / 2+d_{8} q_{h}}{8 d}[/latex] (15.56b)

[latex]\begin{aligned}q_{c 3} &=\frac{d_{4} q_{m}+d_{5}\left(q_{m}+q_{n} ight) / 2+d_{6} q_{n}+d_{7}\left(q_{g}+q_{k} ight) / 2}{8 d} \&=\frac{0.4 imes 71+0.3(71+65) / 2+2.1 imes 65+0.4(65+60) / 2}{8 imes 0.4} \&=66 kg / cm ^{2}=660 t / m ^{2} ext { (metric) }\end{aligned}[/latex]

From Eq. (15.54)

[latex]q_{p}=\frac{(78+71) / 2+66}{2}=70 kg / cm ^{2} \approx 700 t / m ^{2} ext { (metric) }[/latex]

Ultimate Base Load

[latex]Q_{b}=q_{b} A_{b}=q_{p} A_{b}=700 imes 0.4^{2}=112 t ext { (metric) }[/latex]

Frictional Load [latex]Q_{f}[/latex]

From Eq. (15.56d)

[latex]Q_{f}=K \frac{1}{2}\left(\bar{f}_{c} A_{s} ight)_{o-8 d}+\left(\bar{f}_{c} A_{s} ight)_{8 d-L}[/latex] (15.56d)

[latex]Q_{f}=K \frac{1}{2}\left(\bar{f}_{c} A_{s} ight)_{0-8 d}+\left(\bar{f}_{c} A_{s} ight)_{8 d-L}[/latex]

where K = correction factor from Fig. (15.18a) for electrical penetrometer.

For [latex]\frac{L}{d}=\frac{12}{0.4}=30, K=0.75[/latex] for concrete pile. It is now necessary to determine the average

sleeve friction [latex]\bar{f}_{c}[/latex] between depths z = 0 and z - 8d, and z = 8d and z = L from the top of pile from [latex]f_{c}[/latex] profile given in Fig. Ex. 15.20.

[latex]\begin{aligned}Q_{f} &=0.75\left[\frac{1}{2} imes 0.34 imes 10 imes 4 imes 0.4 imes 3.2+0.71 imes 10 imes 4 imes 0.4 imes 8.8 ight] \&=0.75[8.7+99.97]=81.5 t ( ext { metric }) \Q_{u} &=Q_{b}+Q_{f}=112+81.5=193.5 t \Q_{a} &=\frac{Q_{b}+Q_{f}}{2.5}=\frac{193.5}{2.5}=77.4 t ( ext { metric })=759 kN\end{aligned}[/latex]

Question 15.20: A concrete pile of size 0.4 x 0.4 m is driven to a depth of ...

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