A concrete pile of section 30 x 30 cm is driven into medium dense sand with the water table at ground level. The depth of embedment of the pile is 18m. Static cone penetration test conducted at the site gives an average value qc = 50 kg/cm^2. Determine the load transfer curves and then calculate

Question

A concrete pile of section 30 x 30 cm is driven into medium dense sand with the water table at ground level. The depth of embedment of the pile is 18m. Static cone penetration test conducted at the site gives an average value [latex]q_{c}=50 kg / cm ^{2}[/latex]. Determine the load transfer curves and then calculate the settlement. The modulus of elasticity of the pile material [latex]E_{p} ext { is } 21 imes 10^{4} kg / cm ^{2}[/latex] (Fig. Ex. 15.26).

Accepted Answer

It is first necessary to draw the [latex]\left(q_{p}-s ight) ext { and }( au-s)[/latex] curves (see section 15.29). The curves can be constructed by determining the ratios of [latex]q_{p} / s ext { and } t / s[/latex] from Eqs (15.77) and (15.76) respectively.

[latex]\frac{ au}{s}=\frac{0.22 E_{s}}{2 R}[/latex] (15.76)

[latex]\frac{q_{p}}{s}=\frac{3.125 E_{s}}{2 R}[/latex] (15.77)

[latex]\frac{q_{p}}{s}=\frac{3.125 E}{2 R}[/latex]

[latex]\frac{ au}{s}=\frac{0.22 E}{2 R}[/latex]

where R = radius or width of pile

The value of [latex]E_{s}[/latex] for a driven pile may be determined from Eq. (15.78).

[latex]E_{s}=\left(36+2.2 q_{C} ight) kg / cm ^{2}[/latex] (15.78)

[latex]\begin{aligned}E_{s} &=3\left(36+2.2 q_{c} ight) kg / cm ^{2} \&=3(36+2.2 imes 50)=438 kg / cm ^{2}\end{aligned}[/latex]

Now [latex]\frac{q_{p}}{s}=\frac{3.125 imes 438}{2 imes 15}=45.62 kg / cm ^{3}[/latex]

[latex]\frac{ au}{s}=\frac{0.22 imes 438}{2 imes 0.15}=3.21 kg / cm ^{3}[/latex]

To construct the [latex]\left(q_{p}-s ight) ext { and }( au-s)[/latex] curves, we have to know the maximum values of [latex]q_{p} / s ext { and } au[/latex].

Given [latex]q_{b}=q_{p}=50 kg / cm ^{2}[/latex] - the maximum value.

From Table 15.4 [latex] au_{\max }=0.011 q_{c}=0.011 imes 50=0.55 kg / cm ^{2}[/latex]

Now the theoretical maximum settlement s for [latex]q_{p}(\max )=50 kg / cm ^{2}[/latex] is

[latex]s_{(\max )}=\frac{50}{45.62}=1.096 cm =10.96 mm[/latex]

The curve [latex]\left(q_{p}-s ight)[/latex] may be drawn as shown in Fig. Ex. 15.26. Similarly for [latex] au_{(\max )}=0.55 kg / cm ^{2}[/latex]

[latex]\underset{(\max )}{s}=\frac{0.55}{3.21}=0.171 cm =1.71 mm[/latex].

Now the [latex]( au-s)[/latex] curve can be constructed as shown in Fig. Ex. 15.26.

Calculation of pile settlement

The various steps in the calculations are

1. Divide the pile length 18 m into three equal parts of 6 m each.

2. To start with assume a base pressure [latex]q_{p}=5 kg / cm ^{2}[/latex].

3. From the [latex]\left(q_{p}-s ight) ext { curve } s_{1}=0.12 cm ext { for } q_{p}=5 kg / cm ^{2}[/latex].

4. Assume that a load [latex]Q_{1}=Q_{p}=5 imes 900=4500[/latex] kg acts axially on segment 1 .

5. Now the compression [latex]\Delta s_{1}[/latex] of segment 1 is

[latex]\Delta s_{1}=\frac{Q_{1} \Delta L}{A E_{p}}=\frac{4500 imes 600}{30 imes 30 imes 21 imes 10^{4}}=0.014 cm[/latex]

6. Settlement of the top of segment 1 is

[latex]s_{2}=s_{1}+\Delta s_{1}=0.12+0.014=0.134 cm[/latex].

7. Now from [latex]( au-s)[/latex] curve Fig. Ex. 15.26, [latex] au=0.43 kg / cm ^{2}[/latex].

8. The pile load in segment 2 is

[latex]Q_{2}=4 imes 30 imes 600 imes 0.43+4500=30,960+4500=35,460 kg[/latex]

9. Now the compression of segment 2 is

[latex]\Delta s_{2}=\frac{Q_{2} \Delta L}{A E_{p}}=\frac{35,460 imes 600}{900 imes 21 imes 10^{4}}=0.113 cm[/latex]

10. Settlement of the top of segment 2 is

[latex]s_{3}=s_{2}+\Delta s_{2}=0.134+0.113=0.247 cm[/latex].

11. Now from [latex]( au-s)[/latex] curve, Fig. Ex. 15.26 [latex] au=0.55 kg / cm ^{2} ext { for } s_{3}=0.247 [/latex] cm. This is the maximum shear stress.

12. Now the pile load in segment 3 is

[latex]Q_{3}=4 imes 30 imes 600 imes 0.55+35,460=39,600+35,460=75,060 kg[/latex]

13. The compression of segment 3 is

[latex]\Delta s _{3}=\frac{Q_{3} \Delta L}{A E_{p}}=\frac{75,060 imes 600}{900 imes 21 imes 10^{4}}=0.238 cm[/latex]

14. Settlement of top of segment 3 is

[latex]s_{4}=s_{t}=s_{3}+\Delta s_{3}=0.247+0.238=0.485 cm .[/latex]

15. Now from [latex]( au-s) ext { curve, } au_{\max }=0.55 kg / cm ^{2} ext { for } s \geq 0.17 cm[/latex].

16. The pile load at the top of segment 3 is

[latex]\begin{aligned}Q_{T} &=4 imes 30 imes 600 imes 0.55+75,060=39,600+75,060=114,660 kg \& \approx 115 ext { tones (metric) }\end{aligned}[/latex]

The total settlement [latex]s_{t}=0.485 cm \approx 5 mm[/latex].

Total pile load [latex]Q_{T}=115[/latex] tones.

This yields one point on the load settlement curve for the pile. Other points can be obtained in the same way by assuming different values for the base pressure [latex]q_{p}[/latex] in Step 2 above. For accurate results, the pile should be divided into smaller segments.

Table 15.4 Recommended maximum skin shear stress [latex] au_{\max }[/latex] for piles in cohesionless soils (After Verbrugge, 1981)
[latex] au_{\max } kN / m ^{2}[/latex]	Pile type
[latex]0.011 q_{c}[/latex]	Driven concrete piles
[latex]0.009 q_{c}[/latex]	Driven steel piles
[latex]0.005 q_{c}[/latex]	Bored concrete piles
Limiting values
[latex] au_{\max }=80 kN / m ^{2}[/latex] for bored piles
[latex] au_{\max }=120 kN / m ^{2}[/latex] for driven piles

Question 15.26: A concrete pile of section 30 x 30 cm is driven into medium ...

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