Figure Ex. 17.8 shows a drilled pier penetrating an IGM: clay-shale to a depth of 8 m. Joints exists within the IGM stratum. The following data are available: Ls = 8 m (= zc), d = 1.5 m, qu (rock) = 3 x 10^3 kN/m^2, Ei (rock) = 600 x 10^3 kN/m^2, concrete slump = 175 mm, unit weight of concrete

Question

Figure Ex. 17.8 shows a drilled pier penetrating an IGM: clay-shale to a depth of 8 m. Joints exists within the IGM stratum. The following data are available: [latex]L_{s}=8 m \left(=z_{c} ight), d=1.5 m , q_{u}( ext { rock })=3 imes10^{3} kN / m ^{2}, E_{i}( ext { rock })=600 imes 10^{3} kN / m ^{2}[/latex] concrete slump = 175 mm, unit weight of concrete [latex]\gamma_{c}=24[/latex] [latex]kN / m ^{3}, E_{c} ext { (concrete) }=435 imes 10^{6} kN / m ^{2}, ext { and } RQD =70 ext { percent, } q_{u} ext { (concrete) }=435 imes 10^{6} kN / m ^{2}[/latex]. Determine the ultimate frictional load [latex]Q_{f}(\max )[/latex].

Accepted Answer

(a) Determine [latex]\alpha[/latex] in Eq. (17.26)

[latex]f_{a}=\alpha q_{u}[/latex] (17.26)

[latex]f_{a}=\alpha q_{u} ext { where } q_{u}=3[/latex] MPa for rock

For the depth of socket [latex]L_{s}=8[/latex] m, and slump =175 mm

From Eq. (17.27)

[latex]\sigma_{n}=M \gamma_{c} z_{c}[/latex] (17.27)

[latex]\sigma_{n}=M \gamma_{c} z_{c}=0.76 imes 24 imes 8=146 kN / m ^{2}[/latex]

[latex]p_{a}=101 kN / m ^{2}, \sigma_{n} / p_{a}=146 / 101=1.45[/latex]

From Fig. 17.16 for [latex]q_{u}=3 MPa ext { and } \sigma_{n} / p_{a}=1.45, ext { we have } \alpha=0.11[/latex]

(b) Determination of [latex]f_{a}[/latex]

[latex]f_{a}=0.11 imes 3=0.33 MPa[/latex]

(c) Determination [latex]f_{a a}[/latex] in Eq. (17.28)

[latex]f_{a a}=f_{a} R_{a}[/latex] (17.28)

For RQD = 70%, [latex]E_{m} / E_{i}=0.1[/latex] from Table 17.5 for open joints, and [latex]f_{a a} / f_{a}\left(=R_{a} ight)=0.55[/latex] from Table 17.6

[latex]f_{\max }=f_{a a}=0.55 imes 0.33=0.182 MPa =182 kN / m ^{2}[/latex]

(d) Ultimate friction load [latex]Q_{f}[/latex]

[latex]Q_{f}=P L f_{a a}=3.14 imes 1.5 imes 8 imes 182=6,858[/latex] kN

Table 17.5 Estimation of [latex]E_{m} / E_{i}[/latex] based on ROD (Modified after Carter and Kulhawy, 1988)
	[latex]E_{m} / E_{i}[/latex]
ROD (percent)	Closed joints	Open joints
100	1	0.6
70	0.7	0.1
50	0.15	0.1
20	0.05	0.05

Table 17.6 [latex]f_{a a} / f_{a} ext { based on } E_{m} / E_{i}[/latex] (O'Neill et al., 1996)
[latex]E_{m} / E_{i}[/latex]	[latex]f_{aa} / f_{a}[/latex]
1	1
0.5	0.8
0.3	0.7
0.1	0.55
0.05	0.45

Question 17.8: Figure Ex. 17.8 shows a drilled pier penetrating an IGM: cla...

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