NUMERICAL ANALYSIS OF NSF USING FEM
6.3 NSF ON SOCKETED SINGLE PILES
6.3.2.3 Generalized Settlement Behaviour of Socketed Piles with NSF
As noted in the preceding section, owing to the limitation of the centrifuge model test, the model pile was only socketed half pile diameter into the underlying sand layer. As such, the settlement behavior presented in Fig. 6.17 is only representative of a socketed pile with short socket length in the underlying competent stratum. To investigate the effect of socket length on pile settlement, further FEM analyses were conducted with pile socket length of 0.5d, 1d, 2d, 3d and 5d, where d represents the pile diameter. It can be seen from Fig. 6.18 that as the pile socket length increases, the pile settlement reduces consistently. For example, the final pile settlement is about 44 mm for a socket length of 0.5d, and reduces to only 17 mm for a socket length of 5d.
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In order to correlate the settlement of a socketed pile with geotechnical FOS considering dragload as elaborated in Section 6.3.2.1, the geotechnical capacity of socketed piles with various socket lengths must be evaluated first. The total pile resistance in the underlying sand layer can be given by (see for example, Tomlinson, 1994)
(5.33)
where Nq is the pile base bearing resistance factor to be determined by pile load test;
σ’v0 is the effective overburden pressure at pile base; Ab is the pile base area; Ks is the coefficient of horizontal soil stress which, for a jacked-in pile, can assume a value of 2K0 where K0 is the coefficient of horizontal stress at rest before pile installation (Tomlinson, 1994); is the average effective overburden pressure along the embedment length in the competent soil; φ is the frictional angle of the soil; Re is a reduction factor to account for the reduced friction angle at the pile-soil interface which can assume a value of 0.8 according to Tomlinson (1994); and As is the area of shaft in contact with the competent soil. The breakdown of the pile geotechnical capacity from centrifuge model Test SS is detailed in Table 6.4. The geotechnical bearing capacity of the pile in the model test is 3563 kN, consisting of shaft resistance of 123 kN and base resistance of 3440 kN, as given in Table 6.4. The shaft resistance only contributes about 4% to the total bearing capacity, due to the short pile socket length in the model test. The back-calculated base bearing resistance factor Nq is about 28 as shown in Table 6.4, which appears at the lower bound.
' '
0 0R tane
p q v b s v s
Q =N σ A +Kσ φA
'0
σv
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Table 6.4 Breakdown of geotechnical capacity in centrifuge model Test-SS
With the back-analysis of geotechnical capacity for Test SS given in Table 6.4, the calculated geotechnical capacity of socketed piles with various socket lengths is summarized in Table 6.5. Thus, the evolvement of geotechnical FOS considering dragload can be obtained by dividing the geotechnical capacity listed in Table 6.5 by the corresponding maximum loads at the neutral point from the above FEM analyses and the results are plotted in Fig. 6.19. By combining Fig. 6.18 and Fig. 6.19, the correlation between the pile settlement and the geotechnical FOS considering dragload can be readily obtained as shown in Fig. 6.20. It is interesting to note that all the results with various socket length cluster closely together within a narrow band which can be readily fitted by the solid curve as shown in Fig. 6.20. This reveals that
Measured total geotechnical resistance by base sand
Qp = 3563 kN
Pile diameter, d = 1.28 m
Pile section area, Ab = 1.29 m2
Area of shaft in base sand layer, As = 2.57 m2
Friction angle of base sand layer, φ = 38 °
coefficient of horizontal soil stress at rest before pile installation
K0 = 0.38
Coefficient of horizontal soil stress after pile installation
Ks = 2×K0 (Tomlinson, 1993) 0.77
Pile/soil interface reduction factor (Tomlinson, 1993), α = 0.8
tanδ = 0.65
Ks tanδ = 0.50
Average effective overburden at midpoint of shaft in sand layer
= 95 kPa
Shaft resistance, Qs = 123 kN
Effective overburden pressure at pile base level, σ'v = 98 kPa
Base resistance, Qb = 3440 kN
Base bearing capacity factor, Nq = 28
'0
σv
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the effect of various socket length on pile settlement can be effectively normalized by the adoption of Geotechnical FOS considering dragload. This is plausible as to cause a specific pile settlement, the longer the socket length, the larger the maximum load at NP (inclusive of the applied load and dragload) is expected. In the meantime, a longer socket length also leads to a higher geotechnical bearing capacity, and the resulting geotechnical FOS turns out to be consistent regardless of socket length.
Table 6.5 Geotechnical Capacity of Socketed Pile with Increased Embedment Length over That in Centrifuge Model Test-SS
Although the effect of socket length can be normalized by the geotechnical FOS, the stiffness of the underlying competent soil could also affect the pile settlement behaviour. To examine this issue, further extensive FEM analyses have been conducted with the stiffness of the underlying sand layer varying between 1.5E4 kPa and 1.5E5 kPa. For each stiffness, the socket length is again varied from 0.5d to 5d and all the results are plotted together and fitted with best-fitted curves, as shown in Fig. 6.21. Instead of specifying a fixed value of geotechnical FOS considering dragload, as proposed by some researchers elaborated in Section 6.3.2.1, Fig. 6.21 provides a rational means upon which a proper geotechnical FOS can be judiciously selected based on the stiffness of the underlying competent soil and the allowable settlement of socketed piles.
Socket length
in base sand Ks tanδ Effective overburden stress at midpoint of shaft in base sand
Shaft resistance
Effective overburden stress at pile base
Base bearing capacity factor
Base resistance
Total Geotechnical capacity
(m) σ'v0 (kPa) Qs (kN) σ'v0 (kPa) qb Qb (kN) Qp (kN)
0.5d* 0.5 95 123 98 28 3528 3651
1d 0.5 98 252 103 28 3713 3965
2d 0.5 103 531 113 28 4082 4612
3d 0.5 108 836 124 28 4450 5286
5d 0.5 118 1525 144 28 5188 6713
* d is the pile diameter
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