NUMERICAL ANALYSIS OF NSF USING FEM
6.2 NSF ON END-BEARING SINGLE PILES
6.2.3 Back-analysis Procedure and Results
The first FEM analysis was conducted to back-analyse the centrifuge model test ES for the end-bearing single pile. In this analysis, Modified Cam Clay (MCC) was adopted for the soft clay, while Mohr-Coulomb (MC) model was used for the sand layers with the soil parameters shown in Table 6.1. Linear elastic model was used for the hollow tube pile with an bulk unit weight of 9.5 kN/m3 taking into account the hollow section within the pile. Coupled-consolidation analysis was conducted with the duration of each stage replicating that of the centrifuge model test. The typical simulation procedure is given in Table 6.2 which simulates the centrifuge test procedure closely except the pile jack-in process. As FEM simulation of pile jack-in process involves very large deformation and element distortion requiring very complicated adaptive re-meshing techniques, the pile was simply “wish-in-place” in the present analysis. As such, the generation of excess pore pressure as well as the subsequent development of NSF due to pile installation was not captured in the present FEM analysis.
Plaxis treats the pore pressure as two components, namely the hydrostatic pore pressure due to the explicitly defined water table and the pore pressure “in excess of”
the hydrostatic component, or the excess pore pressure. While the hydrostatic pore pressure does not change with time, the excess pore pressure will evolve with time based on the Biot-consolidation process until it fully dissipates and the pore pressure regime of the whole FEM domain converges to the hydrostatic pore pressures defined by the explicitly defined phreatic line. It turns out that such treatment of pore pressure in Plaxis greatly facilitates the simulation of water drawdown in the FEM analysis. As shown in Fig. 6.3(a), the hydrostatic water regime was dictated by the initial water
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table WL1 (refer to Fig. 6.1 as well). For the simulation of water drawdown, a new water table, WL2 (see Fig. 6.1 as well) can be explicitly defined in Plaxis, leading to a new hydrostatic water regime as shown in Fig. 6.3(b). Such water drawdown will cause an increment of effective overburden stress of about 10 kPa on the underlying soft clay which was initially fully taken by the excess pore pressure as illustrated in Fig. 6.3(c). The total pore pressure of the FEM domain immediately after the water drawdown is the combination of Fig. 6.3(b) and 6.3(c). With consolidation, and thus dissipation of excess pore pressure in Fig. 6.3(c), Fig. 6.3(b) presents the final hydrostatic pore pressure regime. As such, the final effective stress regime of the FEM domain thus simulated is representative of the corresponding effective stress regime at the end of water drawdown stage in the centrifuge model test.
As for the subsequent stages of application of deadload, surcharge loading as well as transient live loads, the FEM simulation of the model test procedure is much more straightforward as tabulated in Table 6.2.
Fig. 6.4 shows the comparison of numerical results of the dragload along the pile shaft against centrifuge test data. The interface friction angle at the pile-soil interface is set to 17.3°, as derived using Eq. (6.22). It is evident that the numerical results not only capture the neutral point of the end-bearing pile at the pile toe, but also match the magnitude of the dragload closely. The calculated maximum dragload in the pile is 732 kN and 1375 kN at the end of water drawdown stage (Fig. 6.4a) and surcharge stage (Fig. 6.4b), respectively, compares favorably with the measured dragloads of 680 kN and 1416 kN at the corresponding stages. The discrepancy between the calculated and measured values is within 8%.
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Table 6.2 FEM Back-analysis Steps for End-bearing Pile in Test-ES
To illustrate the crucial effect of the incorporation of the pile-soil interface element and its properly defined property on the FEM analysis, another two analyses were carried out with the interface friction angle set to 10° and 22°, respectively. It can be seen from Fig. 6.4 that the numerical output of NSF essentially increases or decreases in tandem with the value of interface friction angle. A fourth analysis was also conducted without the incorporation of the interface elements along the pile-soil interface and the analysis results are plotted in Fig. 6.4 as well. In this case, the FEM prediction simply grossly over-estimates the NSF along the pile. The above analyses clearly demonstrates that in FEM analysis of NSF problems, the interface elements must be applied at the pile-soil interface and the interface friction angle should be determined according to constitutive model adopted for the soil. For MC and MCC
Step No. Description
Calculation type
Duration (days) 1 Establishment of in-situ stress regime by turning on the self-weight of
soils. The water table was set at ground level for the time being
(shown by WL1 in Fig. 6.1) Plastic /
2 Wish-in of the pile Consolidation 15.3
3 Post-installation consolidation Consolidation 156.5
4 Ground water was lowered down by 2m to the top sand-clay interface
(shown by WL2 in Fig. 6.2) Plastic /
5 Consolidation of the soft clay for 181.3 days for the excess pore pressure
generated due to the water drawdown to dissipate Consolidation 181.3 6 Application of 700 kN axial loading on top of pile Consolidation 26.9
7 Application of 40 kPa surcharge on ground surface Plastic /
8 Consolidation of the soft clay for 830 days for the excess pore pressure
to dissipate. Consolidation 830
9 Application of transient live loads Plastic /
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soil models, the derived Eqs. (6.21) and (6.22) should be used to derive the interface friction angle accordingly.
For comparison purpose, the β curves are also plotted in Fig. 6.4. It is very evident that the β curves match the numerical curves very well at the upper pile shaft but start to deviate from each other as they approach the neutral point. As pointed out in Chapter 4, the relative movement between the pile and the surrounding soil around the neutral point is too small to cause the full mobilization of the negative skin friction.
For the present case, the deviation between the β curve and the numerical dragload profile starts at about 3 m above the neutral point for the water drawdown stage as shown in Fig. 6.4(a). After the application of surcharge, the deviation between the two is only confined to within 1 m above the neutral point, as shown in Fig. 6.4(b).
The above observation of partial mobilization of NSF around the neutral point can be further examined by plotting the plastic yielding zones of the FEM domain as shown in Fig. 6.5. As expected, the soft clay modeled by the elasto-plastic MCC model experiences extensive yielding/hardening at essentially all the stress points for both water drawdown and surcharge stages, as indicated by the blue marks. On the other hand, Mohr Coulomb yielding, which governs the pile-soil interface as explained in the preceding section, is observed to develop along the pile-soil interface, as indicated by the square red marks. It can be seen that at the end of water drawdown stage, the MC yielding along the pile-soil interface develops downwards until about 13 m below the ground surface, leaving a partial mobilization zone of about 3 m above the neutral point. On the other hand, at the end of surcharge stage, the full mobilization zone along the pile-soil interface extends downward further, leaving the partial mobilization zone above the neutral point to be less than 1 m above the pile toe.
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Such observations of the development of the MC yielding along the pile-clay interface are in line with the deviation behavior between the numerical dragload profiles and β curves in Fig. 6.4. The state of mobilization of NSF along the pile-soil interface underscores the fundamental mechanism of the deviation of the actual dragload profile from the β curve which assumes full mobilization of NSF up to the neutral point.
The practical implication of the above finding is the need to apply a “mobilization factor” to the calculated dragload using β method to account for the partial mobilization of NSF around the neutral point. This will be explored further later.