NUMERICAL ANALYSIS OF NSF USING FEM
6.4 NUMERICAL SIMULATION OF NSF ON END-BEARING PILE GROUPS
6.4.2 Back-analysis of End-bearing Pile Groups
The results of the back-analysis for the end-bearing 16-pile group is presented in detail herein as it is the largest pile group conducted in the centrifuge model tests and thus possesses the most prominent pile group effects. Fig. 6.24 shows the 3D FEM mesh of the problem, which essentially preserves most features of the 3D mesh in Fig.
6.22, except that the single pile has been replaced by a 16-pile group connected by a rigid pile cap with the base set at 0.5 m clear of the top surface of surcharge sand. The whole domain is discretized into 37,296 number of 15-node wedge volumetric
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elements with 103,639 nodes. The average element size is 0.88 m, but with the elements around the piles being refined much denser than those further away from the pile group. The whole FEM domain is essentially composed of 2 sub-domains, namely the soil sub-domain shown in Fig. 6.24(b) and the pile group sub-domain shown in Fig. 6.24(c). The 2 sub-domains interact with each other through the defined interface elements along the pile-soil interface as indicated in Fig. 6.24(c) and have been discussed at length in Section 6.2.2.
The identification of “corner pile”, “side pile” and “inner pile” follows those adopted in Chapter 5 and further illustrated in Fig. 6.25. The calculated dragload on the corner, side and inner pile at the end of water drawdown and surcharge stages are extracted from the 3D FEM analysis and plotted in Fig. 6.26, together with the measured data from the centrifuge model test. In general, the 3D FEM results compare favorably with the model test data, capable of re-producing the largest dragload on the corner pile and least dragload on the inner pile. At the water drawdown stage, the FEM analysis correctly captures the tension developed at the corner pile head and compression at inner pile head (see Fig. 6.26(a)) due to the difference in dragloads among the piles and the interaction of the pile cap. The tension at the corner pile head at the original ground surface diminish upon surcharge (see Fig. 6.26(b)) due to the downward dragload on the pile shaft within the filled-up 2.5-m thick surcharge sand above the original ground surface. Comparing with the 3D FEM results on single pile plotted in the same figure reveals much smaller calculated dragloads on various piles in the 16-pile group.
The results of 3D FEM analysis and measured data of all pile groups are summarized in Table 6.6 and plotted in Fig. 6.27. It should be noted that even for the
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16-pile group, the “inner” pile is only surrounded by one row of perimeter piles (see Fig. 6.25). In order to explore whether the shielding effect could be enhanced in case of an inner pile surrounded by more than one row of perimeter piles, a 3D FEM analysis on a 25-pile group was also conducted with the most inner pile surround by two rows of perimeter pile (see pile No. 4 in Fig. 6.25). However, the 3D FEM analysis results reveal that the dragload on the most inner pile (namely pile No. 4 in Fig. 6.25) was only marginally smaller than that on the inner pile (marked as pile No.
3 in Fig. 6.25) surrounded by one row of perimeter pile. This suggests that the number of rows of perimeter piles does not affect the behavior of inner piles substantially. The analysis results of the 25-pile group are also incorporated in Table 6.6 and Fig. 6.27 for completeness. It can be seen that in all cases, the 3D FEM analysis is capable of capturing the general trend of decreasing NSF with increasing number of piles with reasonable accuracy. In all the cases, the calculated dragloads on all the piles in the pile groups are generally within ±8% against the test data (see Table 6.6 and Fig.
6.27). It can be concluded that the above 3D FEM analysis can effectively account for the pile-soil-pile interaction of NSF among piles in a group.
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Table 6.6 Comparison of Measured and Calculated Dragloads for All the End-bearing Pile Group Tests
Magnitude (kN)
Group factor
Magnitude
(kN) Accuracy Group factor
Magnitude (kN)
Group factor
Magnitude
(kN) Accuracy Group factor
Magnitude (kN)
Group factor
Magnitude
(kN) Accuracy Group factor
1 680 0% 637 -7% 0% 680 0% 637 -7% 0% 680 0% 637 -7% 0%
3 584 14% 557 -5% 13% / / / / / 551 / 540 / /
5 521 23% 496 -5% 22% / / / / / 463 / 470 / /
9 468 31% 459 -2% 28% 435 36% 437 0% 31% 403 41% 410 1% 36%
16 443 35% 445 0% 30% 379 44% 408 7% 36% 339 50% 367 8% 42%
25 / / 440 / 31% / / 399 / 37% / / 320 / 50%
Magnitude (kN)
Group factor
Magnitude
(kN) Accuracy Group factor
Magnitude (kN)
Group factor
Magnitude
(kN) Accuracy Group factor
Magnitude (kN)
Group factor
Magnitude
(kN) Accuracy Group factor
1 1416 0% 1419 0% 0% 1416 0% 1419 0% 0% 1416 0% 1419 0% 0%
3 1276 9% 1353 6% 5% / / / / / 1221 / 1321 / /
5 1259 11% 1284 1% 10% / / / / / 1085 / 1237 / /
9 1197 15% 1265 5% 11% 1148 18% 1215 5% 14% 1050 25% 1139 8% 20%
16 1183 16% 1245 5% 12% 1099 22% 1166 6% 18% 1009 28% 1051 4% 26%
25 / / 1240 / 13% / / 1140 / 20% / / 930 / 34%
Model Test SURCHAGE STAGE
Pile number in group
CORNER PILE SIDE PILE INNER PILE
3D FEM 3D FEM
WATER DRAWDOWN STAGE SIDE PILE
3D FEM
INNER PILE 3D FEM Pile number
in group
CORNER PILE
Model Test 3D FEM
Model Test Model Test
3D FEM
Model Test Model Test
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