NUMERICAL ANALYSIS OF NSF USING FEM
6.5 NUMERICAL SIMULATION OF NSF ON SOCKETED PILE GROUPS
The 3D FEM mesh of a socketed pile group resembles that of the corresponding end- bearing pile group, except that the end-bearing block is removed and the group piles are extended half a pile diameter into the underlying sand. The calculated and measured dragload along a corner pile, a side pile and an inner pile of the socketed 16-pile group at the end of water drawdown and surcharge stages from the 3D FEM analysis are plotted in Fig. 6.41 as an illustration. It can be seen that at the water drawdown stage (Fig. 6.41(a)), the analysis competently captures the tension at the corner pile head and compression at the inner pile head, which cause the offset of the dragload profiles with the maximum dragload at the NP very close to each other for the two piles. It appears that the calculated NP elevation at the drawdown stage is discernibly lower than the measured elevation. Since the position of NP is the elevation where the settlement of the pile equals the settlement of the soil, such discrepancy may be due to the assumed soil stiffness in the analysis which may not be an exact replication of that of the actual soil condition, thus resulting in a slightly different pile and soil settlement profiles from those of the actual situation. However, the calculated elevation of NP at the surcharge stage matches the measured elevation reasonably well at around 90% of the pile length within the upper settling soils, as shown in Fig. 4.41(b). By and large, the calculated dragload profiles replicate the trends as well as the magnitudes of the measured data favorably.
The numerical simulations of the other socketed pile groups with 3, 5 and 9 piles were also conducted and all the simulation results are summarized in Table 6.7 and
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plotted in Fig. 6.42, together with those of the test data for comparison. It can be seen that for all cases, the 3D FEM analysis is capable of capturing the general trend of decreasing NSF, and thus increasing of group reduction factors, with increasing number of piles within the socketed pile groups with reasonable accuracy. The calculated dragload on the piles in a group is generally within ±8% against the test data, except it is 14% for the inner pile of the 9-pile group (see Table 6.7 and Fig.
6.42).
The NSF group reduction factors presented in Fig. 6.42 are only applicable for socketed pile groups with the specific pile and soil conditions. Besides factors like pile slenderness ratio, pile-soil stiffness ratio and surcharge intensity which would affect the NSF group reduction factor, other factors like the socket length and stiffness of underlying competent soil also play an important roles in influencing socketed pile group behavior. As such, the permutation of so many factors is too numerous to make a concise generalization of variation of NSF group reduction factors for socketed pile groups. However, as manifested by the test data in Section 5.3, the average NSF group reduction factors for the socketed pile groups with half pile diameter socket length are on average only about 5% smaller than those of the corresponding end- bearing pile groups. As the socket length increases, which is very likely in practical situations, the behaviors of socket piles is expected to become more similar to those of end-bearing piles. Thus, the average NSF group reduction factor generalized in Fig.
6.40 may be used as an approximate average NSF group reduction factor for socketed pile groups.
The calculated pile group settlements due to dragloads on socketed pile groups during the water drawdown and surcharge stages are plotted in Fig. 6.43. It can be seen that consistent with the observed reducing dragload with the increase of pile
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Table 6.7 Comparison of Measured and Calculated Dragloads for All the Socketed 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
1 563 0% 552 -2% 0% 563 0% 552 -2% 0% 563 0% 552 -2% 0%
3 510 9% 497 -3% 10% / / / / / 489 / 478 / /
5 493 12% 466 -6% 16% / / / / / 464 / 444 / /
9 441 22% 417 -6% 24% 394 30% 413 4% 25% 357 37% 408 14% 26%
16 411 27% 392 -5% 29% 385 32% 385 0% 30% 348 38% 381 9% 31%
25 / / 377 / 32% / / 369 / 33% / / 358 / 35%
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 1188 0% 1148 -4% 0% 1188 0% 1148 -4% 0% 1188 0% 1148 -4% 0%
3 1084 8% 1084 0% 6% / / / / / 1028 / 1079 / /
5 1109 6% 1070 -4% 7% / / / / / 1011 / 1030 / /
9 969 18% 1033 6% 10% 973 18% 1019 4% 11% 904 23% 957 5% 17%
16 1062 10% 1026 -4% 11% 997 16% 973 -3% 15% 907 23% 929 2% 19%
25 / / 970 / 16% / / 946 / 18% / / 880 / 23%
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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number in a pile group, the downdrag settlement of a pile group decreases consistently with the increase of pile number in a pile group. The reduction of pile group downdrag settlement tends to taper off after the number of piles exceeds nine, which is consistent with centrifuge test observation that the reduction of dragload tapers off when the pile number exceeds nine. If a socketed single pile subjected to NSF is designed with allowable downdrag settlement based on Fig. 6.21, the downdrag settlement of a socketed pile group is expected to be even less due to the beneficial pile group effects. It should be noted that, as mentioned earlier, due to inconsistent readings of the local potentiometers mounted on top of the pile caps during the pile group model tests, comparison with measured socketed pile group downdrag settlement can not be made.