NUMERICAL ANALYSIS OF NSF USING FEM
6.4 NUMERICAL SIMULATION OF NSF ON END-BEARING PILE GROUPS
6.4.3 Mechanism of Pile Group Effect with NSF
It is believed that the reduction of effective stress of the soils surrounding the piles within a pile group attributes directly to the reduction of dragload on piles within a pile group, which explains why Shibata’s analytical method which adopts such principle gives more favourable results against the present measured data as compared to all the empirical methods which do not capture the essence of NSF group effects and generally grossly overestimate dragload on pile groups. Owing to limitations of centrifuge model setup, the spatial variation of stresses of the soil within the pile group is not available from the test data. As such, the 3D FEM analysis provides a supplementary tool to explore the mechanism of NSF pile group effect by probing into the spatial regime of effective stress distribution within a pile group.
Fig. 6.28 shows the top view of the 3D FEM mesh of the end-bearing 16-pile group presented in Fig. 6.24. The pile cap has been removed in the figure for clarity.
The distributions of effective vertical and horizontal soil stresses at the end of the surcharge loading for Section A-A shown in Fig. 6.28 are illustrated in Fig. 6.29. It can be seen that at the far field away from the pile group, the vertical and horizontal stress contours are more or less horizontal revealing relatively even stress distribution in the clay. However, as the stress contour lines approach the pile group, the lines become distorted and generally show smaller stresses at the pile-soil interface. The stresses inside the pile group are generally further reduced as compared to those outside the pile group. Such phenomenon of stress reduction within a pile group subjected to NSF is quite understandable with the aid of Fig. 6.24. The NSF developed on individual piles within the pile group will generate downward shear stress around the pile shaft, as illustrated in Fig. 6.24(c). Reversely, each pile within
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the pile group will generates counteractive upward shear stress along the surface of each annulus of the soil at the pile-soil interface, as illustrated in Fig. 6.24(b), hence causing a general reduction in effective stresses within the pile group. Such reduction of stress will inevitably lead to the reduction of NSF along the shafts of piles within the pile group and is the fundamental cause of NSF pile group effect.
It is speculated that the reduction of effective stress within a pile group will lead to unbalanced normal stress acting around the shafts of piles within the pile group with a larger normal stress acting on the side of a pile shaft facing the outside of the pile group and a smaller normal stress acting on the side of a pile shaft facing the inside of the pile group. Such unbalanced normal stress may lead to some unfavourable implications like additional bending moments along the pile shafts. To explore this issue, four characteristic lines a-a, b-b, c-c and d-d, are marked along the 4 quadrant points of a centre pile, a side pile and a corner pile in a 9-pile group as shown in Fig. 6.30. The pile cap is omitted in the isometric view in Fig. 4.30(a) for clarity. The effective normal stress acting along the 4 vertical quadrant lines on the pile shaft at the end of surcharge stage were extracted from the 3-D FEM analysis and plotted in Fig. 6.31. It can be seen from Fig. 6.31(a) that for the inner pile, the effective normal stress acting along the four quadrant lines on the pile shaft is essentially identical. Correspondingly, the induced bending moment in the pile is essentially zero along both X-X and Y-Y directions (marked in Fig. 6.30(b)) as shown in Fig. 6.32(a). On the other hand, it can be seen from Fig. 6.31(b) that although the effective normal stress acting on the quadrant lines a-a and b-b on the side pile is essentially identical, the stress acting on the line d-d located inside the pile group (see Fig. 6.30) is substantially smaller than that acting on the line b-b located outside the pile group. As a result, the resulting bending moment around the Y-Y axis (MY-Y) is
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practically zero due to balanced stress on the left and right hand side of the pile, while the bending moment around the X-X direction (MX-X) is quite substantial with a maximum magnitude of about 200 kNm due to the unbalanced stress on the inner and outer faces of the pile shaft, as shown in Fig. 6.32(b). Similarly, it can be seen from Fig. 6.31(c) that the reduction of effective stress within the pile group caused much smaller effective normal pressures acting on the vertical lines a-a and d-d located at the inner faces of the pile group (see Fig. 6.30) as compared to the stress acting on the lines b-b and c-c located at the outer faces of the pile group. As a result, the unbalanced stress along both the X-X and Y-Y direction causes substantial bending moment of about 160 kNm to develop on the pile in both directions, see Fig. 6.32(c).
It is noted that the bending moment around the X-X axis, MX-X, for the corner pile is relatively smaller than that for the side pile (compare Figs. 6.32(b) with 6.32(c)). This can be explained by the relative magnitude of the unbalanced stress in the two cases.
While the normal stress on line b-b of the side pile is very close to that on line b-b of the corner pile, the stress on line d-d of the side pile is smaller than that on line d-d of the corner pile (see Fig. 6.31). This is because the line d-d at the inner face of the side pile is more shielded by other piles as compared to the corresponding line d-d of the corner pile, as shown in Fig. 6.30. As such, the unbalanced stress acting along the Y- Y direction for the side pile is larger than that acting along the Y-Y direction of the corner pile. This explains the relatively larger bending moment around the X-X axis of the side pile than that of the corner pile.
The above probing of effective stress regime within a pile group effectively explores the reduction in effective stress within a pile group which fundamentally reveals the mechanism of NSF pile group effect. The different degrees of reduction in effective stress along the corner piles, side piles and inner piles help to explain the
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different group factors among piles at different locations in a pile group as observed in the model tests. The unfavourable extra bending moment developed on the side piles and corner piles is the direct product of the unbalanced stress on different faces of a pile shaft caused by the reduction of effective stress within a pile group. Such extra bending moment may pose very unfavourable concerns for piles designed purely for axial loads with very nominal steel reinforcement.