Effect of Tunnel Progress on the Settlement of Existing Piled Foundation

Single and group of (3 × 3) piles with an optimum centre-to-centre spacing of s = 3d (Bowles, 1997) were modelled to study the behaviour of the pile groups, where d is the diameter of the pile and D is the diameter of the tunnel. Figure 1 shows the three dimensional finite element mesh that was used in the numerical analyses. The mesh dimensions in the x-direction are 60 m (10 D), that is, 30 m in each side of the centre line of the tunnel, y-direction is 81 m (13.5 D), and in the z-direction is 36 m (6 D). The mesh consists of nearly 28,000 elements (10-node tetrahedrons) with over 32,000 nodes. The boundary conditions of the geometry model are as given below:

Figure 1

A fine mesh was used near the tunnel and pile locations due to the concentration of large shear strains; while a coarser mesh was used outside these zones. The tunnel diameter D is constant throughout the analysis and is equal to 6 m. Figure 2 shows the sectional views of the geometry used in the analysis for a single pile and group of piles, respectively, where E is the lateral distance from the tunnel centre to the pile centre in case of single pile analysis and to the pile group centre in case of pile group analysis, and C is the vertical clearance between the pile tip and the tunnel crown. The pile’s length (L) was assumed to be 18 m with a diameter (d) of 1 m. The connection of piles with the cap was assumed to be a hinge, and the thickness of the pile cap is 1 m. In this study, the behaviour of the centre and corner piles within the pile group was analysed. The pile cap dimensions and the positions of the piles within the group are shown in Figure 3. It is assumed that the construction was performed using the shield tunnelling tunnel boring machine (TBM) (Chapman, 2010). The water table level was assumed to be at the ground surface and the hydrostatic pore pressure was kept constant during the tunnel boring advancement.

Figure 2

Figure 3

An elasto-plastic analysis was adopted to simulate tunnel construction. Pile–soil interaction was included using the embedded pile feature (Brinkgreve et al., 2013). The embedded pile is a pile composed of beam elements that can be placed in an arbitrary direction in the sub-soil and that interacts with the sub-soil by means of special interface elements.

Table 1 summarizes the concrete parameters used in the present study. Tunnel-soil interactions were included using interface elements around the tunnel. Interfaces are composed of 12-node elements consisting of six pairs of nodes, which offer compatibility with the 6-noded triangular sides of the soil and tunnel lining elements, (Brinkgreve et al., 2013). An elasto-plastic Hardening Soil (HS) model was used to simulate the soil structure interaction at the tunnel-soil interface. An isotropic elastic model was used for the pile, piles cap, tunnel lining and tunnel boring machine shield (TBM). Zarev (2016) stated that the advanced models like HS and HS small model are required for obtaining a realistic prediction of the deformations during shield tunnelling. Table 2 summarizes the soil properties adopted from Miro et al., 2012. According to Zarev (2016), the HS model allows for accounting the plastic collapse (isotropic hardening cap plasticity) as well as plastic shearing due to deviatoric loading with shear/frictional hardening (deviatoric yielding). For the deviatoric yielding a non-associated and for the cap plasticity an associated plastic flow rule is prescribed.

The numerical modelling composed of three stages: initial geostatic equilibrium, application of an axial load at the pile head under the service condition and tunnel excavation. The simulation of the tunnelling process started from Y/D = -5 to Y/D = +5 (-30 m to +30 m) in the longitudinal direction (Y), as shown in Figure 4. The pile axis was located at Y/D = 0.0. At the second stage, an axial load of 1000 kN (calculated from static pile capacity) was applied to the pile head in order to simulate the service loading prior to the third stage, that is, tunnel excavation. In case of pile group analysis the load was 140.6 kN/m² distributed on the pile cap. After the application of loading, the tunnel excavation progress was simulated in 40 steps.

Figure 4

The progress of the TBM and the delayed installation of the lining at the tunnel periphery cause a stress release at the soil surrounding the tunnel. Hence, radial and longitudinal deformations will take place in the soil body

that tends to move towards the tunnel’s cavity. This is commonly defined as (volume loss). The ground loss for a TBM excavated tunnel occurs in three stages:

Field observations showed that pile settlement could be classified into three categories, depending on the position of the pile toe relative to the tunnel axis (see Fig. 5). In particular piles with their bases in Zone A settled more than the ground surface, the piles in Zones B settled approximately by the same amount as the ground surface and the piles found in Zones C settled less than the ground surface (Kaalberg et al., 1999).

Figure 5

Several previous studies indicate that piles with their tips directly above the tunnel (i.e., within a horizontal offset of one tunnel radius from the tunnel axis) are likely to settle more than the surface, whereas piles outside this area generally settle less than the surface. This causes a narrowing of the pile head settlement profile with respect to the greenfield surface settlement trough, leading to an increased potential for building damage. Moreover, assessing tunnelling induced deformations in buildings using a tunnel-pile interaction analysis (i.e. assuming that the building follows the settlement curve obtained from a tunnel-pile or tunnel-pile group analysis) does not allow inclusion of the influence of the building on the global interaction; this may be overly conservative in the cases of relatively stiff structures, as illustrated by a case study reported by Goh and Mair (2014).

Figure 6 presents the results of the analysis I (Table 3) with C/D = 0.16 and E/D = 0, and analysis G, where (analysis G) is the Greenfield condition tunnelling analysis without pile presence. Figure 6 shows the development of normalized pile head settlement δnet/δi${{{\delta }_{\text{net}}}}/{{{\delta }_{\text{i}}}}\;$(analysis I) and soil surface settlement δg/δi${{{\delta }_{\text{g}}}}/{{{\delta }_{\text{i}}}}\;$(analysis G) during the tunnel excavation steps (Y/D = -5 to +5). The Greenfield soil settlement (without pile) at the same pile location is also plotted in this figure, where

Figure 6

Figure 7

Negative Y/D value means that the tunnelling progress is towards the pile centre, while positive Y/D means that the tunnelling passes the pile centre.

Figure 6 shows that δnet/δi${{{\delta }_{\text{net}}}}/{{{\delta }_{\text{i}}}}\;$increases as the tunnel excavation proceeds. At the end of the tunnel excavation, δg)max/δi,andδnet)max/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{g)max}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;,\,\,\,\text{and}\,\,\,\,{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net)max}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$reach 2.31, and 2.94, respectively. The δg)max${{\text{ }\!\!\delta\!\!\text{ }}_{\text{g)max}}}$value obtained from analysis G is 4.40 mm, and δnet)max${{\text{ }\!\!\delta\!\!\text{ }}_{\text{net)max}}}$from the analysis I is 5.59 mm. The maximum pile

head settlement of the single pile due to tunnelling only is approximately 1.27 times larger than that computed from the Greenfield condition. The rate of pile settlement increases at each analysis step. Similar results were reported by Lee and Jacobsz (2006). When tunnelling was conducted within a range of Y/D = ± 1, δ at Y/D = -1 and Y/D = +1 were 3.85 mm, 5.78 mm, respectively, and reaches its maximum value at the end of excavation where δmax=7.49${{\text{ }\!\!\delta\!\!\text{ }}_{\max }}=7.49$mm, so that the percentage of settlement at Y/D = ±1D with respect to the maximum settlement at the end of tunnel excavation (δ/δmax)$\left( {\text{ }\!\!\delta\!\!\text{ }}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\max }}}\; \right)$was approximately (51.4% to 77.2%). Similarly, when tunnelling was conducted within Y/D = ±2 from the pile centre, approximately 39 to 88.5 % of total settlement was noticed within this range. Therefore, the zone of influence on the pile head settlement in the longitudinal direction can be considered as ± 2D from the pile centre, based on the large share of settlement that occurs within this range (about 89% of total settlement). This zone of influence is approximately close to those reported by Lee and Ng (2006), and Lee (2013). Figure 7 illustrates the soil displacement at the end of the tunnel excavation. At the end of the tunnel excavation Y/D = +5, the maximum pile head displacement increases by about three times relative to the initial pile head displacement.

The effect of tunnel advancement on a group of piles was studied using analysis (VI) and analysis (G). Figure 8 shows the variations in the normalized pile head settlement δnet/${{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}/$δ_i and soil surface settlement δg/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{g}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$(analysis G) for all the tunnel excavation steps (Y/D = -5 to +5), where, _i is the centre pile head settlement (7.85 mm) from analysis series VI due to the service pile loading prior to tunnelling.

Figure 8

Figure 8 shows that δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$increases as the tunnel excavation progresses. At the end of the tunnel excavation, δg)max/δi,andδnet)max/δi${{\text{ }\!\!\delta\!\!\text{ }}_{\text{g}}})\,{{{_{\max }}/{\text{ }\!\!\delta\!\!\text{ }}\;}_{\text{i}}},\,\,\,\,\,\text{and}\,\,\,\,\,{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}})\,{{{_{\max }}/{\text{ }\!\!\delta\!\!\text{ }}\;}_{\text{i}}}$at the centre of the pile group were 0.56 and 0.80, respectively, the δg)max${{\text{ }\!\!\delta\!\!\text{ }}_{\text{g}}}{{)}_{\max }}$obtained from analysis G was 4.40 mm, and δnet)max${{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}{{)}_{\max }}$obtained from analysis VI for centre pile of group was 6.27 mm. The maximum head settlement of the centre pile due to tunnelling only is approximately 1.42 times that computed from the Greenfield condition. The rate of pile settlement increases at each analysis step. The results are in good agreement with Lee and Jacobsz (2006). It is clear that the longer the distance from the tunnel before reaching the pile, the smaller the pile settlement would be. When tunnelling was conducted within averages of Y/D= ±1 and Y/D= ±2 approximately 71-81% and 63-94% of total settlement was observed respectively. Therefore, the influence zone on the pile head settlement along the longitudinal direction can be considered as ±2D from the centre of pile group, because the pile head settlement almost appeared when tunnelling was restricted from Y/D = -2 to Y/D = +2, which is in a good agreement to those reported by Lee and Ng (2006), and Lee (2013). Figure 8 shows that the centre and corner piles settlement have almost the same behaviour.

Figure 9 illustrates the displacement of soil around the piles group at the end of tunnel excavation Y/D = +5. The total head settlement of the centre pile was 14.12 mm (effect of service pile loading and tunnelling combined). The total pile head settlement at the end of tunnel excavation was 1.8 times the initial pile head settlement (δ_i).

Figure 9

The effect of transverse tunnel location relative to a pile was investigated using the pile head settlement (Table 3). Figure 10 shows the changes in the normalized net pile head settlement for the five series of analysis case, δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$for the entire tunnel excavation steps (Y/D = -5 to +5).

Figure 10

The value of C/D remains constant for all the five cases at 0.16. Figure 10 shows that larger distance in the transverse x-direction of the tunnel from pile results in smaller pile head settlement, which means that dnet at E/D = 0 is 3.25 times dnet at E/D = 2. From Figure 10, in case E/D = 0 the net settlement at the end of tunnel excavation is equal to 2.94 times the settlement due to service load, while in case of E/D = 2 the net settlement equal to 0.91 times the settlement due to service load at the end of the tunnel excavation.

It is shown that δnet/δi${{{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{\text{ }\!\!\delta\!\!\text{ }}\;}_{\text{i}}}$decreases with increasing the lateral distance from the tunnel to the pile. The pile head settlements at the end of the tunnel excavation obtained from Figure 10 are plotted against the lateral distance E/D as shown in Figure 11. As can be seen in this figure, δnet/${{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}/$δ_i decreases with an increase in the lateral distance from the tunnel to the pile, and these values become small when E/D is greater than 2.0, indicating that the effect of tunnelling on piles located beyond 2D from the tunnel is not significant

Figure 11

The effect of tunnel location relative to a group of piles is investigated using the pile head settlement as given in Table 3. Figure 12 shows a variations in the normalized net pile head settlement (centre pile) for the five series of group piles analyses, (δnet/δi)$\left( {{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\; \right)$for the entire tunnel excavation steps (Y/D = -5 to +5), where δ_i is the centre pile head settlement (7.85 mm) due to the service pile loading prior to tunnelling. As seen in Figure 12 when E/D=0 the centre pile suffered the largest head settlement of δnet=${{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}\text{=}$6.27 mm upon the completion of tunnel driving, while δnet=2.03mm${{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}=2.03\,\,\text{mm}$at E/D=2. Figure 12 shows that the larger the distance in transverse X-direction of the tunnel from the centre pile the smaller the pile head settlement, which indicates that δnet${{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}$at E/D=0 is 3.07 times δnet${{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}$at E/D = 2. Figure 12 also shows that in case of E/ D = 0 the increase in pile settlement caused by tunnelling is 80% of settlement due to service load while in case E/D = 2 the increase in pile head settlement caused by tunnelling is 25% of the settlement due to service load. It is evident that δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$in all cases decrease with increasing the lateral distance from the tunnel to the pile. These values are small when E/D> 2.0, indicating that the effect of tunnelling on the group that has its centre located beyond 2D from the tunnel may be ignored.

Figure 12

The effect of Tunnel-pile clearance, C/D is examined using the pile head settlement of analyses series shown previously in Table 3 for single pile analysis. Figure 13 shows the variations in the normalized pile head settlement δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$for all the tunnel excavation steps (Y/D = -5 to +5). It is shown that the settlement increases with increasing C/D up to the tested value of C/D = 2. However, all the curves of different C/D ratios coincide after Y/D = 0, so that once the tunnel face comes under the pile centre there would be no further increase in the settlement with tunnel progress. Therefore, it is reasonable to consider C/D = 2 as the limit after which the tunnelling would be safe enough.

Figure 13

Table 4 also shows the analysis series that represent the group of piles cases under several ratios of (C/D). Figure 15 shows the changes in the normalized pile head settlement δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$for all these series during the tunnel excavation (Y/D = -5 to +5), where δ_i is again the centre pile head settlement (7.85 mm) due to the service pile loading prior to tunnelling.

Figure 15

As shown in Figure 15, the net pile head settlement shows a little increase with the increase of C/D ratios until Y/D = 0, the case when the tunnel comes under the centre of the group; after that the settlement remains approximately constant. At Y/D = 0, δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$for C/D 0.16, 0.5, 0.75, and 1.0 are equal to 0.47, 0.48, 0.48, and 0.49, respectively. At Y/D = -1, δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$for C/D 0.16, 0.5, 0.75, and 1.0 are equal to 0.28, 0.31, 0.33, and 0.34, respectively.

It could be concluded that as the tunnel excavation progresses toward the piles group, δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$slightly increases when C/D increases, but after the tunnel passes the group δnet/δi${{{\text{ }\!\!\delta\!\!\text{ }}_{\text{net}}}}/{{{\text{ }\!\!\delta\!\!\text{ }}_{\text{i}}}}\;$becomes approximately equal for all the suggested values of C/D.