Three Dimensional Finite Element Analyses to Investigate the Impact of Tunneling on Pile

(1)

OHN10109581230

Three Dimensional Finite Element Analyses to Investigate the Impact of Tunneling on Pile

B.Vafaei

¹

, M.R.Jafari

²

1- M.Sc in Geotechnical Engineering, Department of civil engineering, Tafresh University, Tafresh, Iran

2- PhD, PE, Principal Tunnel and Geotechnical Engineer, Geotechnical and Tunnelling Division, CDM, USA



[email protected] [email protected]

Abstract

Tunnels are an integral part of the infrastructure of modern society and are used for a wide range of applications, including subways and railways, highways, material storage, and sewage and water transport. On the other hand, in urban area many of the surface structures are supported by piled foundations. Thus, tunneling-induced ground movements may cause serious damage to the adjacent piles. Several researchers conducted two-dimensional laboratory tests and centrifuge model tests and presented closed-form analytical solution for the preliminary design purpose. In this paper, a series of finite element simulations were performed to investigate the influence of tunneling on adjacent piles. Results of three-dimensional numerical analysis show that, although there is a good agreement between finite element method and closed-form analytical solution when the tunnel lining is located (installed) at the pile level, magnitude of internal forces and displacement imposed on pile due to the tunneling increase significantly even after the passage of tunnel face from the pile

.

Keywords: Tunneling; Pile Foundation; Interaction; Displacement; Internal Forces

1. INTRODUCTION

In urban environments, many high-rise buildings are supported by deep foundations and, if adjacent to a new tunnel excavation, they are likely subject to additional axial and lateral forces caused by tunneling-induced ground movements. Although assessment of the impact of tunneling on the stability and integrity of existing pile foundations is one of the important issues especially in weak soils, relatively little research work associated with this problem can be found in the literature. Mair & Taylor (1997) reviewed case histories, the results of numerical analyses and model tests relating to this problem. Morton and King (1979) investigate the effects of tunneling on the bearing capacity and settlement of pile foundations by carrying out laboratory tests. They concluded that the effects of tunneling on existing adjacent pile foundations in weak soils may be a major and governing concern in the design and execution of underground works. Lee et al. (1994) reported a case where a tunnel was to be driven between newly constructed pile foundations supporting a seven-story building with a two-story basement. The lateral pile deflection was estimated using a 2D finite-element method and the computed maximum value was used to design the piles. Attewell et al. (1986) reported a case in which the pile was anticipated to experience negative skin friction to be caused by a future tunnel construction because bituminous slip coatings were applied to piles. Jacobsz et al. (2001) suggested a critical influence line associated with large settlement of piles during volume loss in the centrifuge model test.

Benton & Phillips (1991) analyzed the stress changes and deformations of two existing tunnels beneath a building founded on bored piles using two-dimensional finite element method, and the effects on tunnel during both construction and loading of the piles were considered. Chen et al. (1999) and Loganathan et al.

(1999) used a two-stage approach to study the pile response to unsupported excavation. This approach is based on the use of closed-form analytical solutions to estimate the soil movement induced by tunneling in

‘free-field’ conditions (i.e. in the absence of the pile) and a boundary element analysis to compute the response of piles to soil movements estimated by analytical solutions. Results of this analysis show that tunneling may cause appreciable bending moment, lateral deflection and compressive and tensile axial forces in adjacent piles. Based on these studies an understanding of soil–tunnel–pile interaction mechanisms under plane strain conditions has developed and simplified design charts for estimating the maximum pile

(2)

responses to tunneling have been produced. H. Mroueh & I. Shahrour (1999) investigated interaction between tunneling and pile foundations using three-dimensional finite element modeling, which concern, the construction of the tunnel in presence of the pile foundations. They concluded that the distribution of internal forces and displacements depends mainly on the position of the pile tip regarding the tunnel horizontal axis and the distance of the pile axis from the center of the tunnel. Lee & Chiang (2007) investigated responses of single piles under various working loads in saturated sandy ground to nearby tunneling using centrifuge model test. As only two-dimensional analyses were found in the literature, it is questionable whether they can properly simulate a truly 3-D problem, since analysis of the impact of the tunnel construction using TBM on the soil movement requires the solution of large 3D non-linear soil–structure interaction problem. Non- linearity results from the non-linear behavior of geo-materials, soil–structure interface and the evolution of the geometry during excavation.

In this study the main purpose is to develop a better understanding of pile responses caused by tunneling.

First, the computed internal force (i.e. bending moments and axial force) and displacements (i.e. lateral displacements and settlements) of pile caused by the tunneling advance from finite element method are determined and discussed. Second, the results of numerical analysis of pile responses are compared with values which have obtained from quasi-analytical approach proposed by Chen et al. (1999) and the surface settlement profile is compared with the approach presented by Loganathan & Poulos (1998).

3. Finite element model

3.1 Tunnel construction simulation

Numerical modeling of the tunnel construction using Tunnel Boring Machine (TBM) constitutes of the three- dimensional behavior and it, requires consideration of a set of complex simulations such as the soil excavation, the overcut or annular space between the tunnel support and the excavation line, the application of the face pressure, the installation of tunnel support consisting of lining rings and the grouting of the annular space. It also requires the description of the non-linear behavior of both the soil and the lining and the condition at the soil–structure interface (Mroueh and Shahrour, 2006). In this study a method proposed by Mroueh & Shahrour (2006) is used to model the TBM process using a three-dimensional model based on the convergence-confinement method (Panet and Guenot, 1982). This method uses a step-by-step procedure. At each step of the procedure, the stress release around the tunnel head is modeled using the parameters αdec and Ldec, which stand for the ratio of the stress release and the length of the unlined zone, respectively.

The soil movement is controlled through the partial release factor αdec and the parameter Ldec. In each step, the tunnel face progresses by a distance Llin. It includes:

(i.) A partial deactivation of soil elements situated in the section to be excavated. The deactivation procedure is governed by parameters αdec and Ldec which stand for the ratio of stress release (unloading level) and the length of the unlined zone, respectively. This procedure permits to take into consideration the presence of the boring machine and the TBM sequences.

(ii.) The construction of a new section of the lining and a full release of stresses in this section. (Mroueh and Shahrour, 2006)

3.2 Geometry and numerical parameters

The tunnel outer diameter and cover depth are equal to D=7.2m and H=2.5D, respectively. The tunnel lining and concrete pile were modeled as linear elastic materials. The concrete circular pile length and diameter are equal to Lp=22.6m and Dp=1m. The Homogeneous silty sand behavior is assumed to be governed by an elastic Perfectly-plastic constitutive relation based on the Mohr–Coulomb criterion with a non-associated flow rules. Table 1. Shows the material properties used in this study.

In this paper for better understanding of pile responses caused by tunneling four different pile distances from tunnel vertical axis are considered which are about Xp=1.5D, Xp=2D, Xp=2.5D and Xp=3D. Fig. 1. Show the relative location of pile and tunnel with dimensions. Figure 2 presents the finite element mesh used in numerical modeling. The left boundary of the model are located a distance 4D from the tunnel axis in order to minimize their interaction with the tunneling construction. The longitudinal length of the mesh is fixed to 6D. The distance of the tunnel center to the bottom boundary (rigid substratum) is assumed to be equal to 3D.

Roller supports were applied on all Vertical sides of the mesh, whereas pin supports were assigned to the base of the mesh. Therefore, the movement normal to all vertical sides of the mesh and the movements in all

(3)

directions at the base of the mesh were restrained. In this study, a circular concrete pile was constructed in the ground.

Fig. 1. Relative pile and tunnel location with dimensions.

Table 1. Material properties

Material E (MPa) C(Kpa) ) )

Soil(Sandy) 30 0.3 5 27 5

Liner(Concrete) 35000 0.25 - - -

Pile(Concrete) 23500 0.25 - - -

3.4 Calculation process

In this study, three different values for volume loss are considered.These values obtained by trial and error with examine the various values for



^dec

and constant Ldec which importance of these parameters in controls the soil movement is described in section 3.1. However, ratios of stress release are 0.97, 0.3, and 0.5 for volume loss equal to VL=2%, VL=3%, and VL=4%, respectively, Where VL denotes for the volume loss at the ground surface. The length of unlined zone Ldec=D/4, and also the length of excavated section at each step L_lin=D/3. The face pressure is assumed to be uniform and equal to to ensure its stability, where

0



h stands for the initial axial stress at the tunnel axis. It corresponds to a ‘compressed-air pressure’

TBM.

4. Results

4.1 General pile response caused by tunneling

Fig. 3. Shows the variation of induced lateral displacement of pile during tunneling, Ux, it can be observed that tunneling induced lateral deflection even after the passage of tunnel face from pile section. The direction of the pile head deflection is toward the tunnel, whereas in the portion of the pile adjacent to the excavated zone the direction of pile deflection is opposite. Variation of induced pile lateral deflection during tunneling

(4)

for Xp=1.5D, Uy, is presented in fig. 4. Pile deflection, Uy, is mainly induce before the passage of the tunnel face and after the passage of tunnel face a decrease of pile deflection is observed. For both, lateral and longitudinal deflection, the maximum values occur at pile head.

Fig. 2.Three-dimensional finite element mesh used for the pile/tunneling interaction.

Fig. 3. Variation of induced lateral deflection of pile during tunneling for Xp=1.5D, Ux

Fig. 4. Variation of induced pile lateral deflection during tunneling for Xp=1.5D, Uy

The variation of induced pile axial force along its length (Fig. 5) Presents the pile axial force is mainly induces in the upper part of the pile due to the downward soil movement, whereas decrease of the axial force is observed in the lower part of the pile, due to the upward movement of the soil in this zone. Furthermore, the maximum axial force occurs in the section located in the section located at the tunnel center depth.

Variation of induced pile bending moment during tunneling, Mx, My are presented in fig. 6 and fig. 7 respectively. The bending moment in the lateral section, Mx induces after the passage of the tunnel face, due to the increasing lateral deflection after the passage of the tunnel face from the pile, whereas The bending

(5)

moment in longitudinal section, My is mainly induce before the passage of the tunnel face. For both, lateral and longitudinal bending moment the maximum values occur in the proximity of the tunnel horizontal axis.

It should be noted that although the results presented in this paper are similar to those shown by (Mroueh and Shahrour, 1999), however, it is still very important to explore pile-tunnel interaction in more details for better. The following sections will provide results and discussion on pile behavior due to tunnel construction.

Fig. 5. Variation of induced pile axial force during tunneling for Xp=1.5D, N

Fig. 6. Variation of induced bending moment on the pile during tunneling for Xp=1.5D,

Mx

Fig. 7. Variation of induced bending moment on the pile during tunneling for Xp=1.5D, My

4.2 Maximum pile response caused by tunneling

Fig. 8 shows pile settlement induced by tunneling in each step of finite element analysis of tunnel progression for three values of volume loss. It can be observed that tunneling significantly induced pile settlement. Pile settlement increase with progression of tunnel face and increasing continue even after the passage of tunnel face from the pile location. The pile settlement stagnates when the distance of the tunnel face from the pile becomes greater than +2D, and after that constant values for pile settlement are observed.

Maximum pile settlements for volume losses of 2%, 3%, and 4% are about 10mm, 13mm and 15mm, respectively. Maximum induced lateral deflection of pile head and lateral deflection of pile in level of the tunnel centerline which obtained in each step of analysis are shown in fig. 9 and fig. 10. As mentioned in pervious section, maximum lateral deflection (Ux,heacd) occurs in pile head. It can be observed increasing in (Ux,heacd) and (Ux,CL) starts when the distance of tunnel face is about -2.5D. Increasing both (Ux,heacd) and (Ux,CL) continue even after the passage of tunnel face from the pile. The maximum amounts of Ux,heacd are about 11mm, 15mm and 18mm, whereas these values for Ux,CL obtained 6.8mm, 8mm and 9.8mm for VL=2%, VL=3% and VL=4%, respectively, which occur when the distance of the tunnel face

(6)

from the pile becomes +2.5D.On the other hand, pile deflection in the longitudinal section behaves differently.

Fig. 7. Variation of induced bending moment on the pile during tunneling for Xp=1.5D, My

Fig. 8. Maximum induced pile settlement in each step of tunneling for various values of volume loss, Xp=1.5D

Fig. 9. Maximum induced lateral displacement of pile head in each step of tunneling for various values of volume loss, Ux,head, Xp=1.5D

Fig. 10. Maximum induced lateral displacement of pile in level of the tunnel centerline in each step of tunneling for various values of volume loss, Ux,cl, Xp=1.5D

(7)

Fig. 11. Maximum induced lateral displacement of pile head in each step of tunneling for various values of volume loss, Uy,head, Xp=1.5D

Fig. 12. Maximum induced lateral displacement of pile in level of the tunnel centerline in each step of tunneling for various values of volume loss, Ux,cl, Xp=1.5D

Fig. 13. Maximum induced pile bending moment in each step of tunneling for various values of volume loss,Mx, Xp=1.5D

Fig. 14. Maximum induced pile bending moment in each step of tunneling for various values of volume loss,My, Xp=1.5D

(8)

Fig. 15. Maximum induced pile axial force in each step of tunneling for various values of volume loss, Xp=1.5D Both (Uy,heacd) and (Uy,CL) tend to decrease after the passage of the tunnel face from the pile(fig. 11 and fig. 12) It can be observed from fig. 11 that (Uy,heacd) tends to be about zero when the distance of tunnel face from the pile becomes greater than +2D. The maximum values for both (Uy,heacd) and (Uy,CL) occur when the lining installs at the level of pile location. In the other word, maximum pile deflections in this case occurs when the distance of the tunnel face from the pile is +0.5D.

Maximum pile bending moment in lateral section induced in each step of tunneling, Mx, is illustrated in fig.

13. It can be observed that Mx increase significantly due to the increasing lateral deflection. Mx increases even after the passage of the tunnel face from the pile. The maximum values of Mx are about 402KN.m, 439KN.m and 471KN.m for volume losses of VL=2%, VL=3% and VL=4, respectively. Furthermore, increasing in Mx stagnates when the distance of tunnel face from the pile becomes +2.5D and after that constant values for bending moment are observed. On the other hand, it can be observed from fig. 14 bending moment in longitudinal section tends to decrease after the passage of tunnel face from the pile. The maximum values for My are computed about 131.9KN.m, 142.1KN.m and 156.3KN.m for VL=2%, VL=3%

and VL=4, respectively. It should also to be noted that maximum My occur when the tunnel lining installs at the same level of the pile location.

Fig. 15. Shows maximum pile axial force induced by tunneling which obtained in each step of analysis. It can be observed tunneling significantly induced pile axial force. Increasing in axial force continue even after the passage of the tunnel face from the pile due to the increasing in vertical soil movement. Maximum values of axial force for volume losses of 2%, 3% and 4% are about 652.7KN, 797.7KN and 923.7KN, respectively. It should also to be noted that maximum values pile axial force occur when the distance of tunnel face from the pile becomes +2.25D and after that these values remain constant.

5. Comparison between surface settlement profiles

Computed surface settlement profiles using finite element method in presence of pile are compared with quasi-analytical expression by Loganathan and Poulos (1998) in ‘free-field’ conditions for volume loss of 2%

in Fig. 16. The maximum vertical displacement for numerical method (Smax) is equal to 3.466 cm, which is about 20.13% of the maximum settlement at the ground surface obtained by analytical approach. Where (Smax) denotes for the maximum settlement induced at ground surface. (Fig. 17) and (Fig. 18) show the comparison of transverse surface settlement trough for volume losses of 3% and 4%, respectively. The Smax is equal to 4.463 cm and 5.91 cm which obtained from numerical method for the VL=3% and VL=4%, respectively. Whereas, these values are about 5.596 cm and 7.39 cm for VL=3% and VL=4% from analytical solution purposed by Loganathan and Poulos (1998). It can also be noted in these cases the amounts of maximum ground surface settlement induced which obtained from finite element analysis are about 20.35%

and 20% of the maximum surface settlement estimated from analytical solution for VL=3% and VL=4%, respectively.

(9)

Fig. 16. Comparison of transverse surface settlement trough using various methods for VL=2%

Table 2. Summarizes the amounts of maximum settlement induced from numerical and analytical approach Difference )%(

Analytical solution (Cm) Numerical method (Cm)

Volume Loss

31.02 4.224

2.433 VL=2%

31.22 2.2.3

4.432 VL=3%

31 9.2.

2..0 VL=4%

It can be observed that the computed settlement profiles from numerical method in presence of pile tend to be shallower and wider than analytical profiles in ‘free-field’ conditions. Furthermore, movements are over predicted. (Potts and Addenbrooke, 1997; Burd et al., 2000) on studies on the simulation of tunnel–soil–

building interaction showed (illustrated) significant differences between settlements that would have been obtained at greenfield sites and at sites with the structure in place.

Table 2 summarizes the amounts of maximum settlement induced which are computed from numerical and analytical approach for three different values of volume losses and also the difference between these methods are showed in terms of percent.

(10)

6. Comparison between Pile responses

Table 3 comparison the results of numerical and analytical methods, X=1.5D

Volume Loss Parameters Analytical solution Numerical solution Difference (%)

Axial Force(KN) 300.2 276.661 7.8

VL=2% Bending moment (KN.m) 174.25 164.970 5.32

Lateral Displacement(mm) 2.63 2.417 8.706

Pile Settlement(mm) 5.4831 5.14 6.25

Axial Force(KN) 400 368.725 7.81

VL=3% Bending moment (KN.m) 330 208.215 2.95

Pile Settlement(mm) 7.298 6.8289 6.42

Axial Force(KN) 547 504.770 7.72

VL=4% Bending moment (KN.m) 393.32 262.238 2.02

Pile Settlement(mm) 9.5 5.. 6.31

Tables, 3 summarizes the comparison the results between numerical and analytical methods for Xp=1.5D, Xp=2D, Xp=2.5D, Xp=3D, respectively.

Details of comparison the results of numerical and the analytical methods for Xp=1.5D are given in Table 3 . The computed displacement and internal forces are compared with the analytical approach. It can be observed the difference between axial force for both method and three different values of volume losses is about 7.77%. the difference between bending moments are about 5.41%, lateral deflections are about 8.6%

and pile settlements are about 6.32%. for the all obtained values analytical solution shows conservable results in comparison with numerical solution.

It should be noted that the numerical results in these tables are for when the tunnel lining is installed in the level of the pile, whereas analytical approach shows the maximum responses of the pile induced by tunneling. In the other word, it can be concluded that although there is a good agreement between simulation results and analytical approach when the lining is installed at the same level of the pile, as it mentioned in pervious section the pile responses increase even after the passage of the tunnel face from the pile location.

As a result, the analytical approach may not be suitable for predict of pile responses due to the tunneling especially in densely built-up area where tunnel-soil-structure interaction plays a significant role, since the analytical approaches limited to tunneling in greenfield sites only.

9. CONCLUSIONS

This paper included a series of elastoplastic three-dimensional finite element simulations of the interaction between tunneling and pile foundations. Numerical results show that tunneling induce significant deflection and internal forces in piles. The results of numerical method show that Pile settlement increase with progression of tunnel face and increasing continue even after the passage of tunnel face from the pile location. The deflection of pile in lateral section increase with progression of tunnel face and even after the passage of tunnel face from pile location, increasing in lateral deflection continues, whereas the deflection of pile in the longitudinal section tend to decrease after the passage of the tunnel face.

(11)

The bending moment in lateral section increases even after the passage of the tunnel face from the pile due to the increasing in lateral deflection, whereas lateral bending moment tend to decrease after the passage of tunnel face from the pile location. Increasing in axial force continue even after the passage of the tunnel face from the pile due to the increasing in vertical soil movement.

Comparison between settlement profiles from numerical and analytical approach was performed. The results show that computed settlement profile from numerical method in presence of pile tends to be shallower and wider than analytical profile in free-field condition.

Comparison between the results of numerical and analytical solution for induced internal forces and displacement of pile show that although there is a good agreement between simulation results and analytical approach when the lining is installed at the same level of the pile, the pile responses increase even after the passage of the tunnel face from the pile location. As a result, the analytical approach may not be suitable for predict of pile responses due to the tunneling especially in densely built-up area where tunnel-soil-structure interaction plays a significant role, since the analytical approaches limited to tunneling in greenfield sites only.

11. REFERENCES

1. Areias, P.M.A. and Belytschko, T. (2005),“Analysis of Three-Dimensional Crack Initiation and Propagation Using the Extended Finite Element Method,”International Journal for Numerical Methods in Engineering, 63 (55), pp. 760–788.

2. Addenbrooke, T.I., Potts, D.M., Puzrin, A.M., 1997. The influence of prefailure soil stiffness on the numerical analysis of tunnel construction. Geotechnique 47 (3), 693–712.

3. Addenbrooke, T.I., Potts, D.M., Puzrin, A.M., 1997. The influence of prefailure soil stiffness on the numerical analysis of tunnel construction. Geotechnique 47 (3), 693–712.

4. Benton, L. J. & Phillips, A., 1991. The behavior of two tunnels beneath a building on piled foundations.

Proc. 10th European Conference on Soil Mechanics and Foundation Engineering: 665-668. Florence.

5. Calabrese, M. & Monaco, P. 2001. Analysis of stresses induced in an old deep tunnel by pile driving from the surface. FLAC and Numerical Modeling in Geomechanics: 199-204. France.

6. Chen LT, Poulos HG, Loganathan N. Pile responses caused by tunneling. ASCE Journal of Geotechnical and Geoenvironmental engineering 1999; 125(3):207–215.

7. Jacobsz, S.W., Standing, J.R., Mair, R.J., Soga, K., Hagiwara, T., Sugiyama, T., 2001. The effects of tunneling near single driven piles in dry sand. In: Proceedings of Asian Regional Conf. on Geotechnical Aspects of Underground Construction in Soft Ground. Tongji University Press, Shanghai, pp. 29–35.

8. Lee, R. G., Turner, A. J., and Whitworth, L. J. (1994). ‘‘Deformations caused by tunnelling beneath a piled structure.’’ Proc., XIII Int. Conf. Soil Mech. Found. Engrg., University Press, London, 873–878.

9. Loganathan, N., and Poulos, H. G. (1998). ‘‘Analytical prediction for tunnelling-induced ground movements in clays.’’ J. Geotech. and Envir.Engrg., ASCE, 124(9), 846–856.

10. Loganathan N, Poulos HJ, Xu KJ. 1999. Ground deformations and pile-group responses due to tunnelling. Proceedings of the III National Conference of the Geo-Institute of ASCE, University of Illinois at Urbana Champain, USA.

11. Loganathan, N., Poulos, H.G., Stewart, D.P., 2000. Centrifuge model testing of tunneling induced ground and pile deformations. Geotechnique 50 (3), 283–294.

12. Mair, R. J. (1993). ‘‘Developments in geotechnical engineering research: application to tunnels and deep excavations.’’ Unwin Memorial Lecture 1992, Proc., Instn. Civ. Engrs. Civ. Engrg., 93, 27–41.

13. Mair, R. J., Taylor, R. N., and Bracegirdle, A. (1993). ‘‘Subsurface settlement profiles above tunnels in clays.’’ Geotechnique, 43(2), 315– 320.

14. Morton, J. D., and King, K. H. (1979). ‘‘Effects of tunnelling on the bearing capacity and settlement of piled foundations.’’ Proc., Tunnelling ’79, IMM, London, 57–68.

(12)

15. Mroueh, H., and Shahrour, I. (1999). “Three-dimensional analysis of the interaction between tunnelling and pile foundations.” Proc., 7th Conf. on Numerical Models in Geomechanics—NUMOG, Austria, Balkema, Rotterdam, The Netherlands, 397–402.

16. Mroueh, H., and Shahrour, I.(2006) “A simplified 3D model for tunnel construction using tunnel boring machines” Tunnelling and Underground Space Technology; 23:38–45