The influence of tunnel boring on foundations and buildings in urban areas - A numerical study

Transcription

1 Int. Workshop on Geotechnics of Soft Soils-Theory and Practice. Vermeer, Schweiger, Karstunen & Cudny (eds.) 2003 VGE The influence of tunnel boring on foundations and buildings in urban areas - A numerical study R.B.J. Brinkgreve Geotechnical Laboratory, Delft University of Technology & Plaxis bv W. Broere Geotechnical Laboratory, Delft University of Technology & A.Broere bv ABSTRACT: The advancement of a tunnel boring machine in the ground has been numerically modelled using a phased excavation scheme. Special attention is given to the possibilities and limitations of numerical modelling of the tunnel boring process and the influence of soil stiffness. The method has been applied to a situation where tunnel boring may lead to damage in adjacent buildings on wooden piles. It is concluded that soil stiffness plays an important role in predicting the width of the settlement trough and consequently the influence on adjacent buildings. 1 INTRODUCTION The increasing performance of desktop computers may eventually lead to the situation that geotechnical engineers can apply non-linear three-dimensional finite element calculations on a daily basis for ordinary design and consulting purposes. However, this situation is not yet reality and requires more than just computer power. Finite element models for settlement analysis due to tunnelling are often known to over-predict the width and to under-predict the gradient of the settlement trough. To obtain realistic results it is, among other things, necessary to use advanced soil models and to carefully select the corresponding model parameters. In this contribution attention will be focused on the possibilities and limitations of 3D finite element models for the analysis of the effects of shield tunnelling on old masonry buildings founded on wooden piles. The situation considered is an arbitrary case based on a real large-scale project in Amsterdam, The Netherlands, where a tunnel is constructed (bored) in the ancient city centre. This large-scale project is known as the North-South (metro) line. The metro tunnels will be constructed near historical masonry buildings, founded on wooden piles, as well as newer buildings, founded on prefabricated concrete piles. Along the main part of the line the tunnels will run close to or beneath the toes of the wooden foundation piles. Both the piles and the masonry structure have little margin for deformation before damage to the construction will occur. In recent years, several papers have been published with details about soil conditions (Teunissen, 1998), design aspects and other issues related to the North-South line project. Extensive tests and monitoring programmes have been carried out during the construction of the Second Heinenoord Tunnel near Rotterdam, in view of the situation at the North-South line (Bakker, 1996). Predictions and back-analyses have been made of the settlement profile that occurs due to the tunnel boring process (Strack, 2000). The numerical modelling of this process itself has also been subject of several papers (Vermeer, 2000, 2001; Van der Vliet, 2001).

2 In the next section of this contribution it will be evaluated to what extent 3D finite element calculations can be used for geotechnical applications and which pitfalls should be taken into account. In the third section the example situation and the corresponding finite element model will be described in detail. Section four deals with the 3D modelling of the tunnel boring process. The fifth section describes the results of the finite element analysis in terms of the influence of the tunnel boring process on the surrounding buildings and the role of soil stiffness in the numerical analysis. Finally, in Section six, the main conclusions of this research are summarised. 2 POSSIBILITIES AND LIMITATIONS OF 3D FEM MODELLING OF SHIELD TUNNELS Apart from the computer power requirements, three-dimensional finite element calculations are difficult to perform due to various reasons. Probably the most important reason is that it is much more difficult to properly construct and interpret a three-dimensional computer model than a 2D model. Modelling errors are easily overlooked. Of course, advanced 3D computer graphics and 3D analysis tools can help, but it definitely requires spatial perception from the user. Particularly for an analysis that involves multiple subsequent construction stages (some modellers call this a '4D analysis', where Time is the fourth dimension), the use of animations can be of great help to evaluate the results or to locate input errors. Regarding the modelling of soil behaviour, a range of soil models is available nowadays in modern finite element computer programs. Simple constitutive laws, like the standard Mohr- Coulomb model, lack aspects of soil behaviour that are vital to obtain accurate results. Nevertheless, most finite element calculations are still performed using this first order model, because it requires a limited amount of parameters and calculation times tend to be smaller than when using advanced soil models. Regardless of the soil model, it should be realised that the strain levels observed even close to a shield tunnel are usually quite small (except in extreme cases) and the stress paths involve unloading rather than primary loading. As a result, the stiffness of the soil tends to be very high and is generally underestimated. Advanced soil models involve stressdependent stiffness relations and distinguish between primary loading and unloading, but the input of a small-strain stiffness is often not recognised. A real small-strain stiffness can only be determined from dynamic soil testing, but this type of testing is not standard. For the modelling of the tunnel boring process of a shield tunnel various methods were developed over the years. Aspects that should be considered are the face pressure (for slurry or earth pressure balance shields), the conicity of the TBM, the weight distribution of the TBM and other equipment, the grout injection in the tail void between the TBM and the final lining, the consolidation process of this grout layer, the segmentation and connections of the final lining, as well as various other aspects. Most modern finite element programs provide facilities to apply various types of loadings (pressure control), volumetric straining (strain control), tunnel lining contraction and, last but not least, staged construction. However, it is usually a tremendous job to correctly enter the necessary conditions for all calculation phases. A special aspect that needs to be considered is the start condition. Finite element models generally model the tunnel boring process on the route, but start from an undeformed mesh with initial soil stresses. These start conditions definitely influence the results. A certain number of construction steps are required to set the proper 'initial' conditions and to avoid influences of the boundary where the tunnelling process is started. Something similar can be said about the face of the TBM. Some soil deformation will already take place in front of the TBM. As soon as the TBM is activated (usually modelled by means of shell elements), these elements are pre-deformed but not properly stressed. However, if the analysis is performed according to the small deformation theory (only first order deformations) rather than an Updated Lagrangian analysis, these initial deformations do not really influence the stresses and forces, whereas in reality initial stresses and forces do exist. In reality, the tunnel boring process involves conditions that depend on the observations and measurements that are made during the tunnelling process and on how the TBM operation crew reacts on these observations. Examples of such conditions are the local pore pressure distribution, the face pressure (depending on TBM advancement and cutting speed) and the grout injection

3 pressure and volume. Hence, when a finite element analysis is used as a true class A prediction, the modelling may deviate significantly from the real process. Nevertheless, it can still be quite useful to perform a finite element analysis to qualitatively analyse the effects of tunnel boring. 3 THE EXAMPLE SITUATION AND FINITE ELEMENT MODEL In addition to an earlier analysis made for The Second Heinenoord Tunnel, an arbitrary but realistic situation is considered here in which an 8.5 m diameter tunnel is bored with its axis at a depth of 20 m below the ground surface (15.75 m soil above the tunnel lining). The situation is modelled using a 3D finite element model which is symmetric with respect to a vertical plane through the tunnel axis. The bottom of the mesh is at a depth of 30 m (5.75 m below the tunnel lining). In addition to the tunnel, a block of houses on piles is modelled adjacent to the tunnel at a distance of 10 m from the tunnel axis (5.75 m from the lining). The block of houses is 18 m long, 10 m wide and 12 m high (above the ground level). The piles are founded on the sand layer in which the tunnel is bored. Above this sand layer (S) there is a 2 m thick clay layer (C), a 7 m thick peat layer (P) and a 3 m thick fill (F). All layers are modelled with the Hardening Soil model (ref). Table 1 gives an overview of the soil layers and their properties and parameters. The stiffnesses are reference stiffnesses at a reference stress level of 100 kn/m 2. The dilatancy angle of the stiff sand layer is 6.5 degrees; the other layers have a zero dilatancy. The power in the stress-dependent stiffness relation is 0.5 for all layers, except for the clay layer, where it is 1.0. The hydrostatic pore pressure distribution in the model is derived from a phreatic level at 2 m below the ground level. The 3D finite element model used consists of 9125 quadratic volume elements, divided into 25 slices with identical cross section. However, in each slice, elements may be (de)activated or may have different properties (see Figure 1). The thickness of most slices is 3.0 m, corresponding with the advancement steps of the tunnel boring process. The 12 piles and the walls of the houses were created using 0.40 m thick columns and slices of volume elements that were filled with 'pile' and 'wall' material (linear elastic model; pile = wall =24 kn/m 3 ; E pile = kn/m 2 ; ν pile =0.0 ; E wall = kn/m 2 ; ν wall =0.2). A small slice is followed by a 2.60 m thick slice to complete the advancement step of 3.0 m. The TBM is modelled as a 9 m long cylinder of shell elements (three tunnel advancement lengths). The flexural rigidity of the shell EI = knm 2 /m and the normal stiffness EA = kn/m. The weight of the shell is taken as w = kn/m 2, representing the full weight of the TBM including equipment. The final concrete tunnel lining was modelled as a 0.35 m thick continuous ring, using volume elements with a volumetric weight γ = 24 kn/m 3, Young's modulus E = kn/m 2 and Poisson's ratio ν = 0.2. Figure 1. Finite element model in final situation (some elements have been made invisible to show the pile foundation)

4 Top [m+nap] Type Table 1. Soil layers and their parameters (Hardening Soil model) γ unsat [kn/m 3 ] γ sat [kn/m 3 ] ν ur [-] E 50 ref E oed ref E ur ref c' F 0.00 Drain P Drain C Undr S Drain φ' [ ] 4 3D MODELLING OF THE TUNNEL BORING PROCESS The modelling of the tunnel boring process consists of different aspects (see Figure 2), as mentioned in Section 2, although not all aspects are considered here. Inside the tunnel the soil is excavated by de-activating the corresponding volume elements and water pressures. At the face of the TBM a face pressure is applied to support the soil during excavation. This face pressure is 234 kn/m 2 at the top of the TBM and increases linearly to 336 kn/m 2 at the bottom. The TBM itself is slightly conical. The tail radius is 20 mm less than the front radius, which effect has been modelled using a total contraction of 0.48% at the TBM tail, i.e. an incremental contraction of 0.16% in each cross section at 3 m, 6 m and 9 m behind the TBM face. contraction of shield TBM face pressure grout pressure final lining Figure 2. Various excavation phases modelled in the phased excavation procedure The influence of the grout injection at the shield tail has been modelled using a distributed load, acting over 6 m (two tunnel advancement lengths). Thereafter it is assumed that the grout has settled and dewatered enough such that no additional deformations occur. The grout pressure has been set to 186 kn/m 2 at the top, increasing to 254 kn/m 2 at the bottom. Behind the grout injection zone the elements that form the tunnel lining are activated and are given concrete properties. The initial stresses are calculated using a coefficient of neutral effective stress according to Jaky. The full finite element analysis is divided into 20 calculation phases. In the first two phases, the piles and the building are constructed, but the corresponding deformations are not taken into account in further steps. In the following phases, the advancement of the tunnel boring process is simulated by advancing the tunnel face 3 m in every phase, starting from the back-side of the model and taking into account the previously described modelling aspects behind the tunnel face as long as they fit in the model. The first tunnel excavation step takes place in the third calculation phase. In the sixth phase the grout pressure becomes active for the first time (TBM shield is locally de-activated). In the eighth phase, when the tunnel heading has advanced to the first row of piles, the concrete lining is activated for the first time at the back-side of the model. In phase 14 the tunnel heading has advanced to the last row of piles. In the final phase 20 the tunnel heading has advanced 54 m, i.e. 18 m behind the last row of piles, such that most deformations of the buildings have occurred. The results of the analysis are presented in Section 5. 5 RESULTS OF THE FINITE ELEMENT ANALYSIS The influence of tunnelling close to pile foundations on the bearing capacity of those foundations and the resulting deformations of the structures founded on them is topic of several research projects (e.g. Teunissen, 1998). In this case it is the aim to investigate numerically and qualitatively

5 Figure 3. Total displacements at the end of Phase 20 (TBM well beyond houses) (deformations enlarged 100 times) to what extent pile foundations that are located primarily above the excavation level may be influenced by the tunnel boring process. Moreover, the importance of soil stiffness in the finite element model is shown. Figure 3 shows the tilting of the houses due to the tunnelling process. At the left side the vertical settlement is 17.8 mm and at the right side the vertical settlement is 5.7 mm, which gives a gradient of , i.e. less than 1:800. The gradient is slightly more than the gradient of the ground surface at the back-side of the model. This is due to the fact that the soil deformation and gradient at the pile tip level are higher than at the ground level. A gradient by itself may not be most harmful for historical buildings, but what might be more harmful is the torsion that occurs when the tunnel boring process passes the block of houses. The torsion effect reaches a maximum when the TBM has advanced about half way the houses (see Figure 4). Figure 4. Displacements at the end of Phase 10 (TBM half way houses) showing torsion of the houses (deformations enlarged 100 times)

6 From Figure 4 it can be seen that the wall at the back-side has settled and is inclined whilst the front wall is still more or less undeformed. This torsion effect may lead to cracks in the masonry walls, although the amount of torsion in this example case is quite limited. It is known that the width of the settlement trough above a tunnel is generally overestimated in a finite element analysis, and, as a result, the gradient of the trough is underestimated. Similar observations have been made for the width of the settlement trough behind a sheet pile wall or a diaphragm wall. It is the authors' opinion that the underestimation of the gradient is mainly due to an underestimation of stiffness in the small-strain region. To validate this statement an additional finite element analysis was performed for the situation as described in Section 3, taking into account small-strain stiffness effects. The analysis was performed by setting the stiffness moduli to values five times higher than used in the first analysis. It is recognized that this approach does not fully replicate the small-strain stiffness effect, since that effect is particularly pronounced at a somewhat larger distance from the tunnel. Nevertheless, the corresponding aspects can, to some extent, still be observed. The deformations around the tunnel are mainly strain-controlled and not stress controlled. Hence, the deformations immediately around the tunnel are not influenced by the larger soil stiffness, so a comparison of deformations is still valid. With the higher stiffnesses, the soil becomes plastic in a zone around the tunnel in an earlier stage, which effectively reduces the stiffness in this zone. As a result, the stiffness is lower around the tunnel and higher at a somewhat larger distance from the tunnel. This effect is similar (but not equal) to the small-strain stiffness effect. Figure 5 shows a comparison of results after Phase 20, where the model has been cut at the back-side wall of the houses. Although the deformations of the tunnel are almost the same, the settlement trough right above the tunnel in the stiff model (b) is indeed more concentrated and steeper than in the soft model (a). Nevertheless, the gradient of the houses in the stiff model is less than in the soft model. This is caused by the fact that in the stiff model the houses and their foundation are located just outside the zone in which most settlements occur whereas in the soft model the settlement area is wider and influences the pile foundation more than in the stiff model. Also the settlements of the ground surface are less in the stiff model than in the soft model (see Figure 6). Especially in the stiff model the inclination of the ground surface near the houses is less than at the back-side of the model. For the soft model the situation is reversed, as mentioned before. Figure 5. Total displacements at the back-side wall and beyond at the end of Phase 20 (deformations enlarged 100 times) a. Original analysis with stiffnesses according to Table 1 b. Modified analysis with five times higher stiffnesses

7 Figure 6. Comparison of settlements at the ground surface at the end of Phase 20 a. Original analysis with stiffnesses according to Table 1 b. Modified analysis with five times higher stiffnesses 6 CONCLUSIONS A 3D finite element analysis can be used quite well to simulate the tunnel boring process and to analyse the effects on adjacent structures. However, it is important to take sufficient modelling aspects into account. Regarding soil behaviour, it is important to realise that the soil behaves quite stiff due to unloading and small-strain stiffness effects. In the model, the selected soil stiffness influences the width of the settlement trough and the effects of the tunnel boring process on adjacent structures. REFERENCES Bakker K.J., van Scheldt W. Plekkenpol J.W. (1996) Predictions and a monitoring scheme with respect to the boring of the Second Heinenoord Tunnel. Geotechnical aspects of underground construction in soft ground. Balkema, Rotterdam, Brinkgreve R.B.J., Vermeer P.A. (2001) Plaxis 3D Tunnel (Validation manual). Balkema, Lisse. Strack O.E., Verruijt A. (2000) A Complex Variable Solutions for the Ovalization of a Circular Tunnel in an Elastic Half-Plane. GeoEng2000, An International Conference on Geotechnical & Geological Engineering. Technomic. Teunissen E.A.H., Hutteman M. (1998) Pile surface settlements at full scale tests North/South metro line. Tunnels and Metropolises, WTC 98. Balkema, Rotterdam Vermeer P.A., Ruse N. (2000) Face stability when tunneling in soil and homogeneous rock. Proc. Developments in Theoretical Soil Mechanics The John Booker Memorial Symposium. Sydney, Vermeer P.A. (2001) On a smart use of 3D-FEM in tunnelling. Plaxis Bulletin (11), 2-7 Van der Vliet C., de Boer A., Blom C.B.M., Ros P.L.M. (2001) Strategy and results of calibration for complex 3D finite element model for tunnel linings in soft soil. Modern Tunneling Science and Technology. Swets & Zeitlinger,