Numerical Simulation of Ground Movements Due To EPB Tunnelling in Clay

Transcription

1 EURO:TUN rd International Conference on Computational Methods in Tunnelling and Subsurface Engineering Ruhr University Bochum, April 2013 Numerical Simulation of Ground Movements Due To EPB Tunnelling in Clay Vasiliki Founta 1, Jelena Ninić 2, Andrew J. Whittle 1, Günther Meschke 2 and Janosch Stascheit 2 1 MIT, Department of Civil and Environmental Engineering 2 Institute for Structural Mechanics, Ruhr University Bochum, Germany Abstract This paper compares the results of two different 3D finite element models for simulating EPB mechanized tunnelling in clay. One model is created in Plaxis 3D TM and the other using the Kratos-Ekate software. The Plaxis model represents the construction process as a sequence of discrete steps, where soil elements are deactivated, and the conical shield is modelled by imposing appropriate boundary conditions at each step. The segmental concrete lining is brought into contact with the surrounding soil by activating an annulus of grout with time-dependent mechanical properties. In contrast, the Kratos model provides a process-oriented simulation that represents the TBM as a distinct deformable structure in frictional contact with the soil. The shield is advanced using an array of hydraulic jacks that react against the lining system and can be used to control the shield orientation. The Kratos model offers advantages in simulating the TBM trajectory, but involves much greater computational complexity. In this paper we compare results from the two FE models, using a linearly elastic-perfectly plastic (MC) soil model and similar grout properties, to establish how details of the tunnel construction simulations affect the predicted ground movements. Keywords: Tunnelling, EPB, finite element model, ground deformations, lining forces 1 INTRODUCTION 1

2 V. Founta, J. Ninic, A.J. Whittle, G. Meschke, J. Stascheit Mechanized tunnelling is an established and flexible technology for the construction of tunnels in urban areas. The tunnel construction process in soft soils causes short and long term ground deformations resulting from a disturbance of the in situ stress state of the soil and pore pressures due to the heading face support, the shield skin friction and the gap grouting. The procedure for controlling the advance of the EPB machine can affect significantly the development of far-field soil deformations, as well as the structural forces within the lining system. Therefore, analyses of the ground response require accurate modelling of the constitutive material behaviour and construction process. Finite element (FE) methods have been used to simulate tunnel construction since the early 1980s, but there are still relatively few studies involving threedimensional modelling of mechanized tunnelling [e.g., 1-4] compared to conventional tunnelling (i.e., open-face, sequential excavation and support). A process-oriented three-dimensional (3D) finite element model for simulating mechanized tunnelling in soft ground conditions has been proposed in [5] and demonstrated in simulations of slurry shield tunnelling in clay [6]. More recently this model has been extended for tunnels in partially saturated soft soils [7]. However, increasing the complexity of the numerical model generates very large computational costs, while each component of the model is still subject to certain assumptions. In order to answer the question of an optimal balance between accuracy of the solution and complexity of the model, two different modelling approaches are presented in this paper. A comparative study investigates the effect of the mechanized tunnel excavation on ground settlements and structural forces in the lining by means of Plaxis 3D TM and Kratos-Ekate [8] model. In order to capture the influence of specific modelling assumptions, the two models are calibrated using a simplified reference excavation procedure (Appendix A). For this reference situation, the model parameters are calibrated such that their response matches the analytical solution presented in [9]. The comparison is focused on the surface deformations, and axial forces and moments in the lining. Further, numerical issues relating to element types and numerical integration are also addressed briefly in this paper. 2

3 Numerical Simulation of Ground Movements Due To EPB Tunnelling in Clay 2 MODELING OF EPB TUNNELLING Two different approaches are used to simulate the shield tunnelling process. One numerical model is created using Plaxis 3D TM FE program and the second model is created using Kratos, an object-oriented FE framework for multi-physics simulations. Both models are based on the geometry of the Herrenknecht EPB machine currently being used to bore tunnels for the Crossrail project in London, with a 7.1 m diameter cutting wheel and 12 m tapered steel shield. The analyses consider ground conditions associated with a "base" tunnel design section with a cover depth of m (16 m to springline) below ground surface, where the tunnel is excavated within the London Clay. The clay extends to a total depth of approximately 60 m and overlies the Lambeth Group (approximately 12 m thick) and the Thanet sands (lower aquifer). The analyses consider an idealized 100m long straight horizontal trajectory for the EPB machine within a uniform 60 m deep clay layer. The FE model assumes a lateral boundary located 300 m from the tunnel centerline (to ensure accurate representation of far field ground movements), with symmetry in the longitudinal plane such that only a halfsection of the tunnel (and EPB machine) is represented. Both models are using same geometry ( m), and the tunnel construction is performed within 66 excavation rounds (each 1.5 m long). The models assume undrained shear conditions within the clay (i.e., the model assumes there is no migration of pore water within the clay mass over the time frame of the tunnel construction), and represent a profile where undrained shear strength varies linearly with depth (Table 1). The analyses assume that the groundwater table is coincident with the ground surface and pore pressures are hydrostatic. Calculations have been performed for two different in situ stress conditions, K 0 = 1.0 and Plaxis Model This section describes the development of the 3-D FE model using the general purpose geotechnical software Plaxis 3D TM. The model uses 10-node solid tetrahedral elements with quadratic interpolation of displacements (and pore pressures) to represent the soil mass, while the tunnel lining is simulated using 6-noded plate elements. The model assumes zero lateral displacements along the exterior vertical boundaries of the mesh. The clay is modelled as an elastic-perfectly plastic material with a Mohr-Coulomb yield criterion [MC] that is subject to undrained shearing. Table 1 lists the input parameters used to represent the London Clay profile using the MC model. 3

4 V. Founta, J. Ninic, A.J. Whittle, G. Meschke, J. Stascheit Figure 1: Modelling approaches for EPB mechanized tunnelling: a) Plaxis 3D TM b) Kratos-Ekate Initial horizontal stresses are specified by an assumed K 0 condition. Figure 1a shows a schematic figure of the boundary conditions used to represent the EPB tunnel-boring machine in the Plaxis 3D FE model. The 12 m long shield is represented by a set of 8x 1.5 m long segments with uniform radial displacement-defined boundaries that approximate the conical surface of the shield. The face conditions are represented through a uniform face pressure (the current base case assumes 150 kpa). Conditions in the tail void and initial ring assembly are represented by a uniform grout pressure (with grout pressure of 100 kpa), which extends over one tunnel segment. The lining is then activated with an initial external diameter, 6.8 m and a ring of hardening grout is activated around the lining. Table 1 summarizes the elastic properties of the lining and grout. In order to account for the effects of grout set-up properties, a time hardening model [6] is used to represent the time dependent stiffness of the activated grout. Since 4

5 Numerical Simulation of Ground Movements Due To EPB Tunnelling in Clay the EPB machine is assumed to advance forward in steps, the time parameter is introduced by assuming a reasonable excavation rate of 1 m/h [11]. As a result, each excavation step corresponds to a 1.5 h time step. Table 1: Soil Grout Material properties used in FE models P K Material Model Mohr Coulomb Drucker Prager ρ [kg/m 3 ] E [MPa] 2, z ν 0.25 undrained effective ( ) stress analysis 0.5 Su [KPa] E1/E z - P Kasper 1,500 [ ] 10 3 [ ] K , Lining P/K Linear Elastic 2,500 20, , Machine P K Linear Elastic 7, , KRATOS Model For this comparative study, a second model has been created using the object-oriented FE framework KRATOS [11]. It has been designed to match the PLAXIS model by means of deactivation of soil elements and installation of tunnel lining and grouting elements. It is a simplified version of the ekate model for process-oriented simulation of mechanized tunneling (see [8]) and accounts for the shield as a deformable body moving through the soil and interacting with the ground through frictional surface-tosurface contact. The volume loss due to the excavation process follows naturally the real, tapered geometry and the overcutting of the shield machine. The soil is modeled as a two-phase fully saturated material [5], accounting for solid and water as distinct phases according to the theory of mixtures, where the plastic behavior of the solid phase is described by a Drucker-Prager plasticity model. Grout is modeled as a fully saturated two-phase material with a hydrating matrix phase, considering for time-dependent 5

6 V. Founta, J. Ninic, A.J. Whittle, G. Meschke, J. Stascheit stiffness and permeability of the matrix material of the cementitious grout [12]. Therefore, the grouting pressures are applied at the front face of the grout elements instead of directly at the soil (see Fig. 1b). The excavation of one slice of soil (1.5 m) is performed in three successive steps, which provides continuous temporal development of excavation-induced settlements. All material properties have been chosen similar to the Plaxis model and have been calibrated by means of a reference excavation model (see Table 1 and Appendix A). The FE mesh of the model uses 27- node hexahedron elements for all components (soil, lining, grouting, shield) and has a total number of DOFs. For future comparisons, the full-featured version of the ekate model will be used, adding simulation of the steering process by means of hydraulic jack elements to study the influence of free movements of the shield and fluctuations in jack forces on the loading of the lining and the behavior of the surrounding ground. 3 RESULTS AND COMPARISONS 3.1 Comparison of surface settlements The two modelling approaches are compared by examining the differences between the ground surface displacements and the structural forces in the lining. Figure 2a-d compares the vertical and horizontal components of surface deformations along the transverse mid-plane of the FE model (y' = 0 m) for different K 0 values ( ) at three reference locations of the EPB machine, y'/d = 7.1, 0.7 and -6.8 (where y' is the longitudinal distance from the center of the FE model and D, the nominal lining diameter). At the first location represents conditions the EPB shield becomes fully embedded in the FE model, at the second the face approaches the central-plane of the model and at the third the face of the machine approaches the rear face of the model. It can be seen that both vertical and horizontal displacements of Plaxis and Kratos show good agreement for K 0 = 1.0, for all the three positions of the machine. This can be explained by the fact that for K 0 = 1.0, the main deformation mode of the excavation boundary is uniform convergence. For this deformation mode Plaxis and Kratos models produce similar deformation shapes at the tunnel cavity i.e., the imposed uniform boundary displacements in Plaxis produce a similar shape for the excavation boundary as the approach used in Kratos, where the excavation boundary freely deforms by means of relaxation of stresses. In general, the analyses with K 0 = 1.5 produce larger far field settlements (x > m) and larger lateral deformations than the analyses with K 0 = 1.0. While the horizontal 6

7 Numerical Simulation of Ground Movements Due To EPB Tunnelling in Clay displacements are similar for the two FE models, the vertical displacements differ substantially for the K 0 = 1.5 case (for x 20-30m). This is explained by the fact that deformations of the excavation boundary for K 0 = 1.5 ovalization as well as uniform convergence modes [12]. The imposed boundary conditions used to simulate the machine in Plaxis do not capture the ovalization but predict a wider settlement trough (than for K 0 = 1.0). In contrast Kratos predicts very small centreline settlements due to passage of the EPB shield (y /D 0.7 to -6.8) with maximum surface settlements occurring at an offset location, x = 10-15m. While these results are readily explained from the numerical models, they have yet to be resolved with respect to real field data. Figure 3 shows the development of surface settlements as a function of time for the longitudinal mid-plane. For K 0 = 1.0 the surface settlements troughs of the two models are similar. Plaxis predicts larger settlements ahead of the EPB machine since the imposed boundary displacements are larger than the free deformations of the tunnel cavity (allowing the formation of the gap) in Kratos. However final settlements of the two models are comparable at y /D =

8 V. Founta, J. Ninic, A.J. Whittle, G. Meschke, J. Stascheit Figure 2: Comparison of surface settlements trough for Plaxis and Kratos FE models for different positions of machine with respect to middle cross section There is a significant difference in surface settlements for the K 0 = 1.5 case seen also in Figure 3. It becomes clear that the ovalization mode is represented in Plaxis, only after the passage of the EPB machine (after 50m advance), where the surface settlement trough starts to diverge from the K 0 = 1.0 case. In contrast differences between the two K 0 cases become apparent at the excavation face, and much smaller settlements are predicted for the K 0 = 1.5 case. Figure 3: Comparison of surface settlements trough for Plaxis (P) and KRATOS (K) model for different positions of machine with respect to middle cross section 3.1 Comparison of structural forces Figure 4 compares the computed structural forces in the lining for the two models after tunnel construction. The structural forces were plotted for a reference lining ring located at the mid-plane. The plotted values correspond to values averaged first over the ring elements and then over the ring width. It can be seen that the differences in structural forces are negligible for K 0 = 1.0. As expected, the bending moment is almost zero for K 0 = 1.0 (uniform convergence), whereas for K 0 = 1.5 it is positive for the springline and negative for crown and invert 8

9 Numerical Simulation of Ground Movements Due To EPB Tunnelling in Clay Figure 4: Structural forces in linings for two different modelling approaches and K0 values, for the lining ring in the middle after construction process is completed (ovalization). For the bending moment there is a good match between the two models for both K0 = 1.0 and K0 = 1.5. For the axial force, the two models give similar results for K0 = 1.0, while for K0 = 1.5 there is a big difference at the springline due to the significant effect of the ovalization mode. The observed mismatch is smaller than expected, due to the small initial stiffness of the grout that allows for significant deformations, absorbing the imposed displacements by the surrounding soil. As a result, only a part of the displacements affects the lining. 9

10 V. Founta, J. Ninic, A.J. Whittle, G. Meschke, J. Stascheit 4 CONCLUSIONS This paper compares results of two three-dimensional FE models for simulating the mechanized tunnel construction. The Plaxis model uses simplified boundary conditions to represent the EPB tunnelling process, while Kratos represents the TBM as a distinct deformable structure in contact with the soil. The analyses simulate the Crossrail EPB machine and assume undrained conditions with stiffness and strength parameters typical of London Clay. Results are compared for cases with K 0 = 1.0 and 1.5. The two FE models produce quite similar predictions of surface deformations and lining forces for the K 0 = 1.0 case. However, there are large differences in the predicted behaviour at K 0 = 1.5 that can be directly attributed to the assumed boundary conditions of the two models. The more comprehensive Kratos model predicts an ovalization of the tunnel cavity resulting in smaller surface settlements above the tunnel. Lining forces are quite comparable for both K 0 cases, although Kratos tends to predict smaller axial thrusts and larger bending moments at the springline for K 0 = 1.5 than Plaxis. While comprehensive process oriented FE models such as Kratos are clearly superior for representing (and controlling) the advance of a tunnel boring machine, the predictions of the simpler Plaxis model appear to provide very reasonable predictions of far-field ground deformations and tunnel lining forces. 5 ACKNOWLEDGEMENTS Research on tunnel modelling at MIT has been supported by Ferrovial-Agroman, the second Author (JN) has been supported by the Ruhr-University Research School funded by Germany's Excellence Initiative (DFG GSC 98/1). This support is gratefully acknowledged. REFERENCES [1] S. Bernat, B. Cambou Soil-structure interaction in shield tunnelling in soft soil. Computers and Geotechnics, 22 (3/4), pp , Ernst& Sohn,

11 Numerical Simulation of Ground Movements Due To EPB Tunnelling in Clay [2] K. Komiya, K. Soga, H. Akagi, T. Hagiwara, M. Bolton Finite element modelling of excavation and advancement processes of a shield tunnelling machine. In Soils and Foundations, 39 (3), pp , [3] D. Dias, R. Kastner, M. Maghazi. Three dimensional simulation of slurry shield tunnelling. In Kusakabe O, Fujita K, Miyazaki Y, editors. Geotechnical aspects of underground construction in soft ground, Tokyo 1999, Rotterdam: Balkema;. p , [4] G. Swoboda, Abu-Krisha Three-dimensional numerical modelling for TBM tunnelling in consolidated clay. In Tunnel Undergr Space Technol, 14, pp , [5] T. Kasper, G. Meschke A 3D finite element model for TBM tunnelling in soft ground. In Int J Numer Anal Methods Geomechanics, 28, pp , [6] T. Kasper, G. Meschke. On the influence of face pressure, grouting pressure and TBM design in soft ground tunnelling. Tunnelling and Underground Space Technology, 21 (2), , [7] F. Nagel, J. Stascheit, G. Meschke, A. Gens, T. Rodic. Process-oriented numerical simulation of mechanised tunnelling. G. Beer (Ed.), Technology Innovations in underground construction, Taylor and Francis, pp , [8] F. Nagel, J. Stascheit, G. Meschke. Numerical Simulation of Interactions between the Shield Supported Tunnel Construction Process and the Response of Soft, Water Saturated Soils. International Journal of Geomechanics (ASCE), 12, , [9] F. Pinto, A.J. Whittle. Ground movements due to shallow tunnels in soft ground: 1. Analytical solutions. ASCE Journal of Geotechnical and Geoenvironmental Engineering, To appear, [10] P. Dadvand, R. Rossi, E. Oñate. An object-oriented environment for developing finite element codes for multi-disciplinary applications. Archives of Computational Methods in Engineering, 17 (3), pp ,

12 V. Founta, J. Ninic, A.J. Whittle, G. Meschke, J. Stascheit [11] M. Melis. A selection and specifications of the EPB tunnelling machines for the Madrid Metro extension. Jornadas Tecnicas sobre la ampliacion del Metro de Madrid. Fundacion AgustÃn de Bethencourt y Comunidad de Madrid, Madrid, Vol 1, [12] A.J. Whittle, C. Sagaseta. Analyzing the effects of gaining and losing ground. Soil Behavior and Soft Ground Construction, ASCE GSP No. 119, pp APPENDIX - VALIDATION OF SOIL MODELS Plaxis (Mohr-Coulomb) and KRATOS (Drucker-Prager) soil models are calibrated using a simple excavation test. A simple model with the same dimensions ( m), boundary conditions and soil characteristics as the tunnelling model is created in both, Plaxis and Kratos. Further, a simple excavation test is performed, where the elements representing the excavation sequence are removed, and the soil freely deforms at the excavation boundary by relaxation of in situ stresses. This test is performed for both software for K 0 = 1.0 and K 0 = 1.5. In Figure 5 the horizontal and vertical displacements at the soil surface for both models are presented. As it can be seen, there is a near-perfect match for the results of both models. Figure A1: Structural forces in linings for two different modelling approaches and K0 values, for the lining ring in the middle after construction process is completed 12