Introduction. I have been working with Luis Vigl on a challenging tunneling project, the Gilgel Gibe II Tunnel in. Ethiopia. I was acting as a consultant on behalf of ...
G. Barla Paper Luis Vigl 60th birthday
Is 3D modeling of TBM excavation in squeezing rock a feasible and useful design tool? G. Barla, Politecnico di Torino, Torino, Italy
1. Introduction I have been working with Luis Vigl on a challenging tunneling project, the Gilgel Gibe II Tunnel in Ethiopia. I was acting as a consultant on behalf of ELC Electroconsult and EEPCO - Ethiopian Electric Power Corporation) and Luis was working for the Contractor (SELI SpA). Going back to this remarkable and unique tunnel case (Barla 2010), it is indeed a matter of course and enjoyable at the same time to write this short note on TBM tunneling in “squeezing rock” on the occasion of Luis’ 60th birthday! In tunneling at great depth, the tunnel excavation may induce a stress change with large deviatoric stresses which, in turn, induce a squeezing behavior. This is shown by time dependent, irreversible and mainly deviatoric deformations, which last long after the excavation and may be relevant in the short term, i.e. in a time span comparable with the excavation time. The magnitude of tunnel convergence or “squeezing” which occurs as the tunnel is excavated and the rate of deformation, including the extent of the plastic zone ahead and around the tunnel, depend on: (1) the rock mass conditions before and after failure; (2) the in situ state of stress relative to the rock mass strength; (3) the support pressure provided by the lining and the consolidation/stabilization measures adopted, if any, ahead and around the tunnel. The combination of high in situ stress (generally related directly to the depth of the tunnel) and weak rock results in the most significant squeezing conditions. In general, if the support installation is delayed, the rock mass moves into the tunnel and a stress redistribution takes place around it. On the contrary, if deformation is restrained, squeezing will lead to long-term load build-up of the support With a TBM tunnel, if rock mass deformation is rapid relative to the progress of the TBM, and insufficient overcutting around the shield has been allowed, the TBM may become entrapped by the squeezing ground. Speed of advance is important in minimizing the entrapment risk. However, this may have an adverse effect on the load on the lining at the rear of the TBM shield. At the design stage, TBM tunneling in squeezing rock is very demanding. Serious difficulties in predicting the extent of squeezing, the performance and even the feasibility of a TBM drive remain. In this respect, analytical, semi-analytical and axisymmetric numerical solutions are often used. More recently, a 3D model which considers all the TBM components has been proposed (Barla et al. 2011, Zhao et al. 2012). 1
G. Barla Paper Luis Vigl 60th birthday If 3D modeling is a feasible and useful design tool is open to questions, given the complexities and uncertainties of the problem under study. Actually, many people feel that it may yet be preferable to rely on experience derived from previous works and on observation and monitoring during excavation. I will give some short evidence, taken from a recent case study, of the results that can be obtained with 3D modeling, hoping to have a comment from Luis, who knows TBM tunneling very well, the next time I will meet him (in Salzburg, for the Geomechanics Colloquy?).
2. Simplified design analysis methods TBM entrapment in squeezing conditions occurs when the available thrust is not sufficient to maintain TBM advancement or to allow for TBM restart. A possible approach to study this problem is to determine the closure of the TBM shield gap. In order to do this, one is to calculate the distance from the face where the gap between the tunnel perimeter and the shield closes completely and the ground gets into contact with the shield. The Longitudinal Displacement Profile (LDP) method represents the simplest solution. Axisymmetric Numerical Modeling (ANM) is also used for a better understanding of the complex interaction process during excavation.
• Longitudinal Displacement Profile (LDP) method The LDP method represents the simplest solution. The LDP of the tunnel, i.e. the closure or displacement versus distance from the tunnel face, is calculated. If contact occurs (e.g. the radial displacement u is equal to the TBM gap uTBM ), a load-build up on the machine will develop which may lead to TBM entrapment. The calculation assumes that the TBM shield is infinitely stiff, i.e. the shield is instantaneously loaded when contact with the ground occurs. The semi-analytical solution due to Vlachopoulos and Diederichs (2009), which gives the radial displacement u versus the normalized plastic zone radius R* = Rpl / a, where Rpl is the radius of the plastic zone and a is the tunnel radius, may be used to compute the LDP. In order to account for the non-isotropic in situ state of stress in the rock mass (Kh= σh/σv ≠ 1; σh=minimum in situ principal stress and σv= maximum in situ principal stress ), one may refer to the mean in situ stress (σv + σh)/2. The first step is to determine the radius of the plastic zone Rpl and the maximum radial displacement umax . The LDP is then computed. In order to account for the presence of the TBM cutter head, the radial displacement at a specific point along the tunnel is calculated by subtracting the displacement uf at the face from the LDP value (in other words the TBM is made to excavate the ground which has undergone displacement before excavation). The thrust required to overcome the friction force acting between the shield and the rock mass can be calculated based on the pressure which develops on the shield after closure of the gap Fr = ps⋅S⋅m , where ps is the pressure acting on the shield, m is the friction coefficient and S is the contact surface between the shield and the rock mass, which is given as S = 2⋅p⋅rs⋅Lc, where rs is 2
G. Barla Paper Luis Vigl 60th birthday the shield radius and Lc is the length where contact occurs. The pressure ps can be calculated from the Ground Reaction Curve (GRC) as the pressure acting when the radial displacement u is equal to uf + uTBM. • Axisymmetric Numerical Modeling (ANM) method Axisymmetric numerical modeling is possible by using either the Finite Element Method (FEM) or the Finite Difference Method (FDM). Due to the advantageous features available with the FDM code FLAC (essentially the large deformation option), reference is made below to the use of FDM. A typical detail of the FDM grid used in such cases is shown in Figure 1.
Figure 1: Axisymmetric Numerical Model. Detail of FDM grid near the face
The rock mass is assumed to be an isotropic elasto-plastic Mohr-Coulomb continuum. Time dependent modeling with an elasto-visco-plastic constitutive law is also possible. The initial state of stress in the rock mass is taken to be equal to the mean stress as previously defined. Special care is used in the simulation of: (1) TBM head-shield interaction, (2) rock mass-segmental lining interaction, (3) application of the TBM thrust, (4) gaps due to overcutting and shield conicity. Given the large deformation option available with FLAC, the progressive closure of the gap between the rock and shield/lining can be well reproduced in order to update the model geometry as the face advance is simulated. To this purpose, interface elements are used. The excavation sequence is simulated with a step-by-step process in order to represent the deactivation of the excavated elements, TBM advancement as new contacts at the face and along the shield occur, and the activation of the segmental lining. The TBM thrust is calculated with reference to the integral of the normal stress acting on the shield.
3. 3D Modeling - TBM Simulator A novel and completely 3D simulator has been developed as described in (Barla et al. 2011 and Zhao et al. 2012). The main TBM components considered (a Double Shield TBM is taken as example) are as follows: shields, cutter-head, backfilling, lining, thrust jacks. These are modeled
G. Barla Paper Luis Vigl 60th birthday with a linearly elastic isotropic law except the backfilling elements. The rock mass is modeled as an isotropic elasto-plastic Mohr-Coulomb material. The model simulates the on-going shielded TBM excavation by a step-by-step method. The excavation length is chosen so as to simulate a continuous and rapid excavation process. The construction stages and the total number of steps to be performed depend on the geometry of the excavation, the TBM type, and the rock mass. A typical simulation process is shown in Figure 2.
Figure 2: TBM Simulator. (a), (b), (c) Typical steps used simulate the ongoing shielded TBM excavation
4. Case Example The excavation of the Headrace Tunnel of the Kishanganga Hydroelectric Project (India), in the Hasthoji Formation, is considered in the following. The rock mass is a very thinly to thinly bedded shale with inter-beds of meta-siltstones. The rock mass parameters are as follows (no dilation is assumed): deformation Modulus Ed=3.6 GPa, Poisson’s ratio νd=0.3, cohesion c=2.8 MPa, friction angle φ=22°. The vertical in situ stress σv is 26 MPa and the horizontal stress σh is 52 MPa (i.e. Kh = 2). A Double Shield TBM is used with length 11 m. The boring diameter is 6 m with uniform overexcavation equal to 90 mm at the front shield, increased to 110 mm at the rear, due to a stepwise conicity of 20 mm. Figure 13 shows the equivalent plastic strain zones in a three dimensional view. Figure 14 illustrates the radial displacement along the tunnel axis (the LDPs) and the principal stresses at the octant point ahead and behind the face. 4
G. Barla Paper Luis Vigl 60th birthday
Figure 3: Case example. Results of TBM Simulator Equivalent plastic strain contours
Figure 4: Case example. (a) Longitudinal Displacement Profile behind the tunnel face. (b) Principal stresses at the octant point along the longitudinal axis
G. Barla Paper Luis Vigl 60th birthday A failure zone develops around the tunnel which extends more at the crown than at the sidewalls (Figure 3). The maximum closure occurs at the crown (Figure 4a). Contact between the ground and the TBM takes place 4 m behind the face, and 3 m behind the front shield, in the rear shield. The principal stresses (Figure 4b) follow the same trend of behavior with the minimum principal stress σ3 showing localised unloading along the shields. A stress concentration occurs at the face and the initial state of stress is reached approximately one diameter ahead of the face. As the annulus grouting is formed simultaneously with face advance, the segmental lining is shown to support the ground 2 m behind the TBM. During the transient phase, the backfilling works as a compressible buffer and the ground undergoes still a significant deformation. As soon as the grout hardens, the backfilling and the segmental lining act as a stiff system. The contact pressure developing on the shields and on the segmental lining is not uniformly distributed along the cross-section. Based on the normal stress distribution, the computed thrust results to be equal to 72 MN. It is of interest to note that the ANM gives a smaller value equal to 60 MN, whereas the LDP method would result in the grossly overestimated value of 130 MN.
5. Conclusion The Longitudinal Displacement Profile (LDP) method and the Axisymmetric Numerical Modeling (ANM) method have been introduced as recognized design analysis tools for the simulation of TBM excavation in squeezing rock. A recently developed 3D simulator has been presented. With a case example the results of typical design analyses performed with the 3D TBM Simulator have been briefly discussed. It has been shown that 3D modeling represents a significant step forward and is highly effective in reproducing the interaction between the rock mass, the TBM components, and the lining.
Acknowledgement Thanks are due to Dr Kai Zhao for the numerical analyses with the 3D Simulator.
References Barla G (2010) Analysis of an extraordinary event of TBM entrapment in squeezing ground conditions. In: No Friction No Tunnelling. Fetschift zum 60. Gebustag von Wulf Schubert, Institut für Felsmechanik und Tunnelbau, Technische Universität Graz. Ed. T. Pilgerstorfer, 66-76. Barla G, Janutolo M, Zhao K (2011) Open issues in Tunnel Boring Machine excavation of deep tunnels. Keynote Lecture. 14th Australasian Tunnelling Conference. Auckland, New Zealand. Vlachopoulos N, Diederichs M S (2009) Improved Longitudinal Displacement Profiles for Convergence Confinement Analysis of Deep Tunnels. Rock Mech Rock Eng, 42 (2): 131-146. Zhao K, Janutolo M, Barla G (2012a) A completely 3D model for the simulation of mechanized tunnel excavation. Rock Mech Rock Eng, 45 (4): 475-497.