POSTER PAPER PROCEEDINGS

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1 ITA - AITES WORLD TUNNEL CONGRESS April 2018 Dubai International Convention & Exhibition Centre, UAE POSTER PAPER PROCEEDINGS

2 Analysis of multilateral interaction between shotcrete, yielding support and squeezing ground by means of two different numerical methods Rohola Hasanpour 1,2, Anna-Lena Hammer 3 and Markus Thewes 4 1 Postdoctoral Researcher, Institute for Tunneling and Construction Management, Ruhr-University Bochum, Germany, ra.hasanpour@gmail.com 2 Project Engineer, Babendererde Engineers GmbH, Lübeck, Germany 3 Research Assistant, Institute for Tunneling and Construction Management, Ruhr-University Bochum, Germany, anna-lena.hammer@rub.de 4 Professor, Institute for Tunneling and Construction Management, Ruhr-University Bochum, Germany, markus.thewes@rub.de ABSTRACT Squeezing behaviour, which might be observed in tunnelling through the weak ground under high in-situ stresses, yield large deformations at tunnel boundaries. To control this ground convergence and provide tunnel stability, it is essential to implement some precaution measures such as implementing the yielding supports. These yielding elements are installed and embedded between the lining segments along with other conventional supports, such as steel ribs, wire mesh, rock bolts and shotcrete. Implementing yielding supports allows the tunnel walls to be deformed to a certain amount that is resulted in redistribution and relaxation of the ground stresses. Although it is recognized that this practical measure is highly effective in providing stability and preventing failures in the other installed supports, there is not a well-stablished method to study the complex multilateral interactions between shotcrete, yielding support and squeezing ground in order to transfer and extend these beneficial effects into the design. To achieve this aim and understand the interaction mechanism between shotcrete, yielding support and squeezing rock in detail, two fully 3D models including a detailed construction sequences using FEM and FDM numerical methods are developed and the relevant results are compared with each other and with the real data from Tauern Tunnel in Austria. Special interface elements are included in the models to represent the yielding supports. Interfaces in the lining-rock contact and time evolution of the shotcrete properties are also incorporated in both 3D models. Based on comparisons of numerical results between stiff supports with and without yielding elements, the effect of the applying ductile supports on the stress states, load-deformation and the failure behaviours of the shotcrete and interfaces are investigated in both 3D models and then compared with the measurement data. To conclude, the advantages and shortcomings that are encountered using FEM and FDM methods within studying the interaction mechanism between different support materials and squeezing ground are reported. Key Words: Yielding elements; squeezing ground; interaction analysis; numerical modelling; interface elements; time-dependent material behaviour. 1

3 1. INTRODUCTION Tunnel construction through adverse geological conditions such as squeezing ground and long fault zones may accompany with large deformations at tunnel walls providing that the tunnel excavated under high overburden which is resulted in high ground stresses. In the case of using a rigid support system, extreme ground pressures can be applied on the linings that lead to the severe damages and sometimes the stoppage of the excavation process. To cope with such challenging conditions, various techniques have been developed in the last decades. Among these methods, applying yielding elements (ductile support), which are embedded between segments of a shotcrete lining, and in combination with other conventional supports such as steel ribs, wire mesh, rock bolts and shotcrete has been acknowledged as an effective precaution measure for controlling the large deformations at tunnel circumference. Using this method allows the ground to be deformed to a certain amount without damage to the shotcrete system that is resulted in redistribution and reduction of the applied pressure on the whole support system. This approach together with installing a set of dense rock bolting, which increases the shear strength of the rock mass, reduces the asymmetrical deformation of the tunnel walls. The application of ductile support system has been introduced firstly in Galgenberg Tunnel after several collapses occurred in this tunnel (Moritz 1999). Before, the concept of the slotted shotcrete lining with deformation gaps had been used in the first tube of Tauern Tunnel. The same concept was also utilized in Galgenberg Tunnel. However, due to several collapses occurred during tunnelling, it was decided to develop the special types of ductile supports as called yielding elements and employing them between shotcrete segments in order to control ground deformations. Then, the embedded upright steel tubes into the shotcrete lining were the first yielding elements have been used in Galgenberg Tunnel. Ever since, there has been an unceasing improvement in the structure and configuration of the yielding elements and their adjustments for different construction objectives. By now, the ductile support approach has been successfully implemented in the construction of several tunnelling projects, for example, Strenger Tunnel (Radoncic 2011), Tauern Tunnel (Weidinger und Lauffer 2009), St. Martin La Porte (Barla et al. 2008), Gotthard-Base Tunnel (Classen 2011) are a number of underground projects in which the ductile support systems have been used. 2 Although it was recognized that this practical measure is highly effective in providing stability and preventing failures at the installed support system, however, there is no a well-stablished method to study the complex multilateral interactions between shotcrete, yielding support and squeezing ground in order to transfer and extend these beneficial effects into the design. To achieve this aim and understand the interaction mechanism between shotcrete, yielding support and squeezing rock in detail, two fully 3D models including a detailed construction sequences using FEM and FDM numerical methods are developed in this paper, and the relevant results are compared with each other and with the measured data from Tauern Tunnel in Austria. The special spring elements and double-yield constitutive models are included in the models to represent the yielding supports. Interfaces in the lining-rock contact and time evolution of the shotcrete properties are also incorporated in both 3D models. Based on comparisons of numerical results between stiff supports with and without yielding elements, the effect of the applying ductile supports on the stress states, load-deformation and the failure behaviours of the shotcrete and interfaces are investigated in the developed 3D models. To conclude, the advantages and shortcomings experienced using FEM and FDM methods within studying the interaction mechanism between different support materials and squeezing ground are reported.

4 2. AN OVERVIEW ON YIELDING ELEMENTS Figure 1 illustrates a schematic of a ductile support system in which the slotted shotcrete lining with the embedded yielding elements are combined with a set of radial rock bolts and lattice girders (steel ribs). The important point here is that the design level of the yielding elements should be selected regarding decreasing at the force levels with respect to continues deformations. The prerequisite for this selection is that the applied stresses on the shotcrete lining at each time point should be lower than the strength of the shotcrete. Therefore, the initial resistance of the yielding elements should not be adopted too high, because the fresh shotcrete has a low strength. Furthermore, the load-deformation behaviour of the yielding elements is supposed to adjust itself according to the strength development of the shotcrete, so that the best-mobilized lining capacity is achieved (Wiese 2011). The interaction of two main support components, shotcrete and yielding elements, determines the passive support concept of the ductile shotcrete lining. When these components are implemented in the calculation models, the initial stiffness of the yielding elements should be precisely represented, and the time-dependent strength or stiffness development of the shotcrete should be described as realistically as possible. To date, there is no general method or material model for taking into account the loaddeformation behaviour of the yielding elements in the numerical calculations. The attempts in this regard can be referred to the study by John et al. (2004) who presented numerical calculations for the design of support system for Strenger Tunnel, in which the yielding elements were simulated by limiting the normal force and the bending moment through individual beams. Radoncic (2011) and Barla et al. (2011) use an elasticperfectly plastic Mohr-Coulomb material model for the modelling the yielding elements by determining stiffness and strength values from the load-deformation behaviour of the applied elements. Further numerical computations with the implementation of yielding elements can be found in the studies by John and Poscher (2004), Cantieni (2011) and Likar et al. (2013), however, the modelling procedure of implemented yielding elements was not explicitly described in these studies. Figure 1. A schematic of shotcrete lining with embedded yielding elements (Hammer et al. 2017) Regarding the recent investigations carried out for simulation of ductile support system numerically, it can be concluded that there is a major shortcoming on a wellstablished method to study the complex multilateral interactions between shotcrete, yielding support and squeezing ground to transfer and extend these beneficial effects into the design. One should become aware of such a complex interaction between the 3

5 squeezing rock mass, shotcrete and yielding supports when designing a tunnel project through squeezing ground. This interaction should be investigated in detail using threedimensional modelling by considering the detailed constitutive properties of the applied supports e.g. yielding elements and shotcrete for correct simulation of this interplay. 3. PROJECT DESCRIPTION AND APPLIED YIELDING ELEMENTS The Tauern Tunnel is a part of the motorway A10 in Austria. The 6.5 km long, twin-tube tunnel passes through the Radstadt Tauern with a maximum overburden of 1000 m. The first tube was excavated in 1975, and the construction operations for the second tube began in Figure 2 shows a lengthwise section of the rock mass along Tauern tunnel with the chosen reference cross sections (green) for numerical calculations. The geological formations mostly consist of 85% phyllite with changing strengths so that it increases with the presence of carbon and decreases with the existence of sericite, graphite and chlorine minerals. Rock strength is reduced due to strong tectonization such as faults, which was also confirmed by observations of metamorphosis degrees of the rock mas encountered at tunnel face. With regards to the rock strength, one should consider the tectonic processes that occur mostly along the bedding, flat to moderately sloping northward (Kohlböck et al. 2010). Figure 3 depicts the cross-sectional profile of Tauern Tunnel at the chainage between 1685 m and 1775 m with two sets of yielding elements applied in this zone. The measured data from this area was used in this study for comparing them to the results from computational modelling. In Tauern Tunnel the Wabe yielding elements have been implemented for controlling the extreme deformations due to squeezing behaviour of the rock mass within tunnelling. This kind of supports are produced by Bochumer Eisenhütte Heintzmann; they consist of hollow steel circular sections joined together lengthwise by intermediary plates (see Figure 4). The cavities between the joining plates in the honeycomb-shaped structure allow the ground to be deformed so that the degree of flexibility for the Wabe elements can be determined by the sum of the inner diameters of the tubes. The dimensions, material properties and resistance or flexibility of this kind of elements can be modified with respect to tunnel deformation and stresses on whole support system (Podjadtke 2009). Furthermore, tube sections can be retroactively inserted into yielding element cavities to increase the bearing capacity even after a partial deformation occurred. When the outer and inner tubes in a support are deformed and met each other, the resistance increases, and new load levels are adjusted. Therefore, the insertion of additional pipes with different diameters and wall thicknesses can allow the different load levels to be adjusted (Figure 4b). Figure 2. Lengthwise section of the second tube (valley tube) of Tauern Tunnel (ASFINAG Construction Management GmbH 2006) 4

6 6,0 m SN 6,0 m Top Kalotte heading +3,00 Strosse Bench -0,40 Sohle Invert 25 cm Figure 3. Cross-sectional profile of Tauern Tunnel at the chainage between 1685 m and 1775 m with utilized support system (ASFINAG Construction Management GmbH 2006) Figure 4. a) Yielding element of Wabe type and b) Wabe Element with inserted steel tubes (Bochumer Eisenhütte Heintzmann) 4. NUMERICAL MODELING 4.1. FEM and FDM In this study, FLAC3D and DIANA FEA, which are based on finite difference method (FDM) and finite element method (FEM) respectively, are used for simulation of the complex interactions between shotcrete, yielding support and squeezing ground. The main goal of using this two software was comparing and illustrating the capability of each method in modelling of a complicated interplay between tunnel supports. Recommendations and guidelines are offered at end of this study with respect to merits and shortcomings for each software within using in the simulation of multilateral interactions in conventional tunnelling. However, regarding a short explanation about the utilized software; FLAC3D is a three-dimensional explicit FDM program in which materials are represented by polyhedral elements within a three-dimensional grid that are adjusted by the user to fit the shape of the object to be modelled (Itasca Consulting Group, 2015). Each element behaves according to a prescribed linear or nonlinear stress/strain law in response to applied forces or boundary restraints. The material can yield and flow, and the grid can deform (in large-strain mode) and move with the material that is represented. The explicit, Lagrangian calculation scheme and the mixed-discretization zoning technique used in FLAC3D ensure that plastic collapse and flow are modelled accurately. Because no matrices are formed, large three-dimensional calculations can be made without excessive memory requirements. 5

7 DIANA FEA is a three-dimensional implicit FEM program in which the solution domain is divided into simply shaped elements. The total solution is generated by linking together the individual solutions to ensure continuity at the inter-element boundaries. In this program by FEM method, every element communicates with every other element during one solution step and several cycles of iteration are necessary before compatibility and equilibrium are obtained. The program solves the physical problem by dividing the geometry into small elements and calculates the stresses and strains in those elements before assembling them back using the theory of superposition (DIANA FEA Manual 10.1, 2016). In this paper, numerical modelling of conventional tunnelling operation using FEM and FDM methods adopted in the second tube of Tauern Tunnel. The modelling was carried out first with the purpose to simulate the observed performance and load-deformation behaviour of the installed supports during excavation without yielding supports. Then, the same models were applied to analyse the response of the yielding support system and interaction behaviour between linings Modelling of rock mass To analyse the interaction mechanism between ductile supports and examine the response of the support system with adopted yielding elements, the developed full 3D models in FLAC3D and DIANA FEA were implemented in two steps as follows; 1) Block modelling, entering ground properties, definition of ground behaviour model, assigning boundary conditions, application of in-situ stress and solving the unexcavated model for damping the unbalanced forces 2) Modelling tunnel advance using step by step excavation, applying tunnel supports systems such as steel ribs, wire mesh, rock bolts and shotcrete by considering their mechanical constative models, deploying interface elements for simulation of interactions between various support system, and modelling the yielding supports using special interface elements A screen shot of the generated 3D models of the tunnel construction is shown in Figure 5. The models were set up to include 905 m overburden per geomechanical properties as given in Table 1. Tunnel alignment from to m was considered for computational calculations. The ground was assumed to follow an elastic-perfect plastic behaviour according to Hoek-Brown failure criterion for describing the stress-strain behaviour in response to applied loads. Moreover, the in-situ state of stresses was determined 0.64 based on information from the field study. To simulate rock mass and in-situ pressures on a virgin ground, damping (solving) of the unbalanced forces was needed, where unbalanced forces reached zero. Furthermore, the large strain analysis was used for computational calculations. The contour lines of estimated initial in-situ stresses after achieving damping (initial) step is presented in Figure 6. This is in an agreement with predicted in-situ stresses using theoretical methods and observed loads in the field study. Then the developed model can be used in the following steps for studying the effect of yielding elements on the stress-stain behaviour of rock mass surrounding the tunnel. 6

8 Table 1. Rock mass properties Parameters Value Unit Elastic modulus of the intact rock 17.6 GPa Poisson ratio Uniaxial compressive strength of the intact rock 25 MPa GSI (Geological Strength Index) 40 - m i (Hoek brown material constant) 7 - Unit weight 2750 Kg/m 3 (a) (b) Figure 5. 3D model of tunnelling using a) FDM method b) FEM method (c) (d) Figure 6. The contour lines of the initial in-situ stresses after damping the unbalanced forces 7

9 4.3. Modelling of support system The linear elastic model was considered for modelling of the shotcrete but, the elastic modulus of material was increased regarding the time-dependent behaviour of shotcrete and tunnel advancing as can be seen in Figure 7a. The average advance rate of 3m/day is assumed here according to the average advance rate of Tauern Tunnel. The simulated shotcrete for 80 m of tunnel excavation is shown in Figure 7b. Depending tunnel advance rate, different values of elastic modulus for shotcrete can be seen in Figure 7b. In FLAC3D beam element are used for modelling of steel ribs and rock bolts with its mechanical properties as given in Table 2. In DIANA FEA embedded reinforcement is used for modelling steel ribs and rock bolts for the same mechanical properties. Figure 7. a) Elastic modulus of the applied shotcrete versus time b) simulation of increasing the strength of shotcrete with 3 m tunnel advance and 80 m total excavation Table 2. Mechanical properties of steel ribs and rock bolts used in the 3D models Elastic Yield Cross Polar Structural Poisson Diameter Moment of modulus strength section elements ratio (mm) (GPa) (MPa) (m 2 inertia (m 4 moment of ) ) inertia (m 4 ) steel ribs e e e- 6 rock bolt (B500B) e e e Modelling of yielding elements 8 In numerical modelling, the Wabe elements were embedded between shotcrete segments in combination with steel ribs and rock bolts to investigate its complex interactions with the surrounding rock mass. Before applying yielding elements in the fully 3D models, two simple models were developed in order to compare the load-deformation behaviour of the selected yielding element obtained from the computational analysis and experimental tests. The Wabe elements were simulated using two different methods in FLAC3D and DIANA FEA. For modelling of yielding elements in FLAC3D, the double yield model was found to be an appropriate constitutive model for simulating the stress-strain behaviour of this type of elements as illustrated in Figure 8a. Material properties of steel such as elastic modulus and Poisson s ratio were implemented into the model. To simulate the

10 load-deformation behaviour of Wabe elements, the cohesion strength (equivalent cohesion) of steel with respect to Figure 8 was replaced using a Table fish code in FLAC3D. Moreover, the spring elements were used to simulate the stress-strain behaviour of Wabe elements in DIANA FEA. For this purpose, the load-deformation curve of the applied elements with respect to Figure 8 was implemented directly in the numerical calculations. Figure 9 illustrates this comparison study, which proves a good agreement between results. The same procedure then was used in the fully 3D models to study the interaction between support system with yielding elements. Figure 8. Stress-strain behaviour of Wabe elements based on experimental results (Wiese 2011) (c) (d) Figure 9. The load-deformation curves of the Wabe element resulted from computational analysis and experimental data a) simulation with FLAC3D and comparing with experimental data b) simulation with DIANA FEA and evaluating with the results from laboratory tests 9

11 4.5. Validation of the developed 3D models To validate the results of numerical modelling, a chainage of Tauern Tunnel in which the yielding supports has been not adopted was selected for study objectives. Tunnel chainage from to was used for this purpose so that the measured radial displacement and loads at tunnel circumference are available for this chainage and can be evaluated regarding numerical calculations. A comparison between computational results with measured values for the selected chainage is shown in Figure 9. As can be seen in this Figure, the calculated radial displacements at the crown are very close to the measured values in the same points. This means that the developed 3D models can be successfully used for the following steps to investigate the impact of adjusting yielding elements between lining segments on rock mass behaviour surrounding the tunnel and evaluation of the response of the Wabe support system in the relevant chainages that the yielding elements were employed. Figure 10. A comparison between computational results with measured values for tunnel section of m 10

12 5. NUMERICAL RESULTS AND DISCUSSIONS 5.1. The impact of implementing yielding elements on stress redistributions around tunnel Figure 11 shows the block modelling of tunnel construction for the Tauern Tunnel at chainage with and without using the Wabe yielding elements. Figure 11a and 11b illustrate the developed 3D models using FLAC3D, while Figure 11c and 11d display the computational models by applying DIANA FEA. The 3D models of the simulated yielding elements can be seen in Figures 11b and 11d. Figure 11. Numerical modelling of Tauern Tunnel construction at chainage a) FDM model without using yielding element b) FDM model with employing yielding element c) FEM model without yielding element c) FEM model with yielding element Large strain mode has been used for simulating the yielding elements using finite difference method. The deformed elements under high ground stresses can be seen in Figure 12. Furthermore, the interface elements were used for simulation of the interaction between rock mass and yielding supports. Figure 12. A schematic of the deformed yielding elements under high ground stresses 11

13 To conduct a comparison study among the results from different numerical solving methods, the contour of displacements in vertical direction are given in Figure 13, in which the impact of applying the yielding support on the amount of deformaton surrounding the tunnel is depicted. While the maximum displacement at the crown of the tunnel is calculated 8.2 cm after a complete excavation of tunnel without employing the yielding supports, the maximum displacement is obtained 17.5 cm when the yielding supports are used between segments of the shotcrete linings. This means that integrating two sets of yielding supports between shotcrete lining allows the ground to be deformed 113% more than the state without implementing the yielding element. (a) (b) (c) Figure 13. Contour of displacements in vertical direction for modelling a) without applying the yielding elements b) with using the yielding supports and FD method c) with simulation of yielding elements and FE method The difference between the state of principal stresses when applying Wabe elements is shown in Figure 14. Furthermore, the amounts of mean stresses applied on the whole support system are calculated and illustrated as contours when a Wabe yielding element has been adopted (See Figure 15). It clearly shows that the applied stresses are significantly affected by the presence of the deformable elements incorporated in the lining. Moreover, the yield states of applied rock bolts are decreased considerably in the case that a set of yielding elements was installed (Figure 16 and 17). 12 (a) Figure 14. The state of principal stresses in the whole lining system with and without yielding supports (b)

14 (a) (b) (c) Figure 15. The contour of mean stresses surrounding tunnel and support system in cases with and without yielding elements (a) Figure 16. The yield state of the rock bolts a) model without yielding element b) Figure 16. The yield state of the rock bolts a) model without yielding element b) model with yielding element 6. CONCLUSION In this paper, two comprehensive 3D simulations of construction sequences of a conventional tunnelling have been conducted using FEM and FDM methods to investigate numerically the interaction of the shotcrete, yielding support and squeezing ground. Two widely used commercial packages in geotechnical applications, namely FLAC3D and DIANA FEA, were utilized in the calculations. Using FDM and FEM methods, two advanced material constitutive models were applied for simulation of the load-deformation behaviour of a Wabe type of yielding elements and defining of the interactions between shotcrete lining, yielding elements and rock mass. Furthermore, the time-dependent evolution of the shotcrete was considered in the 3D simulated models. (b) Based on comparisons of computational results between stiff supports with and without yielding elements, the impact of the applying ductile supports on the stress states, load-deformation and the failure behaviours of the shotcrete and rock bolts were investigated and compared with some measurement data and observations 13

15 from Tauern Tunnel in Austria. The comparison study shows a good agreement between results and observed cross section from numerical analysis and field measured data. The study results also prove that the both of finite difference and finite element methods can be applied with a good precision for modelling a tunnel construction through squeezing ground under high ground stresses. Furthermore, they can be used for simulating of the complex interactions between support systems and modelling the real behaviour of novel elements such as yielding supports that are used in the excavation of long and deep tunnels through difficult grounds. 7. REFERENCES [1] Barla G., di Torino, P., Rettighieri, M., Fournier, C., Fava, A., Triclot J. (2008): Saint Martin squeeze. In: Tunnels & Tunnelling International (May), pp [2] B arla, G., Bonini, M., Semeraro, M. (2011): Analysis of the behaviour of a yield-control support system in squeezing rock. In: Tunnelling and Underground Space Technology 26 (1), pp [3] Cantieni, L. (2011): Spatial effects in tunnelling through squeezing ground. Ph.D. Thesis. ETH, Zurich, Switzerland. [4] Classen, J. (2011): Bautechnische Bewältigung geologischer Problemzonen mittels TBM am Gotthard-Basistunnel (Lucomagno/Piora/Tenelin). Germany. STUVA-Tagung, pp [5] DIANA FEA (2016) multi-purpose finite element in 2D and 3D dimentions, User s Manual, Release 10.1 [6] Itasca FLAC3D Manual (2012) Fast Lagrangian analysis of continua in 3D dimensions. User s guide. [7] John, M., Poscher, G. (2004): Primärspannungen: Zurecht oder zu Unrecht ein Stiefkind der Felsmechanik. In: 2nd Colloqium Rock Mechanics-Theory and Practice. Vienna, Austria, pp [8] John, M., Spöndlin, D., Mattle, B. (2004): Lösung schwieriger Planungsaufgaben für den Strenger Tunnel. In: Felsbau 22 (1), pp [9] Kohlböck, B., Mayer, A., Schnabl, R., Vergeiner, R. (2010): Geotechnics, tunnelling and support of the second tube of the Tauern Tunnel and comparison with the first tube. In: Geomechanics and Tunnelling 3(4), pp [10] Likar, J., Marolt, T., Likar, A. (2013): Adequacy of the yielding elements selection for underground construction in high squeezing grounds. In: Proc. of the 12th international conference underground construction. Prague, Czech Republic. [11] Moritz, B. (1999): Ductile Support System for Tunnels in Squeezing Rock. Ph.D. Thesis. University of Technology, Graz, Austria. [12] Podjadtke, R. (2009): Entwicklung und Einsatz von stählernen Stauchelementen - Das System WABE im modernen Tunnelbau. In: Felsbaumagazin (2), pp [13] Radoncic, N. (2011): Tunnel design and prediction of system behaviour in weak ground. Ph.D. Thesis. University of Technology, Graz, Austria. [14] Weidinger, F., Lauffer, H. (2009): Tauern Tunnel erste und zweite Röhre aus der Sicht des Bauausführenden. In: Geomechanics and Tunnelling 2 (1), pp [15] Wiese, A.-L. (2011): Vergleichende Untersuchungen von Stauchelementen für den Einsatz in druckhaftem Gebirge. Germany. STUVA-Tagung, pp

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