NUMERICAL MODELING OF PRECAST FRC SEGMENTS: THE MONTE LIRIO TUNNEL IN PANAMA

Transcription

1 BEFIB2012 Fibre reinforced concrete Joaquim Barros et al. (Eds) UM, Guimarães, 2012 NUMERICAL MODELING OF PRECAST FRC SEGMENTS: THE MONTE LIRIO TUNNEL IN PANAMA Alberto Meda *, Francesca Nerilli * and Zila Rinaldi * * Civil Engineering Department, University of Rome Tor Vergata via del Politecnico 1, Roma, Italy alberto.meda@uniroma2.it, nerilli@ing.uniroma2.it, rinaldi@ing.uniroma2.it Keywords: precast tunnel segment, tunnelling design, non-linear FE modelling. Summary: The problem of the Tunnel Boring Machine (TBM) thrust effect on the precast FRC segment, without traditional reinforcement, has been faced through a numerical study, combined with an extensive experimental campaign, with reference to the Monte Lirio Tunnel, now in progress in Panama. A numerical modeling, by means of a proper finite element code has been carried out with the aim of simulating the actual actions on the segment. Furthermore, the adopted FE code allows modeling the concrete cracking phenomena and predicting the crack opening, and can be considered a valuable tool for the precast segment design. The obtained results are compared and validated with the evidence of full scale tests. 1 INTRODUCTION The production of precast segments for mechanically excavated tunnels is one of the most interesting applications for fiber reinforced concrete [1]. In these structures, fiber can often totally substitute the traditional reinforcement (steel cage) allowing several advantages. First of all, the use of fiber reinforced concrete in the precast process can increase the quality of the products [2]. The curved geometry of the segment can create problems in the detailing of the reinforcement and its corrected placement, problems that can be avoided by using dispersed fiber reinforcement. Furthermore, the use of fiber reinforced concrete has economical advantages in term of labour cost reduction. The fiber reinforcement increases also the impact strength, and then limits possible damages during the segment handling and storage. Another important advantage of FRC segments is related to the possibility of avoiding the cathodic protection, necessary for ordinary reinforced concrete elements, that represents a significant cost. Several researches have demonstrated the successful possibility of adopting fiber reinforced concrete in tunnel segment, if a proper design procedure is used, i.e. a correct definition of the concrete mix design and a proper choice of the fibers (content, geometry and strength) [3, 4]. A series of three hydraulic tunnels excavated in Panama, was realised with fiber reinforced concrete, without the traditional steel reinforcement. The design of the tunnel segments was based on the Model Code 2010 [5] prescriptions for fiber reinforced concrete, and was assisted by test, in order to check the possibility of fulfilling the Model Code 2010 requirements for completely removing the traditional reinforcement. In particular full-scale tests, aiming at simulating the thrusts of the Tunnel Boring Machine (TBM) on the segments, were performed. This aspect is particularly important, since this load condition, occurring during the tunnel excavation, can be the worst one. The tests showed a good response of the segments in FRC and confirm the effectiveness of the design procedure. Eventually, the tunnels excavation began, with successful results. In this paper, the possibility of correctly modelling the load condition due to the TBM thrusts is analysed, with the aim of obtaining important information before performing full-scale tests. The behaviour of the segments has been modelled by performing non-linear finite element analysis, based on the fracture mechanics. The obtained results are in good agreement with the experimental

2 BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. evidences. 2 EXPERIMENTAL TESTS The case study herein analysed refers to the Monte Lirio tunnel. The tunnel is 7878 m long, with an external diameter equal to 3.7 m. The thickness of the lining, made with precast segment is equal to 250 mm, thus the internal diameter of the tunnel is 3.2 m. Every tunnel ring, having a width of 1.2 m, is composed by six precast elements (Fig. 1). Figure 1. Tunnel segmental lining. Full-scale tests were performed on the segments: bending tests with the aim of evaluating the sectional bearing capacity and point loads tests simulating the TBM thrust. Attention to these last tests will be paid herein. The segments were cast with a concrete strengthened with 40 kg/m 3 of high strength steel fibers. The material was characterised in tension by performing tests on beam according to the EN14651 prescriptions [6]. The results obtained are represented in Figure 2 through nominal stress-crack opening diagrams. In order to reproduce the actual condition, the point load test was performed by applying two point loads on the segment with two 2000 kn jackets. Figure 3 shows the steel shoes placed between every jacket and the segment surface, with the aim to distribute the point load. A uniform support is considered, as the segment is placed on a stiff beam suitably designed. The load was continuously measured by pressure transducers. Four wire transducers (two located at the intrados and two at the extrados) measure the shoes displacement, while one LVDT transducers is applied between the load shoes, in order to measure the crack openings. Four load steps have been imposed: 1. a load step up to 100 kn for the system arrangement; 2. a load step up to 785 kn for each shoe, representing the limit design value; 3. a load step up to 1100 kn for each shoe, representing the maximum load of the TBM jacks; 4. a load step up to 2000 kn for each shoe (maximum load of the Laboratory jacks). The first cracks appeared for a load level of 1650 kn (for each shoes) between the two shoes, as showed in Figure 4a. The crack pattern at the maximum load, equal to 2000 kn (for each shoe) is depicted in Figure 4b, with a small length increase of the two cracks between the load shoes. 2

3 Nominal stress (kn) BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. It has to be remarked that the first crack occurred at a load level (1650 kn) higher than the design value (785 kn) and the maximum load of the TBM (1100 kn). Furthermore, it can be noticed that the fiber reinforcement can control the crack development, with a limited increase of the cracks length when the load is increased from 1650 kn to 2000kN (for each shoe). In Figure 5 the load is plotted versus the LVDT displacement, that measures the elastic displacement and the openings of the two cracks passing through the instruments (Figure 4). More details on the experimental results can be found in [7] crack opening (mm) Figure 2. Bending tests on beams according to EN Shoe 1 Shoe 2 Figure 3. Point loads test set-up. 3

4 Load (kn) BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. Figure 4. Point load test: a) first cracks (1650 kn for each shoe); b) crack pattern at load level of 2000 kn (for each shoe) displacement (mm) Figure 5. Experimental result: load vs LVDT displacement. 3 NUMERICAL MODELLING A non linear FE code (Diana 9.4) was adopted for modelling the problem. A non-linear fracture mechanic approach for the fiber reinforced concrete, based on the smeared crack model (Total Strain Rotating Crack model) was considered [8]. In order to define the material constitutive law in tension, in terms of stress versus crack opening relationship, a back analysis was conducted. Initially the beam tests performed according to EN14651 were modelled in order to define the material stress-strain relationship before cracking and the stresscrack opening relationship after cracking. Eventually the point load test on the segment was modelled by adopted the aforementioned relationship. In particular a 2D analysis was performed for simulating the beam tests. Quadratic elements of about 10mm (Fig. 6), and thus a crack band width equal to 9.3 mm were adopted. The tensile relationship obtained as a result of the back analysis is reported in Figure 7, both in terms of stressstrain and stress-crack-opening. This last parameter is obtained, after the crack formation, by multiplying the tensile strain for the crack band width. Figure 8 shows the comparison between the experimental evidence and the numerical response, made with reference to the constitutive relationship of Figure 7 4

5 BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. Figure 6. Beam test 2D model. a) Figure 7. Stress-strain tension law for the modelled beam (a, blue curve), and the obtained constitutive relationship stress-crack opening through the crack bandwidth (b, red curve). b) 5

6 BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. Figure 8 Experimental load-displacement curve of the beam (blue curve), compared with the numerical load-displacement curve (red curve). The initial stiffness and the ultimate load are very well caught. The differences appearing in the plastic pre-peak range can be considered negligible for the structural global behaviour. The segment was modelled by adopting a 3D FE mesh. The mesh, used in the model, consists in a twenty node isoparametric solid brick element (Fig. 9). It is based on quadratic interpolation and Gauss integration. Typically, a rectangular brick element approximates the following strain and stress distribution over the element volume. The mesh size is almost 50 mm. The crack band width evaluated on the basis of the mesh geometry is set equal to 46.3 mm. Thus, the adopted multi-linear stress strain curve is described in Figure 10 and it is derived from the relationship of Figure 7b, determined with the back analysis. With regards to the boundary conditions, the segment has been constrained to the vertical translation by rigid supports in correspondence of the supported base. In order to avoid translations and rotations in the all directions, a typology of constraints has been chosen, represented in Figure 11. This type of constraints doesn t limit the extension of the lateral side of the element, and reproduces, as similarly as possible, the experimental behaviour of the segment. On the element, two surface pressures have been applied, whose global resultant force is increase from 0 to 2000 kn, in order to reproduce the experimental tests. Figure 9. 3D model mesh, and scheme of utilized quadratic element. 6

7 BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. b) a) Figure 10. Constitutive relationship in tension (stress-crack opening) for the concrete segment (red curve), and the stress-strain law obtained through the crack bandwidth (blue curve). Figure 11. Boundary condition of the concrete segment. 7

8 Load (kn) BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. 4 RESULTS The numerical model shows that the first cracking occurred for a load level, on a single shoe, ranging between 1600 kn 1800 kn, well in accordance with the experimental evidence, where the first crack onsets for load of 1650 kn. The cracks are located between the thrust shoes, as shown in Figure 12. Figure 12. Crack opening between the load shoes, for four load steps displacement (mm) Figure 13. Load versus crack opening curve obtained by the numerical model. The load versus crack opening curve obtained by the numerical model is depicted in Figure 13. 8

9 Load (kn) BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. The effectiveness of the model is shown in Figure 14, where the above mentioned graph is compared with the experimental outcomes. In particular the crack openings from the test are obtained by the LVDT displacement measures (Fig. 5), by subtracting the elastic displacement and by dividing the obtained value by two, due to the presence of two cracks in the instrument length (see Fig. 5) experimental numerical displacement (mm) Figure 14. Load versus crack opening curve comparison between numerical (blu curve) and experimental results (red dots). 5 CONCLUSIONS The results reported in the paper shows the effectiveness of the adopted numerical model in predicting the behaviour of fiber reinforced concrete segment under a thrust simulating the effect of the TBM machine during excavation. Starting from a series of laboratory beam tests, it was possible to determine the constitutive relationship of the fiber reinforced concrete under tension and apply the obtained constitutive relationship for the analysis of the tunnel segment. In particular it is possible to foresee the load related to the first crack formation, the cracks position and their openings. For this reason the adopted procedure can represent a valuable tool for predicting the behaviour of this kind of structures during the design procedure. REFERENCES [1] R. Burgers, J. Walraven, G.A. Plizzari and G. Tiberti, Structural behaviour of SFRC tunnel segments during TBM operations, World Tunnel Congress ITA-AITES 2007, Praga, (2007). [2] di Prisco, M. and Toniolo, G., 'Structural applications of steel fibre reinforced concrete', Proceedings of the international workshop, Milan (Italy), April 4, 2000, (CTE publ., Milan(Italy), 2000). [3] A. Caratelli, A. Meda, Z. Rinaldi and P. Romualdi. Structural behaviour of precast tunnel segments in fiber reinforced concrete. Tunnelling and Underground Space Technology. Vol. 26, N. 2. (2011). [4] A. de la Fuente, P. Pujadas, A. Blanco and A. Aguado. Experiences in Barcelona with the use of fibres in segmental linings. Tunnelling and Underground Space Technology. Vol. 26, N. 2. (2011). 9

10 BEFIB2012: Alberto Meda, Francesca Nerilli and Zila Rinaldi. [5] Fib Bulletins 55-56: Model Code 2010 First complete draft [6] EN 14651: Test method for metallic fibre concrete. Measuring the flexural tensile strength [7] A. Caratelli, A. Meda, Z. Rinaldi, P. Perruzza and P. Romualdi. Precast tunnel segment in fiber reinforced concrete. Fib Symposium Prague (Czech Republic) June [8] Rots, J.C. Computational modeling of concrete fracture, Doctoral Thesis, Delft University of Technology. (1988). 10