Numerical simulations of SFRC precast tunnel segments

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Figure 6. Motivation for the flexure tests performed at UPC (Gettu et al., 2004). Figure 7. Configuration of the flexure test (Gettu et al., 2004). Figure 8. Comparison between the numerical curves and the experimental load displacement (a) and load-crack opening (b) curves obtained by Gettu et al., (2004) for two different materials. 1108 concerns the crack opening displacement measured in the mid-section (Fig. 7); once again, the numerical curves fit the experimental ones quite well. 4 DESIGN ASPECTS An open question for the construction companies and the precast industry concerns the reinforcement for these precast elements. In fact, a heavy conventional reinforcement is undesired in the construction process due to the placement of many curved rebars and for pouring the fresh concrete. Figure 9 shows the conventional reinforcement adopted for the segments of the Barcelona Metro that, as already mentioned, also included 30 kg/m 3 of steel fibers (FF1). In order to verify the structural behavior of the tunnel segments towards an optimization of the reinforcement, several NLFM analyses were performed in the present research work. Based on the material properties described in §2, the damaged plasticity model provided in ABAQUS 6.4.1 (2003) was adopted for the FE simulations of the tunnel segments. The numerical analyses were carried out by adopting a 3D solid model with 4032 first order hexahedral elements (C3D8-eight node linear brick elements). The constitutive law for concrete under compression was assumed according to EC2 (2003). The actions on the tunnel segments result from transportation, placing process and soil pressures in the final state. The numerical results concerning the high compression force exerted by the 30 TBM actuators on the ring during excavation are presented herein. The service load applied by a single actuator for the Barcelona Metro was 3 MN. One single segment with four actuators was considered for the numerical analyses and its boundary conditions (i.e. presence of the adjacent segments) were simulated by elastic springs whose stiffness was calibrated with previous FE analyses of the full ring. Figure 9. Caption of a typical figure. Photographs will be scanned by the printer. Always supply original photographs.
Structural behavior of segments with different types of reinforcement was compared. Numerical results from segments with conventional reinforcement only (RC), with rebars and 35 kg/m 3 of fibers (RC35FF1, similar to the reinforcement adopted in Barcelona), or with 45 kg/m 3 of fiber reinforcement only (45FF1), are presented. To better evaluate the reinforcement effects, a reference specimen of plain concrete was also considered. Figure 11 shows the numerical results in terms of load (from four actuators) versus the longitudinal displacement of the middle section (average value under the four loading areas). One can notice the brittle failure of the plain concrete specimen and the minor contribution of fibers to the bearing capacity of the segment with conventional reinforcement. Specimens with fibers only have the same ultimate load but it is reached with larger displacements and, therefore, larger crack openings. To better understand the structural behavior of segments with fiber-reinforcement only, Figure 12 shows the load-displacement curve of the specimen with 45 kg/m 3 of fibers FF1, without conventional reinforcement. It can be noticed that a splitting crack starts to open at the service load and that, because of the stress-redistribution along the longitudinal direction Figure 10. Scheme of a segment with the load from four actuator and the springs representing the neighbor segments. Load [kN] 30000 25000 20000 15000 10000 5000 0 Tunnel Segments: Non Linear Analyses, Comparison 45FF1 Plain RC RC35FF1 RCO35FF1 0 1 2 3 4 5 6 Displacement [mm] Figure 11. Comparison between the load-displacement curves as obtained from specimens with different types of reinforcement. 1109 of the segment, this crack can propagate in a stable way up to the ultimate load which is almost twice the service load. The distribution of radial stress � r (see Fig. 13) along the longitudinal section at the service load is represented in Figure 14; one can notice the tensile stresses under the actuator (on the left side) up to a distance from the segment surface of about 400 mm. Figure 12. Caption of a typical figure. Photographs will be scanned by the printer. Always supply original photographs. Figure 13. Reference system adopted for stresses and strains. Stress σ R [MPa] 3 2 1 -2 -3 -4 Radial Stress, Fiber FF1-45 0 0 200 400 600 800 1000 1200 1400 1600 1800 -1 Distance [mm] Service Load Figure 14. Distribution of radial strains � r along the longitudinal section of the element under service loads.
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Numerical simulations of SFRC precast tunnel segments

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