Numerical Investigations of RC, SFRC, and Hybrid Segmental Lining Designs
In order to study the performance of concrete lining structures at the tunnel scale and compare them with conventional reinforced concrete lining designs, the structures of different reinforced tunnel linings were analyzed separately using detailed 2D models including grout layers and individual tunnel lining segments. response. For this purpose, a reference tunnel project was defined (cover depth 20 m, sand foundation, lateral earth pressure coefficient 0.5), in which the loading on the lining was determined by a process-oriented tunnel simulation (see details in Section 6.4.1) (at steady state). The analysis focused on durability, quantified by maximum crack opening exceeding the allowed width of 0.2 mm. Reinforced concrete lining segments with minimal reinforcement (an additional 10-10 C of steel bars in high-stress areas), steel fiber reinforced concrete lining segments with 60 kg/m3 60 mm conventional strength hook-end fibers, and hybrid reinforcement were analyzed Lining segments (125 mm steel fiber concrete strips and 200 mm long steel fiber concrete top caps). The total steel mass of the SFRC and RC lining segments is similar (approximately 260 kg/segment), while the hybrid lining segment uses 65% less steel (92 kg/segment). The simulation was performed using C40/50-grade concrete with a design tensile strength of 2.5 N/mm2. For designs containing SFRC, it is assumed that the fibers have isotropic directionality. Comparisons of different safety concepts in fiber and conventional stiffened segments and nonlinear finite element analysis can be found in the literature.
Under typical loads, large cracks do not occur in ordinary concrete segmental linings. However, there are two potential failure modes: in the vault section, a minimum normal force (1375 kN/m) and a maximum bending moment (329 kNm/m) were observed, possibly leading to flexural cracks. The maximum tensile stress occurs near 78° at the longitudinal joint due to a normal force of 1943 kN/m and a bending moment of 217 kNm/m. This may result in breakage of the segmented corners. Based on these observations, two load cases were created for design purposes. For the design of the vault section subject to bending, the loads are modified so that the resulting bending moment is increased by 1.5 times and the normal force is reduced by 0.5 times. For designs around longitudinal joints where crushing is likely to occur, increase the normal force and bending moment by a factor of 1.5 to increase stress transfer and maintain joint rotation.
Load Case: Bending
The response of all lining designs, or reinforcement schemes, to bending loading conditions. Only the flexural response of the vault segment is shown as this is the area where the largest cracks are observed. Furthermore, only the crack width is shown. The lining system was not damaged and continued to function as a load-bearing structure. Therefore, the only factor limiting the selection of any of these cases is the predicted crack width, which cannot exceed the specific project requirements for the durability limit state (approximately 0.2 mm).
As expected, the plain concrete lining ring (PC) showed the largest bending cracks, with the main cracks occurring at the inner edge of the top of the tunnel lining, where the maximum bending moment is predicted. It is worth noting that the PC scheme exhibits multi-crack behavior (due to compressive normal forces) rather than a single global crack leading to segment failure. The reinforced concrete segments showed a similar response to the reinforced concrete segments, with the main difference being that the crack pattern was more regular. Rather than predicting crack sizes that more or less correspond to the bending moment applied at a certain point, as in PC segments, the crack sizes observed in R segments are more or less similar, indicating that the steel bars will effectively move along the Crack response constraints for bar length. The predicted maximum crack width in the reinforced concrete section is 0.158 mm, which is within the tolerable range of less than 0.2 mm specified in the serviceability limit. Happily, SFRC segments were the most effective at reducing crack width. Both reinforcement options result in cracks significantly below the service limit and are therefore effective reinforcement designs. Under the hybrid reinforcement scheme, the full-section bending performance of SFRC is slightly better (0.112 mm vs. 0.142 mm). This corresponds to an increase in crack width of approximately 25%, while the total reduction in SFRC is 75%.
Load case: Spalling at longitudinal joints
The response of all lining designs, or reinforcement schemes, under spalling loading, is shown in Figure 5.28. The largest chipping crack occurred at the longitudinal joint 78° from the top of the tunnel, measured clockwise from the top of the ring. Overall, the predicted trends in maximum crack width are similar to those for the bending variant. However, in the case of spalling, SFRC proved to be more effective in reducing crack width.
It is important to note that the minimum steel crack resistance provided in the design of reinforced concrete is not sufficient to inhibit the formation of cracks that exceed tolerances. This indicates that SFRC is more suitable than RC for resisting spalling cracks. The effectiveness of hybrid reinforcement schemes can be increased by using higher reinforced concrete cap lengths where they perform better than conventional reinforced concrete designs and below normal service limits. Cracks initiate outside the steel fiber layer, and the steel fiber layer cap can only limit the further development of the crack. In order to estimate the optimal SFRC cap length, an optimization algorithm can be used.
