Design of FRC tunnel segments considering the ductility requirements of the Model Code 2010
Graphical abstract
Introduction
Fibre reinforced concrete (FRC) is a composite material used to improve the mechanical response of precast segments for tunnels (di Prisco et al., 2009, Walraven, 2009, Burguers, 2007, Hilar and Vítek, 2012), enhancing their ductility and fire resistance as well as their mechanical performance during transient load stages. Due to these advantages, the use of structural fibres contributes to the replacement of traditional passive reinforcement, accelerating the production process and increasing the competitiveness of the FRC. Proof of this are the numerous experiences in which precast FRC segments have been used in highway (RT), railway (RWT), metro (MT), water supply (WTT), gas transport (GPT) and service (ST) tunnels. Table 1 (Hilar and Vítek, 2012, de la Fuente et al., 2011, de la Fuente et al., 2012) summarizes some of the main applications already in service or under construction.
The structural use of fibres has been regulated by the national codes in Germany in 1992 (DBV-Recommendati, 1992), Italy in 2006 (CNR DT 204/2006) and Spain in 2008 (CPH, 2008), for instance. More recently, recommendations about the design of FRC structures were also included in the MC 2010 (Bulletins 65-66, 2010), with constitutive equations (Blanco et al., 2010, Blanco et al., 2013) and models for the Service Limit State and Ultimate Limit State (SLS and the ULS, respectively). An increase in the use of FRC in tunnels segments has been observed as a result of that (Caratelli et al., 2012). In this regard, it is necessary to update the philosophy applied to the design of tunnel segments in compliance with the particular requirements proposed in the MC 2010, evaluating its applicability and repercussions.
The objective of this paper is to present a critical analysis of the design of FRC segments according to the ductility requirements from the MC 2010 and to propose an alternative approach more compatible with the conditions found in practice. First, the design procedure from the MC 2010 is analyzed and adapted to FRC segmented linings. Then, the alternative approach is presented. The applicability and repercussion of both approaches in terms of fibre consumption are evaluated in the specific case of the Metro Line 9 from Barcelona, using sectional analysis and results obtained in an experimental program with real-scale segments. This study shows the possible consequences of applying the design philosophy of the MC 2010 for FRC segments and it indicates alternative design considerations that could be implemented if certain conditions are fulfilled and it provides an example on how it may be used to optimize the fibre content required.
Section snippets
Design procedure based on the MC 2010
In tunnels with large internal diameter, segments are usually subjected to high bending moments during the transient and the service stages – the latter being generally the most unfavourable design condition. The replacement of traditional reinforcement by fibres is limited, generally leading to expensive solutions since high amounts of fibre are needed to achieve an equivalent mechanical response. In these cases, mixed reinforcement configurations consisting of a minimum amount of steel bars
Metro L9 of Barcelona
The Metro L9 of Barcelona counts 46 stations and 15 interchanges with a total length of 44 km and connects the airport (El Prat), the justice district (Ciutat de la Justicia) and the high speed railway station (Barcelona Sants Station). The construction is performed with a TBM with approximately 12.0 m of diameter. So far, this is probably one of the most studied TBM-bored tunnels and this is still under construction. In this sense, experimental and numerical analysis related with the FRC were
Analysis of sectional response
The structural analysis based on the design approaches presented in Section 2 is used to assess the minimum flexural residual strength that guarantees ductility. The second segment is subjected to its self-weight (Fig. 10a) and the total load transmitted by the upper segments (Fig. 10b). The self-weight of the segment is represented by means of a uniformly distributed load p = 16.2 kN/m and the force applied by the upper segments by F = ns·Ps, Ps being the self–weight of each individual segment (75.2
Repercussion of ductility criteria
To evaluate the repercussion of the two approaches discussed in this study, the minimum average fR3m estimated following each of them was translated into a required fibre content (Cf). For that, the values of fR3m,min calculated for a range of design eccentricities ranging from 0 to 0.15 m were divided by 0.85 to estimate the corresponding strength at 28 days. The latter was then used in Eq. (7) to assess Cf. Fig. 12 shows the curves that relate Cf and e for the critical situation of a pile
Conclusions
The analysis performed in this study sheds light on a fundamental aspect related to the design of FRC tunnel segments that might have a direct practical repercussion. The following conclusions may be derived from the present work.
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The results from numerical simulations of the structural response of the segments under the storage conditions agree with the results obtained in the real-scale experimental program. The good agreement obtained indicates that the constitutive equation derived from the
Acknowledgements
The authors want to thank the Ministry of Science and Innovation for the economic support received through the Research Project BIA2010-17478: Construction processes by means of fibre reinforced concretes. Likewise, the authors want to acknowledge the L9 Barcelona Metro Joint Venture for its economic support to carry out the experimental campaigns. The first author would like to acknowledge the scholarship received from the China Scholarship Council.
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