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load would be increased further until the peak elastic moment would be reached at another location and another hinge would be introduced at this location, and so forth. At the end of this process, the moments of each step would be superimposed and added. While increasing the external loads during this process, the values of the moments at the hinges could not be increased beyond the plastic moment, but the rotation could increase, making the overall system “softer.” Following this approach, the lining would be locally weakened to induce a load redistribution and eventually show a system failure rather than failure at a specific cross section. The ultimate stage would be reached either as a result of system failure or by reaching rotation thresholds at the hinges or some other predefined limits. Given the properties of a tunnel lining as an embedded beam, a system failure would basically mean formation of hinge next to hinge in close proximity. For this reason, other meaningful structural thresholds or definition of a maximum number of hinges seem to be a viable option. The procedure described previously would allow full use of the properties and benefits of FRC in a structural analysis, while still using elastic structural analysis tools. CONCLUSIONS The article has presented and discussed the basics of FRC tunnel lining design using a selected SSR. The impact of normal force within the tunnel lining and the impact of a change of post-cracking behavior from strain softening to strain hardening was discussed in detail by means of a parametric study. Current tunnel lining design does not fully use the potential of FRC because it disregards the positive benefits of the compressive force, which are not related to the material properties itself. Future material specifications for tunnels should consider the expected range of compressive stress in the lining and its beneficial influence on the ductility of FRC. The most advantageous property of FRC is its toughness when the tunnel lining has cracked. The potential of the toughness is currently not typically used when evaluating moment resistance in the cracked state under a simultaneous axial force. A procedure to introduce plastic hinges has been suggested that would allow use of the benefits of FRC using classical structural analysis tools and thereby realize the full structural and economic potential of FRC. References 1. ACI Committee 544, “Report on Indirect Methods to Obtain Stress-Strain Response of Fiber-Reinforced Concrete (FRC) (ACI 544.8R-16),” American Concrete Institute, Farmington Hills, MI, 2016, 22 pp. 2. ACI Committee 544, “Design Considerations for Steel Fiber Reinforced Concrete (ACI 544.4R-88) (Reapproved 2009),” American Concrete Institute, Farmington Hills, MI, 1988, 18 pp. 3. ACI Committee 544, “Report on Design and Construction of Fiber- Reinforced Precast Concrete Tunnel Segements (ACI 544.7R-16),” American Concrete Institute, Farmington Hills, MI, 2016, 36 pp. 4. ACI Committee 506, “Guide to Fiber-Reinforced Shotcrete (ACI 506.1R-08),” American Concrete Institute, Farmington Hills, MI, 2008, 12 pp. 5. German Society for Concrete and Construction Technology (DBV), “Guide to Good Practice – Steel Fibre Concrete,” 2001. 6. Deutscher Ausschuss fuer Stahlbeton (German Committee for Reinforced Concrete) (DAfStb), DAfStb Richtlinie fuer Stahfaserbeton (DAfStb Guideline for Steel Fiber Reinforced Concrte), 2010. (in German) 7. Barton, N.; Lien, R.; and Lunde, J., “Engineering Classification of Rock Masses for the Design of Tunnel Support,” Rock Mechanics, V. 6, No. 4, 1974. 8. Grimstad, E., and Barton, N., “Updating of the Q-System for NMT. In Kompen,” Opsahl & Berg (eds), Proceedings of the International Symposium on Sprayed Concrete—Modern Use of Wet Mix Sprayed Concrete for Underground Support, Fagernes, Norway, 1993. 9. Nitschke, A., “Tragverhalten von Stahlfaserbeton für den Tunnelbau (Load Bearing Behavior of Steel Fiber Reinforced Concrete for Tunneling),” PhD thesis, Technisch-wissenschaftliche Mitteilungen des Instituts für konstruktiven Ingenieurbau der Ruhr-Universität Bochum, TWM 98-5, 1998. (in German) 10. Dietrich, Jörg, “Zur Qualitätsprüfung von Stahlfaserbeton für Tunnelschalen mit Biegezugbeanspruchung (About Quality Testing of Steel Fiber Reinforced Concrete for Tunnel Lining under Flexural Tension),” PhD thesis, Technisch-wissenschaftliche Mitteilungen des Instituts für konstruktiven Ingenieurbau der Ruhr-Universität Bochum, TWM 92-4, 1992. (in German) 11. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14),” American Concrete Institute, Farmington Hills, MI, 2014, 519 pp. 12. ACI SP-17(14), The Reinforced Concrete Design Handbook, Volume 1: Member Design, American Concrete Institute, Farmington Hills, MI, 2015. 13. Maidl, B., Steel Fibre Reinforced Concrete, Ernst & Sohn, Berlin, Germany, 1995. 14. Nitschke, A., and Ortu, M., “Bemessung von Stahlfaserbeton im Tunnelbau. Abschlußbericht. (Design of Steel Fiber Reinforced Concrete for Tunneling. Final Report),” Ruhr-Universität Bochum, Lehrstuhl Prof. Maidl, Research Project funded by the Deutscher Beton-Verein E.V. (DBV-Nr. 211) and the Arbeitsgemeinschaft industrieller Forschungsvereinigungen (AiF-Nr. 11427 N), Fraunhofer IRB Verlag, 1999. (in German) 15. Maidl, B.; Nitschke, A.; and Ortu, M., Bemessung von Tunnelschalen mit dem M/N-Prüfkonzept. (Design of Tunnel Linings with the M/N Testing Concept),” Taschenbuch für den Tunnelbau 1999, Glückauf Verlag, Essen, 1998. Axel G. Nitschke is Vice President of Shannon & Wilson Inc. He received his MSc and PhD in civil engineering from Ruhr University Bochum, Bochum, Germany, in 1993 and 1998, respectively. He has gained more than 20 years of in-depth, on-the-job experience in all aspects of underground construction, geotechnical engineering, and mining. He has worked on the engineering and construction of many tunnel projects in Europe, the United States, Canada, and Colombia. He is well-experienced in all ground conditions, ranging from soft ground to hard rock, and the associated implications for design and construction methods. Nitschke has held key positions, such as Senior NATM Engineer, Contract/Claims Manager, Risk Manager, Design Manager, and Project Manager. He currently serves on the ASA Board of Direction and Chairs the ASA Underground Committee. He is a licensed professional engineer in Virginia, Maryland, the District of Columbia, New Jersey, Washington, and California. 34 Shotcrete | Spring 2017 www.shotcrete.org


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