Title:
Closed-form Solutions for Interaction Diagrams of Hybrid Fiber-Reinforced Tunnel Segments
Author(s):
Yao, Y.; Bakhshi, M.; Nasri, V.; Mobasher, B.
Publication:
Symposium Paper
Volume:
343
Issue:
Appears on pages(s):
173-184
Keywords:
Analytical method; fiber; hybrid fiber-reinforced concrete; interaction diagram; tunnel, lining; residual strength; segment; TBM
DOI:
Date:
10/1/2020
Abstract:
Precast concrete segments are the predominant support method used in tunnels dug by Tunnel Boring Machines (TBM) in soft ground and weak fractured rock, providing the initial and final ground support. Conventionally, steel bars are used in concrete segments to resist tensile stresses due to all loading cases from the time of casting through service condition. With traditional reinforcement, a significant amount of time and labor are needed to assemble the cages and place the reinforcing bars. Fiber reinforced concrete (FRC) has become more attractive for its use in tunnel lining construction as a result of improved post-cracking performance, crack control characteristics and capability of partial
replacement of steel bars. Due to the strength requirements in large-diameter tunnels, which are subjected to embedment loads and TBM thrust jack forces, the use of FRC is not adequate as the sole
reinforcing mechanism. Therefore, the hybrid fiber-reinforced concrete (HRC) combining both rebars and steel fibers is frequently used in practice. Tunnel segmental linings are designed for load cases that occur during manufacturing, transportation, installation, and service conditions. With the exception of two load cases of TBM thrust jack forces and longitudinal joint bursting load, segments
are subjected to combined axial force and bending moment. Therefore, P-M interaction diagrams have been used as the main design tool for tunnel engineers. Standard FRC constitutive laws recently allow for a significant residual strength in tension zone
below the neutral axis. However, design capacity of HRC segment is significantly underestimated using conventional Whitney’s rectangular stress block method, especially for tension-controlled
failure, since the contribution of fibers in tension zone is ignored. Methods that currently incorporate contribution of fibers on P-M diagrams are based on numerical and finite-element analyses, which are normally more complicated and not readily to be implemented for practical design tools. Closed-form solutions of full-range P-M interaction diagram considering both rebar and fiber contributions are presented in this paper for HRC segments. The proposed model is verified with experimental data of compression tests with eccentricity as well as other numerical models for various cases of HRC sections. Results show that using appropriate material models for fiber and reinforcing bar, engineers can use the proposed methodology to obtain P-M interaction diagrams for HRC tunnel segments.
Related References:
ACI 544. (2016). 544.7R-16 Report on Design and Construction of Fiber-Reinforced Precast Concrete Tunnel Segments. ACI Committee 544.
ACI Committee 318, and American Concrete Institute. (2014). Building code requirements for structural concrete (ACI 318-14): an ACI standard : commentary on building code requirements for structural concrete (ACI 318R-14), an ACI report.
Bakhshi, M., and Nasri, V. (2014a). “Review of international practice on critical aspects of segmental tunnel lining design.” Los Angeles, United States.
Bakhshi, M., and Nasri, V. (2014b). “Guidelines and methods on segmental tunnel lining analysis and design-Review and best practice recommendation.” Iguassu Falls, Brazil.
Bakhshi, M., and Nasri, V. (2014c). “Developments in design for fiber reinforced concrete segmental tunnel Lining.” Montreal, Canada.
Bakhshi, M., and Nasri, V. (2014d). “Design considerations for precast tunnel segments according to international recommendations, guidelines and standards.” Vancouver, Canada.
Bakhshi, M., and Nasri, V. (2015). “Design of segmental tunnel linings for serviceability limit state.” Dubrovnik, Croatia.
Bresler, B. (1960). “Design Criteria for Reinforced Columns under Axial Load and Biaxial Bending.” Journal Proceedings, 57(11), 481–490.
Briffaut, M., Benboudjema, F., and D’Aloia, L. (2016). “Effect of fibres on early age cracking of concrete tunnel lining. Part II: Numerical simulations.” Tunnelling and Underground Space Technology, 59, 221–229.
Chiaia, B., Fantilli, A. P., and Vallini, P. (2007). “Evaluation of minimum reinforcement ratio in FRC members and application to tunnel linings.” Materials and Structures, 40(6), 593–604.
Chiaia, B., Fantilli, A. P., and Vallini, P. (2009). “Combining fiber-reinforced concrete with traditional reinforcement in tunnel linings.” Engineering Structures, 31(7), 1600–1606.
CSA. (2014). A23.3-14 - Design of concrete structures. CSA.
fib - federation internatioale du beton. (2013). fib Model Code for Concrete Structures 2010. Ernst & Sohn, Lausanne, Switzerland.
de la Fuente, A., Pujadas, P., Blanco, A., and Aguado, A. (2012). “Experiences in Barcelona with the use of fibres in segmental linings.” Tunnelling and Underground Space Technology, 27(1), 60–71.
Hernandez-Montes, E., Gil-Martin, L. M., and Aschheim, M. (2005). “Design of Concrete Members Subjected to Uniaxial Bending and Compression Using Reinforcement Sizing Diagrams.” Structural Journal, 102(1), 150–158.
Mobasher, B., Yao, Y., and Soranakom, C. (2015). “Analytical solutions for flexural design of hybrid steel fiber reinforced concrete beams.” Engineering Structures, 100, 164–177.
Parme, A. L., Nieves, J. M., and Gouwens, A. (1966). “Capacity of Reinorced Rectangular Columns Subject to Biaxial Bending.” Journal Proceedings, 63(9), 911–924.
Plizzari, G. (2009). Construction methodologies and structural performance of tunnel linings: optimisation of the structural, technological and functional performance, of construction methodologies and materials, in tunnel linings. Starrylink Editrice, Brescia, Italy.
di Prisco, M., Colombo, M., and Dozio, D. (2013). “Fibre-reinforced concrete in fib Model Code 2010: principles, models and test validation.” Structural Concrete, 14(4), 342–361.
Rotter, J. M. (1985). “Rapid Exact Inelastic Biaxial Bending Analysis.” Journal of Structural Engineering, 111(12), 2659–2674.
Soranakom, C., and Mobasher, B. (2007). “Closed-Form Solutions for Flexural Response of Fiber-Reinforced Concrete Beams.” Journal of Engineering Mechanics, 133(8), 933–941.
Steven, G., and Empelmann, M. (2014). “UHPFRC-Columns with high-strength longitudinal reinforcement.” Beton- und Stahlbetonbau, 109(5), 344–354.
Tiberti, G. (2009). “Concrete tunnel segments with combined traditional and fiber reinforcement: optimization of the structural behaviour and design aspects.” Ph.D. Dissertation, University of Brescia, Brescia, Italy.
Tiberti, G., Conforti, A., and Plizzari, G. A. (2015). “Precast segments under TBM hydraulic jacks: Experimental investigation on the local splitting behavior.” Tunnelling and
Underground Space Technology, 50, 438–450.
Whitney, C. S., and Cohen, E. (1956). “Guide for Ultimate Strength Design of Reinforced Concrete.” Journal Proceedings, 53(11), 455–490.
Yao, Y. (2016). “Characteristics of Distributed Cracking for Analysis and Design of Strain Hardening Cement Based Composites.” Ph.D. Dissertation, Arizona State University, Tempe, AZ.
Yao, Y., Bakhshi, M., Nasri, V., and Mobasher, B. (2018). “Interaction diagrams for design of hybrid fiber-reinforced tunnel segments.” Materials and Structures, 51(1), 35.