Closed-form solutions for interaction diagrams of hybrid fiber-reinforced tunnel segments

Yiming Yao, Mehdi Bakhshi, Verya Nasri, Barzin Mobasher

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationFibre Reinforced Concrete
Subtitle of host publicationFrom Design to Structural Applications - Proceedings of the ACI-fib-RILEM International Workshop, FRC 2018
EditorsBruno Massicotte, Barzin Mobasher, Fausto Minelli, Giovanni Plizzari
PublisherAmerican Concrete Institute
Number of pages12
ISBN (Electronic)9782883941427
StatePublished - Nov 3 2020
Event3rd ACI-fib-RILEM International Workshop on Fibre Reinforced Concrete: From Design to Structural Applications, FRC 2018 - Desenzano, Italy
Duration: Jul 28 2018Jul 30 2018

Publication series

NameAmerican Concrete Institute, ACI Special Publication
ISSN (Print)0193-2527


Conference3rd ACI-fib-RILEM International Workshop on Fibre Reinforced Concrete: From Design to Structural Applications, FRC 2018


  • Analytical method
  • Fiber
  • Hybrid fiber-reinforced concrete
  • Interaction diagram
  • Lining
  • Residual strength
  • Segment
  • TBM
  • Tunnel

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Materials Science(all)


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