Interaction diagrams for design of hybrid fiber-reinforced tunnel segments

Yiming Yao, Mehdi Bakhshi, Verya Nasri, Barzin Mobasher

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Fiber reinforcement has emerged as an alternative to traditional reinforcing bars and welded wire mesh reinforcement for precast concrete tunnel segments. This is mainly due to improved postcracking behavior and crack control characteristics of fiber-reinforced concrete (FRC) segments. A hybrid solution of fibers and reinforcing bars is adopted when FRC is not adequate as the sole reinforcing system. Often times, this is the case in large-diameter tunnels with large curved length segments in order to achieve required strength for embedment loads in shallow cover, TBM thrust jack forces, and loading from imperfect construction and irregularities. P–M interaction diagrams are used as one of the main design tools since segment cross section, under most of governing load cases, is subjected to a combined axial force and bending moment. Standard FRC constitutive laws recently allows for a significant residual strength in tension zone below the neutral axis. However, design capacity of hybrid fiber-reinforced concrete (HRC) segment is significantly underestimated using conventional Whitney’s rectangular stress block method. Methods that currently incorporate contribution of fibers on P–M diagrams are based on numerical and finite-element analyses. However, closed-form solutions offer important advantages. This paper presents material models, derivations and for the first time closed-form solutions to construct P–M interaction diagram of HRC segments. Parametric studies are conducted and validity of the model is verified by simulating experimental results of HRC columns and model-predicted results of precast and cast-in-place concrete linings. 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)
Article number35
JournalMaterials and Structures/Materiaux et Constructions
Issue number1
StatePublished - Feb 1 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)
  • Mechanics of Materials


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