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
Appears on pages(s): 173-184
Keywords: Analytical method; fiber; hybrid fiber-reinforced concrete; interaction diagram; tunnel, lining; residual strength; segment; TBM
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.