Assessment of steel-fiber-reinforced segmental lining of Chamshir water conveyance tunnel, Iran: Integrating laboratory experiments, field observations, and numerical analysis

The conventional rebar-reinforced concrete (RRC) segmented lining of the Chamshir water conveyance tunnel (CWCT) in Bushehr Province, Iran, has experienced significant damage issues. This paper presents a comprehensive study involving laboratory experiments, numerical simulations and statistical site-survey analysis aimed at evaluating the mechanical behaviors and structural integrity of steel fiber-reinforced concrete (FRC) and fiber-rebar-reinforced concrete (FRRC) segment types, as compared to the traditional RRC segments. Laboratory compressive, tensile and flexural strength testing provided insights into the impacts of the fiber diameter and content on the ultimate strength capacities of the FRC test specimens. Numerical simulations scrutinized beam and segment models reinforced by the explicit inclusion of traditional rebar and/or randomly orientated and evenly distributed steel fiber reinforcements. The segment simulations were directed at investigating concentrated loading, representative of the jack thrust force applied in installing the segments during the tunnel boring machine (TBM) installation phase. Additionally, a field-monitoring program of the CWCT lining quantified common damage patterns among 545 RRC and 416 FRC segments that had experienced damage during their installation and in-service phases. For FRC beams, increased fiber content correlated with enhanced strength capacity, although the use of larger diameter fibers produced diminishing returns. Compared to the considerable damage expected near the applied TBM jack thrust force for the RRC segments, significantly reduced damage was predicted for both the FRC and FRRC segment types. However, even modest jack force misalignment (of 5 – 7.5 ◦ ) led to cracking damage

across the segment width for all models, although with the fibers included, the chipping damage was reduced substantially.The findings underscore the potential of FRC and FRRC segment types to achieve better structural integrity compared to traditional RRC segments.
The present case study investigates the implemented RRC and FRC segment types used in the construction of the Chamshir water conveyance tunnel (CWCT) lining.Our investigation aims to elucidate the impact of fiber inclusion on the mechanical properties and structural resilience, while also assessing the feasibility and advantages of partially substituting or complementing the rebar with fiber reinforcement (i.e., for fiber-rebar-reinforced concrete (FRRC)).While previous researchers often relied on equivalent constitutive laws in their numerical models, the innovative approach implemented in this study for simulating the physical inclusion of steel fibers Fig. 1.General location and geology of the CWCT crossing beneath the Zohreh river [77,78].
M. Ezazi et al. in concrete for reinforcement purposes gives a more nuanced understanding of the fiber-concrete interactions.By capturing micromechanical properties and processes, such as damage initiation and evolution, the developed finite-element analysis (FEA) provides valuable insights for various applications, including the tunnel segmented lining.In the CWCT case study, we address this knowledge gap by meticulously modelling the steel fibers as being randomly oriented and evenly dispersed throughout the segments.Our investigation examines the mechanical attributes and structural integrity of variously loaded FRC components for three different fiber diameter sizes and fiber quantities (as proportions of the concrete mix investigated), and scrutinizes the damage initiation and progression in RRC, FRC, and FRRC segment types, with a focus on the role of the embedded fibers in damage mitigation.To achieve these goals, this paper presents the results of laboratory experiments, numerical simulations, as well as field observations and statistical analysis of observed damage patterns to in-situ RRC and FRC segment types of the CWCT lining, thereby obtaining a holistic understanding of the tunnel lining performance for the different reinforcement strategies.In synthesizing the laboratory experiment, numerical simulation and field observation results, this research bridges the gap between small-scale controlled laboratory testing conditions and the dynamic realities of tunnel construction.By amalgamating the various methodologies, the study aims to provide a robust basis for assessing the efficacy of fiber reinforcement and combined rebar and fiber reinforcements in enhancing the structural integrity of the segmented lining of the CWCT amidst diverse operational scenarios.

Case studysegmented lining of the Chamshir water conveyance tunnel (CWCT)
The CWCT is located downstream of the Chamshir dam, in the east of Bushehr province, southwest Iran.The tunnel itself is more than 7-km long, with an internal diameter of approximately 4.6 m.The area in which the tunnel is located occurs in the simply folded Zagros (SFZ) zone, with the geology shown in Fig. 1.
From Fig. 1, the main stratigraphic units, which outcrop in the project area, include the mudstones, marlstones, sandstones and siltstones of the Aghajari formation.This region includes very wide and gently folded parallel anticlines and synclines.In some synclines and the lower parts of anticline limbs, the Aghajari formation is covered by conglomerates and sandstones of the Bakhtiari formation and Quaternary deposits.The Bibi-Hakimeh anticline, with a NW-SE trend (parallel to the general trend of the SFZ zone), is the main structure in the project area (see Fig. 1) -the total 7-km length of the CWCT being covered in its northeastern limb.Geological site investigations did not identify any important fault zone along the CWCT's alignment.
Unlike the originally designed hexagonal shape, a trapezoidal-segmented tunnel lining was later adopted to provide better control over inward and outward water flows.Each lining ring is comprised of six separate 1.2-m long by 0.25-m-thick quadrilateral RRC or   FRC segments (see Fig. 2), with the configuration of the six installed segments forming the lining ring illustrated in Fig. 3.
The conventional RRC segments that comprised the CWCT lining exhibited signs of significant damage having occurred during their installation, as evident from the images shown in Fig. 4.Such deterioration of the lining poses a substantial risk to the operational effectiveness of the tunnel's water conveyance system.To address and mitigate this detrimental occurrence, an alternative reinforcement approach of including both fiber reinforcement and traditional rebar [2,10,12,16,24,49] was devised and executed.This strategy was implemented for the CWCT with the objective of augmenting the structural resilience and operational efficacy of the segmented lining, particularly for the demanding conditions encountered during its installation.

Laboratory testing
The laboratory experiments started with casting a diverse set of FRC test specimens (Fig. 5), incorporating 50-mm long hookedended steel fibers of different diameter sizes (i.e., 0.8, 1.0, and 1.2 mm) and for different fiber contents (FCs) of 30, 40, and 50 kg of the steel fibers per cubic meter of the final concrete mix plan.Some unreinforced concrete (UC) specimens were also prepared (as controls).Apart from their different fiber diameters and contents, the test specimens shared identical concrete mix composition.Note, the same concrete mix composition investigated here had been used in fabricating the RRC and FRC segments of the CWCT lining.
Table 1 and Fig. 6 provide detailed information on the geometry (length, diameter and aspect ratio) of the individual steel fibers, and also the numbers of fibers per kilogram mass considering the three different fiber diameters investigated.While Table 2 lists the composition of the C40-Class concrete mix investigated.Note that the FC additions of 30, 40, and 50 kg/m 3 of the final concrete mix plan equate to fiber volume fractions of 0.42%, 0.56%, and 0.69%, respectively.
After fully blending the dry concrete mixture, the water and admixture were introduced, and the entire wet mixture was thoroughly blended before being placed into the specimen molds.The desired compaction was achieved by vibration, applied for 30 s, as per the study by [55].The test specimens were allowed to cure in water for 28 days at ambient laboratory temperature.At 28 days, the cured specimens were subjected to a program of strength testing, in accordance with the European standard EN 12390 [56][57][58], aimed at quantifying how the fiber diameter and content affected the FRC specimens' mechanical properties for various loading conditions.Each scenario was tested in triplicate, with the overall testing program comprised of 18 numbers of uniaxial compression tests on 15×15×15-cm cubic specimens, indirect tension (Brazilian) tests on 15-cm diameter by 30-cm-long cylindrical specimens, and three-point bend (flexural strength) tests on 10-cm-square × 50-cm-long prismatic specimens (i.e., a total of 54 individual strength tests).

Numerical simulations
The numerical simulations were aimed to provide insights into the performances of various rebar and/or fiber reinforcement schemes, investigated for the controlled loading condition of the laboratory three-point bend test (using beam models), as well as   realistic in-situ loading scenarios of the TBM jack thrust force applied to the CWCT segments (investigated using segment models).To accomplish these, we used the powerful capabilities of the ABAQUS FEA software, which offers a wide range of material behaviors suitable for modeling diverse engineering applications.One of its notable features is the provision of explicit analysis capability, enabling modeling of large displacement/strain problems, with the Dynamic Explicit solver employed to solve the quasi-static problem investigated in the present research.Furthermore, ABAQUS provides users with a variety of contact features to model interaction problems between different parts of a model.These include the General Contact formulation, the Hard Contact property for modeling normal impenetrability of a mesh against another mesh, and Penalty/Coulomb tangential behavior employed for modeling friction between different parts of a model.Additionally, ABAQUS offers an embedding formulation for setting constraints between different parts or associated meshes.The software also provides access to a variety of finite-element types, with options for full or reduced integrations.
In our study, we meticulously designed the beam and segment models to incorporate both rebar and fiber reinforcements.While the rebar elements were directly sketched in ABAQUS, the embedded fibers were generated using MATLAB's uniformly distributed random function (unifrnd).This approach ensured our numerical models realistically reflected the actual distribution and orientations of the fibers within the physical C40-Class concrete beams/segments.In other words, for the models, each steel fiber was generated as a pair of points separated by a standardized distance of 50 mm (i.e., the fiber's physical length), with the fibers uniformly distributed and randomly orientated within the interior of the targeted beam or segment volume.The MATLAB code then exported these fibers in .inpfile format, assigned them the beam element type of B31, and integrated them into the main .inpfile generated by ABAQUS.Note, in this study, we used the eight-node linear brick, reduced integration, and hourglass-control element type of C3D8R for the host/ concrete elements.Upon the fibers' importation into ABAQUS, further property assignments, assembly processes, and interaction definitions were performed.This meticulous approach ensured the realistic representation of the fiber reinforcement within the numerical models, enhancing the fidelity and reliability of our simulations.
To model the interactions and interfaces between the C40-Class concrete matrix and steel reinforcement (i.e., rebar and fiber) elements, we utilized the embedded element technique in ABAQUS.This technique allowed for the precise identification of geometric relationships between the nodes of the embedded elements and the host (i.e., concrete) elements.When a node of a reinforcement element was detected within a concrete element, its translational degrees of freedom (DOFs) were eliminated, thereby converting it into an embedded node.Subsequently, the translational DOFs of the embedded node were constrained to the interpolated values of the corresponding DOFs of the host element.Rotational DOFs were permitted for embedded elements (i.e., they were not constrained by the embedment process).This approach ensured the realistic representation of reinforcements within the concrete matrix, thereby enhancing the fidelity and reliability of our numerical models.Additionally, to model the interactions between the loading/reaction parts with the beams or segments, we implemented the General Contact formulation.This involved selecting surface pairs and assigning contact properties to ensure normal impenetrability (Hard Contact) and Penalty tangential behavior (friction coefficient of μ = 0.3) conditions between different parts of a model.Fig. 7 illustrates the dimensions, boundary conditions, and loading conditions considered for the beam and segment models.
For the beam models (see Fig. 7(a)), the bottom surfaces of the two supports (reaction pins) were fixed in all directions (i.e., no transitional or rotational DOFs).In the case of the central loading pin, all DOFs were prevented, except for its vertical transitional movement (along the y-axis direction) that was used to apply the displacement-controlled loading condition.When employing the   explicit analysis, for investigating a quasi-static problem we strive for a balance between the execution time/cost and the manipulation of the results.For instance, as the displacement amount (which can be also interpreted as the loading rate) is increased, the intended analysis will be completed in a shorter time, which is desirable.However, due to the inertia effect, the result of our quasi-static analysis might be manipulated, which is not desirable.Hence, the goal is to determine the maximum loading rate (displacement) that has minimal effect on the numerical results.We conducted a sensitivity analysis in this regard, and found that 0.5 mm of downward displacement (i.e., 0.5 mm/s loading rate) of the central loading pin was the most appropriate amount for the implemented beam model.
For the segment models (see Fig. 7(b)), all DOFs in the TBM shield and adjacent concrete segments were fixed.A 2000-kN force, equivalent to a bearing pressure of 35 MPa, was applied over an area of 22×26 cm on the end surface of the segment (i.e., representing the hydraulic jack's contact area with the end of the segment), to analyze the effect of concentrated applied forces on the structural response of the segments.Additionally, misalignment (of up to 15 • ) between the direction of the TBM jack thrust force and the segment's longitudinal axis were investigated.Symmetric boundary conditions (XSYMM) were assumed to optimize computational efficiency.
For modelling the constitutive behavior of the C40-Class concrete, the concrete damage plasticity (CDP) model was chosen on account of its capability to simulate both compressive and tensile damage progression [59,60].Fig. 8 illustrates the tension stiffening and compression hardening associated with the tensile and compressive responses.
The input parameters for the CDP model, as determined or deduced from the laboratory experiments performed in the present study, are listed in Table 3.
The model parameters include bulk density, elastic modulus, Poisson's ratio, yield stress σ y , plastic strain ε p , the biaxial yield stress to uniaxial yield stress ratio σ b0 /σ c0 , dilation angle ψ ), invariable ratio of tensile to compressive stresses (i.e., K c ), and damage coefficients in compression (d c ) and tension (d t ).With consideration of the experimental results, the initial values for the auxiliary parameters (i.e., σ b0 /σ c0 , ψ , and K c ) of the CDP model were determined based on the reference manuals, related research articles [59,61], and ABAQUS documentation.The initial values of these parameters were then modified/adjusted accordingly through the verification process.
Moreover, the elastic-perfectly-plastic constitutive model was employed for the steel rebar and fiber reinforcements (refer to Table 4).

Laboratory experiments
Table 5 and Fig. 9 present the laboratory test results for the unreinforced concrete (UC) specimens and five distinct FRC sample types (i.e., FRC1 to FRC5), characterized by their three different fiber diameters and contents investigated.Note the UC results serve as a control for gauging the fiber influence on the strength responses.
Referring to sample types FRC1, FRC2 and FRC3 containing 0.8 mm diameter fibers, the mobilized strengths increased overall for increasing the FC from 30 to 50 kg/m 3 (of the final concrete mix plan).The exception was the compressive strength mobilized for steel fibers at 50 kg/m 3 , which was slightly lower than that mobilized for 40 kg/m 3 , this behavior being consistent with the findings reported in [62].This compressive strength decrease may be attributed to slippage or movements between fibers for the higher FC.Notably, the additions of steel fibers at 30 and 40 kg/m 3 produced significant improvements of the tensile strength, with respective strength gains of about 35% and 56% achieved relative to the UC case.Considering each strength test, the greatest strength improvements achieved relative to the UC case were: (i) a 21% increase in compressive strength for steel fibers at 40 kg/m 3 ; (ii) a 62% increase in tensile strength for steel fibers at 50 kg/m 3 ; (iii) a 55% increase in flexural strength for steel fibers at 50 kg/m 3 .These experimental findings are in general agreement with the results reported in [63,64] for indirect tension, [65,66] for flexural strength, and [67][68][69][70] for compressive strength testing.
Comparing the results for sample types FRC2, FRC4 and FRC5 shown in Fig. 9, it is evident that increasing the fiber diameter (from 0.8 to 1.2 mm) for the same fiber content (of 40 kg/m 3 ) causes a progressive reduction in the mobilized compressive, tensile and flexural strengths.Considering each strength test, relative to the 0.8 mm diameter fibers of the FRC2 case, the strength reductions for the FRC5 case employing 1.2 mm diameter fibers were a 62% decrease in compressive strength, 33% decrease in tensile strength, and an 88% decrease in flexural strength.However, it should be noted that in all investigated cases, the compressive, tensile and flexural strengths of the FRC samples were greater than those mobilized for the UC specimens.The strength reductions for increasing the fiber diameter (from 0.8 to 1.2 mm) with the same fiber content (of 40 kg/m 3 ) can be linked to the reducing number of individual fibers distributed throughout the test specimens for increasing fiber diameter.The number of individual fibers decreases by 54% (i.e., from 4830 to 2200 fibers per kilogram of steel fiber reinforcement: see Table 1) for increasing the fiber diameter from 0.8 to 1.2 mm.Consequently, for the larger diameter fibers, the number of interactions between the embedded fibers and concrete matrix decreases, leading to an overall weakening of the reinforced-concrete element.5 for details of the steel fibers incorporated in the FRC samples.

Numerical analyses
This section begins with establishing the validity and accuracy of the employed numerical analyses by comparing the obtained numerical results with experimental data and established analytical solutions.Next, we present and analyze the numerical results obtained from RRC, FRC and FRRC beam model simulations that mirrored the loading conditions of the laboratory three-point bend test.Then, from comparisons of simulated RRC, FRC and FRRC segment types, we investigated the impact of including the fiber reinforcement on the structural performance/integrity of the segments for TBM jack loading.

Verification and validation of numerical analyses
For model verification and validation purposes, we compared the results of the employed numerical analysis to: (i) an experimental FRC anchor-block study reported in Schnüntger and Erdem [71] (which has also been used in [13,72] for validating their models); (ii) the analytical solution proposed by Zhou [73] for a concentrated compressive loading condition.
Schnüntger and Erdem [71] performed a series of line-load compression experiments on twelve 350-mm-square by 700 mm long FRC blocks (Fig. 10(a)).Comparable with the present investigation, their FRC contained 35 kg of steel Dramix hooked-end fibers per cubic meter of the final concrete mix plan, each fiber being 0.75-mm in diameter by 60-mm long.
A 3D model was developed as part of the present study to replicate both the geometry and loading condition of the mentioned test setup.In other words, vertical displacement was constrained at the bottom surface (i.e., u y = 0), while a displacement-controlled loading condition, with a magnitude of 2 mm/s, was applied to a strip area (of 35×15 cm) centered on the top surface of the anchor block element (see Fig. 10(b)).The resulting reaction force (i.e., macroscopic compressive strength) was monitored for each data output increment, with the maximum value of the reaction force equating to the predicted ultimate load capacity of the anchor block.Furthermore, the line-load configuration mobilizes tensile stress (i.e., splitting or bursting pressure, P sp ) orthogonal to the force direction (i.e., acting in the x direction for the model output shown in Fig. 11a), thereby providing insights into the two-dimensional biaxial behavior of the FRC element.
Before validating our numerical results for the anchor block model against the reported experimental results for the physical anchor block tested in Schnüntger and Erdem [71], we first verified our numerical results for loading in the elastic region, comparing them with the elastic analytical solution proposed by Zhou [73] for the concentrated compressive loading condition (see Fig. 11(b)).For this purpose, we considered the case of a 1150-kN compressive force applied to the 35×15-cm strip loading area on the top surface of the anchor block element (i.e., here the applied force is significantly below the element's ultimate load capacity of 3090 kN).As evident  from the plot of tensile stress (i.e., σ xx or S11) against measured distance vertically from the top of the anchor block (i.e., along its y-axis) shown in Fig. 11(b), our numerical model accurately replicates the FRC anchor block behavior in the pre-cracked (elastic) regime.In other words, the developed numerical models in this study faithfully reproduce the elastic stress distribution of FRC material under concentrated compressive loads, to the thrust force exerted by the TBM's hydraulic jack in the field scenario.
To evaluate the validity of our numerical model when considering the damage initiation and evolution in reinforced concrete, we compared the macroscopic compressive force predicted for the anchor block from the simulation with the experimental data reported in [71].Overall, there was a good agreement achieved between the predicted macroscopic behavior and the experimental results for the FRC anchor block, with the maximum experimental load reaching 3.09 MN, while our numerical results showed a comparable maximum load of 2.98 MN (i.e., with 95.5% prediction accuracy)).To further validate the numerical results, we compared Schnütgen and Erdem [71]'s experimental and our numerical axial-force-against-lateral-displacement response/prediction for the LVDT3 position, i.e., for a distance of 175 mm down from the top end of the anchor block (see Fig. 10(a)).Fig. 12 illustrates the good agreement between the experimental and numerical results of axial force plotted against the LVDT3 (lateral) displacement.
Fig. 13 compares the simulated crack pattern with that observed during the FRC anchor block experiments reported in [71].Initially, divergent tensile cracking occurred at the boundary (edge) of the 35×15-cm strip loading region, i.e., near the compressive/crush zone where direct contact occurs between the loading strip and anchor block.Moving down along the block length towards its mid-height, the induced maximum tensile stresses converge, producing a single/concentrated crack that is approximately aligned along the longitudinal axis of the block.The good agreement found between the numerically predicted and observed crack patterns is another key indication of the model's effectiveness in replicating the mechanical response of the FRC block element for the line-load configuration that ultimately leads to splitting/bursting failure.Moreover, the numerical model captured the intricate details of the crack initiation, propagation and interaction, thereby providing valuable insights into the resistance mechanism(s) of the FRC block until failure.

Beam model simulations
This section presents simulations for the 10-cm-square by 50-cm-long FRC, RRC, and FRRC beam elements, focusing on their mechanical behaviors, such as flexural load and bending moment resistances plotted against mid-span deflection, ultimate load capacity, and damage evolution.These serve as a basis for understanding the behaviors of the more complex FRRC segment element scenarios examined in the Section 4.2.3.
The first series of models investigated the flexural behavior of three FRC beams incorporating 0.8-mm-diameter steel fibers at 30, 40 and 50 kg/m 3 (of the final concrete mix plan) (see Fig. 14).
As per the studies by [28,74], three distinct stages are identified in the load-deflection behaviors of the FRC beams: (i) linear elastic; (ii) softening; (iii) fracture instability (expansion).During the softening stage, micro cracking develops continuously, causing a nonlinear load-deflection relationship.For the third stage, the fractures expand rapidly upon reaching the load capacity limits.The presence of the steel fibers hindered crack propagation, thereby contributing to an overall strengthening and toughening of the FRC beam elements.
As evident from Fig. 14, all three FRC beams exhibited similar load against mid-span deflection behaviors leading up to yield (i.e., first peak).However, their post-yield responses varied depending on the FC, i.e., with additions of steel fibers at 30 and 50 kg/m 3 producing the lowest and highest flexural strength capacities, respectively.The hardening response (post-yield) most likely arose due to the engagement and interaction between the embedded fibers and the concrete matrix.An evaluation of the localized cracking damage predicted in the middle section of the beams revealed less damage occurred for increasing FC.In other words, more engagements between the fibers and concrete matrix hindered the progress of micro-cracks.
The second series of models investigated the flexural behavior of three similarly dimensioned RRC beams, each incorporating 8, 10, or 12 mm diameter rebar.Limited by their small (i.e., 10×10 cm) cross-sectional area, two levels of rebars (wire meshes) were included in each beam: the lower wire mesh located in the tension zone, and the upper wire mesh located in the compression zone.This 14. Flexural load/bending moment against mid-span deflection results from FRC beam simulations, investigating 0.8-mm-diameter steel fibers at 30, 40, and 50 kg/m 3 (of the final concrete mix plan).configuration entails incorporating two rebars within each wire layer, i.e., giving four rebars foreach beam.The four rebars were spaced at 4-cm centers (in the x and y directions; see Fig. 7(a)), with a 3 cm concrete cover to each rebar.Elongation of the rebars occurred along the z-axis under the imposed flexural loading.Referring to the simulation results shown in Fig. 15, all three RRC beams behaved identically up to the yield point.However, as expected, their post-yield hardening responses differed, with greater flexural strength mobilized for larger diameter rebar.Moreover, the ultimate flexural strengths mobilized for the RRC beams were more than five times greater than those mobilized by FRC beams.Fig. 16 shows the damage predicted for the RRC beams incorporating 8 and 12 mm diameter rebars, with more extensive damage to the beam occurring for the larger diameter rebar.This is attributed to the higher rigidity and energy absorption of the larger diameter rebar, which makes the adjacent concrete more susceptible to damage.In other words, the rebars primarily enhanced the flexural strength capacity of the beam elements rather than the structural integrity of the concrete, which experienced extensive damage  17.Flexural load/bending moment against mid-span deflection results from FRRC beam simulations (case of two 8-mm-diameter rebars and 0.8 mm diameter fibers, considering FCs of 30, 40, and 50 kg/m 3 (of the final concrete mix plan)).

progression.
The third series of models investigated the flexural behavior of three FRRC beams having the same dimensions (i.e., 10-cm-square by 50-cm long) as the first and second series of models.The reinforcement designs for the FRRC beams were based on the 0.8-mm-dia.fiber consumption requirement of 30, 40 and 50 kg of steel fibers per cubic meter of concrete, along with a lower wire mesh containing two 8-mm-dia.rebars.In other words, the two rebars were spaced at 4-cm centers (in the x direction; see Fig. 7(a)), with a 3 cm concrete cover between them and the beam's bottom surface.Fig. 17 presents the flexural load/bending moment against mid-span deflection results obtained from the three FRRC beam simulations.
Referring to Figs. 15 and 17, the flexural strength capacities of the three FRRC beams and the RRC beam with 8-mm-dia.rebars were approximately equal.In other words, the flexural strength capacity of the FRRC beams was controlled mostly by the rebars, and not the fiber reinforcement.Referring to Fig. 18, greater damage of the FRRC beams occurred for the higher FC (of 50 kg/m 3 ).This is explained by more contacts between the steel fibers and the rebars for higher FC, resulting in more slippage/movement occurring between them, thereby contributing to the formation and development of more severe damage in the concrete.

Structural performance of CWCT segmented lining during installation phase
Using numerical modelling, this section investigates the effect of a concentrated force, applied by the TBM jack during the lining's installation phase, on the stress distribution, deformation patterns, and damage evolution for the RCC, FRC, and FRRC segment types.The magnitude of the applied jack force depends on many variables, including the ground conditions, tunnel overburden, friction forces developed between the TBM shield and surrounding soil, the number of hydraulic jacks employed per segment, the loading plate's contact area, etc.It is also worth noting that the most demanding scenarios loads and concrete cracking may not occur

Table 6
Threshold pressure causing damage to differently reinforced segment types, considering misalignment of the TBM jack thrust force with the longitudinal axis of the already installed tunnel lining.during the tunnel construction stage [5,75].Furthermore, imperfect segment placement, jack misalignment, or operator error can result in improper ring contact (see Fig. 19) and load eccentricity [13,76].
For our numerical simulations, the models considered perfect alignment (i.e., 0 • ) and misalignments of 5 • , 7.5 • , 10 • , and 15 • between the TBM thrust direction and the longitudinal axis of the already installed tunnel lining.The segment model shown in Fig. 7(b) was employed, investigating C40-Class concrete with the following reinforcement schemes (see also Table 6): • RRC segment incorporating 10-mm-diameter main reinforcement (i.e., 12 rebars in two layers, 6 rebars each), along with 8-mmdiameter shear reinforcement (36 rebars in two layers).• Three FRC segments incorporating 0.8-mm-diameter steel fibers at 30, 40, and 50 kg/m 3 (of the final concrete mix plan).Note, the RRC and FRC reinforcement schemes described above are the same as those used in fabricating the RRC and FRC segment types utilized in the actual CWCT lining.The additional analysis for the FRRC segment type serves to explore reinforcement variations, i.e., different from the field reinforcement plan design.
Fig. 20 presents the results from the RRC, FRC and FRRC simulations, considering the cases of the single hydraulic jack in (i) perfect alignment, and (ii) at a 15 • misalignment with the longitudinal axis of the already installed tunnel lining.In the case of their perfect alignment (Fig. 20(a, c, e)), no significant damage was predicted for both the FRC and FRRC segment types, whereas considerable damage occurred for the RRC segments in the vicinity of the applied TBM jack force (refer to Fig. 7(b) for locating the jack thrust force applied to the end area of the segment.This failure/damage mechanism is quite similar to the formation of a crushing zone under the TBM roller disc-cutter, from which tensile fractures can develop.As demonstrated for flexure loading of the model beams in Section 4.2.2, the rebars in the RRC segments merely enhanced the beam's structural strength capacity, whereas the addition of fibers helped to improve the overall mechanical behavior of the reinforced-concrete elements, reducing their tendency for chipping damage formation.
Fig. 20(b, d, f) show the numerical predictions for the case of the jack thrust force applied at a 15 • misalignment with the longitudinal axis of the already installed tunnel lining.Regardless of the reinforcement scheme employed, even modest jack misalignments (of 5-7.5 • ) resulted in the segments experiencing some damage, mostly occurring in the middle section where transverse cracks formed.Table 6 lists the predicted threshold pressure magnitudes above which the segments sustained damage.As expected, increased jack misalignment caused the segments to experience damage for lower jack thrust force, with the threshold damage pressure decreasing proportionately.

Statistical study of observed damage patterns in CWCT lining segments
A field-monitoring program of the installed CWCT lining was performed, involving detailed observations for a total of 961 segments (comprising 545 RRC and 416 FRC) that had become damaged during their installation and in-service phases.The field observations served to document and quantify common damage patterns, with consideration of the six segment locations around (comprising) the lining ring (refer to Fig. 3).Statistical analysis of the collected data provided valuable insights into the performances of the RRC and FRC segment types under their operational conditions, and for comparison with the numerical simulation results.Fig. 21 categorizes into six distinct patterns the observed damages that had occurred to the 961 segments of the CWCT lining.
Fig. 22 presents the frequency of each damage pattern (as a percentage of the 545 RRC and 416 FRC damaged segments examined), with consideration also of their occurrence in the six segment locations comprising the lining ring (i.e., segments labeled A-E and K illustrated Fig. 3).
Referring to Fig. 22, the most frequent damage patterns observed on-site for both the C40-Class RRC and FRC segments were types G, J, and L. Referring to Fig. 21, patterns G and J are related to cracking damage across the entire segment width, while pattern L is associated with chipping damage in the segment corners and along longitudinal/circumferential joints.As observed in the frequency charts of Fig. 22, the FRC segments were notably less susceptible to chipping damage (pattern L) than the RRC segments.However, approximately 70% and 50% of the damaged RRC and FRC segments, respectively, experienced cracking damage (patterns G and J).As observed for the segment models, cracking damage likely occurred due to the concentrated force action arising from the hydraulic jack's misalignment with the longitudinal axis of the already installed tunnel lining, which caused crack formation regardless of the segment reinforcement scheme adopted.

Summary and conclusions
Employing a combination of laboratory experiments, numerical modeling, and statistical analysis of field performance data, this paper presented a comprehensive evaluation of the efficacy of incorporating rebar and steel fiber reinforcement in the C40-Class precast concrete segments that comprise the lining of the Chamshir water conveyance tunnel (CWCT).The laboratory experiments revealed that for steel fiber-reinforced concrete (FRC) elements, an increase in fiber content or reduction in fiber diameter (for investigated ranges of 30-50 kg/m 3 (of the final concrete mix plan) and 0.8-1.2mm, respectively) produced improvements in compressive, tensile, and flexural strengths.Notably, for these FRC elements, the tensile (i.e., Brazilian) strength exhibited the most significant improvement, whereas the enhancement in compressive strength was comparatively modest.
Numerical simulations of three-point load tests on similar dimensioned rebar-reinforced concrete (RRC), FRC, and steel fiber-rebarreinforced concrete (FRRC) beam models demonstrated that, in terms of ultimate flexural strength, the RRC and FRRC beams achieved comparable performance, whereas the FRC beams exhibited significantly lower ultimate flexural strength, albeit that they showed reduced localized cracking damage compared to their counterparts.In other words, the flexural strength capacity of the FRRC beams was controlled mostly by the rebars (and not the fiber reinforcement), whereas the structural integrity performances of the FRC and FRRC beams was superior because of the fiber reinforcement.
Simulations of RRC, FRC, and FRRC segment types subjected to concentrated force (applied by the hydraulic jack during installation of the CWCT lining) indicated minimal damage would occur for the FRC and FRRC segment types, whereas the RRC segments were predicted to sustain considerable damage.In other words, the fiber reinforcement not only enhanced structural strength capacity, but also mitigated the formation of chipping damage, including for modest jack thrust misalignment.Statistical analysis of 961 damaged segments of the CWCT lining highlighted the susceptibility of both RRC and FRC segment types to cracking and chipping damages.This mostly arose due to the concentrated force action in response to the jack misalignment with the longitudinal axis of the already installed tunnel lining.However, compared to the RRC segments, the FRC segments exhibited notably lower susceptibility to chipping damage regardless of the jack thrust misalignment.
In conclusion, this study provides valuable insights into the mechanical behaviors, strengths, and vulnerabilities of FRC segments used in tunnel construction.Additionally, the integration of fiber reinforcement with conventional rebar offers a promising approach to achieve enhanced concrete performance and mitigate damage to tunnel segmented linings, with broad potential applications in various infrastructure projects.

Fig. 3 .
Fig. 3. Configuration and dimensions of the six trapezoidal segments (A-E and K) forming the CWCT's ring lining.

Fig. 7 .
Fig. 7. Boundary conditions for the FRC-type beam and segment models: (a) three-point bend load test; (b) thrust force applied by single hydraulic jack over an area of 22×26-mm centered on the end surface of the 0.25-m-thick quadrilateral segment.

Fig. 9 .
Fig. 9. Laboratory results for unreinforced concrete (UC) and FRC sample types: (a) compressive strength; (b) tensile (Brazilian) strength; (c) flexural strength.Refer to Table5for details of the steel fibers incorporated in the FRC samples.

Fig. 10 .
Fig. 10.Line-load compression test for FRC anchor block: (a) schematic elevation and plan views of the laboratory test setup [71]; (b) numerical model implemented in the present investigation.

Fig. 11 .
Fig. 11.Evolution of tensile (i.e., σ xx or S11) stress for compressive force of 1150 kN applied to strip area (of 35×15 cm) centered on the 35-cmsquare top surface of the FRC anchor block element: (a) numerical predictions in the investigation; (b) comparison of our numerical results with the analytical solution proposed by [73].

Fig. 12 .
Fig. 12. Experimental vs. numerical results of axial force against lateral displacement for FRC anchor block (shown in Fig.10a), considering the LVDT3 position for lateral displacement measurement (experimental data from[71]).

Fig. 15 .
Fig. 15.load/bending moment against mid-span deflection results from RRC beam simulations (cases of four number of 8, 10, and 12 mm diameter rebars, i.e., two each in the tension and compression zones).

Fig. 18 .
Fig. 18.Damage progression in the FRRC beams incorporating two number of 8-mm diameter rebars and 0.8 mm diameter fibers, considering (a) 30 kg/m 3 and (b) 50 kg/m 3 (of the final concrete mix plan).

Fig. 19 .
Fig. 19.Schematic of improper ring contact caused by misalignment of the TBM jacks with the longitudinal axis of the tunnel lining [50].

Fig. 20 .
Fig. 20.Damage predictions for RRC, FRC, and FRRC segment types, investigating the cases of the hydraulic jack thrust applied in (a, c, e) perfect alignment and (b, d, f) at a 15 • misalignment with the longitudinal axis of the already installed tunnel lining.

Fig. 21 .
Fig. 21.Visual classification of six distinct damage patterns identified on the inner faces of individual segments comprising the in-situ CWCT lining (patterns are labelled G, H, I, L, and M).

Fig. 22 .
Fig. 22. Analysis of 961 damaged segments, considering the six distinct damage patterns identified from inspection of the CWCT lining.[Refer to Fig. 21 for illustrations of the damage patterns labelled G, H, I, J, L, and M. Refer to Fig. 3 for the locations of the six individual segments (labelled A-E, and K) that comprise the lining.Data set comprised 545 RRC and 416 FRC segments].

Table 1
Physical characteristics of hooked-end steel fibers.
* Actual fiber length after straightening.

Table 2
Composition of C40-Class concrete mix (per cubic meter of concrete).

Table 3
Input parameters for concrete damage plasticity (CDP) model.

Table 4
Material properties of steel rebar and fibers obtained from direct-tension tests.

Table 5
Compressive, tension and flexural strengths mobilized for five FRC sample types investigated.