Precast Concrete Tunnel Segmentswith GFRP Reinforcement

Simone Spagnuolo, Ph.D.1; Alberto Meda2; Zila Rinaldi3; and Antonio Nanni, F.ASCE4

Abstract: The possibility of substituting traditional steel reinforcement with glass fiber–reinforced polymer (GFRP) bars in precast concretetunnel segmental linings is investigated. The use of GFRP reinforcement in concrete tunnel segments results in several advantages mainlyrelated to durability enhancement or when a temporary lining is required. Full-scale bending tests were performed on concrete segmentsreinforced with GFRP and steel bars in order to compare their structural performance. The results show the effectiveness of the proposedGFRP solution for this type of application. Additionally, a case study is developed presenting provisions for safety checks on GFRP-reinforced tunnel segments. DOI: 10.1061/(ASCE)CC.1943-5614.0000803. © 2017 American Society of Civil Engineers.

Author keywords: Design; Full-scale testing; Glass fiber–reinforced polymer (GFRP) bars; Reinforced concrete; Tunnel lining.

Introduction

Glass fiber–reinforced polymer (GFRP) rebars in concrete struc-tures are an innovative solution that can be proposed as an alter-native to the traditional steel reinforcement, mainly when resistanceto the environmental attack is required. In comparison with steel,GFRP does not suffer corrosion problems and its durability perfor-mance is a function of its constituent parts (Micelli and Nanni 2004;Chen et al. 2007). Compared to steel, GFRP presents higher tensilecapacity, lower elastic modulus, and lower weight (Nanni 1993;Benmokrane et al. 1995; Alsayed et al. 2000). GFRP is electricallyand magnetically nonconductive but sensitive to fatigue and creep-rupture (Almussalam et al. 2006). This type of concrete reinforce-ment is not suitable for all applications and, at present, its cost isgenerally higher than steel. Furthermore, the structural effects ofthe low elastic modulus and bond behavior (Cosenza et al. 1997;Yoo et al. 2015) have to be considered.

The possibility of using GFRP reinforcement in precast concretetunnel segments is investigated. In mechanically excavated tunnels,generally by means of a tunnel-boring machine (TBM), the liningis composed of precast elements, placed by the TBM during theexcavation process and used as reaction elements during theadvancing phase.

In tunneling, two different classes of structures can be recog-nized: temporary and permanent. Regarding temporary structures,the use of precast segments reinforced with GFRP rebars is suitablein parts of the tunnel that have to be eventually demolished. Typicalexamples are metro or railway lines, where stations are built after

the tunnel excavation, or in road tunnels when safety niches haveto be provided. In these cases, the advantage of using GFRPreinforcement is linked to the fast procedures of reinforced concretedemolition and disposal.

Regarding permanent structures, the advantages in using GFRPreinforcement are as relevant. GFRP bars are a good solution whendurability problems could jeopardize the tunnel integrity (e.g., ag-gressive environment as in wastewater tunnels or in presence ofaggressive soils). Furthermore, the possibility of using noncorro-sive reinforcement allows for a reduction of the concrete cover,avoiding possible damage during handling, transportation, andinstallation of the precast segments. Finally, GFRP-reinforced con-crete (RC) creates dielectric joints in tunnels so that the installationof a series of tunnel rings made with GFRP-RC can interrupt straycurrents. Thus, the adoption of GFRP-RC in substitution for tradi-tional steel-RC can be proposed in tunnel applications: the higherGFRP cost is balanced by the aforementioned advantages. Further-more, the lining under service conditions is mainly in compression;as a result, the demand on the reinforcement is greatly diminished.

From the structural point of view, it is important to demonstratethat the behavior of precast GFRP-RC tunnel segments is compa-rable to traditional steel-RC. Accordingly, full-scale tests on bothsystems subject to bending were performed. In addition to a com-parison, considerations on the design of precast GFRP-RC seg-ments are presented in this paper. An abbreviated version ofthe experimental results can be found in the study by Spagnuoloet al. (2014).

Tunnel Lining Design

The design and safety check of GFRP-RC tunnel segments can beperformed by using axial force-bending moment (Pn −Mn) inter-action diagrams. The factored ultimate bending moments, Mu, andthe axial forces, Pu, acting on the segment during the different con-struction phases (or stages) can be evaluated with reference to thestatic schemes described in the following sections and discussed inthe literature (ACI 2016; Caratelli et al. 2012; Di Carlo et al. 2016).The design condition is verified if all demand points (Pu −Mu)are internal to the interaction diagram that includes the strength-reduction factors (ΦPn − ΦMn).

Both the transient stages (i.e., stripping, storage, transportation,and handling) and the final stage (ground pressure on the lining)

1Dept. of Civil Engineering and Computer Science, Univ. of Rome‘Tor Vergata,’ Via del Politecnico 1, 00133 Rome, Italy (correspondingauthor). ORCID: http://orcid.org/0000-0001-6480-4399. E-mail: spagnuolo@ing.uniroma2.it

2Professor, Dept. of Civil Engineering and Computer Science, Univ. ofRome ‘Tor Vergata,’ Via del Politecnico 1, 00133 Rome, Italy.

3Professor, Dept. of Civil Engineering and Computer Science, Univ. ofRome ‘Tor Vergata,’ Via del Politecnico 1, 00133 Rome, Italy.

4Professor and Chair, College of Engineering, Univ. of Miami, 1251Memorial Dr., Coral Gables, FL 33146.

Note. This manuscript was submitted on June 8, 2016; approved onDecember 12, 2016; published online on February 27, 2017. Discussionperiod open until July 27, 2017; separate discussions must be submittedfor individual papers. This paper is part of the Journal of Compositesfor Construction, © ASCE, ISSN 1090-0268.

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have to be evaluated and verified. In order to judge the perfor-mances of GFRP-RC segments, a comparison with traditionalsteel-RC elements is performed. Accordingly, the ΦPn − ΦMninteraction diagrams at the ultimate limit state are drawn in com-pliance with basic assumptions, constitutive material relationships,and design strengths and reduction factors defined according toACI 318 (ACI 2014) and ACI 440.1R (ACI 2015). In particular,the hypothesis of planar section and perfect bond between GFRPand concrete is imposed. Todeschini’s model (Fig. 1) is used todescribe the concrete stress-strain constitutive law, in compression[Eqs. (1), (2a), and (2b)]

σcðεÞ ¼2 · σ 0 0

c

�εεc0

�1þ �

εεc0

�2ðN=mm2Þ ð1Þ

εc0 ¼1.71 · f 0

c

Ecð2aÞ

Ec ¼ 4,700 ·ffiffiffiffiffif 0c

pðN=mm2Þ ð2bÞ

where σ 0 0c ¼ 0.9f 0

c; f 0c = specified compressive strength of the con-

crete; εc0 = compressive strain corresponding to f 0c; Ec = modulus

of elasticity of concrete; and εcu = maximum compressive strain inthe concrete, here assumed equal to 0.003 mm=mm. The tensileconcrete strength is neglected.

GFRP has a linear-elastic behavior in accordance with Eq. (3),up to its nominal tensile failure defined by the limits of Eqs. (4)and (5):

σf ¼ Efε ðN=mm2Þ ð3Þ

ffu ¼ CEf�fu ðN=mm2Þ ð4Þ

εfu ¼ CEε�fu ðmm=mmÞ ð5Þ

where CE = environmental reduction factor equal to 0.7 for GFRPin concrete exposed to earth and weather (ACI 440.1R-15); ffu andεfu = design GFRP tensile strength and strain, respectively; Ef =modulus of elasticity; f�fu = guaranteed tensile strength of theGFRP bar, defined as the mean tensile strength minus three timesthe standard deviation; and ε�fu = guaranteed rupture strain of GFRPreinforcement defined as f�fu=Ef . GFRP compressive strength isneglected.

When traditional segments with steel reinforcement are ana-lyzed, a perfectly elastic-plastic behavior for steel is assumed.

The GFRP-RC design resistance is evaluated in accordance withACI 440.1R-15 including the corresponding strength-reductionfactor (Φ). In particular, Figs. 2(a and b) show the variation ofthe strength-reduction factor for steel and the GFRP reinforcement,respectively. For the case of steel, Φ is expressed in terms of steeltensile strain (εt), while in the case of GFRP, Φ is a function of thereinforcement ratio (ρf).

Interaction Diagrams for GFRP-RC

The safety-check procedure based on the interaction diagrams isclarified through an example of practical application. Further-more, a comparison with a tunnel segment with traditional steelreinforcement is developed in order to show the potential of thetechnology. A typical segment geometry is considered, character-ized by a thickness of 400 mm, length of 4.5 m, and width of1.485 m (Fig. 3).

The reference segment (SR) is reinforced with a traditional steelcage made of 12 Ø12 mm longitudinal rebars placed at the intradosand extrados surfaces (top and bottom mats) with spacings of 100and 200 mm. The 32 Ø14 mm stirrups used as the transversereinforcement have spacings of 125 and 175 mm. The steel rebarsare classified according to ACI 318 as Grade 60 with specifiedyield strength (fy) equal to 414 MPa.

The GFRP-RC segment is designed according to ACI 440.1R-15 to provide the same design capacity of the reference one under

Fig. 1. Todeschini’s model for concrete stress-strain behavior

Fig. 2. (a) Strength-reduction factor Φ versus steel tensile strain εt ACI 318 (ACI 2014); (b) GFRP reinforcement: strength-reduction factor Φ versusGFRP reinforcement ratio ρt, ACI 440.1 R (ACI 2015)

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pure flexure. The guaranteed tensile strength f�fu of the GFRP barsis assumed equal to 755 MPa. The segment is reinforced withnonconventional sand-coated GFRP bars having a rectangularcross-sectional area produced in curvilinear shape. Based on anequivalent diameter Ø definition, the reinforcement is composed of:12 Ø12 mm longitudinal GFRP bars at the extrados; 12 Ø14-mmlongitudinal GFRP bars at the intrados; and 32 Ø14-mm stirrups(produced in continuous close form) as transverse reinforcement.The guaranteed and design properties of the GFRP bars (bothlongitudinal and transverse) are summarized in Table 1. The bar

spacings are the same of the reference segment, and both segmentsuse the same concrete compressive strength (f 0

c ¼ 40 MPa). Allrelevant material guaranteed and design properties are summarizedin Table 1.

The design (ΦPn − ΦMn) interaction diagrams for both seg-ments (steel and GFRP) are compared in Fig. 4 showing the samecapacity under pure flexure (ΦMn ¼ 170 kN · m), adopted as Mu

design criterion and calculated as shown in the Appendix I.The main differences in the two interaction diagrams are mainly

due to strength-reduction factor, Φ, for the two materials. In par-ticular, the Φ-factor accounts for the available ductility under theload. In both cases (steel and GFRP), the same Φ-factor (0.65)is used for compression-controlled sections while for tension-controlled sections, a Φ-factor of 0.90 is used for the steel rein-forcement compared to 0.55 used for the GFRP reinforcement.The differences in the two diagrams in the compression-controlledzones is due to assumption of neglecting the GFRP compressivestrength.

The pure compression capacity is limited to 80% of its nomi-nal value [ACI 318 (ACI 2014) and ACI 440.1R (ACI 2015)] toaccount for the accidental eccentricity.

Fig. 3. Segment geometry

Table 1.Design and Experimental Values of the Material Properties for theInteraction Diagrams Definition

Material Diameter PropertyExperimental

valueGuaranteed

valueDesignvalue

Concrete fca (MPa) 51 40 40

Steel fy (MPa) 510 414 414

GFRP Ø12 mm A (mm2) 126.70b 113.09c 113.09c

Pmax (kN) 105 85.9 85.9ff

d (MPa) 827 760 532Ef

e (GPa) 42 40 40εf

f (%) 2 1.9 1.3

Ø14 mm A (mm2) 162.3b 153.94c 153.94c

Pmax (kN) 137 116 116ff

d (MPa) 844 755 528.5Ef

e (GPa) 42 40 40εf

f (%) 2 1.9 1.3

Note: 1 GPa = 145 ksi; 1 kN ¼ 0.2248 lbf; 1 MPa = 0.145 ksi; 1mm2 ¼0.00155 in:2; the properties of the stirrups used (Ø14 mm) are the same ofthe properties reported in this table but, due to the bent sections, the tensilestrength values will be deemed to be reduced by 50%.afc ¼ fc;ave in experimental values; fc ¼ f 0

c in guaranteed and designvalues.bImmersion testing.cNominal.dff ¼ fu;ave in experimental values; ff ¼ f�fu in guaranteed values; andff ¼ ffu in design values.eEf ¼ Ef;ave in experimental values.fεf ¼ εf;ave in experimental values; εf ¼ ε�fu in guaranteed values; andεf ¼ εfu in design values.

Fig. 4. Design (ΦPn − ΦMn) interaction diagrams

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Experimental Program

The procedure for the safety check of precast RC segments basedon the interaction diagrams is validated and assessed through acomparison with the results of experimental tests carried out atthe University of Rome Tor Vergata. Two full-scale segments,one reinforced with ordinary steel rebars (steel-RC) and one withGFRP rebars (GFRP-RC), whose geometry (Fig. 5) and reinforce-ment were previously described (GFRP cage details in Fig. 6), werecast and tested as shown in Figs. 7 and 8. The two segmentswere cast with concrete from the same batch. The measured aver-age compressive cube strength of the concrete, fcm;cube, was61 MPa.

The segments were subjected to pure bending in order to high-light the performance of the reinforcement. Using a reaction framehaving 4,000-kN capacity, the tests were performed under displace-ment control with the setup illustrated in Fig. 8. A closed loop1,000-kN electromechanical jack was used at a stroke speed of10 ÷ 16 μm=s. The segments were placed on supports (cylindrical150-mm-diameter steel hinges, Fig. 8) with a free span of 3 m. Theload applied at midspan was transversally distributed by a steelspreader beam as shown in Fig. 8(a).

The load was measured with a 1,000-kN load cell. The midspandisplacement (measured with three potentiometers placed along thetransverse line) and the crack opening at midspan (measured withtwo LVDTs) were continuously recorded during the test as shownin Fig. 8(b). Furthermore, the crack pattern was recorded at differ-ent steps, with the help of a grid (100 × 100 mm) painted on theintrados surface.

Test Results

The results expressed in terms of load versus midspan displace-ment, obtained from the two full-scale tests on steel-RC and GFRP-RC segments are compared in Fig. 9. The first crack occurred atload levels of 175 and 130 kN for steel-RC and GFRP-RC seg-ments, respectively. Eventually, several cracks developed in bothsegments as shown in Fig. 10, where the complete crack patternsand widths are plotted. The maximum loads were about 395 and640 kN for steel-RC and GFRP-RC segments, respectively. Thesteel-RC segment showed behavior stiffer than that of the GFRP-RC segment. This was mainly due to higher elastic modulus ofthe steel rebars. The crack patterns for different load levels givenin Fig. 10 show that more cracks are present in the GFRP-RC seg-ment. In both cases, the failure occurred for the attainment ofthe tensile strength in the reinforcement (Fig. 11). Despite the brit-tleness of the GFRP reinforcement, the overall structural behav-ior of the two segments was comparable in terms of maximum

displacements. Table 2 summarizes failure mode, maximum load(Pmax), maximum midspan deflection (δmax), midspan deflectionat steel yielding (δy), and deflection when the stiffness drasticallychanges for GFRP-RC (δ1). Furthermore, an indication of the duc-tility (μ), defined as the ratio δmax=δy=1, is given.

A significantly higher failure load was obtained for the GFRP-RC segment. This is justified by the need of using the differentstrength-reduction factor (Φ) in the design for the two systemsand to the differences between their nominal strengths as comparedto their mean experimental values as shown in the design analysisto follow.

In order to determine the effectiveness of the check procedure,the interaction diagrams of the two tested specimens are con-structed. To reproduce the actual experimental behavior, the meanmeasured values of the material strength are adopted and thestrength-reduction factor (Φ) is assumed equal to 1 for both.

The material properties, experimentally measured and adoptedfor the P−M diagrams, are summarized in Table 1. The actual in-teraction diagrams are shown in Fig. 12. In the same figure, thebending moments measured in the experiments are further super-imposed [symbols X and solid circle (•)]. Since X and • lie

Fig. 5. Segment geometry

Fig. 6. GFRP cage details

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on the related envelopes, the simplified check procedure based onthe interaction diagram and respective material constitutive rela-tionships appears suitable for predicting capacity. Furthermore, theadoption of average material strength values (without CE and Φfactors) leads to highest bearing capacity of the GFRP-RC segmentas demonstrated in the full-scale tests.

Case Study

A case study for a GFRP-RC segment is analyzed with the aim ofshowing the procedure for the definition of the (P−M) values forall relevant construction phases. The TBM thrust phase is notaddressed here due to the different check mode based on numericalor/and experimental analysis (Meda et al. 2016). The same segmentdescribed in previous sections is considered, (section thicknessth ¼ 400 mm, width w ¼ 1.5 m, and length Ltot ¼ 4.5 m). Thecomplete ring is supposed to be composed of six segments. Thematerial properties are those reported in Table 1.

Fig. 7. Segments casting

Fig. 8. Test setup: (a) loading system; (b) instrumentation

Fig. 9. Load versus midspan displacement curves: comparisonsbetween steel-RC and GFRP-RC segments

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Evaluation of the Actions

The design of segmental lining requires different verifications(Di Carlo et al. 2016) for transient phases and for the loads due toground pressure (final stage). The acting forces for each construc-tion phase are summarized in the following subsections. Loads,material properties, and static schemes can be different in the differ-ent phases.

Transient PhasesThe transient phases generally include the stages of stripping,storage, transportation, and handling as described in ACI 544.7R(ACI 2016).

Stripping and Storage. The segments can be demolded witha lifting device resulting, for example, in the static scheme repre-sented in Fig. 13(a) (cantilevered ends loaded by the self-weight)for which the maximum factored bending moment is calculated byEq. (6) ACI 544.7R (ACI 2016). Subsequently the segments arepositioned on the floor (concave side up)

Mstripping ¼ 1.4 · ðwa2=2Þ ð6Þ

a ¼ Ltrans=2 ð7Þ

Referring to the Eq. (6), the segment is modeled as two canti-lever beams that are loaded by their own self-weight; consideringthe transverse pockets placed in the middle of the segment, the can-tilever beams are taken as half the length of the segment [Eq. (7)].Since the load acting on the segment is the self-weight, a load factorof 1.4 is applied.

For storage purpose, rings can be stacked. The static scheme ofthe bottom segment, related to this phase, for the evaluation of theacting bending moments, is represented in Fig. 13(b). An eccentric-ity of the load transmitted by the upper segments to the bottom one,in both the inward and outward directions, can be also introduced totake into account possible positioning errors.

The distance between stack supports (L) and free edge of thesegment (S) is optimized to minimize the bending moments inthe bottom segment. Once again, the load acting on the segmentis only the self-weight for which a load factor of 1.4 is applied. Themaximum factored bending moment is calculated by Eqs. (8)–(10)

Mstorage ¼ maxfMintrados storage;Mextrados storageg ð8Þ

Fig. 10. Final crack pattern: (a) steel-RC segment; (b) GFRP-RC segment

Fig. 11. Failure mode of two segments: (a) steel rebars rupture;(b) GFRP rebars rupture

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Mintrados storage ¼ 1.4 · ½ðwS2Þ=2þ F1e� ð9Þ

Mextrados storage ¼ 1.4 · ½wðL2=8 − S2=2Þ þ F1e� ð10Þ

These two phases occur generally a few hours after casting and,consequently, the check has to be done with reference to a concretestrength related to this age, td (age at stripping/storage).

Transportation and Handling. The transportation occurs witha stack of segments on truck or train bed. The static scheme is pre-sented in Fig. 13(c) considering three segments. In this phase, adynamic shock value (β) equal to 2 is generally applied ACI544.7R (ACI 2016) and, again, it is suggested to account for theeccentricity of the load. Eqs. (11)–(13) are used to calculate themaximum factored bending moment associated with this phase

Mtransp: ¼ maxfMintrados transp:;Mextrados transp:g ð11Þ

Mintrados transp: ¼ 1.4 · β · ½ðwS2Þ=2þ F2e� ð12Þ

Mextrados transp: ¼ 1.4 · β · ½wðL2=8 − S2=2Þ þ F2e� ð13Þ

The handling of a single segment is performed with speciallydesigned lifting devices such as vacuum lifters, both from the stackyard onto trucks and rail cars then inside the TBM. The staticscheme is reported in Fig. 13(d). Similar to stripping, the segmentis modeled as a cantilever beam Eq. (14). However, in addition tothe dead load factor of 1.4, a dynamic shock factor equal to 2 isconsidered for design

Mhandling ¼ 1.4 · β · ðwa2=2Þ ð14Þ

These two phases generally take place at an age of 28 days and,thus, the concrete strength corresponds to this maturity level. Allcalculations are given in the Appendix II.

Final Phase: Ground PressureThe stress state due to the pressure exerted by the soil on the liningrings, and, if present, other conditions such as groundwater, sur-charges, earthquake, fire, and explosions, is provided by the geo-technical analysis in terms of axial forces and bending moments.In the proposed case study, only the pressure exerted by the groundis examined and evaluated with the software program FLAC 7.0

Table 2. Failure Modes of the Segments

Reinforcement Failure modePmax(kN)

δmaxa

(mm)δy

(mm)δ1

(mm) μ

Steel Rebars ruptureb 395 96 10.6 — 9.1GFRP Rebars ruptureb 640 103 — 65.2 1.6

Note: 1 kN ¼ 224.81 lbf; 1 mm = 0.03937 in.aδmax calculated at 0.85Pmax. In this case, no collapse was seen at that point.bThe failure occurred for the achievement of the tensile strength by theintrados rebars.

Fig. 12. Interaction diagram based on experimental material propertiesand no reduction factor

Fig. 13. (a) Scheme of the lifting device for stripping and equivalentstatic scheme; (b) storage on stack and equivalent static scheme for thebottom segment: inward/outward load eccentricity; (c) transportationphase and equivalent static scheme for the bottom segment: inward/outward load eccentricity; (d) handling phase and equivalent staticscheme for the bottom segment

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(ICG 2011). In particular, a Mohr-Coulomb failure criterion isconsidered for a clay soil characterized by a cohesion c ¼0.01 N=mm2 and an internal friction angle ϕ ¼ 27°. The specificweight of the soil is assumed equal to γ ¼ 20 kN=m3. The tunnelgeometry is reported in Fig. 14 together with the results in terms ofaxial forces and bending moments.

Safety Check

The safety check is carried out by drawing the interaction diagramfor the segment. The maximum factored bending moments (Mu)and axial forces (Nu), evaluated for the listed schemes, and sum-marized in Table 3, are compared with the structural resistance,evaluated through the interaction diagrams ΦPn−ΦMn based onconcrete design strength values of Table 3 as related to the con-struction stages. The safety checks are reported in Fig. 15 withreference to the stripping and storage phases (4-h concrete age),

and for all the other phases (related to a 28-day old concrete).In each case, all the points representing the actions are inside theenvelopes and then the safety checks are verified.

Conclusions

A design procedure for tunnel concrete segments reinforced withGFRP bars is proposed and demonstrated. Based on the resultsobtained and the comparison of two experimental full-scale testsfeaturing GFRP-RC and steel-RC construction, the followingobservations are made:• For the flexural structural behavior, there are not significant

differences when the steel reinforcement is appropriately substi-tuted with GFRP reinforcement. In fact, although steel-RC sec-tions are commonly underreinforced to ensure yielding of thesteel before failure, providing ductility and a warning of failure,the lack of ductility of the GFRP-RC segment is compensatedby increasing the strength reserve. Additionally, the warning offailure is guaranteed by extensive cracking due to the significantelongation that GFRP bars experience before failure;

• The simplified check procedure for the tunnel segment based oninteraction diagrams built on the constitutive relationship of thematerials, appears suitable for predicting the capacity of a tunnelsegment; and

• The use of GFRP reinforcement in precast concrete tunnel seg-ments appears to be a promising solution that can be proposedin situations often present in tunnel construction. To obtain suc-cessful results in this type of application, an adequate concep-tual design has to be performed with the aim of highlighting theadvantages of GFRP use and, at the same time, maintaining asustainable cost level.

Appendix I. Bending Capacity

Steel [according to ACI 318-14 (ACI 2014)]

ΦMn Steel ¼ ΦASintfyðd − as=2Þ ¼ 171 kN · m

With

Φ ¼ 0.90

as ¼ ASintðfy=0.85f 0cbÞ ðmmÞ

GFRP [according to ACI 440.1R (ACI 2015)]

ΦMn GFRP ¼ ΦAfintffuðd − β1cb=2Þ ¼ 172 kN · m

Fig. 14. Soil action on the ring: (a) axial force distribution; (b) bending moment distribution

Table 3. Summary of Required Design Checks and Factors for TransientStages and Soil Pressure according to ACI544.7 R (ACI 2016)

Loadcase Phase

Dynamicshock

factor (β)

Key designparameterf 0c (MPa)

Mu(kN · m)

Nu(kN)

1 Stripping — 15 (4 h) 51.7 02 Storage — 15 (4 h) 31.7 03 Transportation 2.0 40 (28 days) 36.9 04 Handling 2.0 40 (28 days) 103.4 05 Soil pressure — — 231.0 1,621.5

Note: 1 kN · m ¼ 0.737 kip · ft; 1 MPa = 0.145 ksi.

Fig. 15. Interaction diagrams: load cases check

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With:

Φ ¼ 0.55

β1 ¼ 0.76

cb ¼ ðεcu=εcu þ εfuÞd ½mm�

Appendix II. Transient Stages [According toACI 544.7 R (ACI 2016)]

Geometry and concrete

lm ¼ 4,503 mm

h ¼ 400 mm

b ¼ 1,500 mm

Ltrans ¼ 4,340 mm

γ ¼ 25 kN=m3

Load Case 1: Segment stripping (f 0c ¼ 15 MPa)

a ¼ L=2 ¼ 2.17 m

W ¼ lmhbγ ¼ 68.1 kN

w ¼ W=L ¼ 15.69 kN=m

Maximum unfactored bending moment

Mstripping ¼ wa2=2 ¼ 36.94 kN · m

Maximum factored bending moment

Mstripping ¼ 1.4 · ðwa2=2Þ ¼ 51.72 kN · m

Load Case 2: Segment storage (f 0c ¼ 15 MPa)

S ¼ 900 mm

L ¼ 2,542 mm

e ¼ 100 mm

Total segments that formed a ring (6 ¼ 5þ 1)

n ¼ 6

lkm ¼ 3,535 mm

Wkey ¼ lkmbhγ ¼ 53.02 kN

F1 ¼ ðn − 1 − 1ÞW=2þWkey=2 ¼ 162.7 kN

Maximum unfactored bending moment

Mintrados storage ¼ ðwS2Þ=2þ F1e ¼ 22.63 kN · m

Mextrados storage ¼ wðL2=8 − S2=2Þ þ F1e ¼ 22.59 kN · m

Maximum factored bending moment

Mintrados storage ¼ 1.4 · ½ðwS2Þ=2þ F1e� ¼ 31.67 kN · m

Mextrados storage ¼ 1.4 · ½wðL2=8 − S2=2Þ þ F1e� ¼ 31.62 kN · m

Mstorage ¼ maxfMintrados storage;Mextrados storageg ¼ 31.67 kN · m

Load Case 3: Segment transportation (f 0c ¼ 40 MPa)

β ¼ 2

F2 ¼�n2− 1

�W=2 ¼ 68.1 kN

Maximum unfactored bending moment

Mintrados transp: ¼ β · ½ðwS2Þ=2þ F2e� ¼ 13.16 kN · m

Mextrados transp: ¼ β · ½wðL2=8 − S2=2Þ þ F2e� ¼ 13.13 kN · m

Maximum factored bending moment

Mintrados transp: ¼ 1.4 · β · ½ðwS2Þ=2þ F2e� ¼ 36.86 kN · m

Mextrados transp: ¼ 1.4 · β · ½wðL2=8 − S2=2Þ þ F2e�¼ 36.76 kN · m

Mtransp: ¼ maxfMintrados transp:;Mextrados transp:g ¼ 36.86 kN · m

Load Case 4: Segment handling (f 0c ¼ 40 MPa)

Maximum unfactored bending moment

Mhandling ¼ β · wa2=2 ¼ 73.88 kN · m

Maximum factored bending moment

Mhandling ¼ 1.4 · ðwa2=2Þ ¼ 103.4 kN · m

Acknowledgments

The authors are very grateful to Angelo Caratelli, who performedthe experimental tests, and to ATP S.r.l. for funding the researchprogram.

Notation

The following symbols are used in this paper:Afint = steel reinforcement area in the segment intrados

(mm2);Asint = GFRP reinforcement area in the segment intrados

(mm2);a1 = distance from edge of vacuum lift pad to edge of

segment in the load case of stripping (mm);b = width of rectangular cross section (mm);

CE = environmental reduction factor;c = ground cohesion (N=mm2);cb = distance from extreme compression fiber to neutral

axis at balanced strain condition (mm);

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d = distance from extreme compression fiber to centroid oftension reinforcement (mm);

Ec = modulus of elasticity of concrete (MPa);Ef = modulus of elasticity of GFRP (MPa);e = eccentricity (mm);F = force acting on bottom segment due to self-weight of

the segments positioned above (kN);F1 = weight force caused by 4þ 1 segments on the bottom

segment (kN);F2 = weight force caused by two segments on the bottom

segment (kN);fc = compressive stress in concrete (MPa);f 0c = specified compressive strength of concrete (MPa);

fc;ave = mean compressive strength of concrete (MPa);fcm;cube = mean compressive cube strength of concrete (MPa);

ff = stress in GFRP reinforcement in tension (MPa);ffu = design GFRP tensile strength (MPa);f�fu = guaranteed tensile strength of GFRP bar (MPa);

fu;ave = mean tensile strength of GFRP bars (MPa);fy = specified yield strength of non-prestressed steel

reinforcement (MPa);fym = mean yield strength of non-prestressed steel

reinforcement (MPa);h = segment height (mm);L = distance between the supports (mm);

Ltot = length of the segment (mm);Ltrans = transversal length refers to midplane (mm);

lm = arc length along the midplane (mm);lkm = average length of the key-segment (mm);

Mn GFRP = GFRP nominal resistance bending moment(kN · m);

Mn Steel = steel nominal resistance bending moment (kN · m);n = number of segments;

Pmax = maximum failure load (kN);S = cantilever length (mm);td = age of the concrete at different established phases;th = thickness of the segment (mm);W = segment self-weight (kN);

Wkey = self-weight of the key-segment (kN);w = distributed segment self-weight (kN=m);β = dynamic shock factor;β1 = factor relating depth of equivalent rectangular

compressive stress block to depth of neutral axis;γ = specific weight of concrete (kN=m3);δ1 = midspan deflection at yielding for steel reinforcement

and when the stiffness drastically changes for GFRPreinforcement (mm);

δmax = maximum midspan deflection at failure (mm);εc = strain in concrete;εc0 = compressive strain of unconfined concrete;εcu = ultimate compressive strain of concrete;

εf = strain in GFRP reinforcement;εfu = design rupture strain of GFRP reinforcement;ε�fu = guaranteed rupture strain of GFRP reinforcement;μ = ductility coefficient defined as the ratio between δmax

and δ1;ρf = reinforcement ratio;Φ = strength-reduction factor; andφ = internal friction angle of the ground (degrees).

References

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Almusallam, T. H., and Al-Salloum, Y. A. (2006). “Durability of GFRPrebars in concrete beams under sustained loads at severe environments.”J. Compos. Mater., 40(7), 623–637.

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Cosenza, E., Manfredi, G., and Realfonzo, R. (1997). “Behavior and mod-eling of bond of FRP rebars to concrete.” J. Compos. Constr., 10.1061/(ASCE)1090-0268(1997)1:2(40), 40–51.

Di Carlo, F., Meda, A., and Rinaldi, Z. (2016). “Design procedure of pre-cast fiber reinforced segments for tunnel lining construction.” Struct.Concr., 17(5), 747–759.

ICG (Itasca Consulting Group). (2011). “FLAC (fast Lagrangian analysisof continua) version 7.0.” Minneapolis.

Meda, A., Rinaldi, Z., Caratelli, A., and Cignitti, F. (2016). “Experimentalinvestigation on precast tunnel segments under TBM thrust action.”Eng. Struct., 119, 174–185.

Micelli, F., and Nanni, A. (2004). “Durability of FRP rods for concretestructures.” Constr. Build. Mater., 18(7), 491–503.

Nanni, A., ed. (1993). Fiber-reinforced-plastic (GFRP) reinforcement forconcrete structures: Properties and applications, Elsevier Science,Amsterdam, Netherlands.

Spagnuolo, S., Meda, A., and Rinaldi, Z. (2014). “Fiber glass reinforce-ment in tunneling applications.” Proc., 10th Fib Int. Ph.D. Symp. onCivil Engineering, Research Centre on Concrete Infrastructure (CRIB),Université Laval, Québec, 85–90.

Yoo, D-Y., Kwon, K-Y., Park, J-J., and Yoon, Y-S. (2015). “Local bond-slipresponse of GFRP rebar in ultra-high-performance fiber-reinforcedconcrete.” Compos. Struct., 120, 53–64.

© ASCE 04017020-10 J. Compos. Constr.

J. Compos. Constr., 2017, 21(5): 04017020