Abstract
This chapter gives an overview on the state-of-the-art about verifications of reinforced concrete structures using Externally Bonded (EB) Fibre Reinforced Polymers (FRP) under particular loading condition. Focus is mainly put on flexural strengthening, nowadays the most common application field for composite materials in structural engineering. The items discussed in this chapter are:
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Serviceability limit states;
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Fatigue behaviour;
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Effects of fire and high temperature;
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Long term behaviour;
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Anchoring systems;
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Mechanically Fastened Systems.
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Keywords
Serviceability Limit States
Introduction
Both excessive cracking and excessive deformations in reinforced concrete elements may lead to drawbacks in service. Appearance, tightness and durability are normally considered as reasons for crack control. For durability considerations, the crack width in the vicinity of reinforcement is more influential than the crack width on the surface of the element. Cracking analysis of reinforced concrete elements externally bonded with FRP can be carried out considering the same principles of reinforced concrete sections.
In particular the cracks may decrease the durability performances, functionality and appearance of the structure or may endanger the integrity of the bond interface between FRP EBR and concrete.
The limitation of tensile stresses in concrete is an adequate measure to reduce the probability of cracking in tension. The limitation of compressive stresses in concrete aims to avoid or limit excessive compression, producing irreversible strains, longitudinal cracks (parallel to the compressive strains) and nonlinear creep phenomena.
In calculating the stress conditions, account shall be taken of whether the section is expected to crack under service loads. Moreover the effects of creep, shrinkage, relaxation of pre-stressing steel and differential temperatures should be taken into account.
The limitation of tensile stresses in the steel is an indirect method to control the cracks conditions in RC elements, since it is aimed to warrant an appropriate safety margin below the yield strength and, thus, prevent uncontrolled, large, permanently open cracks due to inelastic deformations of steel bars.
Finally, the deformability limit state has to be considered, because the limitation of deflections in RC elements is generally applied since excessive deflections may restrict the normal use of the structure, induce damage to not load-bearing members or negatively influence the appearance.
For RC elements, stresses are calculated using section properties corresponding to either the un-cracked or the fully cracked condition depending on the loading conditions. Both concrete and steel are assumed to be elastic, both in tension and in compression. When an external FRP reinforcement is present, it has to be considered as linear elastic. Thus, the calculation of stresses in concrete and steel follow the same rules used for RC elements under serviceability loading conditions, with the only difference of taking into account the external reinforcement in the analysis of the un-cracked and/or the fully cracked section.
Few test results are available for verification of serviceability limit states of RC elements strengthened with FRP EBR; most of tests available in literature have been carried out with reference to ties elements (Matthys 2000; Sato et al. 2002; Ueda et al. 2002; Zhang et al. 2003; Ceroni et al. 2004) and the codes do not always include design formulas.
Moreover, an increase in the load-carrying capacity by applying FRP laminates is not accompanied by a proportional increase in system rigidity, either in global terms (with reference to the values of deflections), or in local terms (with reference to the transfer of stresses at the FRP-concrete interface). Furthermore an increase of the ultimate capacity of an RC member due to the FRP strengthening does not correspond necessarily to a proportional increase of the service load; hence verification of serviceability could be significant in element design.
Since FRP materials have high tensile strength and Young’s moduli, but small cross-sectional areas, in general their effect on the limitation of deflections can be negligible, unless considering very low reinforced section.
A more significant influence on the cracking pattern due to the local bond transfer produced by the external reinforcement can be observed (Ceroni and Pecce 2004).
Clearly, the use of pre-stressed FRP systems can be more and more useful to reduce the width of existing cracks, limit the deflections and control the stresses in critical sections of structural RC members (Kim et al. 2008).
Stress Limitation
Load combinations for verifications at SLS as specified in Eurocode 2 (EN 1992-1-2 2004) should be applied. Partial safety factors for the materials, γ M , are taken equal to 1.0, except if specified otherwise.
Under the hypothesis that the section remains plane, the strains in the steel and in the FRP reinforcement are related to the concrete strains thanks to a linear relation. Due to the assumption of linear elastic behaviour for all materials, the stresses are obtained multiplying the strains by the elastic modulus. In particular, the stress in the FRP is obtained from the following relationship:
where E f is the mean value of the modulus of elasticity of the FRP reinforcement.
Moreover, existing strain at the time of FRP installation shall be accounted for and the principle of superposition can be used.
If the maximum tensile stress in the concrete is lower than its tensile strength, the section is un-cracked and fully active; on the contrary the section should be treated as cracked.
The modular ratios \(\alpha_{s} = \frac{{E_{s} }}{{E_{c} }}\) and \(\alpha_{f} = \frac{{E_{f} }}{{E_{c} }}\) have to be defined to transform the actual section into a homogenized all-concrete section. These values shall be set to account for creep as well as short and long-term conditions. In particular, under permanent loading conditions, a reduced value of the elastic modulus of concrete can be used to take into account the creep effect, while under not-permanent loading conditions the ratio of the effective moduli can be used.
For calculating the strain and stress distribution along the section a linear elastic analysis both of the un-cracked (state 1) and cracked section (state 2) should be carried out.
To this aim the cracking moment, M cr , for a rectangular section with base b and height h, can be evaluated as:
where f ctm is the mean tensile strength of concrete [MPa]. If M is the rate of maximum moment in the element under the service loading conditions applied after the strengthening and M 0 is the moment applied before the strengthening, the stresses induced in the materials by the overall moment \(M_{k} = M_{0} + M\) can be evaluated adding the contributes of both moments.
If M o is higher than M cr , the analysis can be developed referring to the cracked inertia (state 2) of the section for calculating both the stresses in concrete and steel reinforcement under M o and the stresses in concrete, steel and FRP reinforcement under M; the total stress in concrete and steel is the sum of the two contributions.
On the contrary, if M 0 is lower than the cracking moment M cr and the total moment M k is greater than M cr , the inertia of the un-cracked section has to be used for calculating the stresses in concrete and steel reinforcement under M 0, while the cracked inertia has to be used for calculating the stresses in concrete, steel and FRP reinforcement under M.
The case of both values M 0 and M k lower than M cr can be considered not significant for the usual applications.
When cracking has to be avoided, a limit state of decompression can be assumed for verifications and corresponds to have a zero stress at the extreme fibre of the concrete section.
The compressive stresses in the concrete should be limited to 0.6∙f ck under the characteristic combination of loading and 0.45∙f ck under the most unfavourable quasi-permanent load combination.
About the limitations of the tensile stress in the steel reinforcement, under the characteristic combination of actions the limit 0.8∙f yk should not be exceeded.
The stress limit above introduce are in agreement with the indications of Eurocode 2.
The FRP stress under service load should be limited in order to avoid excessive creep or creep rupture of the FRP:
for the most unfavourable quasi-permanent load combination.
The FRP stress limitation coefficient, η < 1, depends on the type of FRP and should be obtained through experiments. The Italian Guidelines (CNR DT 200/R1 2012) suggest the following ranges depending on the type of fibres: 0.75–0.95 for internal environment, 0.65–0.85 for external environment, and 0.50–0.85 for aggressive environment. The lower values are for glass fibres and the upper for carbon fibres. The same values are furnished also in ACI 440.2R-08.
Control of Cracking Phenomena
Limitation of Longitudinal Cracks
Application of the FRP reinforcement substantially changes the cracking scenario of the element, since tension stiffening phenomena develop not only at the steel-concrete interface, but also at the FRP-concrete interface. In RC elements strengthened with FRP, the crack width is thus generally smaller than for unstrengthened elements either considering the same service load or considering the same tension level in the steel, due, in both cases, to the additional tension stiffening of the external reinforcement that reduces the crack spacing. Since new cracks will appear in between existing cracks, in general, a more diffuse crack patterns, with smaller crack widths, are observed.
A real crack bridging effect due to the external FRP reinforcement has been observed in experimental tests with a further tension stiffening effect in addition to the one produced by the internal steel reinforcement (Yoshizawa and Wu 1999; Tripi et al. 2000; Matthys 2000; Ueda et al. 2002; Ceroni et al. 2004; Ceroni and Pecce 2007; Ferrier et al. 2003). Moreover as the stiffness of the FRP strengthening grows the global tension stiffening results considerably increased. In Ceroni and Pecce (2007), bending tests on beams externally bonded both with carbon and steel cords sheets were carried out and evidenced that: (1) the steel cords and carbon fibres, both impregnated with epoxy, gave very similar results when the equivalent reinforcement percentage was the same, (2) when the steel cords were bonded with cementitious grout, the tension stiffening effect was lower compared with the epoxy.
Modelling of tension stiffening in RC elements is based on many experimental tests and on a consolidated knowledge of the steel–concrete bond. On the contrary the tension stiffening effect and the cracking behaviour has not been well investigated yet for RC elements externally bonded with FRP, due also to the lack of experimental results concerning this aspect. Numerical models taking into account the tension stiffening effects of the external FRP reinforcement can be used to predict the crack width (Ceroni and Pecce 2004; Aiello and Ombres 2004; Ferretti and Savoia 2003). However for design purposes, empirical equations based on regression analysis of experimental data can be obtained to calculate directly the crack width (Tan and Saha 2008) or the crack spacing (Ceroni and Pecce 2009).
Applying the technical report (fib bulletin 14 2001) the crack width can be estimated by using the Model Code approach (Model code 90) and a specific formula is furnished for the crack spacing for taking account the external FRP reinforcement.
where f ctm is the mean tensile strength of concrete [MPa], u s and u f are the perimeter of the steel bar and FRP laminates [mm] bonded to concrete, t f the thickness of FRP [mm], τ s,m and τ f,m the bond stresses [MPa] along the steel-concrete and the FRP-concrete interfaces, assumed constant in s rm .
According to American guidance ACI 440.2R-08, verification of cracking under service loads can be done by applying the provisions of ACI 318-11 (2013) for RC elements. The FRP external reinforcement has to be taken into account in the calculation of the inertia of the transformed section. In particular in (ACI 318-95) an empirical formula is proposed to evaluate directly the maximum crack width, w, without evaluating crack spacing:
where E f and f f are the modulus of Young and the tensile stress in the steel reinforcement, respectively, k b is a bond parameter, experimentally calibrated at 1 for ribbed steel, β is the ratio of distance between neutral axis and tension face to distance between neutral axis and centroid of internal reinforcement, d c is the concrete cover, s is the bar spacing. The presence of the external reinforcement is taken into account only in the calculation of the inertia.
Currently in the Italian Guidelines (CNR DT 200/R1 2012) no specific formulas are available for calculating crack width in RC elements externally bonded with FRP materials, but only general indications referring to well-known approach as the one proposed by Model Code or Eurocode 2.
Under a stabilized cracking condition, the indications given by Eurocode 2 (EN 1992-1-2 2004) and the new Model Code (MC 2010) for RC elements can be, indeed, extended to RC elements externally bonded with FRP materials. Verification of serviceability in the new Model Code for RC elements includes again a cover term in the crack spacing formula in order to emphasize possible deformations in the concrete cover. The cracking model kept the philosophy that the maximum crack width (called herein as design crack width) is the multiple of 2∙l s,max (slip lengths) and the average strain differences between two cracks.
According to the new Model Code, the design crack width, w d may be calculated by:
where:
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σ s is the steel stress in a crack,
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σ sr is the maximum steel stress in a crack at the crack formation stage which for pure tension, defined as:
where:
and A c,ef is the effective area of concrete in tension, defined as follows:
b, d and c are the width, the depth and the inferior cover of the concrete element;
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β is an empirical coefficient to assess the mean strain over l s,max depending on the type of loading (0.6 for short term loads, 0.4 for long term loading);
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k is an empirical parameter to take the influence of the concrete cover into consideration; according to the present knowledge, k = 1.0 can be assumed;
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η r is a coefficient for considering the shrinkage contribution;
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ε sh is the free shrinkage strain.
Note that in Eurocode 2 (EN 1992-1-2 2004), the following provision for the maximum crack spacing is provided:
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k t a factor of load duration (0.6 for short and 0.4 for long term loading);
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k 1 is a bond coefficient: 0.8 for ribbed and 1.6 for smooth steel bars;
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k 2 takes into account type loading: 0.5 for flexural and 1.0 for tensile loading.
When FRP reinforcement is present, the percentage of reinforcement normalized to the effective area of concrete in tension can be modified as follows:
being A s , E s and A f , E f the area and the Young’s modulus of the internal steel and the external FRP reinforcement, respectively.
Moreover, the expression of 2l s,max can be calculated by means of specific formulae according to the type of FRP reinforcement. In particular, Ceroni and Pecce (2009) proposed a formulation for the average and the characteristic value of the crack spacing in RC elements externally bonded with FRP sheets. The formulation is empirically based on a best-fitting procedure considering experimental results about crack spacing according to a ‘design by testing’ procedure suggested in Eurocode 0 (EC0, Monti et al. 2009).
The database used for assessing the crack spacing is made by experimental results of RC beams and ties externally bonded with FRP sheets carried out by the authors in different experimental programs: beams (Ceroni and Pecce 2007; Ceroni 2010) and ties (Ceroni et al. 2004). The experimental results of these tests evidenced that at the same steel stress as more cracks form and the crack spacing is reduced, crack width decreases depending on the amount of external reinforcement that influences the total load applied. Considering the full load history, the tension stiffening effect due to the fibres grows for all the types of beams after the steel yielding due to the elastic behaviour of FRP. The external reinforcement produces the highest tension stiffening effect for beams with the lowest steel reinforcement. The greater the amount of FRP is used, the greater are the effects. In the tests on RC tie-specimens carried out according to the same dimensions and set-up used by Matthys (2000), a pre-load cycle established the crack spacing of the unstrengthened element and, after application of the external FRP reinforcement, new cracks formed about in the middle. Ceroni and Pecce (2009) made several comparisons in terms of crack spacing by defining a variable δ as the ratio of the code to the experimental value. For the provision given by EC2 (EN 1992-1-2 2004), where the FRP reinforcement is taken into account by the effective reinforcement percentage, the average value of δ is 0.48 meaning that the experimental values are overestimated; this can be justified by the assumption that such a formulation provided ‘maximum’ values of crack spacing. On the contrary, for the fib bulletin the mean value of variable δ is 2.14 which means a large underestimation of the experimental results.
The structure of the formulation proposed by Ceroni and Pecce (2009) for crack spacing is similar to Eq. (6.7) or (6.13) and the stiffening effect of the internal steel and the external FRP reinforcement is separately taken into account.
where s 0, k, α, β, γ and δ are parameters calibrated by the statistical procedure. In Fig. 6.1, the comparison between experimental and theoretical results given by Eq. (6.16) is reported assuming the following values of the parameters: s 0 = 20 mm, k = 4; α = 1; β = 0.75; γ = 0.5; δ = 0.75.
Experimental versus theoretical average values of crack spacing given by Eq. (6.16)
Equation (6.16) refers to the average value of the crack spacing, while for characteristic provision the following can be assumed:
In terms of crack width a more extended database was collected (107 data) by adding results of (Yoshizawa and Wu 1999; Matthys 2000). Equation (6.16) has been introduced in Eq. (6.12) for calculating the crack width: Fig. 6.2 shows the experimental-theoretical comparisons (mean values of δ = 0.777 and 0.715 for 64 and 107 data, respectively, CoV = 32 and 37 %).
On the contrary, the formulas of EC2 (EN 1992-1-2 2004) (Eqs. 6.12–6.14), adjusted to take into account the FRP external reinforcement, furnishes a mean value of δ = 0.67 (CoV = 50 %).
A model for considering the influence of NSM on the cracking is reported in (Zehetmaier and Zilch 2008) that based the formulation on experimental studies on NSM systems made of CFRP strips. The authors propose a modification both for the expression of the mean strain and the slip length in presence of NSM reinforcement.
In general, it is worth noticing that in reinforced concrete elements the spacing of internal stirrups can influence the crack spacing both with and without the FRP strengthening.
Verification of Bond Interface
Under service loading conditions, the initiation of bond interface cracks should be prevented as they may reduce the long-term integrity of the bond interface zone under e.g. cyclic loading and freeze/thaw actions. Concentrations of stresses develop especially at the end of the FRP reinforcement and the location of flexural or shear cracks.
At these locations, to avoid local debonding phenomena under the quasi-permanent load condition, the maximum principal stress, calculated based on the shear stress and the normal stress according to a linear elastic analysis (e.g. Taljsten 2004; Roberts 1989), should be smaller than the tensile strength of concrete.
According to the Italian guideline (CNR DT 200/R1 2012), the verification is developed checking that an equivalent tangential stress \(\tau_{\text{b,e}}\) at the adhesive-concrete interface, under the rare or frequent load condition, is lower than the bond strength \(f_{\text{bd}}\) of the FRP strengthening–concrete interface. The equivalent tangential stress \(\tau_{\text{b,e}}\) is defined through a mean tangential stress \(\tau_{\text{m}}\) evaluated in the section at the FRP strengthening–concrete interface according to the Jourawski’s formulation (Jourawski 1858) and a factor, k id , that introduces by a simplified way the effect of the normal stresses.
The stresses have to be calculated under the only rate of loads applied after the adding of the FRP strengthening.
As in flexural strengthening, also in shear and torsion strengthening the externally bonded reinforcement shall not have debonding phenomena at the serviceability limit state.
Limitation of Deflections
The low axial stiffness E f ·A f of FRP external reinforcement is often insufficient to reduce significantly curvatures and deflection in the strengthened beams under service load condition if the internal steel reinforcement is not yielded. On the contrary, a relevant stiffening effect is given by the external reinforcement, after the steel is yielded and is clearly proportional to the axial stiffness of the external FRP reinforcement (Ceroni et al. 2004). Also steel fabrics externally bonded to concrete beams (Balsamo et al. 2013a; Pecce et al. 2006) have evidenced an effectiveness into limiting the deflection after the yielding of internal steel reinforcement. Moreover, the bending tests reported by Balsamo et al. (2013b), evidenced that no significant difference was in using epoxy adhesive or cement-based mortar for impregnating the steel fabrics in term of deformability.
For the evaluation of deflections, the same method used for RC elements can be implemented to take into account the tension stiffening effect of both the internal and external reinforcement: (1) the most refined one is based on the double integration of the curvature, which can be determined by a cross-section analysis along the RC element; (2) a simplified calculation is based on the definition of an effective moment of inertia (Branson 1977; ACI 2005; El-Mihilmy and Tedesco 2000; Bischoff 2007) or on the calculation of a mean deflection according to the Eurocode (EN 1992-1-2 2004) and Model Code 2010 (fib bulletin 65 2012 and 66 2012) approaches.
The more refined procedure is able to take into account the tension stiffening effects in RC members due to both the internal and external strengthening based on the correspondent bond stress-slip laws (Ceroni and Pecce 2004; Aiello and Ombres 2000; Matthys 2000). Closed form equations have been also obtained assuming bi or tri-linear simplified moment–curvature responses (Razaqpur et al. 2000; Charkas et al. 2003; Rasheed et al. 2004).
The simplified formulation according to the Eurocode and Model Code approach is based on the calculation of the deflection in the FRP externally strengthened elements under the hypothesis of un-cracked and cracked section and on a ‘tension stiffening coefficient’ that synthesizes the tension stiffening phenomena along the element between two cracks due to both the internal and external reinforcement:
where:
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β is a coefficient taking into account the loading type (1.0 for single short-term loads and 0.5 for sustained loads or many cycles of repeated loading);
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σ s is the tensile stress in the steel reinforcement under the service loading condition in the cracked section;
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σ sr is the stress in the steel reinforcement calculated in the cracked section under the loading condition causing the first cracking (see Eq. 6.9).
The ratio σ sr /σ s may be replaced by M cr /M for flexure and N cr /N for pure tension, where M cr is the cracking moment and N cr is the cracking force and M and N are the maximum moment and normal force in the load combination considered.
The deflection at the un-cracked state, α 1, and the cracked state, α 2, can be calculated by an elastic analysis, referring to the flexural stiffness of the un-cracked section and the cracked state, respectively.
In the calculation of Eq. (6.18) the presence of the FRP external reinforcement has to be taken into account in the computation of the moment of inertia of the cracked section.
According to ACI 440.2R-08, the deflection under service loads can be calculated by applying the provisions of ACI 318-11 for RC elements. The FRP external reinforcement has to be taken into account in the calculation of the effective inertia, I e , of the transformed section:
where I g and I cr are the inertia of the un-cracked and cracked section, respectively, M cr and M a are the cracking and the maximum moment along the element.
In the case of NSM strengthening there are still few experimental results (Barros and Fortes 2005; Barros et al. 2007; Ceroni 2010; Balsamo et al. 2013b) to validate design formulations, but in general the same approach used for EBR systems can be assumed effective, introducing the specific modified moment of inertia. In particular, according to Ceroni (2010) and Balsamo et al. (2013b), the tension stiffening effect on the deflection provided by the NSM systems was founded to be less effective compared with the EBR technique. This was probably due to the application of the FRP reinforcement in the grooves that could lead to have higher slips along the FRP-concrete interface. In Fig. 6.3 the experimental load-deflection of the reference unstrengthened RC beams is compared with the curves of two equal beams strengthened with 2 and 3 CFRP strips, evidencing the low effect of the reinforcement on the beam stiffness.
Load-deflection curves of reference and NSM strengthened beams (Balsamo et al. 2013b)
Fatigue Behaviour
Introduction
Increasing traffic loads and aggressive environmental conditions are leading to an accelerated aging of reinforced concrete bridges and a loss in their load-carrying capacity. A well-established method to counteract effects of aging and increasing traffic loads is to strengthen bridges with fibre-reinforced polymers (FRP). With FRP strengthening, two objectives can be pursued: the increase of the load-carrying capacity and the extension of service life. The FRP material shows symptoms of fatigue when applied as an external reinforcement. The effect of cyclic loads on FRPs and hybrid FRPs is described in Wu (2010). Especially externally bonded FRPs (EBR) are affected by traffic induced vibrating and fluctuating loads, because cyclic loads also lead to a fatigue of concrete to FRP bond. The FRP debonding process under fatigue loading is the main objective in this chapter.
Experimental Tests
The debonding process of FRP under fatigue loading has been tested with different types of experimental tests. Commonly large scale bending tests at reinforced concrete beams strengthened with FRP under cyclic loading were carried out; see Heffernan (2004) and Kim (2008). In many cases fatigue loading leads to a failure of the interior reinforcing steel, in some cases FRP debonding could be observed followed by steel failure, see Kim (2008). If debonding is prevented, FRP strengthening leads to a higher load range or an increasing number of cycles at the strengthened RC beam, see Fig. 6.4.
Schematic of load range versus load cycle curves of RC beams according to Kim (2008)
According to Kim (2008), notable fatigue damage in FRP-strengthened beams is accumulated within the first cycles. The rate of damage accumulation then slows considerably until a linear damage rate is reached. Prior to fatigue failure of beams, rising damage propagation can be observed. The propagation of flexural cracks, maximum crack width, midspan deflection and steel strain show a similar trend.
These results are global measurements and do not attempt to directly evaluate the applied force in the external FRP reinforcement or the strain distribution along the fibres. Furthermore, the applied load range is not directly related to the load-carrying capacity of the interface, but rather to the load-carrying capacity of the beam. The published experimental work on the fatigue response of strengthened beams does not provide an insight into the fatigue response of the FRP-concrete interface.
A few studies, which directly investigate the fatigue response of the FRP-concrete interface using direct-shear tests of FRP-concrete joints, have been reported in Bizindavyi et al. (2003), Budelmann (2013), Carloni (2012, 2013), Dai (2005), Diab (2009), Ferrier (2005) and Ko (2007). The maximum, F OL , and minimum, F UL , load of the fatigue cycle are defined as a percentage of the load-carrying capacity of an equivalent specimen under monotonic quasi-static conditions. The available literature suggests that the fatigue response depends on the load range, mean value, and frequency.
The most common test set-ups for direct-shear tests are described in Yao (2005). Most of the setups were also used for investigations on the fatigue response of FRP bond. Near-end supported single shear tests were carried out by Bizindavyi et al. (2003) and Carloni (2012, 2013). Far-end supported double shear tests by Ferrier (2005) and near end supported double shear tests by Budelmann (2013) and modified beam tests were carried out by Dai (2005). An extensive literature review can be found in Carloni (2013) and Kim and Heffernan (2008).
Bond Stress-Slip Behaviour Under Fatigue Loads
With an increasing number of fatigue cycles, the stiffness of the bond stress-slip response decreases (Bizindavyi et al. 2003; Carloni 2013; Ferrier 2005). This indicates that fatigue damage propagates at the interface between FRP and concrete. The translation in self-similar manner of a certain strain profile along the bond length supports this damage propagation theory such that the point, where the free strain at debonding \(\bar{\varepsilon }_{yy}^{fatigue}\) is reached, propagates from the loaded end toward the other end (see Bizindavyi et al. 2003; Budelmann 2013; Carloni 2013; Ferrier 2005). A similar behaviour was observed by Hankers (1996) at externally bonded steel plates under cyclic loads.
Generally the strain profiles were measured with strain gauges. In Carloni (2013) the strain components were determined on the surface of the FRP and surrounding concrete during fatigue and monotonic tests from the displacement field, which was measured using a full-field optical technique known as digital image correlation (DIC) see (Sutton 1983, 2009).
An example of longitudinal strain distribution along the direction of the fibres determined with DIC is plotted in Fig. 6.5. Details on the strain analysis can be found in Carloni (2012, 2013) and Ali-Ahmad et al. (2006).
FRP strain profile determined with DIC
The nonlinear strain distribution was approximated by the following function after Ali-Ahmad et al. (2006):
where α, β, ε0, y0 were determined using nonlinear regression analysis of the computed strains. This approach was previously used for static tests and it can be used for fatigue as well.
The approximated strain distribution along the FRP obtained from Eq. (6.20) is also shown in Fig. 6.5. The stress transfer zone (STZ) can be identified in Fig. 6.5 as the intermediate region where the load is actually transferred from the FRP to the substrate. The length of STZ is the effective length whereas STZ itself is the fracture process zone of the interface. The length of the STZ (\(L_{STZ}\)) is termed effective bond length or anchorage length. The constant value of the strain in the fully debonded region was identified as \(\bar{\varepsilon }_{\text{yy}}\).
From the best-fit strain distribution, the cohesive material law parameter \(\tau_{\hbox{max} }^{fatigue}\) and the fracture parameter \(G_{F}^{fatigue}\) were obtained. In Table 6.1 the average values of the fracture parameters and the value of the strain at debonding \(\bar{\varepsilon }_{yy}^{fatigue}\), calculated at the peak of ten slow cycles after a certain global slip gD, measured by two LVDTs, was reached, are reported for three fatigue tests carried out by Carloni and Subramaniam (2013). Ten images, processed with DIC and corresponding to the peaks of the ten slow cycles, were used to calculate the average values reported in Table 6.1. The length of the STZ during fatigue loading \(L_{STZ}^{fatigue}\) appeared to be smaller than the one reported in static tests.
Carloni (2013) postulated that the sub-critical crack growth might occur in the epoxy layer rather than in a thin mortar-rich layer of concrete, as typically occurs in monotonic quasi-static tests. A similar observation was found in Carloni (2012) and in Ferrier (2005), in which the authors noticed that the fatigue performances of FRPs were greatly influenced by the physical and mechanical properties of the epoxy. This circumstance was supported by the visual analysis of the FRP sheets after failure. In fact, the debonded surface of the FRP strip was smoother in the first 40 mm close to the loaded end, which approximately corresponded to the length of the cohesive crack a during fatigue (see Carloni 2013).
Carloni (2013) used the relationship of Eq. (6.21) between the load-carrying capacity and the fracture energy of the FRP-concrete interface to prove indirectly that the load at the peak of the ten cycles \(P_{crit}^{Cycles}\), after reaching the slip gD, was related to the corresponding fracture energy \(G_{F}^{fatigue}\) and, therefore, the approximation of the strain profiles with Eq. (6.20) was acceptable.
\(P_{crit}^{Cycles}\) is provided in Table 6.1 for the three tests and should be compared to the applied load at the peak of the cycles P max , which was equal to 4.2 kN. The calculated loads \(P_{crit}^{Cycles}\) were in good agreement with the applied load Pmax.
Database
From the experimental test data described in Bizindavyi (2003), Budelmann (2013), Carloni (2012), Dai (2005) and Ferrier (2005) the S-N curve can be determined. For determining the number of load cycles N30 needed for reaching a debonded length of 30 mm, a linear increase of the debonded length is assumed. The number of load cycles needed for reaching a decoupled length of 30 mm is calculated for the tests from Bizindavyi (2003), Carloni (2012), Dai (2005) and Ferrier (2005) by linear interpolation using the bond length lb and the number of load cycles until full decoupling. For the tests from (Budelmann 2013) the number of load cycles is taken from the strain measurements. A decoupling length of 30 mm is reached when the strain measured with the strain gauge A0 or B0 placed 30 mm from the loaded end exceeds the free strain measured with the strain gauge A1 or B1 located in the unbounded region of the CFRP-plate.
For fitting the S-N curve unified related load ranges S0;i at a lower load level of 0 and the corresponding number of load cycles is needed. The unified load range S0;i is determined in a projection analysis using the Goodman relation and Eq. (6.22).
Experimental data from Bizindavyi (2003), Budelmann (2013), Carloni (2012), Dai (2005) and Ferrier (2005) with the calculated number of load cycles N30 and the corresponding load range S0, as well as the width bL, the thickness tL, the number of layers nL and Young’s modulus EL of the tested FRP, can be found in Tables 6.2 and 6.3. Figure 6.6 shows the S-N curve fitted to the experimental data compared with the approach given in the DAfStb-guideline (2012). The load range α is the difference between maximum and minimum load \(F_{L}^{O}\)–\(F_{L}^{U}\) related to the monotonic quasi-static load-carrying capacity of the interface F Lb .
A fracture mechanics based method to describe the fatigue behaviour was proposed by Diab (2009) and successively modified by Carloni and Subramaniam (2013).
In Diab (2009) the rate of debonding growth da/dN is related to the interfacial fracture energy:
The coefficients m1, n1 and β can be determined from experimental results. In particular, β takes into account that the crack propagation rate decreases as the debonded region increases. In Eq. (6.23) an additional coefficient, related to the effect of the frequency, was considered equal to 1. \(G_{F}^{fatigue}\) is the interfacial fracture energy during fatigue loading, see Table 6.1. Its relationship with the amplitude and mean value of the load range has not been investigated in the available literature.
Carloni and Subramaniam (2013) modified Diab’s formula, as the relationship between the applied load and fracture energy during cycles was indirectly proven:
where \(\varDelta P = P_{\hbox{max} } - P_{\hbox{min} }\) and \(\bar{P} = {{\left( {P_{\hbox{max} } + P_{\hbox{min} } } \right)} \mathord{\left/ {\vphantom {{\left( {P_{\hbox{max} } + P_{\hbox{min} } } \right)} 2}} \right. \kern-0pt} 2}\) are the amplitude and the mean value of the load range, respectively. \(P_{crit}\) is the monotonic quasi-static load-carrying capacity of the interface. The coefficients \(\bar{m}_{1} , \, \bar{n}_{1} , \, \bar{\beta }\) can be calibrated through the experimental results. \(\alpha\) is the frequency coefficient, which takes into account that the fracture properties during fatigue loading depend on the frequency.
With the experimental data and the projection method presented above, another formulation of Eq. (6.24) can be found:
where \(F_{L}^{O}\) and \(F_{L}^{U}\) are the maximum and the minimum values of the load range. F Lb is the monotonic quasi-static load-carrying capacity of the interface. The parameters N*, c and k can be set to 2 × 106, 0.295 and 23.1 using the S-N curve from the DAfStb-guideline (2012) for calculating the crack growth rate in mm per load cycle.
Equation (6.25) neither takes into account that the crack propagation rate decreases as the debonded region increases nor the effect of the frequency. However, it represented an extension of the classical formulation of the Paris’ law in which the effect of the amplitude and mean value of the cyclic loading were explicitly considered, see Anderson (2004).
Codes and Guidelines
Most of the existing standards and guidelines consider aspects of fatigue only in a rough way. In all cases the steel stress is limited to avoid a fatigue steel failure and in some cases the FRP strain is limited. A detailed analysis method to avoid intermediate crack debonding under cyclic load only can be found in the DAfStb-guideline (2012). A summary of fatigue aspects in different guidelines can be found in Kim (2008):
ISIS Canada (2001) assumes that fatigue failure of FRP strengthened reinforced concrete beams will occur as a result of fracture of the reinforcing steel and, thus, recommends that the stress levels in the externally bonded FRP be limited such that the steel reinforcing bars do not yield.
fib bulletin 14 (2001) regards the fatigue state of strengthened reinforced concrete beams as a special design consideration. This document recommends that the steel stress range in the fatigue design of CFRP-strengthened beams be restricted to those allowed for an unstrengthened beam.
ACI Committee 440 (2008) gives a creep and fatigue limit for FRP. The magnitude of maximum applied stress including both sustained and repeated loads for CFRP should not exceed 55 % of its ultimate strength.
The Italian code for strengthening existing structures (CNR-DT 200-R1 2004) provides a conversion factor of η1 = 0.5 for all types of FRP subjected to fatigue load to account for the potential degradation of FRP-strengthening systems.
The DAfStb-guideline (2012) considers fatigue debonding at the end anchorage of FRPs and between cracks. The steel stress range is restricted after EC2 (EN 1992-1-2 2004) as for an unstrengthened RC structure. The design concept for bond fatigue given in the DAfStb-guideline (2012) is based on the bilinear limit curve of the upper load from Fig. 6.7 and this depends on two verifications. It can be verified whether the load difference ΔF OL is within the elastic range ΔFL;el with Eq. (6.26).
Design concept after DAfStb-guideline (2012)
The load difference has to be checked at the end and in the middle part of a strengthened RC structure. In the end part, the load difference ΔF OL has to be calculated from the plate end to the first flexure crack. In the middle part the load difference ΔF OL between two cracks of a theoretical crack pattern has to be calculated. For the calculation of the crack spacing and the maximum plate force difference ΔFLb between cracks the model given in DAfStb-guideline (2012) and German Committee for Structural Concrete (2013) is used. If the condition given by the equation above is not met, the fatigue range ΔFLb;fat can be verified as follows:
The load range between the load difference at the upper load level ΔF OL and the lower load level ΔF UL has to be smaller than the fatigue range ΔFLb;fat. The fatigue range ΔFLb,fat depends on the lower load level ΔF UL and decreases with a rising lower load level ΔF UL . It also depends on the number of load cycles N.
The reduction of the fatigue range ΔFLb,fat based on an increasing number of load cycles N is described with the factor c given in Eq. (6.27). The Goodman-Smith Diagram shown in Fig. 6.7 illustrates the fatigue design concept. The horizontal line marks the elastic limit calculated with Eq. (6.26). The related load range α used in Eq. (6.27) and its dependence on the lower load level ΔF UL and the number of load cycles N is explained by the linear functions plotted above.
To prevent debonding and damage the limit for the load amplitude has to decrease with an increasing lower load level and an increasing number of load cycles. The design concept after DAfStb-guideline (2012) presented above shows a simple method to calculate the limit for the load amplitude.
Effects of Fire and High Temperature
Introduction
Fire is one of the most serious potential risks for buildings and structures, and for this reason international codes provide specific guidelines to take account of fire in the design of structures (ACI 318-11, EN 1991-1-2, EN 1992-1-2). In some countries (e.g. Italy, Greece, Turkey, Spain, Portugal), the earthquake, which is often follow by fire events, is an event with greater risk for physical injury and damage to objects and properties. However, also in some of these countries, national codes (NTC 2008) have recently introduced more regulation for the fire risk, by considering that human activities are in continuous development and evolution and can be more dangerous than natural events. In this chapter, the main effects of high temperatures on fibre-reinforced composite materials are summarized. In particular, some studies carried out in the last two decades on this topic are cited, mainly to show actual knowledge and future challenge about the degradation of the mechanical properties of FRP materials at high temperatures.
At first, some information about the critical temperatures for FRP are given. Then, some studies related to testing on structural members reinforced with FRP and numerical simulations of the behaviour of FRP materials at high temperatures are mentioned. Although for many applications there is a clear need for protection against high temperatures, the chapter closes with an example that shows how in some cases the protection is already self-provided by non-structural elements having other functions.
Critical Temperatures for the Mechanical Properties
As stated in previous sections, FRP are composite materials successfully applied to repair and/or strengthen RC structures. For external strengthening, the FRP plates are easily bonded on concrete using adhesive, like epoxy resins, which ensure the transfer of forces between concrete and FRP. However, degradation of mechanical properties of composites (strength, stiffness and bond) due to high temperature (Dai et al. 2013; Nigro et al. 2013), moisture absorption (Jia et al. 2005) and cycling loads (Dai et al. 2005) is a key aspect for a durable efficiency of composite materials.
Concerning high temperature, a critical condition occurs when the glass transition temperature, T g , of the polymer matrix is achieved, due to the softening of the resin, which reduces the capacity of transfer of forces between the fibres. The precise definition of the value of T g is still under discussion in the scientific community, because the progressive nature of the softening process makes it difficult to identify a precise temperature limit. Nevertheless, the safety check often is conservatively performed, in the temperature domain, with reference to the value of T g properly reduced (ACI 440.2R-08 2008).
FRPs which polymerize in ordinary conditions, typical of in situ applications, are characterized by very low T g (between 45 and 80 °C for normal and heat resistant resins, respectively). For preformed FRPs, used as internal reinforcement, is easily possible to obtain, reinforcements with T g above 100 °C. Curing processes carried out at temperatures and pressures different from ordinary ones, allow to further increase the T g .
Although overcoming the T g implies a reduction in strength of the reinforcement, the drastic degradation of the resistance is reached at temperatures close to melting of the resin (temperature of crystallization, T c > T g ) or even higher. The reduction of stiffness, instead, depends on the type of fibre reinforcement and it is generally negligible compared to the reduction of resistance. Therefore, the real capacity of the concrete members reinforced with FRP reinforcement, at high temperatures, can be considerably high (Nigro et al. 2011a, b, 2013).
Review of Experimental Studies
Recent experimental studies showed that the softening of the resin which begins when T g is achieved, involves a drastic reduction of the adhesion properties (Bisby et al. 2005). Hence, the efficiency of the strengthening system for existing structures, which mainly depends on the effectiveness of the bond between FRP and concrete, is strongly affected by the temperature.
Some experimental tests (Deuring 1993) showed similar problem when conventional steel strengthening are used without mechanical anchoring. The comparison between steel and FRP strengthening systems showed that FRP, in particular sheets, without protection behave better than steel plates because of the lower heat conductivity and their smaller weight. Clearly, FRP externally strengthened RC beams or slabs need the protection with additional insulation in order to avoid the debonding between FRP sheets or laminates and concrete support. Consequently some researches were devoted to study the performances of FRP strengthened elements protected by different insulation systems in order to individuate the minimum requirements to obtain satisfactory performances in fire (Bisby et al. 2005).
No information is apparently available on the specific mechanical or bond properties of typical FRP systems used for strengthening RC structures after short-term exposure to elevated temperatures, although limited information is available on the residual mechanical properties of specific FRP materials used in the marine, aerospace, and automotive industries after exposure to high temperature (Mouritz and Mathys 1999; Mouritz and Gibson 2006; Bai et al. 2007). Basic research has been reported on the post-heating residual performance of FRP wrapped concrete cylinders (Cleary et al. 2003; Saafi and Romine 2002), although the data presented in these studies do not elucidate the specific performance of the FRP systems. Only one limited study is available on the high temperature performance of the FRP-to-concrete bond loaded in shear (Gamage et al. 2005), although residual properties are not addressed. Several large-scale standard fire tests have also been performed (Deuring 1993; Blontrock et al. 2001; Kodur et al. 2007), but the data do not address the specific performance of the FRPs either during or after high-temperature exposure.
A significant research effort over the past decade has demonstrated that appropriately designed and adequately insulated FRP strengthened RC beams, slabs, and columns, are capable of achieving adequate fire endurances (Kodur et al. 2007). However, these researches have not provided much insight into the specific performance of the FRP strengthening systems or the bond between the FRP systems and the substrate concrete, either during exposure (i.e., at high temperature) or once they have cooled to room temperature (i.e., residual performance). Information is thus required before defensible strengthening limits and allowable thermal exposures can be suggested for FRP strengthening systems, particularly in cases where the FRP system is required to be effective during or after a fire (Porter and Harries 2005). Information is also needed to develop economical fire insulation schemes for FRP strengthened members, even in cases where the FRP is not required to be structurally effective during a fire.
Numerical Modeling
Probably, in order to extend the results of experimental tests to different cases, using a numerical model could be appropriate. Indeed, the behaviour of structures exposed to fire is usually described in terms of fire resistance but, in real buildings, structural members are part of a continuous assembly, and building fires often remain localized, since the fire affected region of the structure receiving significant restraint from cooler areas surrounding it. The real behaviour of these structural elements can therefore be very different from that indicated by standard furnace tests and should be investigated, as is usual within the Fire Safety Engineering approach.
Clearly, the accuracy of the thermo-mechanical analysis is dependent on the main properties required to calculate the temperature distribution (i.e. specific heat, thermal expansion and thermal conductivity) and the constitutive laws used to define the mechanical behaviour of materials (i.e. strength, stiffness and bond properties), both at ambient and elevated temperatures. For many of these parameters suggestions in technical code are not univocal for concrete and are still lacking for FRP. Thus, more research is needed to improve the accuracy of the numerical models.
Obviously, if the FRP strengthening is not directly heated by fire or other sources of heat, the performances may be better. Hence, FRPs can be successfully used to strengthen bridges, where fire is not a primary action to be considered during design (Bisby et al. 2005). Nevertheless, it should be noted that bituminous paving casting on a bridge deck can easily lead to have high temperature (e.g. 200 °C).
On this issue Nigro et al. (2013a, b) investigated the thermo-mechanical behaviour of RC bridge decks strengthened with externally bonded FRP plates. The results are summarized in the following section.
The Effects of High Temperatures in a Practical Application
In Nigro et al. (2013a, b) two possible environmental conditions leading to thermal states different from the normal ones were studied with reference to bridge decks: (a) fire exposure over the bridge deck due to an accident involving camions; (b) bituminous paving casting on a bridge deck. Indeed, in both case the temperature at the FRP-to-concrete interface can overcome the above mentioned glass transition temperature, T g .
The relationships suggested by Italian and American codes, to evaluate the limit strain for FRP debonding at normal temperature, were modified to take into account the effect of high temperature on the debonding of FRP. Then, thermo-mechanical analyses were performed by varying the thicknesses of the slab and the protection layer in order to assess their influence on the thermal field in the structural member. Furthermore, normal resin (NR) with T g = 45 °C and heat-resistant resin (HR) with T g = 80 °C were considered. The results were discussed in terms of both temperatures and safety checks carried out for both ultimate and serviceability limit states (ULS and SLS).
The ULS checks were always satisfied, mainly because the flexural capacity provided by FRP can be neglected during fire or maintenance activity. By contrast, the SLS checks performed to assess the damage levels in the FRP strengthening system during these events show that constructive details and type of resin play a key role.
In the case of fire event over the bridge deck, if the strengthening is on the bottom side, for typical design load level η fi = 0.7, FRP damages (i.e. debonding) were not attained for long time of fire exposure, even if the resin achieved the glass transition temperature, T g . If the strengthening is located on the top side of the slab, the use of heat resistant (HR) resins is suggested. If normal resin (NR) is used, a protection layer on the FRP strengthening is recommended, in order to increase the maximum time of fire exposure without FRP damage.
In order to show that the achievement of the T g may be not a critical condition for the strengthening system, in Fig. 6.8 the bending moment of the FRP strengthened slab, M Rd,fi,FRP , reduced for the effect of the fire exposure, is plotted versus the time for the 15 cm thick slab, normal resin and four thicknesses of protective layer, t prot . Moreover the bending moment in fire situation M Ed,fi = 49.7 kNm is shown. Note that M Rd,fi,FRP was calculated by using the relationships suggested by CNR DT 200/2004 to evaluate the debonding strain at ambient temperature. As stated above, the relationships were modified to take into account the effect of high temperature.
Slab safety check in hogging moment region (fire on the bridge)—Te = 25 °C—Slab thickness = 15 cm—(NR)
Figure 6.8 shows that the time of fire exposure before the debonding of the FRP ranges between 82 and 120 min. Note that these values are higher than those related to the achievement of the T g at the FRP-to-concrete interface (i.e. 50 and 80 min) and probably more realistic to assess the FRP damage.
In the case of bituminous paving realization, for strengthening on the bottom side, the results are quite similar to those obtained in case of fire. On the other hand, if the strengthening is located on the top side of the slab, the use of HR resins is necessary in order to avoid damages in the FRP strengthening. Otherwise thick protective layer of concrete is required also for low load levels.
The results obtained through the relationships provided by different codes (i.e. Italian and American codes) for ambient temperature and refined with the suggested model are in a good agreement (see Fig. 6.9). However, so far, more research is needed to improve the reliability of codes suggestion.
Comparison between codes
Long Term Properties of FRP Systems
Introduction
Regarding the long term performance of a composite system, few authors have dedicated their efforts to the assessment of the performance of the intervening materials (Diab and Wu 2007; Wu and Diab 2007; Meaud et al. 2011).
Apart from changes in applied external actions, the long term performance of a CFRP-adhesive-concrete system is only expected to be affected by the creep, shrinkage or relaxation of each of the components of the system. While the creep and shrinkage of concrete have already been comprehensively studied over the years, limited information is available regarding the creep/shrinkage/relaxation of composite materials. In this chapter a resume on the collected information in this respect is provided.
FRP Relaxation
Bibliographic research has shown that FRPs are known to present low pre-stress losses, as a result of their relatively low elastic modulus (Lopez-Anido and Naike 2000), and lower stress relaxation than steel strands (Dolan et al. 2001; Sayed-Ahmed 2002). In fact, even though FRP materials are able of exhibiting an elastic modulus, E f , close to 200 GPa, most of the materials available reveal to have an average maximum E f of about 160 GPa.
Wang et al. (2012) carried out relaxation tests in CFRP sheets and concluded that the relaxation loss due to sustained deformation levels ranging between 40 and 56 % of the material’s tensile strength was determined to be 2.2–6.6 %, as demonstrated in Fig. 6.10. Moreover, this relaxation was mostly concentrated in the first 100 h of sustained deformation, as depicted in Fig. 6.10 and, after this period it becomes almost negligible. These authors have even suggested that the measured relaxation is primarily caused by the relaxation of the resin and straightening of fibres. The carbon fibres themselves are identified as having no relaxation whatsoever (Dolan et al. 2001).
Stress relaxation in CFRP sheets. Adapted from Wang et al. (2012)
According to Dolan et al. (2001) the relaxation losses in FRP tendons can be caused by three main sources: the relaxation of resin that bonds the fibres together, the lack of parallelism between individual fibres, and the relaxation of fibre itself. Due to these reasons, the relaxation is a characteristic attributable to the fibre type and is generally lower than 12 % over the life of the structure. In the case of CFRP tendons, relaxation losses of approximately 5 % are reported.
Based on these assumptions, it is suggested that FRP relaxation is not a relevant effect for the long-term performance of CFRP laminates. Since in FRP laminates the fibre content is particularly large when compared to FRP sheet coupons, the matrix bonding them together will take only a small portion of the applied load and, therefore, the first source of relaxation may be ignored. Regarding the alignment of the fibres, since FRP laminates are produced by machines, in opposition to FRP sheets, which are manually applied, no significant eccentricities are expected along each fibre and as a result, the second source of relaxation may also be disregarded. Finally, as carbon fibres themselves are reported to have no relaxation, the total amount of relaxation expected is even more reduced.
Adhesive Shrinkage
The volumetric shrinkage of epoxy-based adhesives is generally restricted to the shrinkage occurred during the curing process and is found to be within the range 2–7 % (Li et al. 2004; Yu et al. 2005; Khoun and Hubert 2010).
Concerning the epoxy-based adhesives used in structural applications they reveal such an insignificant shrinkage coefficient, that this parameter is often not even quantified in most materials’ datasheets. However, when complete cure is achieved, the shrinkage coefficient variation becomes negligible, as suggested by (Yu et al. 2005; Khoun and Hubert 2010), and the long-term behaviour of the adhesive is no longer shrinkage dependent, but creep-dependent as it will be revealed hereafter.
Adhesive Creep
Introduction
The creep behaviour of plastics is usually fragmented in three major creep stages (ASTM 2990 2001, Majda and Skrodzewicz 2009): primary creep, secondary creep and tertiary creep. As depicted in Fig. 6.11, in the first phase the material adjusts its deformation level to the installed level of stress. This phase is followed by a stationary stage where creep gradually increases until a third phase is reached, where strain suddenly increases and fracture occurs. It is believed that this behaviour is valid under any applied stress, temperature and humidity. However, for low levels of applied stress, the time necessary to reach the tertiary creep state may be so long that it may never be achieved.
The three stages of creep (at constant stress, temperature and humidity)
The primary function of an adhesive in structural applications is to transmit stress equally over large areas without loss of integrity (Feng et al. 2005). Structural adhesives exhibit, however, notable viscoelastic behaviour, since their deformation, \(\varepsilon\), under a constant stress, \(\sigma\), varies significantly in time. This behaviour is frequently modelled using rheological models and is usually illustrated by means of Hookean springs and Newtonian dashpots that replicate, respectively, the elastic and viscous components of the material’s behaviour (Brinson and Brinson 2008). In Fig. 6.12, the most common rheological models are presented:
a Maxwell model, b Kelvin model, c Burgers model—common configuration, d Burgers model—alternative configuration
-
Maxwell Model—illustrated in Fig. 6.12a, this model is a 2-parameter model that results of associating, in series, a spring with \(E_{M}\) elasticity and a dashpot characterized by \(\eta_{M}\) dynamic viscosity;
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Kelvin Model—depicted in Fig. 6.12b, it is also a 2-parameter model that consists in combining, in parallel, a spring of elasticity \(E_{K}\) and a dashpot of \(\eta_{K}\) dynamic viscosity;
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Burgers Model—schematized in Fig. 6.12a–d, this 4-parameter model can be obtained by joining in series Maxwell and Kelvin’s Model (\(E_{M}\), \(\eta_{M}\), \(E_{K}\) and \(\eta_{K}\) in Fig. 6.12c or, in alternative, by connecting two Maxwell models in parallel (\(E'\), \(\eta '\), \(E''\) and \(\eta ''\) in Fig. 6.12d).
It is possible to create models like the generalized Maxwell Model or generalized Kelvin Model, depicted in Figs. 6.13 and 6.14 (Brinson and Brinson 2008).
Generalized Maxwell fluid
Generalized Kelvin solid
It is relatively simple to obtain the solution of each of these models and, the deduction of each equation can be found in Costa and Barros (2011).
Standards on Creep Behaviour
According to ISO 899-1 (2003) test method, load shall be applied smoothly to a standard specimen, as defined in ISO 527-2 (1993), within 1–5 s and maintained for at least 1000 h (approximately 42 days). Strains, temperature and humidity should be measured according to the schedule presented in Fig. 6.15.
Data acquisition schedule (ISO 899-1 2003)
ISO 527-2 (1993) recommends bone-shape specimens to be moulded using the geometry depicted in Fig. 6.16 (see also Table 6.4).
Directly-moulded specimens (Type 1A, ISO 527-2 1993)
For different temperature and/or humidity level, one creep curve shall be obtained. To construct the desired creep curves, creep strains and/or creep moduli (defined in Eq. 6.28) are plotted against the logarithm of time, for every initial level of applied stress, \(\sigma\), (see Fig. 6.17). Isochronous curves, which consist in Cartesian plots of stress versus strain at specific time instants, similar to those depicted on Fig. 6.17c, can also be presented.
Example of creep curves (ISO 899-1 2003): a creep strain curves, b creep modulus curves and c isochronous stress–strain curves
ASTM 2990 (2001) also addresses creep of plastic materials under specified environmental conditions. Loading shall also be applied in the specimen rapid and smoothly in 1–5 s, and the strains shall be recorded at the time instants shown in Fig. 6.18. To evaluate creep, the use of the normalized specimens produced according to ASTM D 638 (2003) is suggested (Fig. 6.19; Table 6.5).
Strain measurement schedule (ASTM 2990 2001)
Directly-moulded specimens (Type 1A, ISO 527-2 1993)
Research on Creep Behaviour
Feng et al. (2005) suggested that it is possible to estimate the tensile creep strain, \(\varepsilon_{creep} \left( {t,T} \right)\), by the exponential function:
where \(\sigma_{0}\) is the applied stress level, \(E_{0}\) the initial Young modulus, \(E_{e}\) is the equilibrium modulus given in Eq. (6.28), \(t^{*}\) is the relaxation time and \(n\) a coupling parameter related to moisture absorption.
where \(G_{r}\) is the rubbery plateau shear modulus, and \(\nu\) the Poisson’s ratio (\(\nu\) = 0.5 since the material is in the rubbery state). Feng et al. (2005) obtained in their tests values of \(n\) ranging from 0.51 to 0.73. Majda and Skrodzewicz (2009) proposed a model purely based on Burgers Model:
where
Majda and Skrodzewicz (2009) also suggested that the coefficients of dynamic viscosity, \(\eta_{0}\) and \(\eta_{1}\), as well as the elastic modulus are primarily dependent on the applied stress, and:
The rheological properties (\(E_{0}\), \(E_{1}\), \(\eta_{0}\) and \(\eta_{1}\)) were quantified by means of nonlinear regression analysis of the experimental creep tests at four different levels of applied stress, at a constant temperature of 22 °C (Table 6.6). Later, the different \(a_{i}\) coefficients can be obtained applying ordinary trend lines (logarithmic/quadratic regressions) as well as by non-linear regression (Table 6.7).
Choi et al. (2007) presents the results of creep tests performed in double-shear specimens during 6 months, where creep specimens with different adhesive layer thickness and applied stress were considered. The authors suggest that the total strain due creep also follows the following exponential law:
with the values for the parameters indicated in Table 6.8.
By carrying out tensile tests with a current type of adhesive used to bond CFRP laminates to concrete in the NSM technique, Costa and Barros (2013) and Costa (2014) have concluded that after 2 days of curing, the properties of the adhesive are nearly the same as obtained for the recommended curing time (7 days). By performing creep tensile tests with three series of specimens of this type of adhesive, these authors have verified that up to sustained stress levels of 60 % of the adhesive’s tensile strength, the adhesive behaves as a classic visco-elastic material and can easily be parameterized using the modified Burgers model (Figs. 6.20, 6.21 and 6.22; Table 6.9). In the experimental tests performed, the results suggest that the properties of the adhesive tend to deteriorate with time and therefore, a special attention should be taken regarding the time between adhesive production and application. It is also noteworthy that after 1000 h of loading, the adhesive samples exhibited about 4 times the deformation at time of loading (creep modulus of roughly 25 % of the initial stiffness) without rupturing. According to the initial tensile tests performed, a maximum strain at rupture of about 3 ‰ was obtained, while during the creep tests the material was able of somehow reorganizing its internal structure to withstand almost the double of this deformation.
Modified Burgers model—Series I
Modified Burgers model—Series II
Modified Burgers model—Series III
Based on the experimental results the following equation was proposed to estimate the tensile creep modulus (Costa and Barros 2013):
where its good predictive performance is visible in Fig. 6.23 by considering the data from Table 6.9.
Creep modulus curves based on the analytical results: a series I, b series II, c series III and d all analytical curves (Costa 2014)
Anchorage Systems for External Strengthening with FRP
Special Anchorage for Flexural Strengthening
For flexural strengthening the most common anchorage system is given by a FRP sheet or a FRP or steel laminate glued transversally to the strengthening direction. The good performance of such a type of anchoring was tested in Ceroni et al. (2008) on specific bond tests. This is a reliable solution when the FRP-to-concrete width ratio is less than 1, because the transversal sheet/laminate allows extending the width of concrete covered by the FRP strengthening. In Ceroni and Pecce (2010) a simple method based on geometrical considerations is proposed in order to take into account such an enlargement of the bonded width in the theoretical expression of the debonding load.
When the FRP-to-concrete width ratio approaches to 1, a simple transversal strip becomes unhelpful and U-shaped fibre sheets result more efficient. For example one strip at the end or strips distributed along the beam can be considered (see Fig. 6.24): relevant increasing of the ultimate strength and ductility at failure can be obtained by using these systems (Ceroni 2010) allowing a better use of the tensile strength of the fibres. Sharp edges of the section are recommended to be mechanically rounded before application. In this case, a minimum radius of 30 mm is recommended.
Possible shear U-shaped anchoring devices (Ceroni 2010)
In Al-Mahaidi and Kalfat (2011) the efficiency as anchor devices of unidirectional CFRP fabric wrap applied orthogonally or parallel to the direction of the FRP reinforcement was tested by means of bond tests. In the former configuration the load increase was of 19–28 % mainly due to a strut-tie resistant mechanism resulting from the fabric fibres inclining towards the load direction; in the latter configuration the load increase was 18–37 % due to a transfer of bond stresses to a greater distance from the loaded end.
Steel U-shaped devices as the ones tested by Blaschko (2001) and Mukhopadhyaya et al. (1998) can be an alternative solution for end anchorage. The basic scheme of tests made with special anchoring devices for CFRP strips is shown in Fig. 6.25 (Zehetmaier 2000). This system can be applied in case of strengthening of slabs, where no wrapping is possible, or local strengthening and as an anchorage for pre-stressed strips. A minimum concrete cover of about 20 mm is required.
Anchorage for CFRP strips special anchorage system (Zehetmaier 2000)
In general, anchoring devices that may influence the integrity of the strengthening system should be avoided. For example, anchoring solution with bolts need of holes that could lead to interlaminar shear failure or splitting of the strip. Moreover, holes reduce the cross section of the strip. However, in case of using bolted systems, it is not adequate to drill through the strengthening strip omitting special provisions, as compressive forces can weaken the strip. Multidirectional fibres at the location of the bolts can be used in order to allow the end tabs take the full force to be anchored (Tan 2001). Bolts should be anchored in the concrete to a depth beyond the steel reinforcement.
Bolted devices could give a better performance if used to anchor prefab laminates with suitable systems provided by manufacturers.
Nail anchors made by wide ringed head nylon anchor with zinc plated hammer screw were used by (Prota et al. 2006) to mechanically anchor beams strengthened with steel tape and cementitious grout.
Fibre fan anchor systems (see Fig. 6.26) are becoming very diffuse. A hole is drilled in the concrete on the same plane of the strengthening. A glass or carbon fibres tow (see Fig. 6.26a) is forced through the impregnated fabric end into the predrilled hole and the ends are splayed outwards on the continuous sheet reinforcement with epoxy resin (see Fig. 6.26b).
a Carbon fibre fan anchor; b splaying of fibres outwards the hole
Experimental studies about the effectiveness of fan shaped anchors were made by (Özdemir 2005); he founded that: (1) anchors have to be inserted at least 50 mm into the core of the concrete (depth of 130–150 mm); (2) the cross-sectional area of anchor has to be at least two times greater than the cross-sectional area of the longitudinal sheet; (3) splitting the anchor into as many smaller anchors at about a 40 mm spacing as possible.
Such type of anchoring system was tested also by (Ceroni and Pecce 2010) that achieved an increasing of ultimate strength at least of 25 % in bond tests on concrete blocks externally strengthened with carbon sheets when carbon FRP fans were used as end anchoring devices. It is worth to note that the details and accuracy of application procedures can be very influential on the strength increase.
Also (Orton et al. 2008) focused attention on the constructive detailing requested during the installation phase for warrant the efficiency of fan shaped anchor systems.
The effects of anchor splay diameter, anchor diameter and thickness of the FRP sheet have been investigated in (Niemitz et al. 2010).
In Eshwar et al. (2008) the effect of the location and the embedment of spike anchors (10 mm diameter) was experimentally investigated; the experimental results evidenced a significant improvement of strength (25–200 %). A minimum embedment depth of 50 mm in the concrete substrate is suggested, since further increase of the depth resulted ineffective. Multiple anchor spikes significantly increase the strength (+200 %).
In Zhang and Smith (2012a) the influence of FRP anchor fan configuration and dowel angle on the effectiveness of such an anchoring system for FRP reinforcement was investigated in several shear bond tests. In particular, bow-tie FRP anchors (fans oriented in opposite direction along the longitudinal FRP reinforcement) and single fan FRP anchors (fan fibres oriented only in one direction) were tested (see Fig. 6.27). Tests evidenced that single fan FRP anchors with the fan oriented in the direction of load allowed an increasing of the failure load of about 100 % compared with the not anchored specimens. The same load increase was attained using the bow-tie FRP anchors, although the fibre content was twice in this case. When the single fan anchor is positioned with the fan in the reverse direction of the applied load the efficiency into increase the failure load was lower (+60 %). Moreover, the load-slip experimental curves evidenced that the FRP fan anchors enabled a friction resistance that gave to the joint a post-peak reserve and larger ultimate slip, especially in the case of bow-tie configuration. For the single fan anchor the increasing of the angle of the anchor dowel (in the range 45°–157°, while in the basic configuration the angle is 90°) respect to the led to an increase of the failure load (25–160 %) and a decrease of the ductility of the joint due to the brittle failure of the anchor.
a Bow-tie anchor, b single fan anchor (Zhang and Smith 2012a)
In Zhang and Smith (2012b) multiple single fan anchors (one, two, three) were tested in bond tests that substantially evidenced higher maximum load as the number of fan increase, even if the results were more scattered, and lower maximum slip. The concept of flexible and rigid anchors was also introduced and tested: in the flexible anchor there is no epoxy impregnating the region where the fibres of the anchor bend 90° at the junction of the fan and dowel components in order to provide larger slippage of the reinforcement. Experimental results evidenced that in the rigid anchored joints, after the plate debonding, the anchors failed immediately and no post-peak reserve of strength was observed with a consequent reduction of maximum slip that was on average only 36 % of the value attained in the flexible anchored joints. The maximum load in the rigid anchored joints was on average 32 % greater than the load in flexible ones.
The efficiency of single and bow-tie fan anchors located at the plate end or distributed along the plate into increase strength and ductility of RC slabs was proved by (Smith et al. 2013).
An alternative anchoring solution is represented by the application of a FRP bar placed transversally to the direction of the strengthening in a groove filled with resin according to the Near surface mounted bars technique (Khalifa et al. 1999, 2000). This solution can be reliable when the strengthening-to-concrete width ratio is approaching 1. Different solutions can be performed by positioning the FRP bar on a plane surface or in the corner (see Fig. 6.28). For such a technique a sufficient cover is requested for realizing the groove and installing the NSM bar inside. In (Eshwar et al. 2008) the location of the FRP bar, the grove size and the size of the anchoring bar were investigated in an experimental study. The strength was sensibly increased (also until 50 %) compared with not anchored specimens, even if the best performances were obtained when the anchor bars are located after re-entrant corner (see Fig. 6.28a) instead of before the re-entrant corner (see Fig. 6.28b), larger grooves are executed and more bars applied transversally to the reinforcement. In particular, a minimum groove size varying between 1.5 and 2.5 times the bar anchoring diameter and a minimum of 3 GFRP bars are suggested.
NSM bars for plane surface anchorage for beams/slabs flexural strengthening: a after the re-entrant corner; b before the re-entrant corner
The use of FRP bars as anchoring system could create local concentrated stresses where fibres are turned into the groove with cutting of fibre on the corner (Ceroni et al. 2008). However an increasing of ultimate strength at least of 25 % has been experimentally observed if NSM bars are used as end anchorage (Ceroni and Pecce 2010). In Eshwar et al. (2008) a minimum radius of 13 mm is suggested at the corners of the groove to limit stress concentration.
Special Anchorage for Shear Strengthening
For EBR shear strengthening anchoring systems could be particularly useful due to the reduced bond length available in order to avoid debonding. Proper anchorage can be made by systems suitably anchored in the compression zone of the strengthened section.
For shear strengthening solution similar to those proposed for flexural strengthening can be performed. Steel or FRP laminates glued or bolted transversally to the direction of the fibres can be successfully utilized when the not completely wrapped shear reinforcement configuration is adopted.
Special fan anchors can be used also in shear strengthening according to several configurations as tested by Jinno et al. (2001), Kobayshi et al. (2001) to solve the problem of passing fibres of reinforcement through the web of a ‘T-section’ in order to anchor fibres in the compressive zone (see Fig. 6.29).
Near surface mounted bars have been successfully applied as anchorage systems also at the end of shear strengthening (Fig. 6.30), according to the same applying procedure above described.
NSM bars as anchors for U-wrap shear strengthening of an R.C. beam
Special Anchorages for Confinement
For confinement of columns where walls physically obstacle the complete wrapping of the elements, application of fan fibres (Jinno et al. 2001; Kobayshi et al. 2001) can give continuity to the reinforcement (see Fig. 6.31a).
a Fibre fan anchor device for confinement of columns; b fibre fan splayed on the confining strengthening
Since the application of EBR on rectangular columns or pier walls with large aspect ratio does not actually confine the internal concrete, the EBR jacket need to be constrained on both sides along the length through the use of dowels or bolts or spike anchors. Such systems anchor the jacket to the pre-existing structure, thereby creating shorter distances which are confined between bolts (Fig. 6.31b). The positive effect of fibre anchors on the strength enhancement of wall-like columns confined with FRP was tested by (Tan 2002).
Spike anchors provide a low cost solution also to anchor the confinement jacket to the existing structure and has been tested with very good results for the attachment of FRP jackets at the reentrant corners of L-shaped cross section columns (Karantzikis et al. 2005). Experimental tests evidenced that the partial depth anchors give a good effectiveness in terms of deformability and strength increasing, while the benefit provided by full depth anchors are not justified by the high difficulty of installation.
Special Anchorages for Flexural Strengthening of Columns
The anchorage of flexural reinforcement of footing-column/wall joints should be provided. Possible solutions based on the use of steel spike anchors (Fig. 6.32) were tested by (Prota et al. 2005), where the flexural reinforcement was successively wrapped with a FRP jacket, and by (Ascione and Berardi 2011), where the FRP composite was bonded to the device steel plates bolted to each other (double lap bolted joint, see Fig. 6.33).
Flexural strengthening at the footing joint of a RC column using steel spikes wrapped with a FRP jacket (Prota et al. 2005)
Flexural strengthening of a RC column using anchorage device (Ascione and Berardi 2011)
The flexural strengthening of columns can be realized also with NSM CFRP rods that can be anchored at the beam-column joint by wrapping the end with FRP carbon sheets (Prota et al. 2004).
In Antoniades et al. (2003, 2005) U-shaped devices made by FRP fibres or by steel or FRP laminates glued or bolted were successfully tested as anchoring systems of flexural reinforcement of column and walls at the footing zone. Effectiveness of bolted laminates into improve bond of FRP laminates in flexural strengthening of RC walls was tested by Tan et al. (2003) and Nagy-Gyorgy (2005).
Mechanically Fastened Systems
Description of the MF-FRP System
The implementation of mechanically fastened Fibre Reinforced Polymer (MF-FRP) systems for the flexural strengthening of RC members has emerged as an alternative to FRP materials adhesively bonded to the concrete substrate. The MF-FRP system consists of pre-cured FRP laminates with enhanced bearing strength that are connected to the concrete substrate by means of steel nails, anchor bolts, concrete screws, or combinations thereof.
Compared to the adhesive bonding FRP method, the benefit of MF-FRP is the speed of installation with unskilled labour, minimal or absent surface preparation under any meteorological condition and immediate use of the strengthened structures; also, the MF-FRP system is less vulnerable to fail prematurely by FRP delamination, which abruptly reduces the flexural strength gain and affects the member ductility. Some of the potential shortcomings are: possible concrete damage during anchoring and limited opportunity of installation in the presence of congested internal reinforcement in the members to be strengthened. Laboratory testing and a number of field applications have shown the effectiveness of the MF-FRP method.
FRP Strips
Unidirectional pultruded laminates currently used to be adhesively bonded onto the concrete surface are not suitable to be mechanically attached with steel anchors. These laminates are designed to have high modulus and strength in the longitudinal direction and low mechanical properties in the transverse direction of the laminate. Consequently, unless reinforcing fibres in the transverse direction of the laminate are inserted to provide adequate bearing strength, the orthotropic nature of the material causes the splitting failure of the laminate when a fastener is driven through it (Lamanna 2002). Precured laminates commercially available for strengthening with MF-FRP systems were developed in collaboration with Strongwell (USA, www.strongwell.com) and consist of a glass and carbon hybrid pultruded strip embebbed in a vinyl ester resin (see Fig. 6.34). The one shown has thickness and width of 3.2 and 101.6 mm, respectively; the 3.2 mm width is a suitable size for handling in the field. Continuous glass fibre strand mats are used to provide transverse and bearing strength, while 16–113 yield E-glass roving and 40–48 k standard modulus carbon tows are utilized to provide longitudinal strength and stiffness.
Laminate available for the MF-FRP system
Table 6.10 summarizes the relevant mechanical properties of the FRP strips (Arora 2003). More details about the mechanical characterization of the FRP laminate in the longitudinal and transverse direction can be found in some papers (Arora 2003; Rizzo 2005; Rizzo et al. 2005a).
Fasteners
As mentioned earlier, fastener types that have been investigated for the MF FRP systems include: power-actuated fasteners (PAF), wedge bolts and wedge anchors (see Fig. 6.35).
Fasteners used for MF-FRP systems
The PAF system consists of pins embedded into base materials by means of a gunpowder charge. The effects of fastener type, washer, diameter, length, embedment depth have been investigated and discussed elsewhere (Lamanna et al. 2001; Lamanna 2002). Pre-drilling holes in the concrete is strongly recommended in order to reduce detrimental cracking phenomena. The use of the PAF system is particularly suitable when the compression strength of the concrete is less than 27 MPa. The presence of hard aggregates can prevent the fasteners to fully penetrate the concrete substrate (Bank 2004). The PAF installation requires times shorter than for wedge bolts and wedge anchors.
Wedge bolts are single-piece, heavy duty anchors that are driven into pre-drilled holes. Driving of the wedge bolt can be performed with a common rotary drill or impact wrench. As for the PAFs, the efficiency of wedge bolts is dependent on the presence of hard aggregates. Preliminary studies (Rizzo et al. 2005b) indicate that the use is not recommended for concrete with compression strength greater than 27 MPa, and with hard aggregates in the mix design.
In spite of longer installation times, wedge anchors can be used for any type of concrete; they are driven through the laminate into predrilled holes until the nut and washer are firmly secured against the laminate. The anchors are typically tightened by turning the nut with an electrical drill with torque control, according to the specifications of fastener manufactures.
Failure Modes of FRP-Fastener-Concrete Connection
The behaviour of MF-FRP connections is related to any of the components constituting the connection, which are the concrete substrate, the fastener and the FRP material. As a result, failure modes can involve the concrete, the yielding/rupture of fastener, or the FRP laminate.
The pry-out or spalling of the concrete (Fig. 6.36a) depends on the local composition of the concrete surface around the fastener. Once pry-out failure develops, the fastener rotates and the FRP laminate pulls it out of the concrete. Several factors promote the initiation of the concrete failure, such as a fastener hitting a hard aggregate during installation, low concrete strength, cracked concrete substrate conditions, short edge distance that may cause spalling, and poor fastener embedment depth (Lamanna 2002; Arora 2003).
a Concrete pry-out failure; b typical failure modes of mechanically fastened connections in FRP
The fastener failure usually occurs for deep embedment length, low steel strength and large edge distance (Rizzo 2005).
Four typical failure modes can involve the MF-FRP laminate (Fig. 6.36b): net-tension, cleavage-tension (or block shear), bearing and shear-out. The bearing failure is the most desirable failure mode because the connection is able to maintain its strength until significant levels of displacement (Lamanna 2002; Arora 2003). This failure is characterized by crushing on the material around the bolt-contact area followed by elongation of the hole. The other failure modes tend to develop in a more brittle way (Rosner and Rizkalla 1995). In particular, the net-tension failure is characterized by a fracture in the reduced cross section through the bolt hole, perpendicular to the direction of load. The cleavage failure consists of a crack parallel to the applied load that starts at the edge of the composite and propagates toward the bolt hole, leading to the initiation of other cracks across the net section due to in-plane stress. This failure mode is attributed to a combination of shear and tensile stress in the material. The shear-out failure, considered as a special case of bearing, is characterized by the formation of two cracks parallel to the applied load that propagate from the bolt hole toward the free edge.
State of Advancement and Current Research
The MF-FRP systems were firstly employed to strengthen RC bridges and infrastructures (Oliva et al. 2003; Rizzo 2005). After the first successful field applications, a number of experimental studies have been performed around the world with the aim of investigating the performance of RC members externally strengthened by MF-FRP laminate and quantifying the benefits obtained in terms of strength, stiffness and displacement capacity (Rizzo 2005; Lamanna et al. 2001, 2004a, b; Martin and Lamanna 2008; Lee et al. 2007).
To this aim, a recently published state-of-the-art review of the experimental research has provided compelling evidence of the effectiveness and viability of using MF-FRP laminates to rehabilitate RC beams and slabs (Brown et al. 2011). In the review, a database of collected test results was assembled to provide a valuable source of information on the performances of MF-FRP strengthened beams and one-way slabs. In a more recent paper, Martinelli et al. (2014) published an updated database of experimental results from four point-bending tests performed on MF-FRP strengthened RC members. As observed, the specimens tested so far have different sizes of the cross-section, with values of the height to-width ratios spanning from 0.5 (“slab” type) to 1.67 (“beam” type”); the clear lengths range from 1067 (small scale members) to 3505 mm (large scale members). The mechanical fastening mostly consists of shot fasteners with diameters ranging from 3.5 to 4.5 mm and lengths from 22 to 47 mm. Screw anchors were also frequently used, for which the diameters span from 4.76 to 12.7 mm and the lengths from 37 to 50.8 mm. Only in a few cases, instead, the mechanically fastening was performed by using wedge anchors (Ekenel et al. 2005; Galati et al. 2007); they were installed into the concrete by using epoxy resin as a gap filler. In these tests, the fasteners were arranged on single or multiple rows (1, 2, 4) according to aligned or staggered configurations or combinations thereof.
From the experimental investigations it has been shown that with appropriate fastener layout and FRP laminate properties, the strength increases are comparable to those of externally bonded-FRP strengthened members but with greater displacements exhibited at collapse. Also, it has been highlighted that the MF-FRP technique allows for preventing the strip delamination before concrete crushing. As an example, the experimental study performed by Napoli et al. (2010) is mentioned (see Fig. 6.37). The authors studied the effects of fastener layout and FRP strip length on flexural strength and deformability and failure mode of MF-FRP strengthened one-way slabs. Concrete screws were used to fasten the FRP strips to the concrete. At failure of specimens, the authors observed that the high concentration of shear force caused spalling of the concrete cover but the FRP strip was firmly attached to the member. All MF-FRP strengthened specimens attained ultimate strength levels comparable to that of a benchmark slab strengthened with an externally bonded (EB) carbon FRP laminate, with greater deformability, as shown in Fig. 6.37c. Specimens MF-1L and MF-1S that used a larger number of anchors in the shear span (Pattern No. 1 in Fig. 6.37b), achieved marginally larger ultimate strengths but at lesser deformability than corresponding slabs MF-2L and MF-2S (using Pattern No. 2 in Fig. 6.37b).
Tests by Napoli et al. (2010): a specimens; b fastener layouts; c results
Comparative experimental studies (Quattlebaum et al. 2005; Ekenel et al. 2006) on the static and fatigue performance of RC beams strengthened in bending by either MF- or EB-FRP laminates, showed that similar strength levels can be attained.
The feasibility of this strengthening technique was widely demonstrated experimentally in the upgrading of two-way slabs (Elsayed et al. 2009b).
Other experimental investigations examined the suitability of connecting an FRP laminate to the concrete substrate by both adhesive and mechanical anchors (EB + MF-FRP system) (Ekenel et al. 2006; Sena-Cruz et al. 2011; Ebead 2011).
One of the latest studies also showed that the MF-FRP system is viable for strengthening existing reinforced-concrete beams in shear (Johnson 2011).
Also, experimental tests have proven that the mechanically fastened composite system is an effective technique to improve the flexural capacity of corrosion damaged RC beams (El-Maaddawy 2013).
Finally, MF-FRP laminates were recently employed for enhancing the flexural capacity of timber structural members (Dempsey and Scott 2006; Schorer et al. 2008).
Design Rules
Despite the interest and promising experimental results obtained by researchers, there are no international guidelines dealing with MF-FRP till now. However, several analytical and numerical studies have been carried out through years with the aim to predict the flexural behaviour of RC members strengthened with MF-FRP systems: a state-of-the-art review has been recently published in Napoli et al. (2013). As highlighted therein, the first analytical models were based, for the sake of simplicity, on the hypothesis of “conservation of plane sections” between the concrete and the FRP, as generally accepted for EB-FRP strengthened members (Lamanna 2002; Bank et al. 2002; Bank 2004; Bank and Arora 2007; Rizzo et al. 2005b). Despite their ease of application, such models have often provided inaccurate predictions which were primarily attributed to ignoring the slip between the concrete and FRP strip. Therefore, novel proposals accounting for the concrete-FRP interfacial behaviour were recently formulated by (Lee et al. 2009; Nardone et al. 2011).
Lee et al. (2009), after observing and verifying the slip effect at the connection between FRP and concrete, introduced a FRP strain reduction factor calibrated on the basis of experimental results in order to evaluate the nominal moment capacity. However, even after this, an assumed reduction factor can lead to an incorrect evaluation of the neutral axis depth at ultimate limit state and does not provide useful information under service conditions.
Nardone et al. (2011) proposed analytical procedures for the evaluation of the flexural behaviour at both serviceability and ultimate limit states. Their analytical models account for equilibrium, compatibility and constitutive relationships of materials; in particular, they account explicitly for the slip behaviour between the concrete surface and the FRP strip due to the fasteners. The proposed models, coupled with an appropriate computation algorithm, are able to predict the fundamentals of flexural behaviour of RC members strengthened with MF-FRP strips also in terms of load versus deflection curves, failure modes, strain profiles and curvatures.
The models are capable of predicting the three failure modes experimentally found for well-designed applications, namely: bearing failure or net tension failure of the FRP laminate and concrete crushing.
The comparison between the analytical predictions and the experimental results shows a good agreement in terms of strain profiles in MF-FRP strips and moment deflection curves at serviceability limit state. Similarly, comparison of nominal flexural capacity, ultimate curvature and FRP strain at ultimate limit state show good agreement. This agreement is higher if bearing failure of many fasteners is accepted and included in the evaluations (Nardone et al. 2012). However from a design point of view, it is suggested to design for the desired sustained bearing failure of the first outermost fastener.
The knowledge of the relationship between the force acting on the fastener and the slip is fundamental in order to apply the proposed model and more research to address this fundamental parameter is needed.
To this aim, Elsayed et al. (2009a) and Realfonzo et al. (2013) recently proposed nonlinear bearing stress-slip σ-s models to describe the effect of the partial interaction between the concrete and the FRP laminate. These models, shown in Fig. 6.38, were calibrated by best-fitting experimental results of direct shear tests (DSTs) performed on MF-FRP/concrete joints with a single connector.
Bearing stress-slip models
Two different σ-s models were found by Elsayed et al. (2009a), suitable for shot (Model 1) and screwed (Model 2a) fasteners, respectively, both with steel washers (Fig. 6.38). The first model was calibrated for MF-FRP/concrete joints having a single shot fastener with a 47 mm shank length, a 3.7 mm shank diameter and a 13 mm washer where the fastener was driven into the concrete using a powder actuated gun. The second model was for the case of a single screwed fastener with a 37 mm shank length, a 4.8 mm shank diameter and a 16 mm washer installed into the concrete using a drilling tool.
Trilinear σ-s models were proposed by (Realfonzo et al. 2013) for a single screwed fastener with (w/washer) or without (w/o washer) washer (Models 2b and 3 in Fig. 6.38); the screw had a 45 mm shank length, a 6 mm shank diameter, a 32 mm washer (when used) and was driven into the pre-drilled hole using a common torque wrench.
Once the first studies on the FRP-concrete interfacial behaviour were published in the literature, refined moment-deflections models were developed. Among them, the numerical model developed by Napoli et al. (2010) was based on a general algorithm formulated by implementing the differential equation of Newmark’s theory for steel-concrete composite beams with linear-elastic shear connectors (Newmark et al. 1951) into an ‘exact’ two-node finite element (FE) developed for the analysis of partial interaction in composite beams with flexible shear connectors (Faella et al. 2008). The finite element introduced is used for nonlinear analysis through fibre discretization of the beam cross-section, and by implementing an iterative convergence procedure based on the secant value approach to account for material non-linearity, including concrete, steel and concrete-FRP interface. For the latter, the interface bearing stress-slip Model 2a in Fig. 6.38 and its resulting simplification in a bilinear law (Napoli et al. 2010) were successfully implemented and verified to evaluate applicability for analysis and design purposes.
A different 1-D numerical model was presented by Martinelli et al. (2014) to explicitly account for the discrete connection between FRP laminate and RC beam. Later, the model was also used by the authors to investigate the cracking process in RC members (and its implications on the structural response including the tension-stiffening effect) which is generally neglected (Martinelli et al. 2013).
Figure 6.39a depicts the considered finite element which is obtained by assembling the following three components: (a) a 1-D element that models the behaviour of an Euler-Bernoulli RC beam; (b) a rod element that simulates the mechanical behaviour of an FRP laminate; (c) two springs used as axial constraints between the FRP laminate and the RC beam. The two springs simulate the behaviour of the fasteners connecting the FRP laminate to points on the beam surface, i.e., at the points where the fasteners are actually screwed or shot. Four degrees of freedom are considered in each node to take into account the possible axial displacements of both RC beams and FRP strips, along with deflections and rotations of the former component. The stiffness matrix of the proposed FE is derived by assembling the key mechanical components of the RC beam/slab, the FRP strip and the mechanical fasteners. The nonlinear behaviour of the aforementioned components and materials is handled through well-established numerical techniques usually adopted in nonlinear FE analysis.
FE model by Martinelli et al. (2014): a schematic and b validation
The procedure was validated by comparing the numerical simulations in terms of load-deflection curves with the results of some experimental tests reported in the literature. In particular, Fig. 6.39b shows a comparison for an MF-FRP strengthened slab tested by Napoli et al. (2010). In this case, the behaviour of the screws w/o washers was modelled by adopting the trilinear Model 3 (Fig. 6.38). For comparison, the nonlinear Model 1 for shot fasteners (Fig. 6.38) was also considered. It is shown that the numerical simulations do not significantly change with the use of the two different bearing stress-slip relationships, thus suggesting that both of them are suitable to model MF-FRP strengthened members.
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Fatigue Behaviour
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Mechanically Fastened Systems
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Ceroni, F. et al. (2016). Special Problems. In: Pellegrino, C., Sena-Cruz, J. (eds) Design Procedures for the Use of Composites in Strengthening of Reinforced Concrete Structures. RILEM State-of-the-Art Reports, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-7336-2_6
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