Assessment of fib Bulletin 90 Design Provisions for Intermediate Crack Debonding in Flexural Concrete Elements Strengthened with Externally Bonded FRP

With the assessment of intermediate crack debonding (ICD) being a subject of main importance in the design of reinforced concrete (RC) beams strengthened in flexure with externally bonded fibre-reinforced polymer (FRP), several approaches to predict the debonding loads have been developed in recent decades considering different models and strategies. This study presents an analysis of formulations with different levels of approximation collected in the fib Bulletin 90 regarding this failure mode, comparing the theoretical predictions with experimental results. The carried-out experiments consisted of three RC beams strengthened with carbon FRP (CFRP) tested under a four-point bending configuration with different concrete strengths and internal steel reinforcement ratios. With failure after steel yielding, higher concrete strength, as well as a higher reinforcement ratio, lead to a higher bending capacity. In addition, the performance of the models is assessed through the experimental-to-predicted failure load ratios from an experimental database of 65 RC beams strengthened with CFRP gathered from the literature. The results of the comparative study show that the intermediate crack debonding failure mode is well predicted by all models with a mean experimental-to-predicted failure load ratio between 0.96 and 1.10 in beams tested under three- or four-point bending configurations.


Introduction
The strengthening of reinforced concrete (RC) structures with fibre-reinforced polymer (FRP) materials has been extensively performed in construction during the last two decades due to the advantages in the mechanical and durability properties of these materials over traditional techniques such as reinforcement with steel plates. FRPs are composite materials made of a polymeric matrix (resin) reinforced with continuous fibres of glass (GFRP), carbon (CFRP), basalt (BFRP), or aramid (AFRP). Some of the reasons why these materials are increasingly used are their durability and resistance to corrosion, high tensile strengthand stiffness-to-weight ratio, low weight resulting in ease of installation and reduction in labour costs, and large availability of sizes and geometries [1][2][3]. CFRP strengthening has been shown to increase the stiffness and strength performance of flexural members. It is currently a widespread strengthening methodology for RC members with a variety of applications, for example, the strengthening of sea sand RC members [4].
Two techniques are typically used to retrofit the RC structures with FRP materials: externally bonded reinforcement (EBR) and near-surface mounted (NSM). The EBR method is widely used to effectively strengthen RC structures in flexure, shear, and torsion, as well as to introduce favourable confinement effects [5]. However, members with flexural reinforcement often suffer from premature debonding of the FRP from the concrete surface before the sectional failure due to FRP rupture or concrete crushing [1,2,6], leading to a high underutilisation of the FRP reinforcement mechanical properties. The utilisation rate of the tensile strength may be improved by prestressing the CFRP plates before bonding them to the substrate. In the latter, the choice of the end anchorage system will be of importance to avoid a significant loss of the prestressing forces [7,8].
In the system FRP/adhesive/concrete, debonding may take place within the concrete (cohesive failure), the adhesive (cohesive failure), the laminate (delamination failure), or in the interfaces between these materials (adhesion failure). If a proper application of the strengthening system is carried out, the weakest part of the system is the concrete layer near the interface with the adhesive as the tensile strength of the concrete is usually much lower than the adhesive strength [9]. Considering the origin of the debonding, failure modes can be classified as intermediate crack debonding (ICD), starting at an intermediate section of the beam due to flexural (or flexural-shear) cracks and propagating to the support, and end debonding (ED), which occurs at the curtailment region of the FRP reinforcement. As observed from experiments in the literature, ICD is usually the governing failure mode in flexural applications [9,10].
In an EBR FRP-concrete joint, normal stresses in the FRP are transferred to the concrete through shear stresses applied to its surface. When these stresses attain the value of the bond strength, the debonding process initiates. The bond behaviour of the interface can be described in terms of the shear stresses (τ b ) and the slip (s) of the laminate from the substrate. Several models can be found in the literature coming from experimental assessment and simplifications [11][12][13][14][15][16][17][18]. The bond behaviour is often well represented by a bilinear bond law ( Figure 1, Equation (1)) with an initial ascending branch up to the maximum shear stress τ b1 (bond strength), followed by a linear descending branch (due to the damage of materials) until the maximum slip s 0 . The fracture energy G f of the system is defined as the area under the bond stress-slip curve, which, for a bilinear law, can be expressed by Equation (2).
f or s > s 1 (1) G f = τ b1 ·s 0 2 (2) leading to a high underutilisation of the FRP reinforcement mechanical properties. The utilisation rate of the tensile strength may be improved by prestressing the CFRP plates before bonding them to the substrate. In the latter, the choice of the end anchorage system will be of importance to avoid a significant loss of the prestressing forces [7,8].
In the system FRP/adhesive/concrete, debonding may take place within the concrete (cohesive failure), the adhesive (cohesive failure), the laminate (delamination failure), or in the interfaces between these materials (adhesion failure). If a proper application of the strengthening system is carried out, the weakest part of the system is the concrete layer near the interface with the adhesive as the tensile strength of the concrete is usually much lower than the adhesive strength [9]. Considering the origin of the debonding, failure modes can be classified as intermediate crack debonding (ICD), starting at an intermediate section of the beam due to flexural (or flexural-shear) cracks and propagating to the support, and end debonding (ED), which occurs at the curtailment region of the FRP reinforcement. As observed from experiments in the literature, ICD is usually the governing failure mode in flexural applications [9,10].
In an EBR FRP-concrete joint, normal stresses in the FRP are transferred to the concrete through shear stresses applied to its surface. When these stresses attain the value of the bond strength, the debonding process initiates. The bond behaviour of the interface can be described in terms of the shear stresses (τb) and the slip (s) of the laminate from the substrate. Several models can be found in the literature coming from experimental assessment and simplifications [11][12][13][14][15][16][17][18]. The bond behaviour is often well represented by a bilinear bond law ( Figure 1, Equation (1)) with an initial ascending branch up to the maximum shear stress τb1 (bond strength), followed by a linear descending branch (due to the damage of materials) until the maximum slip s0. The fracture energy Gf of the system is defined as the area under the bond stress-slip curve, which, for a bilinear law, can be expressed by Equation (2).
This bilinear bond behaviour is usually described using direct shear tests [19,20]. Although in flexural applications (i.e., beams), curvature may cause peeling stresses perpendicular to the FRP surface, shifting the shear failure mode II to a mixed mode I-II, the normal component is usually neglected, and, as a simplification, debonding is treated as a pure shear (mode II) failure [9].  This bilinear bond behaviour is usually described using direct shear tests [19,20]. Although in flexural applications (i.e., beams), curvature may cause peeling stresses perpendicular to the FRP surface, shifting the shear failure mode II to a mixed mode I-II, the normal component is usually neglected, and, as a simplification, debonding is treated as a pure shear (mode II) failure [9]. Several analytical models have been developed to predict ICD failure and adopted by codes of practice [1,2,6,21], involving different levels of approximation. There is still uncertainty in the precise role of the influencing parameters in the debonding phenomena, hence simplified design formulations based on the direct calibration of empirical expressions against experimental results are often presented in the literature. Usual models are based on different approaches: a limitation of the stress or strain in the FRP strengthening at the critical section of the beam [2,6,[22][23][24]; a limitation of the maximum mean bond stress [25]; or a limitation of the increment of tensile force/stress in the FRP [21,[26][27][28][29].
In the fib Bulletin 90 [1], different approaches to predicting ICD are presented, addressing different levels of approximation and parameters defining the bond-slip law, which may lead to different predictions. This paper aims to assess these proposals in order to understand their basis, highlight their differences, and compare their predictions with experimental results.
In this study, a detailed description of the different approaches is presented along with an experimental campaign that was performed to compare the theoretical predictions with experimental results. The experimental results are presented and discussed in terms of modes of failure, flexural capacity, load-deflection response, and load-strain response in the CFRP. As a further element of assessment, a database of 65 EBR CFRP RC beams that failed by ICD gathered from the literature is analysed using the different proposals. Experimental-to-predicted failure load ratios are presented, and the differences in the approaches are highlighted.

Analysis of the Current Formulations for ICD
Three main approaches are presented in the fib bulletin 90 [1] to predict ICD failure. All of them are based on the transfer of bond stresses in an FRP-strengthened concrete element between two cracks. However, the limiting value is established by following two different approaches, either the maximum stress or the maximum increment of tensile force in the FRP reinforcement.
The transfer of bond stresses is limited by the maximum transferrable (anchorage) stress in the FRP, which can be derived from a non-linear fracture mechanics (NLFM) analysis of direct shear tests [11,12,14,[30][31][32]. Equation (3) is suggested to calculate the anchorage strength, where E f and t f are the elastic modulus and thickness of the FRP, respectively, and β l (Equations (4) and (5)) is the reducing factor for bonded lengths (l b ) lower than the effective length (l e ), thus taking into consideration that the full bond-slip law will not be developed, and the maximum anchorage force will not be attained. The effective length for a bilinear bond law can be calculated using Equation (5).
Two proposals to calculate the model parameters of the bilinear local bond-slip law (Table 1) are indicated. Considering that debonding takes place in the concrete, the bond strength is determined by using the Mohr-Coulomb failure criterion, assuming that in a pure shear stress state, normal stresses are null. The differences between both proposals are:

•
The dependence on the concrete strength in the formulation for the shear strength; • The value of the maximum slip; • The influence of the relationship between FRP and concrete surfaces, introduced by the shape factor k b (Equation (6)), where b f and b represent the widths of the FRP reinforcement and of the strengthened element, respectively. Table 1. Suggested mean values for the parameters in the bilinear bond law [33,34].
Note: f cm and f ctm are the mean compressive and tensile strength of the concrete, respectively.
The two approaches are compared in Figure 2 through the resulting fracture energy for a typical range of values of the factor k b . It can be observed that according to the approach from [33] G f is higher in specimens with sheet reinforcements than in those with strips. By using the approach from [34], G f increases proportionally to k b 2 , and, therefore, decreases proportionally to the ratio b f /b.

•
The influence of the relationship between FRP and concrete surfaces, introduced by the shape factor kb (Equation (6)), where bf and b represent the widths of the FRP reinforcement and of the strengthened element, respectively. Table 1. Suggested mean values for the parameters in the bilinear bond law [33,34].
The two approaches are compared in Figure 2 through the resulting fracture energy for a typical range of values of the factor kb. It can be observed that according to the approach from [33] Gf is higher in specimens with sheet reinforcements than in those with strips. By using the approach from [34], Gf increases proportionally to kb 2 , and, therefore, decreases proportionally to the ratio bf/b.

Simplified FRP Stress Limit Method (S1, S2)
This approach limits the ultimate FRP tensile stress at the most unfavourable section to a certain value ffb,IC, which depends on the end anchorage capacity of the FRP (Equation (3), considering βl equal to 1). In flexural applications, the transferred force in the FRP is higher than the end anchorage capacity due to the gradient of stresses in the FRP reinforcement. This phenomenon is considered through the calibration factor kcr, which has been defined with a value of 2.10 according to the assessment of the database described in [1].

Simplified FRP Stress Limit Method (S1, S2)
This approach limits the ultimate FRP tensile stress at the most unfavourable section to a certain value f fb,IC, which depends on the end anchorage capacity of the FRP (Equation (3), considering β l equal to 1). In flexural applications, the transferred force in the FRP is higher than the end anchorage capacity due to the gradient of stresses in the FRP reinforcement. This phenomenon is considered through the calibration factor k cr , which has been defined with a value of 2.10 according to the assessment of the database described in [1].
Bilinear and design-by-testing approaches (Table 1) will be used for calculating G f and designated as S1 and S2, respectively. The proposal of the German committee DAfStb was adopted, consisting of a more accurate method in which the maximum allowable increase in tensile force in the FRP reinforcement between two adjacent cracks is computed, considering a modified version of the bilinear bond law (Figure 3). According to the analysis of the experimental tests performed in [35,36], a significant increase in the bond force with respect to the typical bilinear bond law represented in Figure 1 was achieved, due to the contribution of friction (τ bF ) and curvature components (τ bC ). Bilinear and design-by-testing approaches ( Table 1) will be used for calculating Gf and designated as S1 and S2, respectively.

More Accurate Method (MA1, MA2)
The proposal of the German committee DAfStb was adopted, consisting of a more accurate method in which the maximum allowable increase in tensile force in the FRP reinforcement between two adjacent cracks is computed, considering a modified version of the bilinear bond law (Figure 3). According to the analysis of the experimental tests performed in [35,36], a significant increase in the bond force with respect to the typical bilinear bond law represented in Figure 1 was achieved, due to the contribution of friction (τbF) and curvature components (τbC). The calculation of the maximum allowable increase in tensile force in the FRP (ΔFfR) can be performed in a detailed manner as in Equations (8)- (15) or in a simplified one as in Equation (22). Both formulations involve the calculation of FRP stresses at each crack, which implies the solution of equilibrium and compatibility equations at each iteration. Moreover, the resisting increment of force in the detailed analysis is dependent on the level of FRP force, changing at every crack and iteration, whereas in the simplified analysis, a unique value of ΔFfR needs to be computed, which was determined through a numerical approach to the more accurate method [22].
In the evaluation of the different methods, the detailed analysis will be addressed as MA1, whereas the simplified analysis will be MA2. Bilinear approach (Table 1) will be used for calculating the bond-slip parameters in both analyses.

Detailed Analysis of FRP Force Difference (MA1)
As mentioned before, the bond resistance to change in the FRP force between cracks (Equation (8)) is the result of the addition of three components: where ΔFf,B is the bond strength from the bilinear bond stress-slip curve, ΔFf,F is the term due to the frictional bond in the already debonded surface, and ΔFf,C is the contribution of the curvature of the member. The term related to the adhesive bond (ΔFf,B) is calculated using Equation (9). The first linear branch represents the cases where the stresses are not high enough to develop the whole bond stress-slip relationship in the crack spacing, as the value of s0 has not been attained (line G-D in Figure 4). Point G is obtained from Equation (10) assuming that the stress in the lower stressed crack is zero, and point D is calculated by Equations (11) and The calculation of the maximum allowable increase in tensile force in the FRP (∆F fR ) can be performed in a detailed manner as in Equations (8)- (15) or in a simplified one as in Equation (22). Both formulations involve the calculation of FRP stresses at each crack, which implies the solution of equilibrium and compatibility equations at each iteration. Moreover, the resisting increment of force in the detailed analysis is dependent on the level of FRP force, changing at every crack and iteration, whereas in the simplified analysis, a unique value of ∆F fR needs to be computed, which was determined through a numerical approach to the more accurate method [22].
In the evaluation of the different methods, the detailed analysis will be addressed as MA1, whereas the simplified analysis will be MA2. Bilinear approach (Table 1) will be used for calculating the bond-slip parameters in both analyses.

Detailed Analysis of FRP Force Difference (MA1)
As mentioned before, the bond resistance to change in the FRP force between cracks (Equation (8)) is the result of the addition of three components: where ∆F f,B is the bond strength from the bilinear bond stress-slip curve, ∆F f,F is the term due to the frictional bond in the already debonded surface, and ∆F f,C is the contribution of the curvature of the member. The term related to the adhesive bond (∆F f,B ) is calculated using Equation (9). The first linear branch represents the cases where the stresses are not high enough to develop the whole bond stress-slip relationship in the crack spacing, as the value of s 0 has not been attained (line G-D in Figure 4). Point G is obtained from Equation (10) assuming that the stress in the lower stressed crack is zero, and point D is calculated by Equations (11) and (12) when the required transfer length (l e ) is equal to the crack spacing. The second branch of Equation (9) Figure 4). In the latter, as a certain area of FRP reinforcement has detached, crack spacing becomes not relevant.
where F fu is the ultimate force of the FRP reinforcement and: Polymers 2023, 15, x FOR PEER REVIEW 6 of 24 (12) when the required transfer length (le) is equal to the crack spacing. The second branch of Equation (9) considers the cases in which s0 has already been attained (line beyond point D in Figure 4). In the latter, as a certain area of FRP reinforcement has detached, crack spacing becomes not relevant.
where Ffu is the ultimate force of the FRP reinforcement and: For this approach, according to [1], the term ffb(sr) is calculated through Equation (3), considering lb equal to sr and the bond parameters of approach [33] (Table 1). The term related to the bond friction (ΔFf,F) is calculated using Equation (13). This term considers the friction that is produced in the surfaces where the debonding process starts, before the failure of the whole element between cracks.
When the tensile stress in the FRP is lower than , , the slip is lower than the maximum slip s0; therefore, debonding cannot happen, and friction is not produced (first branch of Equation (13)). After attaining the maximum slip, the friction stress developed in the debonded area will increase the bond strength. The debonded length is calculated by deducting from the crack spacing an effective length, derived from the bilinear bond law (second branch of Equation (13)). For this approach, according to [1], the term f fb (s r ) is calculated through Equation (3), considering l b equal to s r and the bond parameters of approach [33] (Table 1).
The term related to the bond friction (∆F f,F ) is calculated using Equation (13). This term considers the friction that is produced in the surfaces where the debonding process starts, before the failure of the whole element between cracks.
When the tensile stress in the FRP is lower than F D f ,B , the slip is lower than the maximum slip s 0 ; therefore, debonding cannot happen, and friction is not produced (first branch of Equation (13)). After attaining the maximum slip, the friction stress developed in the debonded area will increase the bond strength. The debonded length is calculated by deducting from the crack spacing an effective length, derived from the bilinear bond law (second branch of Equation (13)). The bond friction strength is obtained by calibration from the experimental results [27]. In Equation (14), α cc considers long-term loading effects with a value between 0.8-1.0. In this study, α cc = 1.
The term related to the contribution of the member curvature (∆F f,C ) is calculated using Equation (15). Due to the curvature of the beam caused by deflection, a pressure is applied onto the bottom of the concrete element so that the FRP can transfer higher stresses before debonding. Based on experimental tests [36], an empirical coefficient κ m = 33.3 × 10 3 N/mm multiplies the curvature of the concrete element between cracks to compute the increment of transferred force due to the effect of curvature, where ε f and ε c are the strains in the FRP reinforcement and concrete at the lower stressed crack of the intermediate crack element, respectively.
where tensile strains are considered positive and compressive strains, negative. For determining the crack spacing at the ultimate limit state, the formulation in Equations (16)-(21) is proposed, where l e,0 is the transfer length of the reinforcing steel, M cr is the cracking moment, z s is the steel lever arm approximated to 0.85 h, W c,0 is the section modulus of the uncracked concrete gross section, F bsm is the bond force per unit length, n s,i is the number of steel rebars with diameter ø s,i , f bsm is the mean bond stress, and the parameters κ νb1 and κ νb2 can be assumed equal to 1.0 for good bond conditions and κ νb1 = 0.7 and κ νb2 = 0.5 for medium bond conditions.
Based on a numerical analysis from the previous detailed procedure [22], a constant value for the increment of resisting the tensile force of each element between cracks is proposed. This formulation, also accounting for the three terms related to bond resistance, friction, and curvature is deemed to be more conservative than the detailed approach, providing a simpler methodology and reducing the computational effort.
where κ h = 2739, s r is the crack spacing, limited to 400 mm, and h, the member height, is greater than 100 mm. The maximum strain in the FRP reinforcement should not exceed the value of 0.01.

Layout and Instrumentation
An experimental campaign was performed to assess the different approaches presented above. Three CFRP-strengthened RC beams from two different series were tested under a four-point bending configuration ( Figure 5). The differences between series I and II were the concrete strength (properties are reported in Table 2) and the concrete cover.  [37]. 2 Determined according to [38]. 3 Determined according to [39]. 4 Determined according to [40] 5 Provided by the manufacturer (S&P).   The dimensions of the specimens are shown in Figure 5. The total length of the beams was 2400 mm, with a distance between supports of 2200 mm and a shear span of 900 mm. The beams were designed with a relatively high ratio between the shear span and the effective depth to induce failure by ICD [41]. All beams had a cross-section of 140 × 180 mm. The tensile steel reinforcement consisted of two bars of diameter 8 mm or 10 mm (depending on the beam, see Figure 5) and two bars of diameter 6 mm in the compression zone to hold the internal shear reinforcement. The latter consisted of steel stirrups of diameter 8 mm with a spacing of 100 mm placed along the beam length. All beams were externally strengthened with a CFRP laminate of 50 × 1.4 mm. The properties of the steel and CFRP are reported in Table 2.

Material
The specimens were designated as EBR-X-dY, where X is the series (I or II) and Y is the diameter of steel tensile reinforcement (8 mm or 10 mm).
To ensure a sufficient bonding between the concrete and the CFRP laminate, the outer layer of concrete in all beams was removed by bush-hammering the surface and then cleaned with compressed air. After this procedure, a thin layer of a two-component epoxy resin was applied onto the CFRP laminate, which was immediately placed on the concrete surface. The adhesive used in this study was S&P Resin 220 HP, a thixotropic and solventfree adhesive. Its properties after a curing time of 7 days, according to the manufacturer data sheet, are reported in Table 2. The specimens were cured for 135 days, in the case of series I, and 37 days in the case of series II, in laboratory conditions.
The test was performed under a displacement-controlled mode with a rate of 0.60 mm/min. The load was applied by a hydraulic jack to a spreader beam, which transmitted the load to the beam specimens within the span of 400 mm.
A 200-kN load cell was placed under the actuator to measure the applied force. Three linear variable displacement transducers (LVDT) were placed to measure the mid-span deflection: one LVDT was located at the central section of the beam, and the other two were located at each one of the two supports. The concrete strain at the mid-span was measured in beams of series II using two strain gauges (SG): one at the concrete top section and another at 2 cm from the top, attached to the beam face. The CFRP strain at the mid-span was measured using one SG attached to the CFRP surface.

Experimental Results
The values of the load, mid-span deflection, and CFRP strain and concrete strain at failure are reported in Table 3  The dimensions of the specimens are shown in Figure 5. The total length of the beams was 2400 mm, with a distance between supports of 2200 mm and a shear span of 900 mm. The beams were designed with a relatively high ratio between the shear span and the effective depth to induce failure by ICD [41]. All beams had a cross-section of 140 × 180 mm. The tensile steel reinforcement consisted of two bars of diameter 8 mm or 10 mm (depending on the beam, see Figure 5) and two bars of diameter 6 mm in the compression zone to hold the internal shear reinforcement. The latter consisted of steel stirrups of diameter 8 mm with a spacing of 100 mm placed along the beam length. All beams were externally strengthened with a CFRP laminate of 50 × 1.4 mm. The properties of the steel and CFRP are reported in Table 2.
The specimens were designated as EBR-X-dY, where X is the series (I or II) and Y is the diameter of steel tensile reinforcement (8 mm or 10 mm).
To ensure a sufficient bonding between the concrete and the CFRP laminate, the outer layer of concrete in all beams was removed by bush-hammering the surface and then cleaned with compressed air. After this procedure, a thin layer of a two-component epoxy resin was applied onto the CFRP laminate, which was immediately placed on the concrete surface. The adhesive used in this study was S&P Resin 220 HP, a thixotropic and solventfree adhesive. Its properties after a curing time of 7 days, according to the manufacturer data sheet, are reported in Table 2. The specimens were cured for 135 days, in the case of series I, and 37 days in the case of series II, in laboratory conditions.
The test was performed under a displacement-controlled mode with a rate of 0.60 mm/min. The load was applied by a hydraulic jack to a spreader beam, which transmitted the load to the beam specimens within the span of 400 mm.
A 200-kN load cell was placed under the actuator to measure the applied force. Three linear variable displacement transducers (LVDT) were placed to measure the mid-span deflection: one LVDT was located at the central section of the beam, and the other two were located at each one of the two supports. The concrete strain at the mid-span was measured in beams of series II using two strain gauges (SG): one at the concrete top section and another at 2 cm from the top, attached to the beam face. The CFRP strain at the midspan was measured using one SG attached to the CFRP surface.

Experimental Results
The values of the load, mid-span deflection, and CFRP strain and concrete strain at failure are reported in Table 3  Analysing the experimental values of maximum CFRP and concrete strains, the premature nature of the debonding failure mode can be observed. Considering the ultimate CFRP strain of 16 × 10 -3 according to the manufacturer, the tested laminates were working at between 30% and 40% of their tensile capacity. As for the concrete, the Analysing the experimental values of maximum CFRP and concrete strains, the premature nature of the debonding failure mode can be observed. Considering the ultimate CFRP strain of 16 × 10 -3 according to the manufacturer, the tested laminates were working at between 30% and 40% of their tensile capacity. As for the concrete, the maximum compressive strain in series II was approximately 50% of the design compressive strain (3.5 × 10 -3 ) [42]. The maximum concrete strain in specimen EBR-I-d10 could not be recorded due to damage in the corresponding SG during the test.
Experimental load versus mid-span deflection and maximum CFRP strain are represented in Figure 7a,b, respectively, along with the theoretical predictions. The theoretical behaviour was calculated considering force equilibrium and strain compatibility in the cross-section. The EC-2 [42] parabola-rectangle diagram for concrete (ε c0 = 2‰ and ε cu = 3.5‰) and a bilinear diagram for steel were considered. The shrinkage effect was taken into account in the calculations through a value of the shrinkage strain of 2.30 × 10 -4 , gathered from the characterisation of the concrete, following the methodology of [42]. The values of the ICD failure load predictions were calculated according to the approaches presented above. As the interest of this study was to compare the theoretical with the experimental results, mean values were considered; therefore, strength reduction factors were not taken into account (γ c = γ s = γ f = γ fb = 1). maximum compressive strain in series II was approximately 50% of the design compressive strain (3.5 × 10 -3 ) [42]. The maximum concrete strain in specimen EBR-I-d10 could not be recorded due to damage in the corresponding SG during the test. Experimental load versus mid-span deflection and maximum CFRP strain are represented in Figure 7a,b, respectively, along with the theoretical predictions. The theoretical behaviour was calculated considering force equilibrium and strain compatibility in the cross-section. The EC-2 [42] parabola-rectangle diagram for concrete (εc0 = 2‰ and εcu = 3.5‰) and a bilinear diagram for steel were considered. The shrinkage effect was taken into account in the calculations through a value of the shrinkage strain of 2.30 × 10 -4 , gathered from the characterisation of the concrete, following the methodology of [42]. The values of the ICD failure load predictions were calculated according to the approaches presented above. As the interest of this study was to compare the theoretical with the experimental results, mean values were considered; therefore, strength reduction factors were not taken into account (γc = γs = γf = γfb = 1). As was expected, all beams followed a trend with three branches defined by the cracking, yielding, and failure loads. The predicted behaviour agreed well with the experimental one. In all specimens, ICD took place after the yielding of the internal tensile steel reinforcement, which is one of the desirable flexural failure modes [1]. Debonding in series I occurred near the theoretical concrete crushing failure load, whereas in series II, the difference between the debonding and theoretical concrete crushing was much higher. This shows that a higher concrete strength, which is the case of the beams in series II, improved the bending capacity of the beam, yet concluded in a higher underutilisation of the CFRP reinforcement. As was expected, all beams followed a trend with three branches defined by the cracking, yielding, and failure loads. The predicted behaviour agreed well with the experimental one. In all specimens, ICD took place after the yielding of the internal tensile steel reinforcement, which is one of the desirable flexural failure modes [1]. Debonding in series I occurred near the theoretical concrete crushing failure load, whereas in series II, the difference between the debonding and theoretical concrete crushing was much higher. This shows that a higher concrete strength, which is the case of the beams in series II, improved the bending capacity of the beam, yet concluded in a higher underutilisation of the CFRP reinforcement.
The values of the CFRP strain at failure were similar among specimens EBR-I-d10 and EBR-II-d10, despite the differences in concrete strength. However, specimen EBR-II-d8, with a lower steel reinforcement ratio but higher concrete strength than EBR-I-d10, achieved a lower maximum value of CFRP strain. This implies that a higher amount of internal tensile steel reinforcement was more effective in terms of the use of FRP reinforcement than a high concrete compressive strength. It should be noted that the experimental CFRP strain in Figure 7b corresponds to the SG that gave the maximum value in each beam, which, due to the nature of crack patterns, was in a different location depending on the specimen. The appearance of cracks in the tensile face of the beam may change the CFRP strain distribution, which inherently implies a certain lack of precision in capturing the maximum value along the laminate.
Experimental failure load and CFRP strain have been compared with the predicted values in Table 4. For this experimental campaign, values of ICD load are well predicted by all approaches, with a mean experimental-to-theoretical ratio between 0.93 and 1.09 and a coefficient of variation (CoV) between 0.03 and 0.08. The variation in the CFRP strain values is higher, probably due to the difficulty of capturing the maximum value as mentioned above. Approaches S1 and MA2 are shown to be the most conservative, with a mean experimental-to-predicted failure load ratio of 1.09. On the other hand, MA1 has been the least conservative approach (0.93), over-predicting the ICD load in terms of average values.
The parameters of the bond law used for the predictions in the different approaches are reported in Table 5. When using [34], higher values of the maximum shear stress and ultimate slip are attained, resulting in a higher fracture energy than in the former. This is the reason why, comparing both simplified approaches, S1 is more conservative than S2. The bonded length is not taken into account in the simplified methods as it is considered that the effective length, and, therefore, the full anchorage capacity, are attained between the point of maximum strain in the CFRP laminate and the support. On the contrary, in MA1, the effective length is compared with the crack spacing, using the most restricting value of both for the calculations. In MA2, the value of the crack spacing is used without considering the effective length. This means that in cases where the crack spacing is lower than the effective length (reducing the anchorage capacity of the CFRP reinforcement according to Equations (3) and (4)), as in beams EBR-I-d10 and EBR-II-d10, the bond strength considered in the accurate approaches is lower than in the simplified ones. However, due to the contribution of the bond friction and beam curvature, MA1 is still less conservative than the simplified approaches. Regarding MA2, as it is devel-oped from a simplification of the detailed model MA1 on the safe side, it gives similar experimental-to-predicted failure load ratios as S1 and S2.

Database
A database of 65 FRP-strengthened RC beams that failed by ICD [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] has been analysed, in addition to the 3 specimens described in the previous section, thus giving a total of 68 specimens. The geometrical and material properties of the beams are listed in Table 6, as well as the debonding failure load (P u,exp ) and bending moment (M u,exp ). The specimens were externally strengthened with bonded CFRP reinforcement; 36 (55%) of them were pre-cured, and 30 (45%) of them were wet laid-up. Most of the beams were tested under three-or four-point bending tests, the most common configuration found in the literature due to the simplicity of the test and the advantage of being able to separate moment and shear failure modes, with the exception of specimens LP4SP1000 and LP8SP1000 [55], which were tested under six-and ten-point bending configurations, respectively. With the purpose of having the same conditions in all specimens in the database, none of them had anchorages.
All beams have rectangular sections with a geometry defined by the distance between supports (L beam ), the shear span (L shear ), the sectional width (b) and total depth (h), the effective depth (d), the tensile and compression steel reinforcement (A s1, A s2 ), and the CFRP width (b f ), thickness (t f ) and type (P for pre-cured and W for wet lay-up).
Concrete properties are given by the mean concrete compressive strength (f cm ) and the mean tensile strength (f ctm ). The values of f cm range between 16.8 MPa and 55.8 MPa. Where f ctm is not defined, it has been computed as specified in the fib Model Code [60] (Equation (23)). Steel properties are given by the yielding strength (f y ) and the elastic modulus (E s ). Where f y and E s were not defined, 500 MPa and 200 MPa have been considered, respectively. CFRP properties are given by the tensile strength (f fu ), the ultimate strain (ε fu ), and the elastic modulus (E s ). According to [1], in cases of wet lay-up systems where the geometrical and material properties of the CFRP sheet were not specifically detailed, only the properties of the fibres in its cross-section have been considered. The properties of the adhesive are not listed as they are not used in the calculations.

Discussion
Predictions based on the models described in the previous section are reported in Table 7 for all beams in the database. The results are presented in terms of failure load (P u,th ) and experimental-to-predicted failure load ratio (P u,exp /P u,th ). Furthermore, the theoretical location of the initiation of debonding (x failure ), as well as the tensile force in the FRP at failure (F fR ) for the simplified methods and the increment of force for the accurate ones (∆F fR ) are also reported in Table 7 as further elements of comparison. The mean values of the ratio P u,exp /P u,th , standard deviation (StDev), and CoV are shown in Table 8. Moreover, theoretical predictions and experimental results are presented in Figure 8. White circles represent theoretical ICD failure, while black triangles represent beams that, theoretically, should have arrived at their rupture load (either concrete or FRP) before ICD.        For the beams in the present database, the values of the ICD load are well predicted by all approaches, with a mean ratio of Pu,exp/Pu,th between 0.96 and 1.10 and a CoV between 0.12 and 0.17. As was also observed in the experimental campaign, MA1 is the least conservative approach in terms of average values (0.96), whereas S2 is the second least conservative one (1.04). The latter, although being a very simple method, presents highly accurate results. The most conservative methods in this study were S1 and MA2, with an For the beams in the present database, the values of the ICD load are well predicted by all approaches, with a mean ratio of P u,exp /P u,th between 0.96 and 1.10 and a CoV between 0.12 and 0.17. As was also observed in the experimental campaign, MA1 is the least conservative approach in terms of average values (0.96), whereas S2 is the second least conservative one (1.04). The latter, although being a very simple method, presents highly accurate results. The most conservative methods in this study were S1 and MA2, with an experimental-to-predicted failure load ratio of 1.09.

Analysis of the Location of Initiation of Debonding
Regarding the location of the theoretical initiation of debonding, for the beams analysed in this study under three-or four-point bending configurations, the maximum values of bending moments and shear forces are located under the load application point. Considering this, jointly with a constant increment of the FRP force along the FRP in the shear span due to a constant shear force, the load application point becomes the critical point in the beam, as it can be observed from the x failure values. For this reason, the ratios between the experimental and predicted failure loads are similar within the different approaches. However, the critical point might be shifted from the central zone to the shear span due to a higher increment of force in the FRP caused by the yielding of the steel. This effect will only be appreciated by the more accurate (or stress increment-based) approaches, which is the reason for the difference in x failure values between those and the simplified approaches.
If a more distributed load is applied (common case in practice), the relationship between the bending moment and the shear force would change. The maximum moment region would be located at the same point, leading to the same predictions when considering the simplified (or strain-based) approaches. However, the shear and increment of the FRP force would not be constant, being lowest at the maximum moment region and highest at the support, leading to higher ICD load predictions according to the more accurate methods. In that scenario, the differences between simplified and more accurate methods would be greater, the simplified approaches being more conservative than the accurate ones, as was also observed in [29].

Analysis of Simplified Methods
Similar to the beams in the experimental campaign, S1 predictions were more conservative than in S2 for the specimens in the database strengthened with pre-cured laminates. The reason for this is that, theoretically, a higher bond fracture energy (G f ) was attained considering the formulation in [34] (used in S2) instead of [33] used in S1. On the contrary, in specimens reinforced with wet lay-up sheets, the fracture energy and ICD predictions in S1 were higher than in S2. By analysing the results, the reason of this fact was found to be the shape factor k b , affecting the bond parameters in the formulation in [34].

Analysis of More Accurate Methods
Analysing the contribution of bond, friction, and curvature in the more accurate methods, it can be observed that in MA1, friction was the least contributing factor in all specimens. Regarding the other components, specimens with high CFRP reinforcement ratios and/or high concrete strength had a high contribution of the bond component but lower curvature contribution, whereas specimens with low values of those properties had the opposite effect. As MA2 is developed from a simplification on the safe side of the MA1 model with calibration factors, this tendency was not that clear.
When one or more of the conditions listed below are met, the predicted failure mode might be concrete crushing (CC) or FRP rupture (FR) instead of ICD, although beams experimentally failed by ICD. As reported in Table 8, this mostly happened when using the MA1 approach, in which only 63% of the specimens theoretically failed by ICD. However, it was observed that the experimental-to-predicted failure load ratios considering the specimens that theoretically failed by CC or FR (case 1 in Table 8) were similar to those not  Table 8). Some possible reasons for this difference in the failure mode prediction could be the following:

•
The similarity of the experimental failure load due to ICD with the predicted ultimate capacity of the beam without considering debonding; • The value of the concrete strain, which may have exceeded the ultimate value of 3.5‰ considered in this study; • The difficulty of finding the exact position of the cracks and the point where failure initiates; • The differences in the experimental and predicted parameters of the bond law; • A combination of these with other factors such as concrete strength, steel, and CFRP reinforcement ratio and the geometry of the beam.

Conclusions
In the present study, the formulation published in the fib Bulletin 90 [1] regarding the intermediate crack debonding (ICD) has been assessed through comparison with a database of 68 RC beams strengthened with EB CFRP. Moreover, an experimental campaign of three beams tested under a four-point bending configuration was carried out to have a better understanding of the ICD failure mode, as well as to be able to compare the results with the theoretical predictions in more detail. Based on these results, the following conclusions can be drawn:

•
In all specimens, ICD took place after the yielding of the internal tensile steel reinforcement, corresponding to the desirable flexural failure modes. The results showed that a higher concrete strength improved the bending capacity of the beam (series II-44.8 MPa vs. series I-23.9 MPa), yet it was much lower than the theoretical prediction in the absence of debonding. Likewise, a higher amount of steel reinforcement led to a higher bending capacity with similar CFRP strains at failure; • The values of the ICD load were well predicted by all approaches, with a mean experimental-to-predicted failure load ratio between 0.96 and 1.09 and a CoV between 0.12 and 0.17; • Predictions more similar to the experimental results were obtained with the more accurate method MA1 (0.96) approach in comparison with the MA2 (1.09) and simplified methods S1 (1.09) and S2 (1.04), although with more computational effort. However, for the beams in the database following the usual test configurations with a three-or four-point bending configuration, the differences between the methods were low; • The value of the bond fracture energy affects the ICD load. For this database, the formulations used in S2 considering the shape factor kb were slightly more accurate predictions than S1.  Data Availability Statement: The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.