7.1 FAILURE DUE TO DEBONDING
The main failure modes of FRP-strengthened structural members due to debonding are summarized as follows:
•
Mode 1 (plate end debonding) (Figure 7-1). The end portions of the FRP system are sub- jected to high interfacial shear stresses for a length of approximately 100-200 mm.RC beam
direction of delamination
delamination at laminate end
laminate
Figure 7-1 – Plate end debonding.
•
When strengthening is carried out with FRP laminates, tensile stress perpendicular to the in- terface between FRP and support (normal stress) may arise due to the significant stiffness of FRP laminate (Figure 7-2(a)). Such a normal stress may reduce the value of interfacial shear stress as shown in Figure 7-2(b). Failure mode by end debonding is characterized by brittle behavior.(a) (b)
Figure 7-2 – (a) Interfacial shear and normal stress
along the length of a bonded FRP laminate (linear-elastic analysis); (b) Strength domain represented by interfacial shear and normal stresses.
•
Mode 2 (Debonding by flexural cracks in the beam) (Figure 7-3). Flexural cracking gener- ates discontinuity within the support that enhances interfacial shear stress responsible for FRP debonding. Cracking may be oriented perpendicular to the beam axis when flexural FRP cut-off sectionInterfacial shear stress
loads are predominant; inclined when there is a combination of flexure and shear.
Figure 7-3 - Debonding starting from vertical cracks in concrete.
• Mode 3 (Debonding by diagonal shear cracks) (Figure 7-4). For members where shear stresses are predominant compared to flexural stresses, a relative displacement between the edges of the crack is displayed. Such displacement increases normal stress perpendicular to the FRP laminate responsible for FRP debonding. Such a debonding mechanism is active irrespectively of the presence of stirrups. Collapse due to debonding by diagonal shear cracks is peculiar of four-point-bending laboratory tests; it is not common for field applica- tion where the applied load is distributed over the beam’s length. For heavily strengthened beams with low transverse reinforcement, debonding usually generates at the end plate sec- tion due to peeling.
Figure 7-4 – Debonding by diagonal shear crack.
•
Mode 4 (Debonding by irregularities and roughness of the concrete surface). Localized debonding due to surface irregularities of the concrete substrate may propagate and cause full debonding of the FRP system. This failure mode can be avoided if the concrete surface is treated in such a way to avoid excessive roughness.7.2 BOND BETWEEN FRP AND CONCRETE
In the following, additional recommendations related to bond between FRP and concrete support are given. Reference is made to Figure 7-5; symbols are those introduced in Section 4.1.
lb≥ le
b bf
tf Fmax
Figure 7-5 – Maximum force allowed to FRP reinforcement.
7.2.1 Specific fracture energy
When the stiffness of the concrete support is much greater compared to the stiffness of the FRP sys- tem, the following relationship applies:
max f 2 f f F
F = ⋅b ⋅E t⋅ ⋅Γ (7.1)
between the maximum force, Fmax, allowed to the FRP reinforcement considered of infinite length and the fracture energy, Γf, assuming:
max f b 0 ( ) F b τ x dx ∞ =
∫
, F b 0 ( )s ds Γ τ ∞ =∫
(7.2)where tf, bf , Ef represent FRP thickness, width, and Young modulus of elasticity in the direction of the applied force, respectively.
The fracture energy depends on the strength properties of both concrete and adhesive, as well as on the characteristics of the concrete surface. For properly installed FRP systems, failure by debonding takes place on the concrete support and the specific fracture energy may be written in a similar fash- ion to that used for failure mode 1 of the concrete:
ctm ck b G F k k f f Γ = ⋅ ⋅ ⋅ [force in N, length in mm] (7.3)
where the coefficient k shall be experimentally adjusted. The value of such coefficient has been G
computed over a large population of experimental results available in the literature. The statistical analysis of the results has provided an average value equal to 0.064, a standard deviation equal to 0.023, and a 5th percentile of the statistical distribution equal to 0.026. When the latter value is used in Eq. (7.3), the characteristic value, ΓFk, of the specific fracture energy is obtained. On the basis of this consideration, this Guideline suggest adopting the value of 0.03 for k . G
7.2.2 Bond-slip law
Bond between FRP and concrete is typically expressed with a relationship between interfacial shear stress and the corresponding slip (“τb−s“ relationship). Both FRP and concrete mechanical char- acteristics as well as geometry of the FRP system and concrete support shall be considered in the analysis.
The τb−s relationship is typically non linear with a descending branch; for design purposes, it may be treated as a bi-linear relationship as shown in Figure 7-6. The first ascending branch is defined by taking into account the deformability of adhesive layer and concrete support for an appropriate depth. Unless a more detailed analysis is performed, the average mechanical parameters defining the τb−s relationship, can be evaluated as follows:
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.00 0.05 0.10 0.15 0.20 s [mm] τb [N/mm 2 ] arctg K1 fb
Figure 7-6 – Bi-linear “τb−s“ relationship ( fck =20 MPa, kb =1).
- Maximum bond strength, fb:
The maximum experimental average bond strength can be expressed as follows: ctm
ck b
b 0.064 k f f
f = ⋅ ⋅ ⋅ [force in N, length in mm] (7.4)
where f and ck fctm represent the concrete characteristic compressive strength and the average con- crete tensile strength, respectively; and the geometrical factor k can be written as follows: b
f b f 2 1 1 400 b b k b − = ≥ + [length in mm] (7.5)
where b and bf represent beam and FRP width, respectively. Equation (7.5) is valid when
33 . 0
f b≥
b (when bf b<0.33 the value corresponding to bf b=0.33 shall be adopted for k ). b
- Slope, K1, of the ascending branch:
1 1 a a c c c K t G t G = + (7.6)
where G , a G represent shear modules of adhesive and concrete, respectively; c t is the nominal a
thickness of the adhesive; and t is the effective depth of concrete (suggested values for tc c and c1
- Interface slip corresponding to full debonding, sf :
f 0.2 mm
s = (7.7)
This value of s ensures the specific fracture energy, f Γf, (represented by the area subtended the “τb−s“ relationship) is equal to the value reported in Equation (7.3). At SLS, the “τb−s“ rela- tionship reduces to the ascending branch only and K1 is given by Equation (7.6) for c1=1.
7.3 SIMPLIFIED METHOD FOR DEBONDING DUE TO FLEXURAL CRACKS (MODE 2) AT ULTIMATE LIMIT STATE
As an alternative to the general method reported at item 1(P) of Section 4.1.4, this simplified method is based on the definition of the maximum design strain, εfdd, for FRP reinforcement to be evaluated with Equation (4.7), hereafter reported for the sake of completeness:
fdd Fk fdd cr cr f f d c f f 2 1 , f k k E E t Γ ε γ γ ⋅ = ⋅ = ⋅ ⋅ ⋅ ⋅ (7.8)
This relationship is similar to that proposed for maximum stress or strain in FRP reinforcement when mode 1 FRP debonding controls. However, for a constant applied force, the maximum inter- facial shear stresses are significantly smaller compared to that achieved close to the end of the FRP itself due to the reduced distance between cracks. This implies that the value of maximum FRP strain related to failure mode 2 is greater than that pertaining to failure mode 1. These considera- tions have suggested adopting a magnifying coefficient kcr >1 for Equation (4.7).
The calibration of kcr has been carried out on reinforced concrete beams strengthened with FRP
laminates or fabrics failed by FRP intermediate debonding (mode 2). The statistical analysis of the results has provided an average value equal to 4.289, a standard deviation of 0.743, and a 5th per- centile value equal to 3.070. Given the limited scattering exhibited by the application of Equation (4.6) and considering the lower brittleness of FRP intermediate debonding compared to FRP end debonding, it is suggested to use Equation (4.6) for the evaluation of the design strain, assuming
cr