Experimental and nonlinear finite element studies of RC beams strengthened with FRP plates

Abstract

This paper presents a joint experimental–analytical investigation aimed at studying the brittle failure modes of RC members strengthened in flexure by FRP plates. Both midspan and plate end failure modes are studied. The finite element analyses are based on nonlinear fracture mechanics. The model considered the actual crack pattern observed in the tests by using a smeared and an interface crack model. This paper shows how concrete cracking, adhesive behavior, plate length, width and stiffness affect the failure mechanisms. The numerical and experimental results show that debonding and concrete cover splitting failure modes occur always by crack propagation inside the concrete.

Introduction

Gluing fiber reinforced polymers plates or sheets to the soffit of RC members is by now a well-established technique used to strengthen reinforced concrete (RC) members in flexure. Several experimental studies [1], [2], [3], [4], [5], [6], [7], [8] have indicated that bonding FRP plates or sheets to the soffit of RC members is a very effective technique to enhance the ultimate load capacity of RC members. However, experimental tests have also shown that strengthened RC members lose ductility due to the application of externally bonded FRP (EB-FRP) reinforcement. The possible failure mechanisms observed in experimental tests are summarized in Fig. 1. Failure modes RC1 and RC2 are similar to those observed in unstrengthened RC structures and can be predicted with standard methodologies [4], [9]. If the FRP is well anchored and the ultimate flexural capacity is reached, the strengthened RC member fails by concrete crushing (RC1 in Fig. 1). When the shear demand exceeds the shear capacity of the strengthened RC member in the shear span, the beam fails in shear in the shear span (RC2 in Fig. 1).

The other failures depicted in Fig. 1 are caused by the application of the FRP reinforcement. If the composite tensile stress reaches the ultimate strength, the FRP fails in tension (FRP^r in Fig. 1). Alternatively, the bond between the FRP and the concrete may fail due to the formation of cracks that may initiate in different places at the FRP-to-concrete interface [9]: inside the resin, at the interface between the concrete and the adhesive or at the interface between the adhesive and the FRP, inside the FRP or within the concrete cover. The interface between the concrete and the adhesive fails because of lack of surface preparation. The adhesive may reach its ultimate strength if not designed adequately. The above two failure modes can be predicted and avoided by following a proper design and ensuring a good preparation of the gluing surface.

End plate plastic hinge failure (P^end in Fig. 1) was observed by Seim et al. [7], it is not common and can occur if the FRP glued to the RC member is very short. In this case, steel yielding progresses towards the composite plate end and into the non-strengthened zone. A crack forms at the plate end, followed by the formation of a plastic hinge. As the applied load increases, flexural-shear failure is observed without separation between the composite and the concrete. This failure mode shows a pseudo-ductile behavior. After reaching the ultimate load the strengthened slab follows a yield plateau, similarly to a traditional one way reinforced RC member.

The most common failures of EB-FRP RC structures strengthened in flexure occur within the concrete cover (failures labeled Cc in Fig. 1) either near the interface between the adhesive and the concrete or along a plane immediately below the steel reinforcement. This failure type has been observed in a number of tests [6], [7], [10] and numerical studies [10], [11]. The corresponding failure mechanisms are abrupt, brittle and complex to predict. They can be classified into three categories depending on where they initiate: near midspan, within the shear span or at the plate end.

Close to midspan the strengthened members can fail within the concrete cover because of either concrete debonding or concrete cover splitting, ${\mathrm{Cc}}_1^{\mathrm{mid}}$ and ${\mathrm{Cc}}_2^{\mathrm{mid}}$, respectively, in Fig. 1. Midspan debonding and midspan concrete cover splitting are triggered by different mechanisms. Midspan debonding starts near the region of maximum moment and usually propagates towards the nearest plate end [10]. It is caused by high interface stresses induced by the opening of a major crack. Midspan concrete cover splitting is caused by a combination of diagonal and flexural cracks. Past experimental results have shown that, prior to failure, shear cracks develop at the toes of the flexural cracks due to high shear stresses. Sebastian [12] shows that these inclined cracks cause localized bending of the plate. The localized bending pulls the concrete causing the formation of a horizontal crack, which triggers the failure in the concrete cover along a plane below and parallel to the steel reinforcement.

In the shear span, the strengthened RC member can fail because of FRP plate debonding starting from an intermediate shear crack (${\mathrm{Cc}}_3^{\mathrm{sp}}$ in Fig. 1). In this case, an intermediate shear crack induces a relative vertical displacement between the two faces and produces peeling stresses. These peeling stresses, in combination with the high shear stresses caused by the crack opening, trigger failure. According to Teng et al. [10], however, the opening of the crack has a predominant effect compared to the vertical relative displacement of the two crack faces. For this reason, this mechanism can be very similar to midspan debonding.

At the plate end, the beam can fail by either end concrete cover splitting or end debonding, ${\mathrm{Cc}}_4^{\mathrm{end}}$ and ${\mathrm{Cc}}_5^{\mathrm{end}}$, respectively, in Fig. 1. End concrete cover splitting is a complex phenomenon and is still not well understood. It starts at the end of the plate and propagates toward midspan in a RC member. The failure is initiated by a combination of shear and normal stress concentrations near the plate cut-off end, as shown in ${\mathrm{Cc}}_4^{\mathrm{end}}$ in Fig. 2. The failure starts at the plate end in mode I and propagates because of a combination of modes I and II. Whether the failure propagates along a plane immediately below the reinforcing steel bars (concrete cover splitting) or near the interface between the glue and the concrete (debonding) appears to be related to material properties and to the RC beam and the EB-FRP geometry. These parameters influence the crack pattern and in particular the distance between the cracks at the plate end shown in Fig. 2. The available bond length at the plate end, L_bond, is given by the smaller between the critical bond length [9], b_d, and the distance between the two cracks at the plate end. Increasing the distance between two adjacent cracks at the plate end leads to an increase in the bond length, as shown in Fig. 2. For the longer bond length, the mode II contribution to the mixed mode I/II crack is larger [13]. This is the case of end debonding in which the spacing of the crack at the end of the FRP plate is larger than the bond length, as shown in ${\mathrm{Cc}}_4^{\mathrm{end}}$ in Fig. 2. Therefore, although end debonding starts in mode I, it develops predominantly in mode II. However, mode I crack opening is responsible for crack initiation. Hence, a correct description of the end failures must account for an accurate crack pattern and the contribution of both modes I and II.

This paper presents a joint experimental–analytical investigation carried out at the University of Ljubljana, at the University of Colorado at Boulder and at the University of Chieti-Pescara to study the mid span failure modes of RC members strengthened in flexure by FRP plates. The experimental tests carried out at the University of Ljubliana are accompanied by a series of FE analyses based on NLFM. The model considers the actual crack pattern observed in the tests. The FEM uses both discrete and smeared crack discretization, because only a combination of the two crack model accurately traces the stiffness degradation of the strengthened members, as already discussed in Camata et al. [13]. The smeared crack model was used for the beam concrete; the discrete crack model was used for the interfaces where delamination can be expected. Because the tests performed at the University of Ljubljana showed only midspan debonding failure modes, end concrete cover splitting is also considered by analyzing three tests performed by Dong et al. [8].