A fracture-based model for FRP debonding in strengthened beams

This paper presents an experimental and analytical research study aimed at understanding and modeling of debonding failures in fiber reinforced polymer (FRP) strengthened reinforced concrete (RC) beams. The experimental program investigated debonding failure modes and mechanisms in beams strengthened in shear and/or flexure and tested under monotonic loading. A newly developed fracture mechanics based model considers the global energy balance of the system and predicts the FRP debonding failure load by characterizing the dominant mechanisms of energy dissipation during debonding. Validation of the model is performed using experimental data from several independent research studies and a design procedure is outlined.     

Numerical simulation of rebar/concrete interface debonding of FRP strengthened RC beams under fatigue load

The aim of this paper is to simulate the rebar/concrete interface debonding of FRP strengthened RC beams under fatigue load and also, to ascertain the influence of design parameters such as the elastic modulus, thickness and length of the FRP plate on the debonding performance. In order to simplify the simulation, some basic equilibrium equations are formulated and then the stresses of the rebar and FRP plate are numerically solved, and stress intensity factor is avoided in the simulation by fundamentals of fracture mechanics because of its complexity around the crack tip of bi-material interface. With the combination of finite element method and difference approximation, authors program the degradation model of coefficient of friction, debond criterion, propagation law and loop of load process into a commercial finite element code to investigate the fatigue debonding. The relationships between the debond length as well as other fatigue parameters and number of cyclic load are obtained and discussed.     

Viscoelastic analysis of FRP strengthened reinforced concrete beams

External bonding of FRP plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP-concrete interface are critical to the effectiveness of this technique because high stress concentration along the FRP-concrete interface can lead to the FRP debonding from the concrete beam. Although the short-term stress distribution along the FRP-concrete interface has been studied extensively, very few studies have been conducted on the long-term stress distribution, which closely simulates the behavior of the structure during the service-life. In this study, we develop a viscoelastic solution for the long-term interface stress distribution in a FRP plate strengthened reinforced concrete beam. In this solution, the RC beam and the FRP plate are modeled as elastic materials; while the adhesive layer is modeled as a viscoelastic material using the Standard Linear Solid model. Closed-form expressions of the interface stresses and deflection of the beam are obtained using Laplace transform and calculated using the Zakian’s numerical method. The validation of this viscoelastic solution is verified by finite element analysis using a subroutine UMAT based on the Standard Linear Solid model.     

Performance of reinforced concrete beams strengthened by hybrid FRP laminates

In the last two decades, the use of advanced composite materials such as Fiber Reinforced Polymers (FRP) in strengthening reinforced concrete (RC) structural elements has been increasing. Research and design guidelines concluded that externally bonded FRP could increase the capacity of RC elements efficiently. However, the linear stress–strain characteristics of FRP up to failure and lack of yield plateau have a negative impact on the overall ductility of the strengthened RC elements. Use of hybrid FRP laminates, which consist of a combination of either carbon and glass fibers, or glass and aramid fibers, changes the behaviour of the material to a non-linear behaviour. This paper aims to study the performance of reinforced concrete beams strengthened by hybrid FRP laminates.

This paper presents an experimental program conducted to study the behaviour of RC beams strengthened with hybrid fiber reinforced polymer (HFRP) laminates. The program consists of a total of twelve T-beams with overall dimensions equal to 460 × 300 × 3250 mm. The beams were tested under cyclic loading up to failure to examine its flexural behaviour. Different reinforcement ratios, fiber directions, locations and combinations of carbon fiber reinforced polymer (CFRP) and glass fiber reinforced polymer (GFRP) laminates were attached to the beams to determine the best strengthening scheme. Different percentages of steel reinforcement were also used. An analytical model based on the stress–strain characteristics of concrete, steel and FRP was adopted. Recommendations and design guidelines of RC beams strengthened by FRP and HFRP laminates are introduced.     

Sensitivity analysis of reinforced concrete beams strengthened with FRP laminates

Numerical procedures are proposed to predict the failure of reinforced concrete (RC) beams strengthened in flexure with fiber-reinforced polymeric (FRP) laminates. The framework of damage mechanics was used during the modeling. Numerical results were validated against experimental data obtained from 19 beams strengthened with different types of FRP. These beams failed by concrete crushing, cover failure and plate debonding. The numerical models were capable of predicting the experimentally observed load–deflection, failure load and failure modes. The sensitivity of the numerical results was studied. In particular, the effect of the concrete constitutive behavior and different modeling considerations was evaluated. It was found that the fracture energy of the concrete–repair interface plays a central part in predicting plate-debonding failures.     

Diagonal macro-crack induced debonding mechanisms in FRP rehabilitated concrete

The effectiveness of externally bonded fiber reinforced polymer (FRP) composites to strengthen concrete components depends intrinsically on bond and transfer related aspects. Premature debonding, initiated from ends or from cracks in the concrete, often limits potential performance gains. While end initiated debonding and peeling mechanisms have been researched extensively, crack initiated debonding has not been studied to the same extent. This paper investigates mechanisms associated with diagonal cracks and models debonding initiation and propagation through a fracture mechanics based finite element approach. It is seen that debonding propagation is mainly caused by mode II fracture mechanisms and that the interfacial failure path is primarily governed by relationships between concrete cracking behavior and interfacial properties.     

Shear enhancement of reinforced concrete beams strengthened with FRP composite laminates

This paper presents the results of an experimental investigation on shear strength enhancement of reinforced concrete beams externally reinforced with fiber-reinforced polymer (FRP) composites. A total of nine full-scale beam specimens of three different classes, as-built (unstrengthened), repaired and retrofitted were tested in the experimental evaluation program. Three composite systems namely carbon/epoxy wet layup, E-glass/epoxy wet layup and carbon/epoxy precured strips were used for retrofit and repair evaluation. Experimental results indicated that the composite systems provided substantial increase in ultimate strength of repaired and strengthened beams as compared to the pre-cracked and as-built beam specimens. A comparative study of the experimental results with published analytical models, including the ACI 440 model, was also conducted in order to evaluate the different analytical models and identify the influencing factors on the shear behavior of FRP strengthened reinforced concrete beams. Comparison indicated that the shear span-to-depth ratio (a/d) is an important factor that actively controls the shear failure mode of beam and consequently influences on the shear strength enhancement.     

Static strength tests of steel plate strengthened concrete beams

The behaviour of damaged concrete beams strengthened by externally bonded steel plates is experimentally investigated. The study includes an investigation of the mode of failure, including flexural failure and the interface separation of the steel plate. Simply supported beams under monotonically increasing loads are considered exclusively. A total of five plain concrete beams externally reinforced with bonded steel plates were tested under static loads to determine their strength and behaviour. The variables tested were the thickness of the external steel plate, length and location of the interfacial crack, and the degree of surface preparation of the steel plate. In all five beams the thickness of adhesive was kept constant. The results indicate that (i) the behaviour of a damaged open sandwich beam is similar to that of a singly reinforced concrete beam when no debonding occurs between the concrete and the adherent steel plate; (ii) when debonding occurs, the failure is sudden and at loads smaller than for a case where failure is either by yielding of steel or crushing of concrete; (iii) the case with an interfacial crack between the steel and the adhesive is more critical than the case when the interfacial crack is between the adhesive and the concrete; and (iv) the failure load and the mode of failure are dependent on the degree of surface preparation of the steel plate. Analytical investigation to predict the interfacial debonding is summarized, and the results suggest that linear elastic fracture mechanics is suited for predicting the failure load for open sandwich beams which fail by interface debonding.     

Modeling of crack propagation in strengthened concrete disks

Crack propagation in strengthened concrete disks is a problem that has not yet been addressed properly. To investigate it, a cracked half-infinite disk of concrete is strengthened with a linear elastic material bonded to the surface, and analyzed using two different finite element modeling approaches. The first method is 3D modeling of strengthening, interface and disk, and the second method is modeling of an equivalent disk in 2D, with an effective cohesive crack, equivalent thickness and equivalent stiffness. The 2D modeling approach simplifies modeling of the problem significantly and reduces the computational efforts and time. A good prediction of the cracking response, global response and load was obtained with the 2D model, whereas prediction of the size and shape of the interface debond was only approximate. It is concluded that the effective cohesive modeling approach can be used instead of 3D calculations to predict the response of a structure and that it opens up for simpler evaluation of strengthened concrete structures using the finite element method.     

Prediction of intermediate crack debonding failure in FRP-strengthened reinforced concrete beams

The present paper addresses with intermediate crack (IC) debonding failure modes in FRP-strengthened reinforced concrete beams; a non-linear local deformation model, derived from a cracking analysis based on slip and bond stress, is adopted to predict the stresses and strains distribution at failure. Local bond-slip laws at the longitudinal steel-to-concrete and FRP-to-concrete interfaces, as well as the tension stiffening effect of the reinforcement (steel and FRP) to the concrete, are considered. Model predictions are compared to experimental results available in the literature together with predictions of other models. Reasonable agreement with experimentally measured IC debonding loads and FRP strains is observed for all examined strengthened beams. Results of a parametric analysis, varying geometrical and mechanical parameters involved in the physical problem are also presented and discussed.     

Failure diagrams of FRP strengthened RC beams

Amongst various methods developed for strengthening and rehabilitation of reinforced concrete (RC) beams, external bonding of fibre reinforced plastic (FRP) strips to the beam has been widely accepted as an effective and convenient method. The experimental research on FRP strengthened RC beams has shown five most common modes, including (i) rupture of FRP strips; (ii) compression failure after yielding of steel; (iii) compression failure before yielding of steel; (iv) delamination of FRP strips due to crack; and (v) concrete cover separation. In this paper, a failure diagram is established to show the relationship and the transfer tendency among different failure modes for RC beams strengthened with FRP strips, and how failure modes change with FRP thickness and the distance from the end of FRP strips to the support. The idea behind the failure diagram is that the failure mode associated with the lowest strain in FRP or concrete by comparison is mostly likely to occur. The predictions based on the present failure diagram are compared to 33 experimental data from the literature and good agreement on failure mode and ultimate load has been obtained. Some discussion and recommendation for practical design are given.     

Modeling of flexural behavior of RC beams strengthened with mechanically fastened FRP strips

An alternative to fiber reinforced polymer (FRP) materials adhesively bonded to the concrete substrate is the implementation of mechanically fastened FRP (MF-FRP) systems using steel anchors to secure the laminate to the substrate. The benefit of MF-FRP, compared to adhesive bonding for FRP flexural strengthening, is the speed of installation with unskilled labor, minimal or absent surface preparation under any meteorological condition and immediate use of the strengthened structures. 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. In this paper, an analytical model is discussed for reinforced concrete (RC) members strengthened with MF-FRP strips. The model accounts for equilibrium, compatibility and constitutive relationships of the constituent materials; in particular, it accounts explicitly for the slip between the substrate surface and the FRP strip due to the behavior of the fasteners. The proposed flexural model, coupled with the computation algorithm, is able to predict the fundamentals of the behavior of RC flexural members strengthened with MF-FRP strips, in terms of both ultimate and serviceability limit states. Comparisons between the analytical predictions and the experimental results have been successfully performed.     

Modelling of mixed mode debonding in externally FRP reinforced beams

In this paper a refined model able to analyze edge debonding problems in beams strengthened with externally bonded composite laminated plates, is presented. The structural system is viewed as composed by three physical different components: the base beam (made of steel or concrete), the adhesive layer and the bonded plate. Each component may be comprised by one or several mathematical layers which adopts the first-order shear deformation laminate theory. Bonding and continuity conditions between different layers are simulated by using the interface modelling technique. Strong and collapsed interface models are introduced in order to capture stress singularities and to reduce the complexity of the analysis, respectively. Governing equations for displacement fields complemented with boundary and continuity conditions, are obtained by a variational approach. According to a fracture mechanics approach, the analysis is carried out by evaluating the total and individual mode components of energy release rate (ERR).Applications for typical strengthened systems, carried out by numerical integration procedures, are proposed in which the energy release rates are evaluated by means of interface displacement jumps, leading to a very efficient numerical procedure. The approximations introduced in the model with respect to the adopted number of mathematical layers are analyzed and comparisons with existent models are given. For the simpler two-layer model of the structure, comparisons are given with the closed-form solutions obtained in [Greco F, Nevone Blasi P, Lonetti P. An analytical investigation of debonding problems in beams strengthened using composite plates. Eng Fract Mech 2006, in press]. The convergence to the results from continuum analysis is investigated when a refined assembly of layers is adopted, by means of comparisons with predictions from very careful FE solutions. Finally, the effect of different debonding modes on the overall behaviour of the structural system is analyzed. These results show the capability and the accuracy of the proposed approach to predict debonding failure behaviour in both steel and concrete strengthened beams. As a matter of fact, the proposed approach involves reduced computational cost with respect to FE solutions based on 2D continuum elements and the use of a multi-layer structural model leads to avoid some complexities related to the classical elasticity theory for bimaterial interface cracks.     

Experimental investigation on fire endurance of insulated concrete beams strengthened with near surface mounted FRP bar reinforcement

Fiber reinforced polymer (FRP) composites are known to be susceptible to deterioration at elevated temperature. To evaluate the feasibility of achieving a fire-rated FRP system an investigation was undertaken to examine and document the performance of near surface mounted (NSM) FRP strengthened concrete beams under fire conditions. Twelve reinforced concrete beams were strengthened in flexure with NSM FRP bars and insulated with different insulation systems. The specimens were subsequently exposed to a standard fire while subjected to full service load. Tests results on fire indicated that insulated NSM FRP strengthened beams can achieve a fire endurance of at least 2 h. Moreover structural testing to failure at room temperature of the fire testes beams has shown that well insulated members are able to retain (part of) their original strengthened flexural capacity.     

Comparison of numerical behaviors of FRP reinforced concrete beams using three smeared crack models

The numerical behaviors of fiber reinforced polymer (FRP) bar reinforced concrete beams using three non-linear finite element models are compared with the recorded data. First approach is based on strain decomposition into elastic and crack strain and is capable of simulating multiple non-orthogonal cracks. The remaining two approaches are based on the total strain crack model and include a rotating crack model (RCM) and an orthogonal fixed crack model (FCM). The analysis is carried out with the help of 2D-isoparametric plane-stress elements. Compression softening and tension stiffening effects of cracked concrete are considered. Tension reinforcement consists of either steel or FRP bars. The accuracy of the models has been discussed with reference to the authors?? tests as well as various studies reported in the literature. Both RCM and orthogonal FCM models showed good agreement with the recorded data which was also found consistent with every type of FRP bar.     

CFRP-PCPs复合筋嵌入加固钢筋混凝土梁裂缝试验及计算方法研究

通过5根嵌入不同张拉控制应力的碳纤维增强塑料预应力混凝土棱柱体(CFRP-PCPs)复合筋加固钢筋混凝土梁受弯试验,对比分析试验梁的裂缝分布与发展,得到最大裂缝宽度与平均裂缝宽度在静力荷载作用下的变化特性。结果表明: 嵌入CFRP-PCPs复合筋能有效的减少被加固钢筋混凝土梁的裂缝宽度和高度。在试验基础上,根据国家现行混凝土规范,对平均裂缝间距和最大裂缝宽度计算公式进行参数修正,建立了CFRP-PCPs复合筋嵌入加固钢筋混凝土梁最大裂缝宽度计算公式,计算值与试验值吻合较好。     

Modeling of composite/concrete interface of RC beams strengthened with composite laminates

In this paper a finite element model for predicting shear and normal stresses in the adhesive layer of plated reinforced concrete beams has been developed. The numerical results carried out agree with those obtained in previous studies by other authors. It is found that shear stresses and high concentrations of peeling forces are present at the ends of the plates when the composite beam is loaded in flexure. These concentrations can produce premature failure of the strengthened beam because of debonding of the plate or cracking of the concrete cover along the level of internal steel reinforcement. The numerical simulation captures the actual interfacial stresses and, in particular, the maximum values of shear and normal stresses.     

Flexural behaviour of strengthened reinforced concrete beams

A large experimental research programme has investigated the flexural strength of simply supported reinforced concrete beams. The beams were first damaged so that they could be strengthened by means of jackets (cast-in-place shotcrete or pre-packed special mortar plus additional new reinforcement). This paper analyses the flexural strength of these beams. The behaviour in service and ultimate state as well as the bond characteristics are studied.

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Résumé Au cours d'un vaste programme expérimental, on a étudié la résistance en flexion de poutres en béton armé à appui simple. Ces poutres ont d'abord été endommagées, pour ensuite être renforcées par du béton projeté ou par du mortier spécial préconditionné, avec l'adjonction de nouvelles armatures. Cet article discute de la résistance en flexion de ces poutres. Le comportement en service et à l'état limite ultime, ainsi que les caractéristiques d'adhérence, sont étudiés.

     

Reinforcement delamination of metallic beams strengthened by FRP strips: Fracture mechanics based approach

The delamination failure of metallic beams reinforced by externally bonded fibres reinforced polymers (FRP) is addressed in this paper and a simplified fracture mechanics based approach for the edge delamination of the reinforcement strips is illustrated. The criterion is based on the evaluation of the energy release rate (ERR) using both analytical and numerical models. The analytical models consist of a simplified version of a “two parameters elastic foundation” and “transformed section” model while the numerical analyses refer to the modified virtual crack closure technique (MVCCT). The main aim of the paper is to establish a fracture mechanics failure criterion based on the ERR and the specific fracture energy of the bonded strips. The criterion is an alternative approach to the well known stress based method to asses the load carrying capacity of the adhesive joint. The accuracy of the simplified approaches is shown through a numerical example which refers to a steel beam strengthened by carbon fibres reinforced polymers (CFRP).     

Flexural performance of FRP reinforced concrete beams

A numerical method for estimating the curvature, deflection and moment capacity of FRP reinforced concrete beams is developed. Force equilibrium and strain compatibility equations for a beam section divided into a number of segments are numerically solved due to the non-linear behaviour of concrete. The deflection is then obtained from the flexural rigidity at mid-span section using the deflection formula for various load cases. A proposed modification to the mid-span flexural rigidity is also introduced to account for the experimentally observed wide cracks over the intermediate support of continuous FRP reinforced concrete beams.