Interface stress redistribution in FRP-strengthened reinforced concrete beams using a three-parameter viscoelastic foundation model

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. In this study, a novel analytical solution has been developed to predict the interface stress redistribution of FRP-strengthened reinforced concrete beams induced by the viscoelastic adhesive layer. Both the FRP plate and the RC beam are modeled as Timoshenko’s beams, connected through the adhesive layer. The adhesive layer is modeled as a three-parameter viscoelastic foundation (3PVF) using Standard Linear Solid model. The 3PVF model satisfies the equilibrium equation of the adhesive layer and the zero shear-stress boundary condition at the free edge. Closed-form expressions of the time-dependent interface stresses and deflection of the beam are obtained using Laplace transform. Finite element analysis is also conducted to verify the analytical solution using a subroutine UMAT based on the Standard Linear Solid model. Numerical results suggest that the stress concentrations within the FRP–concrete interface relax with time. The axial force in the FRP plate also reduces with time due to the creep of the adhesive layer. However, this relaxation is limited to a small zone close to the end of the FPR plate.     

Interfacial shear stress in FRP-plated RC beams under symmetric loads

A recently popular method for retrofitting reinforced concrete (RC) beams is to bond fibre-reinforced polymer (FRP) plates to their soffits. An important failure mode of such plated beams is debonding of the FRP plates from the concrete due to high level interfacial stresses near the plate ends. A closed-form rigorous solution for the interfacial stresses in simply supported beams bonded with thin plates and subjected to arbitrary loads has been found, in which a non-uniform stress distribution in the adhesive layer was taken into account. This paper uses the rigorous solution to investigate the impact of symmetric loading configurations on the interfacial shear stress distributions, and concludes that the bending moments on the cross sections at the plate ends play a significant role in terms of stress concentration, while the shear forces on the same cross-section contribute little to the concentration. On the basis of this observation, this paper proposes a simplified approximate solution to the shear stress along the interface between concrete and adhesive layer. Compared with the rigorous and other approximate solutions, the simplified solution exhibits sufficient accuracy in terms of stress distribution and stress concentration localized near the plate ends. Due to its compact feature, the simplified solution is more suitable for engineering applications using a portable calculator and to be adopted in the codes of practices.     

Stress–strain and deflection relationships of RC beam bonded with FRPs under sustained load

Fiber-reinforced polymer (FRP) systems that have a strong resistance against long-term deformation must provide improved serviceability to reinforced concrete (RC) members under sustained loads. Consequently, there is a need to develop a method for accurately predicting the time-dependent behavior of RC beams that are externally bonded with FRPs. However, there are very few previous studies that have been carried out or experimental results available, on the time-dependent behavior of RC beams externally bonded with FRP. In order to enable a reasonable prediction, correlations should first be clarified between the stress–strain relationship of the concrete, the reinforcement and the FRP that changes over time. By using these correlations, deflections under sustained loads should then be forecast. In this study, RC beams were fabricated for this purpose. Carbon reinforced polymer (CFRP) and glass reinforced polymer (GFRP) materials were bonded to the tension face of the two respective RC beams. The beams were then placed under sustained loads for 300 days. For the specimens that were externally bonded with FRPs and for the conventional specimen, the strain of the compression and tension reinforcement and the strain of FRP and deflection were measured respectively for comparison. In order to theoretically predict the time-dependent behavior of the RC Beam externally bonded with FRPs, creep coefficients for concrete and shrinkage strains were calculated by using the CEB-FIP and the ACI-209 Codes. For the method used to forecast the stress–strain relationships of the concrete, reinforcement and FRPs that change over time were theoretically clarified and were then compared with the experimental results. The deflection of the RC Beams externally bonded with FRP was predicted by using the ACI 318 Standard, EMM, AEMM, Branson’s method, and Mayer’s method. They were also compared to the experimental results. Subsequently, in the case of RC Beams externally bonded with FRPs under sustained loads, the proposed method proved that it is possible to accurately predict long-term deformations.     

CFRP加固混凝土梁各受力阶段的剥离机理

粘贴碳纤维片加固混凝土梁的试验数据和破坏模式表明,在锚固措施可靠的情况下,界面粘贴失效或基面混凝土剥离是加固混凝土梁的主要早期破坏形态。为研究混凝土梁不同受力阶段对界面粘结失效或混凝土剥离的影响程度,针对实际加固工程中常见的混凝土梁损伤状况并结合室内试验结果,分别研究了粘贴碳纤维片加固完整梁及不同开裂程度梁在不同受力阶段中的界面应力分布与剥离机理,指出了加固梁的开裂或裂缝扩展是导致界面或粘贴基面混凝土剥离的主要原因。最后,结合实际混凝土梁的损伤特点,提出了加固设计施工过程中的注意事项及应采取的技术措施。     

Cohesive zone model for the prediction of interfacial shear stresses in a composite-plate RC beam with an intermediate flexural crack

In this paper, an analytical method is developed to predict the distribution of interfacial shear stresses in concrete beams strengthened by composite plates. Accurate predictions of such stresses are necessary when designing to prevent debonding induced by a central flexural crack in a FRP-plated reinforced concrete (RC) beam. In the present analysis, a new theoretical model based on the bi-linear cohesive zone model for intermediate crack-induced debonding is established, with the unique feature of unifying debonding initiation and growth. Adherent shear deformations have been included in the present theoretical analyses by assuming a parabolic shear stress through the thickness of the adherents, verifying the cubic variation of the longitudinal displacement function, whereas all existing solutions neglect this effect. The results obtained for interfacial shear stress distribution near the crack are compared to the Jialai Wang analytical model and the numerical solutions are based on finite element analysis. Parametric studies are carried out to demonstrate the effect of the mechanical properties and thickness variations of FRP, concrete and adhesive on interface debonding. Indeed, the softening zone size is considerably larger than that obtained by other models which neglect adherent shear deformations. However, loads at the limit of the softening and debonding stages are larger than those calculated without the thickness effect. Consequently, debonding at the interface becomes less apparent and the lifespan of our structure is greater.     

Plate end debonding in the constant bending moment zone of plated beams

Reinforced concrete (RC) beams strengthened in flexure by externally bonding fibre reinforced polymer (FRP) or steel plate on their tension face are susceptible to premature plate end debonding failures. Safe design of such a strengthened RC beam demands a reliable and predictive debonding strength model. There are two special cases of plate end debonding failures: flexural debonding for cases when the plate terminates within a constant bending moment region (CMR), and shear debonding for the case when the plate terminates where the shear force is large but the bending moment is minimal. A general plate end debonding case is usually considered as an interaction between these two special cases. This paper is concerned with flexural debonding. A brief review of existing models is presented before the plate end interfacial stresses are examined. Three new models with different levels of accuracy are then developed: a closed-form theoretical model based on a simplified interfacial fracture mechanics analysis; a semi-empirical model; and a wholly empirical model. These three models together with two existing models are assessed against a carefully constructed test database containing 67 test data from an extensive literature survey.     

Plate end debonding in the constant bending moment zone of plated beams

Reinforced concrete (RC) beams strengthened in flexure by externally bonding fibre reinforced polymer (FRP) or steel plate on their tension face are susceptible to premature plate end debonding failures. Safe design of such a strengthened RC beam demands a reliable and predictive debonding strength model. There are two special cases of plate end debonding failures: flexural debonding for cases when the plate terminates within a constant bending moment region (CMR), and shear debonding for the case when the plate terminates where the shear force is large but the bending moment is minimal. A general plate end debonding case is usually considered as an interaction between these two special cases. This paper is concerned with flexural debonding. A brief review of existing models is presented before the plate end interfacial stresses are examined. Three new models with different levels of accuracy are then developed: a closed-form theoretical model based on a simplified interfacial fracture mechanics analysis; a semi-empirical model; and a wholly empirical model. These three models together with two existing models are assessed against a carefully constructed test database containing 67 test data from an extensive literature survey.     

Long-term bond stresses and debonding failure of FRP-strengthened RC cracked members

Most of the existing models to prevent debonding failure in beams externally strengthened by fiber reinforced polymer (FRP) laminates were developed focusing on the short term response. This paper studies the effect of concrete creep on the interfacial shear stresses and consequently, on the debonding failure load. A simplified formulation for the instantaneous and time-dependent bond stresses under sustained load is provided. Its reliability is analysed through the results obtained by a non-linear time-dependent analysis model. Previously, this model has been checked to evaluate the long-term response of existing experimental programmes in terms of deflections and strains.     

On the reduce of interfacial shear stresses in fiber reinforced polymer plate retrofitted concrete beams

One major problem when using bonded fiber reinforced polymer (FRP) plate is the presence of high interfacial shear stresses near the end of the composite (edge effect) which might govern the failure of the strengthening schedule. It is known that the decrease of plate thickness reduces the magnitude of stress concentration at plate ends. Another way is to use a plate end tapering. In this paper, the analytical solution of interfacial shear stresses obtained has been extended by a numerical procedure using the modal analysis of finite element method (FEM) in a retrofitted concrete (RC) beam with the FRP plate with tapered end, which can significantly reduce the stress concentration. This approach allows taking into consideration the variation of elastic properties of adhesive and plate as well as the complicated geometrical configurations and effects of thermal loads.     

FRP debonding from a concrete substrate: Some recent findings against conventional belief

For beams strengthened with FRP plates, many existing theories and concepts related to debonding failure are challenged by recent experimental observations in our laboratory. For debonding initiated by stress concentrations at the plate end, ultimate failure is always preceded by the formation of a major crack in the concrete member, causing interfacial stresses to change significantly from the elastic distribution. Existing elastic models are therefore not applicable to failure prediction. For debonding initiated from a flexural crack near mid-span, fracture mechanics based models indicate that the plate stress at failure is inversely proportional to the square root of the thickness. Test results from beams of various sizes and retrofitted with plates of different thickness show a different trend. To delay debonding failure, bonding of U-shape FRP ‘stirrups’ to the end of the FRP plate has been proposed. Test results indicate that ‘stirrups’ applied away from the plate end can indeed be more effective under some practical situations.     

Analytical study on RC beams strengthened for flexure with externally bonded FRP reinforcement

This paper presents analytical study on reinforced concrete (RC) beams strengthened for flexure with externally bonded fiber reinforced polymer (FRP) reinforcement. A simple yet rational numerical model is developed and proposed for this purpose. The model is based on cross-sectional analysis satisfying strain compatibility and equilibrium conditions. The moment–curvature relationship can be generated for an RC beam section using an incremental strain technique. The model can also generate the load–deflection relationship of the beam with respect to its configuration, loading system, and preloading conditions. The model can predict the flexural capacity of FRP-strengthened section based on full composite action and IC debonding failure modes. This also allows for designing the FRP strengthening area according to the desired failure mode. Various IC debonding criteria were adopted in the model and compared with test results from the literature. The result of comparison indicated that the accuracy of the model is dependent on the adopted IC debonding criterion. Furthermore, the model was verified against test data related to full composite action failure mode and good agreement was found.     

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.     

A discrete spectral model for intermediate crack debonding in FRP-strengthened RC beams

One of the common failure modes of reinforced concrete (RC) beams strengthened in flexure with a bonded fibre-reinforced polymer (FRP) is intermediate crack (IC) debonding, which is originated at a critical section in the vicinity of flexural cracks and propagates to a plate end. Despite considerable research over the last years, few reliable and simplified IC debonding strength models have been developed. This paper firstly presents a one-dimensional model based on the discrete crack approach for concrete and the spectral element method for the numerical simulation of the IC debonding process. The progressive formation of flexural cracks and subsequent concrete–FRP interfacial debonding is formulated by the introduction of a new element able to represent both phenomena simultaneously without perturbing the numerical procedure. Furthermore, with the proposed model, high frequency dynamic response for these kinds of structures can also be obtained in a very simple and non-expensive way, which makes this procedure very useful as a tool for diagnoses and detection of debonding in its initial stage by monitoring the change in local dynamic characteristics.     

Experimental study on RC beams with FRP strips bonded with rubber modified resins

This paper presents the effects of adhesive properties on structural performance of reinforced concrete (RC) beams strengthened with carbon fiber reinforced plastic (CFRP) strips. The epoxy adhesives modified with liquid rubber of different content were used to bond the CFRP strips, and four point bending experiments were carried out on RC beams. The experimental results show that different CFRP strip thickness of 0.22 and 0.44 mm resulted in a transition of failure mechanism from interfacial debonding along the CFRP-concrete interface to concrete cover separation starting from the end of CFRP strips in the concrete. Moreover, it is suggested that no matter interfacial debonding or concrete cover separation, the rubber modifier enhanced the structural performance by increasing the maximum load-carrying capacity and the corresponding ductility, compared with the beams bonded with a neat epoxy resin. The improvement of structural performance due to modified adhesive was associated with the modification of stress profiles along the CFRP-concrete interface especially the stress concentration at the end of FRP, and the enhanced interlaminar fracture toughness. Rubber modified epoxy therefore is worth further studying in practical repair applications.     

碳纤维布加固RC梁中粘结性能的非线性有限元分析

碳纤维布加固钢筋混凝土(RC)梁中,碳纤维布与梁底混凝土的剥离破坏使碳纤维布的强度不能得到充分发挥。分析碳纤维布与梁底混凝土的粘结应力,是研究碳纤维布加固剥离破坏承载力的基础问题。根据4根碳纤维布加固RC梁的试验研究结果,采用商业有限元程序MSC.Marc建立有限元模型,进行了非线性计算分析。通过分离总粘结应力中的局部粘结应力,得到粘结延伸长度范围内的锚固粘结应力分布,并结合试验数据对其分布规律进行了研究。根据分析和试验结果,引入了“有效锚固粘结长度”和“锚固粘结应力”的概念,给出了极限荷载下锚固粘结应力的计算建议。     

Effect of variations in the plate modulus of elasticity on the failure modes of FRP plated R.C. beams

In the absence of FRP plate/glue/concrete interface bond failure (i.e. interfacial debonding), eight possible flexural modes of failure are identified for reinforced concrete beams experiencing lateral loading, and strengthened in flexure with external FRP or steel plates glued to their soffits. All possible changes in such modes of failure, as a result of variations in the modulus of elasticity of the FRP material (assuming an associated constant value of ultimate tensile strength for the FRP plate in a given beam design), have been addressed in some detail, with a quantitative treatment of the critical values of the FRP modulus of elasticity associated with various failure mode transitions (i.e. changes).     

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.     

Interfacial shear stress concentration in FRP-strengthened beams

This paper reports the results of an experimental programme designed to study the interfacial shear stress concentration at the plate curtailment of reinforced concrete (RC) beams strengthened in flexure with externally bonded carbon fibre-reinforced polymer (CFRP). Specifically, the study looks at the relationship between the CFRP plate thickness and the interfacial shear stress concentration at the plate curtailment, the failure modes of the CFRP-strengthened beams as well as the efficiency of the CFRP external reinforcing system. Comparing the experimental results with existing models' predictions is another objective of this study. The experimental programme included five RC beams 115 mm×150 mm in cross-section and 1500 mm in length. Four of the RC beams were reinforced externally with CFRP plates of different thicknesses. Tests in this study showed that the thickness of CFRP plate affects not only the load-carrying and deflection capacities of the strengthened beam, but also the shear stress concentration at the CFRP/concrete interface and the beam failure mode.     

Flexural strengthening of RC beams using Hybrid Composite Plate (HCP): Experimental and analytical study

Hybrid Composite Plate (HCP) is a reliable recently proposed retrofitting solution for concrete structures, which is composed of a strain hardening cementitious composite (SHCC) plate reinforced with Carbon Fibre Reinforced Polymer (CFRP). This system benefits from the synergetic advantages of these two composites, namely the high ductility of SHCC and the high tensile strength of CFRPs. In the material-structural of HCP, the ultra-ductile SHCC plate acts as a suitable medium for stress transfer between CFRP laminates (bonded into the pre-sawn grooves executed on the SHCC plate) and the concrete substrate by means of a connection system made by either chemical anchors, adhesive, or a combination thereof. In comparison with traditional applications of FRP systems, HCP is a retrofitting solution that (i) is less susceptible to the detrimental effect of the lack of strength and soundness of the concrete cover in the strengthening effectiveness; (ii) assures higher durability for the strengthened elements and higher protection to the FRP component in terms of high temperatures and vandalism; and (iii) delays, or even, prevents detachment of concrete substrate. This paper describes the experimental program carried out, and presents and discusses the relevant results obtained on the assessment of the performance of HCP strengthened reinforced concrete (RC) beams subjected to flexural loading. Moreover, an analytical approach to estimate the ultimate flexural capacity of these beams is presented, which was complemented with a numerical strategy for predicting their load-deflection behaviour. By attaching HCP to the beams' soffit, a significant increase in the flexural capacity at service, at yield initiation of the tension steel bars and at failure of the beams can be achieved, while satisfactory deflection ductility is assured and a high tensile capacity of the CFRP laminates is mobilized. Both analytical and numerical approaches have predicted with satisfactory agreement, the load-deflection response of the reference beam and the strengthened ones tested experimentally.     

Strengthening of RC beams with epoxy-bonded fibre-composite materials

Strengthening of concrete beams with externally bonded fibre-reinforced plastic (FRP) materials appears to be a feasible way of increasing the load-carrying capacity and stiffness characteristics of existing structures. FRP-strengthened concrete beams can fail in several ways when loaded in bending. The following collapse mechanisms are identified and analysed in this study: steel yield-FRP rupture, steel yield-concrete crushing, compressive failure, and debonding. Here we obtain equations describing each failure mechanism using the strain compatibility method, concepts of fracture mechanics and a simple model for the FRP peeling-off debonding mechanism due to the development of shear cracks. We then produce diagrams showing the beam designs for which each failure mechanism is dominant, examine the effect of FRP sheets on the ductility and stiffness of strengthened components, and give results of four-point bending tests confirming our analysis. The analytical results obtained can be used in establishing an FRP selection procedure for external strengthening of reinforced concrete members with lightweight and durable materials.