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.     

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.     

Fracture-mechanics failure criteria for RC beams strengthened with FRP strips––a simplified approach

A simplified approximation approach for the evaluation of a fracture mechanics based criterion for the edge delamination failure of reinforced concrete beams strengthened with externally bonded composite materials is presented. The proposed approach is based on evaluation of the energy release rate (ERR) through the virtual crack extension method using various analytical and numerical stress analysis models. The investigated models include the high-order model, two types of “elastic foundation” or “springs” models, a simplified beam model, and finite elements analysis. The stress and displacement fields, the governing equations and their closed form solutions, and the expressions for the release rate of the total potential energy of the various models are presented. The proposed approach sets up the basis for an energetic failure criterion, in which the ERR is compared to the specific fracture energy of the bonded system. This criterion replaces the traditional allowable stress approach in describing the initiation and stable or unstable growth of the delamination crack. The capabilities of the proposed approach and its ability to evaluate the ERR through simplified and approximated models is investigated numerically. The accuracy of the simplified approach is numerically examined through comparison with the J-integral formulation. Numerical results in terms of stresses near the edge of the bonded strip, the ERR associated with initiation and growth of the interfacial crack, and the critical loads and crack lengths are presented. The paper closes with a summary and conclusions.     

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.     

Width effect in the interface fracture during shear debonding of FRP sheets from concrete

The increasing use of carbon fiber reinforced polymer (FRP) sheets for strengthening existing reinforced concrete beams has generated considerable research interest in understanding the debonding mechanism of failure in such systems. The influence of the width of the FRP on the load-carrying capacity is investigated in this paper. The interfacial crack propagation and strain distribution during shear debonding are studied using a full-field optical technique known as digital image correlation. The results indicate the development of high stress/strain gradients at the interface as a consequence of the relative slip between the FRP and the concrete. The interface stress transfer between the FRP and concrete produces axial strain gradients in the FRP along its length. In the vicinity of the edges along the width of the FRP, edge regions comprising of both FRP and concrete are established. The edge region is characterized by high strain gradients in a direction perpendicular to the length and is of fixed width throughout the debonding process. The size of the edge regions is also found to be quite independent of the width of the FRP. Mode-II fracture condition exists in the interface directly below the FRP away from the edge regions. The interfacial crack is shown to be associated with a cohesive stress transfer zone of fixed length. During debonding, the stress transfer zone is shown to propagate in a self-similar manner at a fixed load. The interface fracture properties obtained from the portion of FRP away from the edge regions are shown to be independent of the FRP width. It is shown that when the width of concrete is larger than that required for establishing the edge regions, the nominal stress at debonding increases with an increase in the width of FRP. The scaling in the load carrying capacity during shear debonding is shown to be the result of the edge regions which do not scale with the width of the FRP.     

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.     

Direct determination of cohesive stress transfer during debonding of FRP from concrete

Interface cohesive stress transfer between FRP and concrete during debonding is typically obtained using measured surface strains on the FRP, along the direction of the fibers. The cohesive material law is derived under a set of assumptions which include: (a) the bending stiffness of the FRP laminate is insignificant with respect to that of the concrete test block; (b) the strains in the bulk concrete produced by debonding are negligible, thus concrete substrate can be considered rigid; (c) there is stress transfer between FRP and concrete through the FRP–concrete interface which is of zero thickness; and (d) the axial strain in the FRP composite is uniform across its thickness. In this paper, a test procedure for directly obtaining the through-thickness strains in the FRP and the concrete substrate during cohesive stress transfer associated with debonding is presented. The displacement and strain fields are measured on the side of a direct-shear specimen with the FRP strip attached on the edge. Based on the experimental results, the influence of the assumptions which have been introduced to determine the cohesive law is discussed. Within the stress transfer zone there is a sharp gradient in the shear strain. The location of the interface crack within the stress transfer zone and the cohesive stress transfer during the propagation of the interface crack are determined.     

An analytical investigation of debonding problems in beams strengthened using composite plates

This work deals with an enhanced analytical model for the analysis of typical edge debonding problems in concrete or steel beams strengthened/repaired with externally bonded composite laminated plates induced by beam/adhesive interface fracture phenomena. The strengthened system is viewed as composed by three physical different layers: the strengthened beam, the adhesive layer and the bonded plate. On the other hand, the structural model consists of two shear deformable mathematical layers, the upper one representing the beam and the lower one incorporating the adhesive layer and the bonded plate. Bonding conditions between layers are simulated by using the Lagrangian multipliers method and governing equations are obtained by a variational approach. In the context of a fracture mechanics approach, analytical solutions for both total and mode components of energy release rate are obtained by using stress resultant and strain discontinuities across at the crack tip. Closed form solutions are obtained for specific loading conditions and geometric configurations. Comparisons with predictions from very careful FE investigations point out the effectiveness of the proposed results which may form the basis for a design process taking into account properly of debonding failure modes triggered by interface fracture at the edge of the repairing composite plate. Finally, the significance of the paper relies in the analytical approach to the problem, which avoids the complexities commonly shared by FE-based methodologies, related to stress singularities and differences in length scales and in mechanical properties of the single components of the system.     

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.     

Cohesive-bridging zone model of FRP-concrete interface debonding

External bonding of FRP plates or sheets has emerged as a popular method for strengthening reinforced concrete structures. Debonding along the FPR-concrete interface can lead to premature failure of the structures. In this study, a combined cohesive/bridging zone model is presented to simulate the debonding procedure between the FRP and concrete interface. In this model, the crack processing zone of the interface is modeled by a cohesive zone model and the particle interlocking zone of the interface is modeled by a bridging zone model. Two different linearly softening bond stress-slip laws are used to describe these two different zones. Closed-form solutions of interfacial stress, FRP stress and ultimate load are obtained for a typical single-lap specimen and verified with experimental results. The pulling force applied to the FRP plate is found to be proportional to the square root of the energy release rate at the debonding tip for this model. Such a relationship is then extended to any general shapes of bond stress-slip law through J-integral method. A new approach to experimentally determine the bond stress-slip law is also proposed.     

Suitability of optimized truss model to predict the FRP contribution to shear resistance for externally bonded FRP strengthened RC beams without internal stirrups

Shortcoming in the current design guidelines on externally bonded FRP shear strengthened members has initiated a motivation to relook the whole shear design approach. It is understood that effective FRP strain models used in present design guidelines are basically calibrated from the experimental data based on the conservative and unrealistic 45-deg truss model. This paper is intended to propose an optimized truss model that derived from the principle of minimum total strain energy theorem to improve the present 45-deg truss model. The proposed optimized truss model is characterized with limiting failure criteria that reflects truly to the actual FRP strengthened beam behaviour. One of the most important failure criteria is the FRP debonding failure. To characterize it, limiting effective FRP strain ε_frp,e model is incorporated into the optimized truss model. Six most recent effective strain models are chosen for the analysis, included three of the international design guidelines. Performance of each effective strain model will be evaluated along with the optimized and 45-deg truss models in order to assess their respective accuracy in predicting the FRP contribution to the shear strength. The validation of optimized truss model is done through comparing with experimental test results collected from the literature. The results obtained indicated that the optimized truss model is indeed more viable representative to the actual internal stress distribution and accurate than existing 45-deg truss model. So it might have a great potential to be used in the derivation of a new effective FRP strain model that can be implemented in the current design guidelines.     

Strengthening RC beams with composite fiber cement plate reinforced by prestressed FRP rods: Experimental and numerical analysis

This paper deals with the development of a new strengthening system for reinforced concrete beams with externally-bonded plate made of composite fiber cement reinforced by rebars made of fiber-reinforced plastic (FRP) [1]. The proposed strengthening material involves the preloading of FRP rod before mortar casting. The paper presents experimental and numerical analysis carried out on many large-scale beams strengthened by well-known reinforcement techniques, such as externally bonded Carbon Fiber-Reinforced Plastic (CFRP) plate and the Near Surface Mounted (NSM) technique, which are compared to the proposed new strengthening material through four-point bending tests. Results are analyzed with regard to the load-displacement curve, bending stiffness, cracking load, yield strength and failure load. The developed numerical model is in agreement with the experimental results. It clearly shows the effects of prestressed FRP rod on cracking mechanisms and internal strength distribution in the analyzed beams.     

Artificial intelligence techniques for prediction of the capacity of RC beams strengthened in shear with external FRP reinforcement

The prediction of the shear capacity of reinforced concrete beams retrofitted in shear by means of externally bonded FRP is very complex as demonstrate the studies carried out up to date. As alternative to the conventional methods two approaches based on artificial intelligence are proposed for the first time. Firstly, the use of neural networks as a means of predicting shear capacity without the need of using complex models and, secondly, the use of genetic algorithms as a means of determining suitably how the shear mechanism works. Predictions obtained with both approaches are compared to experimental values.     

Development of P-I diagrams for FRP strengthened RC columns

In this study, numerical simulations are performed to construct the Pressure-Impulse (P-I) diagrams for FRP strengthened RC columns to provide correlations between the damage levels of FRP strengthened RC columns and blast loadings. Numerical model of RC columns without or with FRP strengthening is developed using LS-DYNA. The accuracy of the model to simulate RC column responses to blast loads is verified by comparing the numerical simulation results with the tests results available in the literature. Dynamic response and damage of RC columns with different FRP strengthening measures are then calculated using the developed numerical model. The residual axial-load carrying capacity is utilized to quantify the damage level since the columns are primarily designed to carry the axial loads. Parametric studies are performed to examine the influence of column dimension, concrete strength, steel reinforcement ratios, FRP thickness and FRP strength on the P-I diagrams. The empirical formulae are derived based on numerical results to predict the impulse and pressure asymptote of P-I diagrams. These empirical formulae can be straightforwardly used to construct P-I diagrams for assessment of blast loading resistance capacities of RC columns with different FRP strengthening measures.     

A design model for fibre reinforced concrete beams pre-stressed with steel and FRP bars

This paper presents a design oriented model to determine the moment–curvature relationship of elements of rectangular cross section failing in bending, made by strain softening or strain hardening fibre reinforced concrete (FRC) and reinforced with perfectly bonded pre-stressed steel and fibre reinforced polymeric (FRP) bars. Since FRP bars are not affected by corrosion, they have the minimum FRC cover thickness that guaranty proper bond conditions, while steel bars are positioned with a thicker FRC cover to increase their protection against corrosion. Using the moment–curvature relationship predicted by the model in an algorithm based on the virtual work method, a numerical strategy is adopted to evaluate the load–deflection response of statically determinate beams. The predictive performance of the proposed formulation is assessed by simulating the response of available experimental results. By using this model, a parametric study is carried out in order to evaluate the influence of the main parameters that characterize the post cracking behaviour of FRC, and the pre-stress level applied to FRP and steel bars, on the moment–curvature and load–deflection responses of this type of structural elements. Finally the shear resistance of this structural system is predicted.     

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.     

FE homogenized limit analysis model for masonry strengthened by near surface bed joint FRP bars

A homogenized limit analysis model for the prediction of collapse loads and failure mechanisms of masonry walls reinforced with near surface bed joint GFRP bars is presented. Reinforced masonry homogenized failure surfaces are obtained by means of a compatible identification procedure, where each brick is supposed interacting with its six neighbors by means of finite thickness mortar joints, filler epoxy resin and FRP rods.In the framework of the kinematic theorem of limit analysis, a simple constrained minimization problem is obtained on the unit cell, suitable to estimate – with a very limited computational effort – reinforced masonry homogenized failure surfaces.A FE strategy is adopted to solve the homogenization problem at a cell level, modeling joints, bricks, filler and FRP rods by means of eight-noded infinitely resistant parallelepiped elements. A possible jump of velocities is assumed at the interfaces between contiguous elements, where plastic dissipation occurs. For mortar and bricks interfaces, a frictional behavior with possible limited tensile and compressive strength is assumed, whereas for epoxy resin and FRP bars some formulas available in the literature are adopted in order to take into account in an approximate but effective way, the delamination of the bar from the epoxy and the failure of the filler at the interface with the joint.In order to validate the model proposed, two meaningful examples are critically analyzed. The first relies on a reinforced masonry beam in four-point bending, whereas the second is a full scale wall constrained at three edges and loaded until failure with a distributed out-of-plane pressure. While the first example is useful to test the model at a cell level, since only horizontal ultimate bending moment is involved in the failure mechanism, the second provides a full assessment of the procedure proposed at a structural level. In both cases, very good agreement is found with literature data, meaning that the model proposed may provide useful information for all practitioners interested in the design of masonry walls reinforced with bed joint FRP bars.     

Strengthening R/C beams with opening by externally installed FRP rods: Behavior and analysis

This paper discusses the strengthening of opening in R/C beams by FRP rods. A total number of thirteen beams with circular and square opening have been tested. The opening is shown to significantly reduce the shear capacity of beam. Two patterns of strengthening by FRP rod are investigated: one is to place FRP rods enclosing the opening and the other is to place FRP rods diagonally throughout the entire depth of the beam. It is found that simply placing FRP rods around the opening is not fully effective because a diagonal crack can propagate through the beam with the crack path diverted to avoid intersecting with the FRP rod. When FRP rods are placed throughout the entire beam’s depth, a significant improvement in loading capacity and ductility is achieved, similar to strengthening by pre-fabricated internal steel bars. The flexural failure mode is restored. A nonlinear finite element analysis, based on smeared crack approach, is conducted for numerical verification and examining the effect of length, position and inclination of FRP rods. The plot of analytical principal compressive stress illustrates two strut mechanisms associated with FRP rod. The inclined rods are found to be more effective than vertical ones.     

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).