粘贴钢板加固钢筋混凝土梁的分离式有限元模型

提出了外粘钢板加固受弯钢筋混凝土梁的非线性有限元模型。该模型中采用了一种特殊的、具有剥离破坏功能的界面单元来模拟混凝土梁和外粘钢板之间的粘结层,这种剥离破坏主要发生在粘贴钢板端部区域和弯曲、剪切裂缝附近。影响这种剥离破坏的主要因素有两个:一是粘贴钢板的端部与加固梁支座距离;二是粘贴钢板的厚度。传统的梁理论不能描述这种加固梁破坏模式,采用有限元方法能全方位地描述这种加固梁的各种性状和破坏模式。数值计算结果与粘贴不同厚度钢板加固梁的试验结果相吻合。     

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.     

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.     

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.     

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.     

Fracturing behaviors of FRP-strengthened concrete structures

In this paper, we focus on the study of concrete cracking behavior and interfacial debonding fracture in fiber reinforced polymer (FRP)-strengthened concrete beams. An experimental program is systematically reviewed according to the observed failure modes, in which it is found that the interfacial debonding may propagate either within the adhesive layer or through concrete layer in the vicinity of bond interface. A finite element analysis is performed to investigate the different types of debonding propagation along FRP-concrete interface and crack distribution in concrete. For the numerical fracture models, interfacial debonding that initiates and propagates in adhesive layer is modeled by fictitious interfacial crack model. And concrete cracking, including the debonding fracture through interfacial concrete, is modeled by smeared crack model. Properties of the interfacial adhesive layer and concrete are considered to significantly influence the debonding propagation types and crack distribution. The interactions between interfacial bond strength, interfacial fracture energy of bond adhesive layer and tensile strength, fracture energy of concrete are discussed in detail through a parametric study. According to the results, the effects of these properties on different types of interfacial debonding, concrete cracking behavior and structural load-carrying capacity are clearly understood.     

Time-dependent behavior of RC beams strengthened with externally bonded FRP plates: interfacial stresses analysis

External bonding of fibre reinforced polymer (FRP) composites has becomes a popular technique for strengthening concrete structures all over the world. An important failure mode of such strengthened members is the debonding of the FRP plate from the concrete due to high interfacial stresses near the plate ends. For correctly installed FRP plate, failure will occur within the concrete. Accurate predictions of the interfacial stresses are prerequisite for designing against debonding failures. In particular, the interfacial stresses between a beam and soffit plate within the linear elastic range have been addressed by numerous analytical investigations. In this study, the time-dependent behavior of RC beams bonded with thin composite plate was investigated theoretically by including the effect of the adherend shear deformations. The time effects considered here are those that arise from shrinkage and creep deformations of the concrete. This paper presents an analytical model for the interfacial stresses between RC beam and a thin FRP plate bonded to its soffit. The influence of creep and shrinkage effect relative to the time of the casting and the time of the loading of the beams is taken into account. Numerical results from the present analysis are presented to illustrate the significance of time-dependent of adhesive stresses.     

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.     

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.     

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.     

Fatigue behaviour of the bond interface between carbon fibre‐reinforced polymer sheets and concrete

Externally bonded carbon fibre‐reinforced polymers (CFRPs) have been applied to retrofit and strengthen civil structures. In this study, four‐point bending beams were manufactured and tested to examine the fatigue behaviour of the CFRP–concrete interface. The results indicated that the specimens exhibited debonding failure in the concrete beneath the adhesive layer under static loading. However, when cyclic loads were imposed on the small beams, debonding failure may occur in the adhesive layer. Moreover, fitting expressions were proposed to predict the shear stress–slip relationship between the CFRP sheets and concrete and the flexural strength of the CFRP‐strengthened beams under static loads, and good agreement with the test data was obtained. Finally, a fatigue life prediction model was also presented to capture the fatigue life of the CFRP–concrete interface under cyclic loads. The calculation results showed that the fatigue strength of the CFRP–concrete bond interface was approximately 65% of the ultimate load capacity.     

粘结层和预应力对CFRP板加固损伤钢梁抗弯性能的影响

为了对比粘结层和预应力对碳纤维增强聚合物复合材料(CFRP)板加固损伤钢梁抗弯性能的影响,进行了5根H型损伤钢梁的抗弯试验,分析了特征荷载、荷载-挠度曲线、CFRP板应变及其强度利用率的变化。试验结果表明:有粘结和无粘结CFRP板具有相近的加固效果,特征荷载差值小于2%;非预应力CFRP板在正常使用阶段的加固效果很小,而预应力CFRP板加固钢梁的特征荷载比非预应力CFRP板提高了近30%。平截面假定适用于有粘结CFRP板-钢梁复合截面,而不适用于无粘结CFRP板-钢梁复合截面。相比于非预应力CFRP板,对CFRP板施加预应力可以显著提高CFRP板的强度利用率。建立的有限元模型可以较好地预测试件的抗弯性能,增加CFRP板的预应力、厚度和弹性模量可以提高损伤钢梁的抗弯加固效果。      

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.     

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.     

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.     

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).     

U形CFRP条带混锚加固混凝土梁抗剪试验

为解决纯粘贴U形纤维增强聚合物基复合材料（FRP）加固钢筋混凝土梁中FRP端部容易发生剥离破坏等问题,自主研发了对纤维布条带端部进行自锁锚固的方法和锚板,提出了端锚与粘贴并用的混锚U形条带抗剪加固方法。通过2根未加固梁、1根纯粘贴和2根混锚U形碳纤维增强聚合物基复合材料（CFRP）带抗剪加固梁的对比试验,证实了混锚抗剪加固的有效性：混锚能够对纤维带端部进行可靠锚固,阻止端部剥离破坏的发生,实现纤维拉断破坏,大幅度提高材料强度利用率。混锚加固在抑制混凝土梁斜裂缝开展、延缓箍筋屈服、提高箍筋和CFRP的极限应变以及提高抗剪承载力等多个方面的表现均明显优于纯粘贴加固。     

Flexural behavior of steel beams strengthened by carbon fiber reinforced polymer plates – Three dimensional finite element simulation

Debonding, as a mode of failure, is one of the major limitations when using externally bonded carbon fiber reinforced polymer (CFRP) plates in strengthening of steel beams. In this work, mode of failure and flexural behavior of both steel and steel–concrete composite beams strengthened by different lengths of CFRP plates were numerically investigated. The effect of both splicing position (at mid-span and near supports) and CFRP plate ends configuration were studied. Three dimensional finite element analysis (3D FEA) was adopted to simulate the nonlinear behavior of these beams loaded under four point bending configuration. The present numerical analysis assisted by previously valuable experimental results found in the literature succeeded to predict the critical CFRP plate length at which, full efficiency of the adhesively bonded plate is achieved.     

Bond behaviour of CFRP reinforcement for torsional strengthening of solid and box-section RC beams

The economic and time constraints in the repair or upgrading of existing infrastructure have become a major issue, particularly extending the service lifespan of bridges. Fibre reinforced polymer (FRP) has shown great promise as a state-of-the-art material in flexural and shear strengthening as external reinforcement. However, little attention has been paid to torsional strengthening in terms of both experimental and numerical research. This paper focuses on the bond-behaviour of externally bonded CFRP in an overall investigation of torsional strengthening of solid and box-section reinforced concrete beams. Significant levels of debonding prior to failure by CFRP rupture were measured in experiments with photogrammetry. Numerical work was carried out using non-linear finite element (FE) modelling. Good agreement in terms of torque-twist behaviour, steel and CFRP reinforcement responses, and crack patterns was achieved. The addition of a bond-slip model between the CFRP reinforcement and concrete meant that the debonding mechanisms prior to and unique failure modes of all the specimens were modelled correctly as well.     

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.