Use of Mixed-Mode Fracture Interfaces for the Modeling of Large-Scale FRP-Strengthened Beams

In this study, numerical models of fiber-reinforced polymer (FRP)-strengthened beams were developed using nonlinear fracture mechanics for the modeling of the concrete-FRP (longitudinal and U-wrap) interfaces. Mode 1, Mode 2, and mixed-mode interfacial behaviors were considered. Results from the finite-element models were compared with experimental tests of large-scale strengthened beams using FRP U-wraps as anchors. The numerical program assessed the effect of the interfacial modeling in the global and local responses. A parametric study was conducted to determine the effect of additional longitudinal FRP sheets in strengthened beams with and without FRP U-wraps. Results from this study indicate that the use of a mixed-mode concrete-FRP interface is a robust numerical approach for the prediction of the global and local responses of large-scale FRP-strengthened beams. The parametric study shows that the use of FRP U-wraps could improve the strength and ductility of the FRP-strengthened beams by changing their failure mode and deflection response. Appropriate modeling of the concrete-FRP interfaces is needed to successfully predict these effects.     

Peel and Shear Fracture Characterization of Debonding in FRP Plated Concrete Affected by Moisture

The objective of this paper is to develop a new mechanistic understanding of moisture affected debonding failures in carbon fiber reinforced polymer (CFRP) plated concrete systems by mechanically testing accelerated moisture conditioned mesoscale peel and shear interface fracture specimens. Central to the investigation is the use of interface fracture toughness as the quantification parameter of the CFRP-epoxy-concrete trilayer system, which is considered a bond property, to analyze, compare, and correlate physical observations. Results have shown that fracture toughness of the CFRP bonded concrete systems significantly degrades, and its value becomes asymptotic with increasing moisture ingress. This asymptotic behavior is associated with certain moisture concentration levels as predicted by a three-dimensional moisture diffusion simulation. The generally observed debonding mode by concrete delamination for the dry specimens changes to an epoxy/concrete interface separation mode for the wet specimens. Finite element fracture computation, mixed-mode characterization, and kink criterion implementation synergistically suggest that the interface separation mode is attributed to an interfacial material toughening and an interface weakening mechanism as a consequence of moisture diffusion.     

Energy-Based Modeling Approach for Debonding of FRP Plate from Concrete Substrate

For concrete beams and slabs strengthened with bonded fiber reinforced plastic (FRP) plates, plate debonding from the concrete substrate is a common failure mode. In this paper, the debonding process is modeled as the propagation of a crack along the concrete/adhesive interface, with frictional shear stress acting behind the crack tip. Crack propagation is taken to occur when the net energy release of the system equals the interfacial fracture energy. The analysis is first performed for the special case with constant shear stress along the debonded interface, and then for the general case with slip softening in the debonded zone. From the results, a direct correspondence between energy-based and strength-based analyses can be established for arbitrary softening behavior along the interface. Specifically, through the proper definition of an effective interfacial shear strength, the conventional strength-based approach can be employed to give the same results as the much more complicated energy-based analysis. Also, based on the relation between the effective shear strength and other material parameters, it is possible to explain the very high interfacial shear stresses observed in experimental measurements. As an application example, distribution of plate stress and interfacial shear stress for the linear softening case is derived. The model results are found to be in good agreement with experimental measurements, showing that the simple linear softening model can describe the debonding process in real material systems.     

Durability Evaluation of Glass Fiber Reinforced-Polymer-Concrete Bonded Interfaces

In this investigation, 90-cm-long plain concrete beam specimens reinforced with externally bonded wet-laid glass fiber reinforced-polymer sheets are investigated. The specimens are precracked with a three point flexural load, subjected to a constant four point flexural load of about 25% of the initial ultimate moment, and placed into different environmental conditions. The four environmental conditions under investigation are indoor laboratory, outdoor, elevated temperature/dry, and freeze/thaw. By varying the exposure time in different environments and using the photoelastic coating method to evaluate strain distributions, the durability of the externally reinforced concrete beams is evaluated. An innovative approach based on fracture mechanics and local bond shear stress-slip relationships is proposed to explain the degradation mechanism. This approach is capable of qualitatively and quantitatively characterizing the environmental effect in terms of the parameters of the shear stress-slip law. Four one-dimensional shear stress-slip relationships are evaluated in terms of their ability to model the environment-dependent strain distribution and debond data obtained in the present investigation.     

Flexural and Torsional Properties of Pultruded Fiber Reinforced Plastic I-Profiles

Experimental determination of the full section flexural and torsional properties of pultruded fiber reinforced plastic I-profiles is described. Based on beam theory approximations, test configurations for determining the various section properties are established. Tests were conducted on three different I-profiles with a range of span-to-depth ratios. Major and minor axis flexural rigidities and flexural moduli, determined from three- and four-point bending tests, show close correlation. Major and minor axis transverse shear rigidities and shear moduli show significant variation, due to differing effective areas of the cross section resisting transverse shear and differing fiber content and orientation in the web and flanges. St. Venant torsional shear moduli, determined from uniform torsion tests, are consistent but significantly greater than the transverse shear moduli, which may be due to variations in fiber content, orientation, and lay up. Warping torsional rigidities, determined from nonuniform torsion tests, are consistent with values deduced from minor axis flexural rigidities, indicating that the influence of shear deformation on restrained torsional warping is insignificant.     

Bonding Characteristics of Fiber-Reinforced Polymer Sheet-Concrete Interfaces under Dowel Load

Based on a series of experimental tests on notched concrete beams externally bonded with unidirectional fiber-reinforced polymer (FRP) sheets, this paper investigates the bond characteristics of FRP sheet-concrete interfaces under dowel load, which acts vertically on the FRP sheet and leads to a mix-mode interface peeling. The peeling properties of FRP sheet-concrete interfaces under the dowel load are evaluated in terms of their interface dowel load-carrying capacity, critical interface peeling angle, and interface peeling fracture energy. Experimental parameters include strength of concrete substrate, tension stiffness of FRP sheets, properties of bonding adhesives, concrete surface treatment methods, and length of precrack set between the FRP sheet and concrete substrate. Analytical models clarifying the relationships among the interface dowel load-carrying capacity, the interface peeling angle, and the interface peeling fracture energy are built up and also verified by test results. Further, this paper shows how to use the interface peeling fracture energy calibrated from the present dowel tests for the practical design of spalling prevention, which is now becoming a popular application of FRP sheets for the maintenance and repair of existing concrete structures in Japan.     

Fiber Reinforced Polymer Composite–Wood Pile Interface Characterization by Push-Out Tests

Structural restoration of spliced or damaged wood piles with fiber reinforced polymer (FRP) composite shells requires that shear forces be transferred between the wood core and the encasing composite shells. When a repaired wood pile is loaded, shear stresses develop between the wood pile and the FRP composite shell through the grouting material. Alternatively, shear force transfer can be developed through mechanical connectors. The objective of this study was to characterize the interfaces in wood piles repaired with FRP composite shells and grout materials. Two interfaces were studied: wood pile/grout material and a grout material/innermost FRP composite shell. A set of design parameters that control the response of both interfaces was identified: (1) extent of reduction of cross section of wood pile due to deterioration (necking); (2) type of grout material (cement-based or polyurethane); (3) use of mechanical connectors; and (4) addition of frictional coating on the innermost shell. Push-out tests by compression loading were performed to characterize the interfaces and discriminate the effect of the design parameters. The outcome of the push-out tests was evaluation of the shear stress and force versus slip response and characterization of the failure mechanism. A set of repair systems that represent different combinations of the design parameters was fabricated and the interfaces evaluated. It was found that the combination of cement-based grout and polymer concrete overlay on the innermost shell provided the most efficient shear force-slip response. A simplified piecewise linear model of shear stress versus slip at the wood/grout and grout/FRP composite interfaces with and without mechanical connectors is proposed to synthesize the experimental response.     

Determination of Nonlinear Softening Behavior at FRP Composite/Concrete Interface

For concrete beams and slabs, the bonding of fiber reinforced plastic (FRP) plates to the bottom surface is an effective and efficient technique for flexural strengthening. Failure of strengthened members often occurs due to stress concentrations at the FRP/concrete interface. For debonding failure initiated at the bottom of shear or shear/flexural cracks in the concrete, experimental results clearly indicate a progressive failure process accompanied by gradual reduction in shear transfer capability at the interface. Several existing models for FRP debonding have taken interfacial shear softening into account. However, the assumed shear stress versus slip relations employed in the models have never been properly measured. In this investigation, a combined experimental/theoretical approach for the extraction of interfacial stress versus slip relation is developed. With loading applied to a bonded FRP plate, strain is measured at various points along its length. Based on the strain measurements, the interfacial softening curve is derived from a finite element analysis. The present paper will present the proposed approach in detail, demonstrate its application to typical experimental data, and discuss the implications of the results.     

Shear Strengthening of RC Beams with Externally Bonded FRP Composites: Effect of Strip-Width-to-Strip-Spacing Ratio

The results of an experimental and analytical investigation of shear strengthening of reinforced concrete (RC) beams with externally bonded (EB) fiber-reinforced polymer (FRP) strips and sheets are presented, with emphasis on the effect of the strip-width-to-strip-spacing ratio on the contribution of FRP (Vf). In all, 14 tests were performed on 4,520-mm-long T-beams. RC beams strengthened in shear using carbon FRP (CFRP) strips with different width-to-spacing ratios were considered, and their performance was investigated. In addition, these results are compared with those obtained for RC beams strengthened with various numbers of layers of continuous CFRP sheet. Moreover, various existing equations that express the effect of FRP strip width and concrete-member width and that have been proposed based on single or double FRP-to-concrete direct pullout tests are checked for RC beams strengthened in shear with CFRP strips. The objectives of this study are to investigate the following: (1)?the effectiveness of EB discontinuous FRP sheets (FRP strips) compared with that of EB continuous FRP sheets; (2)?the optimum strip-width-to-strip-spacing ratio for FRP (i.e., the optimum FRP rigidity); (3)?the effect of FRP strip location with respect to internal transverse-steel location; (4)?the effect of FRP strip width; and (5)?the effect of internal transverse-steel reinforcement on the CFRP shear contribution.     

Fracture Analysis of Shear Deformable Bi-Material Interface

Based on a novel split bi-layer shear deformable beam model capable of capturing the local deformation at the crack tip, the explicit closed-form solutions of bi-material interface fracture are presented in this paper. A recently developed novel shear deformable bi-layer beam theory is briefly reviewed, from which the deformation at the crack tip is explicitly derived. A new expression for the energy release rate is then obtained using the J integral, in which several new terms associated with the transverse shear force are present; this represents an improved solution compared to the one from the classical beam model. By exploiting the two concentrated crack tip forces, the general loadings acting at the crack tip are decomposed into two groups which produce only the mode I and mode II energy release rates, respectively; the total energy release rate is thus decomposed into the mode I and II components in a global sense. The stress intensity factor referred to as local decomposition is also obtained including the transverse shear effect. The difference between the global and local mode decompositions is clarified, and a simple relationship between them is provided. The effect of the existence of a thin layer of adhesive on the stress intensity factor is further studied by an asymptotic analysis. A simple and improved expression for the T stress, the nonsingular term of stress at the crack tip, is also given. The fracture parameters of several commonly used interface fracture specimens are summarized. The present fracture analysis including the transverse shear effect is in better agreement with finite element analyses and shows advantages and improved accuracy over the available classical solutions.     

Fracture Mechanics of Plate Debonding

This paper presents a fracture mechanics model to determine the load at which FRP plates will debond from reinforced concrete beams. This will obviate the need for finite-element analyses to be used in situations where there is an infinite stress concentration and where the exact details of the interface geometry and properties are unknowable. The paper shows how fracture mechanics concepts based on energy release rates, can be used to answer the question “Will this existing interface crack extend?” Possible modes of debonding are analyzed as is the effect of the plate curtailment location on the debonding mode.     

Development of the Nonlinear Bond Stress–Slip Model of Fiber Reinforced Plastics Sheet–Concrete Interfaces with a Simple Method

A new analytical method for defining the nonlinear bond stress–slip models of fiber reinforced plastics (FRP) sheet–concrete interfaces through pullout bond test is proposed. With this method, it is not necessary to attach many strain gauges on the FRP sheets for obtaining the strain distributions in FRP as well as the local bond stresses and slips. Instead, the local interfacial bond stress-slip models can be simply derived from the relationships between the pullout forces and loaded end slips. Based on a series of pullout tests, the bond stress–slip models of FRP sheet–concrete interfaces, in which different FRP stiffness, FRP materials (carbon FRP, aramid FRP, and glass FRP), and adhesives are used, have been derived. Only two parameters, the interfacial fracture energy and interfacial ductility index, which can take into account the effects of all interfacial components, are necessary in these models. Comparisons between analytical results and experimental ones show good accordance, indicating the reliability of the proposed method and the proposed bond stress–slip models.     

Tension Stiffening of Reinforced Concrete Ties Strengthened with Externally Bonded Fiber-Reinforced Polymer Sheets

Externally bonded laminates of fiber reinforced polymers (FRPs) are becoming more and more common for rehabilitation and strengthening of RC structures, to solve problems either in serviceability or at ultimate conditions. This paper focuses on the behavior in the serviceability state: in particular, verifications in terms of cracks widths and crack spacing, used to warrant the functionality of FRP-RC structures, are considered. Test results on RC ties externally reinforced with FRP laminate are reported and the applicability of the Eurocode2 formulation used for RC elements is discussed. Provisions given by the International Federation for Structural Concrete are also analyzed.     

Behavior of Reinforced Concrete Beams Strengthened with Externally Bonded Hybrid Carbon Fiber–Glass Fiber Sheets

A comparative test program including six beams was carried out. Two strengthening systems, namely hybrid carbon fiber glass fiber-reinforced polymer (H-CF/GF-RP) strengthening and CF-reinforced polymer strengthening were used. The test results showed that the H-CF/GF-RP strengthening led to a significant increase of ductility with a slight influence on stiffness of strengthened beams.     

Experimental Investigation of the Influence of Moisture on the Bond Behavior of FRP to Concrete Interfaces

The effects of moisture on the initial and long-term bonding behavior of fiber reinforced polymer (FRP) sheets to concrete interfaces have been investigated by means of a two-year experimental exposure program. The research is focused on the effects of (1) moisture at the time of FRP installation, in this paper termed “construction moisture,” consisting of concrete substratum surface moisture and external air moisture; and (2) moisture, in this paper termed “service moisture,” which normally varies throughout the service life of concrete. Concrete beams with FRP bonded to their soffits were prepared. Before bonding, concrete substrates were preconditioned with different moisture contents and treated with different primers. The FRP bonded concrete beams were then cured under different humidity conditions before being subjected to combined wet/dry (WD) and thermal cycling regimes to accelerate the exposure effects. Adhesives with different elastic moduli were used to investigate the long-term durability of each adhesive when subjected to accelerated WD cycling. Pull-off tests and bending tests were conducted at the beginning of the cycling and then again after 8 months, 14 months, and 2 years of exposure so as to evaluate the tensile and shear performance of the FRP-to-concrete interfaces. It was found that the effect of the concrete substrate moisture content on short-term interfacial bond performance could be eliminated if an appropriate primer was used. All FRP-to-concrete bonded joints failed at the interface between the primer and concrete after exposure while those not exposed usually failed within the concrete substrate. After exposure to an environment of accelerated WD cycles, it was also found that the interfacial tensile bond strength degraded asymptotically with the exposure time while the flexural capacity of the FRP sheet bonded plain concrete beams even increased. The mechanism behind the above, which is an apparently contradictory phenomenon, is discussed.     

New Approach for Modeling the Contribution of NSM FRP Strips for Shear Strengthening of RC Beams

This paper presents the main features of an analytical model recently developed to predict the near-surface mounted (NSM) fiber-reinforced polymer (FRP) strips shear strength contribution to a reinforced concrete (RC) beam throughout the beam’s loading process. It assumes that the possible failure modes that can affect the ultimate behavior of an NSM FRP strip comprise: loss of bond (debonding); concrete semiconical tensile fracture; mixed shallow-semicone-plus-debonding; and strip tensile fracture. That model was developed by fulfilling equilibrium, kinematic compatibility, and constitutive law of both the adhered materials and the bond between them. The debonding process of an NSM FRP strip to concrete was interpreted and closed-form equations were derived after proposing a new local bond stress-slip relationship. The model proposed also addressed complex phenomena such as the interaction between the force transferred to the surrounding concrete through bond stresses and concrete fracture as well as the interaction among adjacent strips. The main features of the proposed modeling strategy are shown along with the main underlying physical-mechanical concepts and assumptions. Using recent experimental data, the predictive performance of the model is assessed. The model is also applied to single out the influence of relevant parameters on the NSM technique effectiveness for the shear strengthening of RC beams.     

Behavior of RC Beams Shear Strengthened with Bonded or Unbonded FRP Wraps

Reinforced concrete (RC) beams shear-strengthened with fiber-reinforced polymer (FRP) fully wrapped around the member usually fail due to rupture of FRP, commonly preceded by gradual debonding of the FRP from the beam sides. To gain a better understanding of the shear resistance mechanism of such beams, particularly the interaction between the FRP, concrete, and internal steel stirrups, nine beams were tested in the present study: three as control specimens, three with bonded FRP full wraps, and three with FRP full wraps left unbonded to the beam sides. The use of unbonded wraps was aimed at a reliable estimation of the FRP contribution to shear resistance of the beam and how bonding affects this contribution. The test results show that the unbonded FRP wraps have a slightly higher shear strength contribution than the bonded FRP wraps, and that for both types of FRP wraps, the strain distributions along the critical shear crack are close to parabolic at the ultimate state. FRP rupture of the strengthened beams occurred at a value of maximum FRP strain considerably lower than the rupture strain found from tensile tests of flat coupons, which may be attributed to the effects of the dynamic debonding process and deformation of the FRP wraps due to the relative movements between the two sides of the critical shear crack. Test results also suggest that while the internal steel stirrups are fully used at beam shear failure by FRP rupture, the contribution of the concrete to the shear capacity may be adversely affected at high values of tensile strain in FRP wraps.     

Analysis of the Flexural Behavior of Partially Bonded FRP Strengthened Concrete Beams

An investigation was conducted on the flexural behavior of partially bonded fiber-reinforced polymer (FRP) strengthened concrete beams focusing on the improvement of ductility. An analytical model was developed based on the curvature approach to predict the behavior of beams strengthened with partially bonded FRP systems. The result of the analysis showed that ductility of the partially bonded system was improved while sustaining high load carrying capacity in comparison to the fully bonded system. To verify the analytical model, an experimental program was carried out with reinforced concrete beams strengthened with the externally bonded FRP system. A comparison of the analytical prediction and experimental results showed good agreement.     

Debonding in RC Beams Shear Strengthened with Complete FRP Wraps

Substantial research has been conducted on the shear strengthening of reinforced concrete (RC) beams with bonded fiber reinforced polymer (FRP) strips. The beams may be strengthened in various ways: complete FRP wraps covering the whole cross section (i.e., complete wrapping), FRP U jackets covering the two sides and the tension face (i.e., U jacketing), and FRP strips bonded to the sides only (i.e., side bonding). Shear failure of such strengthened beams is generally in one of two modes: FRP rupture and debonding. The former mode governs in almost all beams with complete FRP wraps and some beams with U jackets, while the latter mode governs in all beams with side strips and U jackets. In RC beams strengthened with complete wraps, referred to as FRP wrapped beams, the shear failure process usually starts with the debonding of FRP from the sides of the beam near the critical shear crack, but ultimate failure is by rupture of the FRP. Most previous research has been concerned with the ultimate failure of FRP wrapped beams when FRP ruptures. However, debonding of FRP from the sides is at least a serviceability limit state and may also be taken as the ultimate limit state. This paper presents an experimental study on this debonding failure state in which a total of 18 beams were tested. The paper focuses on the distribution of strains in the FRP strips intersected by the critical shear crack, and the shear capacity at debonding. A simple model is proposed to predict the contribution of FRP to the shear capacity of the beam at the complete debonding of the critical FRP strip.     

Evaluation of Bending Strength of RC Beams Strengthened with FRP Sheets

This paper deals with reinforced concrete beams strengthened by means of externally bonded fiber-reinforced polymer (FRP) sheets. The scope of the work is to discuss and compare an exact and an approximate approach to the computation of the flexural load-carrying capacity of the strengthened beam. The two approaches differ from one another in the way they take into account the extent of the load already acting throughout strengthening operations. To achieve this goal a numerical model is presented and validated by comparing its output with that of 46 experimental tests taken from the literature. The numerical model is then adopted to perform a numerical parametric analysis of a wide range of practical applications, excluding all cases of FRP delamination, and useful conclusions are drawn.