Bond-slip Law Research Articles

Numerical modelling of the bond between concrete and CFRP laminates at elevated temperatures

This paper presents numerical investigations on the bond between concrete and CFRP strengthening systems at elevated temperatures. The numerical study was developed using the commercial package Abaqus and comprised the simulation of double-lap shear tests previously performed by the authors, in which the influence of the strengthening technique – externally bonding reinforcement (EBR) or near surface mounted (NSM) – on the bond behaviour was evaluated along with the temperature increase. In those tests, the two types of specimens (EBR and NSM) were first heated up to elevated temperatures (20°C, 55°C, 90°C, 120°C and 150°C), and then loaded up to failure. Three-dimensional finite element (FE) models of the specimens were developed, in which the global behaviour of the CFRP-concrete interaction was simulated by means of bi-linear bond–slip laws. These laws, which can be used for design purposes, were derived for each of the tested temperatures based on an inverse analysis, in order to maximize the agreement between experimental and numerical results in terms of (i) failure loads, (ii) load vs. slip responses, and (iii) strain distributions. Compared to the EBR specimens, the bond–slip relationships derived for the NSM specimens at ambient temperature presented (i) similar stiffness and (ii) higher values of maximum shear stress. With increasing temperatures, although both strengthening techniques exhibited comparable stiffness decrease, the maximum shear stresses for the NSM technique were higher than the EBR counterparts, attesting the better performance of the former technique.

Bond slip model in cylindrical reinforced concrete elements confined with stirrups

An analytical model able to evaluate the bond-slip law of confined reinforced concrete elements is developed and presented in this paper. The model is based on the studies developed by Tepfers and by den Uijl and Bigaj on the thick-walled cylinder model and extended to the case of the presence of transverse reinforcement. The bond strength and the considered failure modes (splitting or pull-out failure) are expressed as a function of the geometrical (concrete cover and transverse reinforcement) and mechanical (concrete strength) parameters of the element. The application of the proposed methodology allows to forecast the failure mode, and equations for the bond-slip law are finally proposed for a range of steel strain lower than the yielding one.

SRG/SRP–concrete bond–slip laws for externally strengthened RC beams

The goal of the paper is to assess the effectiveness of some Fiber Reinforced Polymer (FRP)–concrete bond–slip laws, widely used in the numerical analyses, to model Steel Reinforced Grout (SRG)–concrete and/or Steel Reinforced Polymer (SRP)–concrete interfaces. The assessment was carried out through a suitable Finite Element (FE) study developed on a set of externally strengthened Reinforced Concrete (RC) beams. For this purpose a database of experimental results, available in literature, was collected.A two-dimensional FE model was defined for each tested beam. The linear and nonlinear behavior of all materials was adequately modeled, whereas the connection between concrete surface and external reinforcing layer was simulated by a cohesive element with a suitable damage model.The numerical and experimental comparisons were used to evaluate the reliability and adaptability of the FRP–concrete bond–slip laws to predict the structural behavior of RC beams externally strengthened to flexure with SRG and SRP innovative systems.The study showed that among a set of bi-linear FRP–concrete bond–slip laws one was also suitable to simulate the behavior of SRG–concrete interface. For the SRP–concrete interface a modification of the same bond–slip law was proposed, calibrated and validated against the available experimental data.

Glass beams reinforced with GFRP laminates: Experimental tests and numerical modelling using a discrete strong discontinuity approach

This paper presents an experimental and numerical study about the bond behaviour between glass panes and glass fibre reinforced polymer (GFRP) laminates and the structural response of glass–GFRP beams. For this purpose, tests on glass–GFRP double-lap joints and tests on glass–GFRP hybrid beams were carried out. The finite element method was used and a discrete crack approach based on non-linear fracture mechanics was adopted. The bond between glass and GFRP is modelled by means of zero thickness interface elements. The material properties that characterize the interface, namely the shear stiffness, the cohesion and the mode-II fracture energy, are evaluated with the objective of simulating the experimental results obtained from double lap shear tests on glass–GFRP bonded joints. The obtained parameters, describing the bond-slip law between glass and GFRP, are then used to model the structural response of glass beams reinforced with GFRP. The numerical model is assessed by comparing the simulated structural responses and corresponding crack patterns with the experimental counterparts. This work contributes for a better understanding of the stress transfer mechanisms between glass and GFRP and the failure mechanisms found in the above-mentioned experimental tests, as well as to clarify the interpretation of the results obtained from those tests.

Theory and calculation of stress transfer between fiber and matrix

For the better use of composites and a deeper insight into the fracture propagation and stress transfer of the interface between fiber and matrix, a theoretical solution of closed form is presented with the assumed bilinear local bond-slip law and a parabolic shear stress distribution along the thickness of the matrix. The load-displacement relationship and interfacial shear stress are obtained for four loading stages. Finally, the effects of Young’s modulus of fiber (matrix) and bond length on the performance of the interface are illustrated.

A modified fiber-reinforced plastics concrete interface bond-slip law for shear-strengthened RC elements under cyclic loading

The objective of this article is to realistically analyze fiber-reinforced plastics (FRP) retrofitted reinforced concrete structures under cyclic loading taking into account FRP–concrete bond-slip law with cyclic bond degradation. In literature, even though numerous studies have been conducted in FRP–concrete interface bond-slip modeling under cyclic loads, a small number of them consider the influence of cyclic degradation on FRP–concrete interface bond behavior. Within this framework, the bond-slip law for carbon fiber-reinforced plastics–concrete interface is revised by utilizing Harajli's and Ko-Sato's approaches. The procedure is distinct from others because it develops existing deficiencies of these approaches, whereas a more reliable modeling process is proposed for use in practice. Conventional bond-slip law of Lu et al. is compared with this interface relationship stated in this investigation and the difference is clearly shown in terms of structural parameters. Experimental tests are conducted at the same time for verification. It is proved that cyclic bond degradation affects the interface behavior; thus, the structural response cannot be omitted in structural evaluations. Structural performance measures are obtained in good agreement for each level of cycles. The technique proposed clearly exhibits structural response difference between monotonic and cyclic loadings while good agreement is reached with experimental results. POLYM. COMPOS., 2015. © 2015 Society of Plastics Engineers

Numerical simulation of the fire behaviour of thermally insulated reinforced concrete beams strengthened with EBR-CFRP strips

This paper presents numerical investigations on the fire behaviour of reinforced concrete (RC) beams flexurally strengthened with externally bonded reinforcement (EBR) carbon fibre reinforced polymer (CFRP) strips, simultaneously subjected to a service load and the ISO 834 standard fire. Two dimensional (2D) finite element (FE) models were developed in order to simulate previous fire resistance tests on CFRP-strengthened RC beams comprising different fire protection schemes, with a thinner insulation layer along the bottom soffit of the beams and a thicker one in the CFRP anchorage zones. The variation with temperature of the thermal and mechanical properties of the constituent materials was considered and the CFRP-concrete interaction was modelled by means of bi-linear bond-slip laws previously calibrated for different temperatures. The numerical results were compared with experimental temperatures, midspan deflections and time for CFRP debonding. The models provided accurate predictions of the thermo-mechanical fire response of the beams, confirming that it is possible to exploit the CFRP mechanical contribution through a cable mechanism, provided that a thicker insulation is applied in the CFRP anchorage zones. The models predicted the CFRP debonding when the average temperature at the CFRP-concrete interface along the anchorage zones ranged from 1.1 to 1.4 times the adhesive glass transition temperature, which also compared well with test measurements. The numerical study presented in this paper, besides providing useful data to understand in further depth the structural effectiveness of CFRP strengthening systems during fire (namely, the strains/stresses in the materials and CFRP-concrete interface during fire exposure), allowed validating the global bond-slip laws for the CFRP-concrete interaction previously proposed by the authors, showing their adequacy for simulating the behaviour of EBR-CFRP strengthening systems under fire exposure, and a strategy for the design of fire protection systems that is based on the fulfilment of two main requirements: (i) the CFRP temperature along the central zone must remain below a certain critical temperature, avoiding its tensile rupture; and (ii) the temperature of the CFRP-concrete interface along the anchorage length must be kept below the adhesive Tg of the adhesive in order to prevent the CFRP debonding for the required time of fire exposure.

Nonlinear Analysis for RC Beams Strengthened by Externally Bonded Steel Plates with Bond-Slip

The RC beams strengthened by externally bonded steel plates are regarded as composite beams which consist of steel plates and reinforced concrete with bond-slip. Based on the deformation compatibility relationship between steel plates and reinforced concrete, the constitutive relationship which can reflect the mechanical properties of steel plates and reinforced concrete and the bond-slip constitutive law, a nonlinear differential equation for the beam, expressed in the form of the tensile force of steel plates, is derived. A nonlinear analytical solution under the double concentrated load of the RC beams strengthened by externally bonded steel plates is obtained. By which a coordination coefficient in the form of the characteristic value of the beam is deduced. By using the coordination coefficient, a practical nonlinear analysis method, which can exactly reflect the bearing capacity and deformation of the beam is established.

Prediction of the bond–slip law in externally laminated concrete substrates by an analytical based nonlinear approach

To attain a suitable strengthening system for concrete structures, adequate stress distribution between externally bonded fibre reinforced polymer (FRP) materials and the substrate is required. With the growing application of the FRP in strengthening of the structures and in order to be able to sufficiently model the strengthened structure behaviour, the need for a generic bond relationship is increasing. Hence, this article introduces a simplified analytical method to define the bond–slip law of the FRP–concrete interfaces. The advantage of this procedure is that the model is developed only based on boundary conditions and therefore can be applied to any type of the adhesively bonded joints. Subsequently, the bond characteristics obtained from the proposed model is compared with the experimental results and the previous models. A modified single lap shear test set-up is adopted during the experiments. In addition, a new relationship is proposed for determination of the fracture energy corresponding to antisymmetric in-plane shear mode. Analytical analysis indicates that the interfacial fracture energy increases for the samples with thicker bondline or lower FRP-to-concrete width ratio.

Analysis of the bond between Fabric Reinforced Cementitious Mortar (FRCM) strengthening systems and concrete

The paper is devoted to the analysis, both experimental and theoretically, of the bond between a cement based fiber reinforced strengthening material and the concrete substrate. Results of tests on concrete specimens strengthened with the PBO-FRCM system, made by PBO (short of Polypara-phenilene-benzo-bisthiazole) fiber meshes embedded into a cementitious mortar (FRCM, Fabric Reinforced Cementitious Mortar), are presented and discussed. Tests were carried out varying both the bond length, the amount of the strengthening system and the service temperature. Obtained results furnish useful information (i) to determine the loss of bond between the PBO-FRCM system and the concrete, (ii) to define the failure modes and (iii) to evaluate both the influence of environmental conditions (service temperature) and mechanical and geometrical parameters on the loss of bond PBO-FRCM-to-concrete. Test results were, then, utilized to calibrate a local bond-slip relation. A comparison between experimental results and theoretical predictions of the bond-slip law PBO-FRCM-to-concrete is, finally, presented and discussed.

Analytical Modeling of Composite-to-Masonry Prisms Bond

The composite-to-substrate interfacial stresses transfer mechanism is one of the critical issues in externally-bonded structural strengthening by means of composite fabrics. In this work, an analytical approach for modeling the debonding process of a composite on a non-homogeneous substrate is developed and applied to simulate the loss of bond of FRP on brick masonry. The analytical formulation is based on the experimental outcomes of bond shear tests, which are part of a Round Robin activity involving several laboratories. The experimental work is the follow up of a previous one [1], and comprises 12 single-lap shear tests of four kinds of unidirectional reinforcement, i.e., glass, carbon, basalt and steel, applied with epoxy resin to masonry prisms composed by five clay bricks and four mortar joints. The analytical simulations of the experimental tests rely upon a bi-linear non-homogeneous bond-slip law that was calibrated using the experimental population. Eventually, the analytical results are compared to experimental ones both, in terms of global (load to displacement curve) and local behavior (strain profile on the reinforcement for increasing load values).

Numerical analysis of FRP anchorage zones with variable width

The use of Fibre Reinforced Polymers (FRP) has recently become widespread in the construction industry. However, some drawbacks related to premature debonding of the FRP composites from the bonded substrates have been identified. One of the solutions proposed is the implementation of mechanical anchorage systems. Although some design guidelines have been developed, the actual knowledge continues to be rather limited. Thus, designers and researchers have not yet achieved any consensus on the efficiency of any particular anchor device in delaying or preventing the premature debonding failure mode that can occur in Externally Bonded Reinforcement (EBR) systems. This paper studies the debonding phenomenon of FRP anchoring systems with a linear variable width, with a numerical analysis based on the Distinct Element Method (DEM). Combined systems with constant and variable width are also discussed. The FRP-to-parent material interfaces are modelled with a rigid-linear softening bond–slip law. The numerical results showed that it is possible to attain the FRP rupture force with a variable width solution. This solution is particularly attractive when the bonded length is shorter than the effective bonded length because the strength of the interface can be highly incremented.

Analytical and numerical modeling of composite-to-brick bond

In masonry components strengthened with externally bonded composites, good bonding is one of the most important aspects governing structural behavior, since failure usually takes place with detachment between reinforcement and substrate. This type of event is a brittle, sudden and therefore undesirable failure mechanism; nor does it allow the full strength of the reinforcement to be exploited. Many experimental data on bonding have recently become available from a Round Robin Test carried out within the framework of RILEM TC-223. In the present paper, experimental tests were simulated at increasing levels of complexity; bond behavior was first studied with an analytical model based on bi-linear representation of bond law. Two-dimensional and three-dimensional finite element analyses were then performed, according to various bond-slip laws. In particular, a number of bi-linear and non-linear interface laws were used, calibrated according to several strategies but with the same experimental population. Lastly, several commercial codes and types of finite elements were examined. This work may be said to represent a numerical Round Robin Test, with various simulations and modeling approaches. Analytical and numerical results are compared with experimental ones, in terms of both overall behavior (load to displacement curve) and local behavior (strain profiles on reinforcements at increasing load values), showing the importance of both types of information in order to obtain reliable predictions of experimental results.

Delamination process analysis of FRP-to-parent material bonded joints with and without anchorage systems using the Distinct Element Method

This study looks at the analysis of the interface between Fiber Reinforced Polymer (FRP)-to-parent material bonded interfaces. The performance of FRP-to-parent material bonded joints for the Externally Bonded Reinforcement (EBR) technique is numerically modelled with the PFC2D software which is based on the Distinct Element Method (DEM). It is believed that this represents the first time the DEM has been used to simulate the delamination process of FRP-to-parent material bonded joints. In order to validate the analysis performed with the DEM, a Pull-out test with no slip constrains was modelled and different linear bond-slip laws were assumed. The numerical results revealed that the DEM is capable of estimating with good accuracy the exact solutions of bond stresses, strains or slippages along the bonded length for linear bond-slip laws. The bi-linear law available in PFC2D was then compared to the numerical results obtained from other another code developed by the author. The delamination process of Pull-out tests with slip constrain at one of the free ends of the FRP plate is also described and analyzed. The results obtained from the DEM revealed that the delamination process ends with stiffness equal to the axial stiffness of the FRP plate. This evidence highlights the need to design mechanical anchor devices capable of preventing premature debonding which is known to occur on EBR systems.

Bond behavior of SRG-strengthened masonry units: Testing and numerical modeling

Innovative materials such as steel reinforced grout (SRG) have shown superior behavior in terms of sustainability and compatibility comparing to their FRP counterparts for external strengthening of masonry structures. Considering the critical bond mechanisms at interfaces, this paper addresses an experimental and numerical investigation on bond in SRG-strengthened masonry by performing conventional single-lap shear bond tests revealing the importance of substrate preparation for application of SRG followed by a numerical model proposing suitable interfacial bond-slip laws. The numerical model, once validated against experimental results, is used to investigate further aspects of the bond behavior and the results are discussed.

Role of multiaxial state of stress on cracking of RC ties

This paper aims to investigate the role and effect of stress diffusion and bond deterioration in the analysis of reinforced concrete ties. Although tension ties seem to be basically in a uniaxial state of stress, after the onset of cracking the problem presents a multiaxial diffusion of stresses. In this paper, a uniaxial 1D numerical model has been compared with more sophisticated 2D and 3D Finite Element (FE) models, in order to investigate the different level of accuracy and information that can be attained considering or not the multiaxial state of stress. The obtained results show that the contribution of stress diffusion in concrete blocks between cracks has a certain importance for the evaluation of the global and local behavior of investigated tension ties, but it does not alter completely the response. Furthermore, the inclusion of damage in the bond–slip law due to the presence of “cone” cracks improves the description of the element behavior especially in the stabilized cracking stage. The same applies if thin secondary cracks are taken into account.

Numerical Simulation of the Behavior of Cracked Reinforced Concrete Members

Refined non-linear static or dynamic analyses of reinforced concrete structures require the knowledge of the actual force-displacement or bending moment-rotation curves of each structural member, which depend on the crack widths and on the crack pattern, and after all on the slip between concrete and reinforcing steel. For this reason the definition of improved local models taking into account all these local aspects is a fundamental prerequisite for advanced assessment of r.c. structures. A numerical procedure which allows to predict the relative displacement between steel reinforcement and the surrounding concrete in a reinforced concrete element, once assigned the stress in the naked steel bar and the bond-slip law is discussed. The method provides as final outcomes the sequence of crack openings and the individual crack widths, regardless of the particular bond-slip correlation adopted. The proposed procedure is implemented referring to two relevant experimental case studies, demonstrating that it is able to predict satisfactorily actual strain fields and slips along the investigated reinforced concrete elements.

Modelling of the bond behaviour of tuff elements externally bonded with FRP sheets

The performance of fibre reinforced plastic (FRP) materials used for external strengthening depends strongly on the bond behaviour at the FRP-substrate interface. In this paper, the results of an analytical model and of two Finite Element (FE) models (bi-and three-dimensional) for simulating bond behaviour in FRP-strengthened masonry elements using zero-thickness interface elements are presented. The primary parameters of bilinear and nonlinear bond-slip laws were determined from experimental results of single shear bond tests that the authors conducted on masonry blocks of yellow tuff bonded with FRP carbon and glass fabrics. Several parametric analyses were conducted to estimate the effect of the primary bond law parameters on the global behaviour of the specimens and to determine the effective bonded length for the investigated masonry support.

Bond–slip on CFRP/GFRP-to-concrete joints subjected to moisture, salt fog and temperature cycles

Research on bond between composite and concrete on beams externally reinforced with fiber reinforced polymers (ERBs) has generated many publications, but uncertainties remain. The issue of the long term behavior of those joints, especially the effect that severe and prolonged environmental actions may induce, justifies the search for additional data and recommendations to avoid premature debonding and failures.The present paper devotes attention to the effects of environmental aging on the constitutive bond-slip curves. Aging was imposed on an accelerated manner and several actions used to degrade the behavior of the joints evaluated by mechanical testing.Prismatic blocks of reinforced concrete linked on the upper side by a stainless steel hinge and externally bonded by a continuous strip of carbon or glass fiber reinforced polymer (CFRP or GFRP) adherent to the soffit were made so as to fit in commercially available laboratory climatic chambers. After aging, they were tested till failure under four point loading.Aging conditions imposed on the CFRP beams were (i) cycles of high-low relative humidity, (ii) salt fog cycles, and, on the GFRP beams, (iii) salt fog cycles, (iv) dry/wet cycles (water with 5.0% weight of NaCl), (v) total immersion in salt water, and (vi) freeze/thaw cycles.The results of the experimental program enabled the proposal of bond-slip laws that take into account the aging of the beams. They also showed that salt fog cycles were more severe in the case of CFRP, while freeze/thaw cycles were more degrading on bond of GFRP-to-concrete. The salt water effects on the GFRP beams appeared to be beneficial, most likely by improving the tensile strength of concrete. Numerical modeling certified by the obtained experimental data is presented that allows more general estimates of the environmental effects.

Critical Analysis of Fibre‐Reinforced Polymer Near‐Surface Mounted Double‐shear Pull‐out Tests

ABSTRACTThe study of the bond behaviour between fibre‐reinforced polymer (FRP) systems and concrete is an issue that nowadays attracts many researchers. The scientific community dedicated to the research of FRP reinforcement has been conducting numerous experimental programmes aiming to assess the local bond–slip law of the FRP–adhesive–concrete connection. This paper reports the relevant results obtained by the Structural Composite Research Group of Minho University in the scope of an international Round Robin Test. The suitability of the recommended test setup to derive a local bond constitutive law for modelling the bond behaviour of near‐surface mounted reinforcement systems is discussed based on a deep interpretation of the results.