Development length and bond strength equations for FRP bars embedded in concrete

Highlights

• Code equations estimate bond strength and bond length of FRP bars conservatively.

• Proposed equations predict development length and bond strength of FRP bars closely.

• Quadratic terms increase accuracy of analytical estimates from regression equations.

• FRP strength, elastic modulus and concrete cover have minor influence on accuracy of estimates.

• Modified hinged beam method allows examining effects of all parameters on FRP-concrete bond.

Abstract

The present study pertains to the linear multiple regression analyses on a database of 185 hinged-beam experiments on FRP bars. The database was compiled from 51 tests conducted within the scope of the present study and 134 tests conducted by previous researchers. Bond strength and development length equations, taking different types of FRP bars and surface finishes into account, were developed and the estimates from the proposed equations were compared to the estimates from the respective equations of various international FRP-reinforced concrete codes. The proposed equations, addressing all kinds of FRP bars and surface finishes, were shown to be in much closer agreement with the experimental results compared to all previous equations according to different statistical evaluation criteria, i.e. the Coefficient of Determination, Root Mean Square Error and Mean Absolute Percentage Error. The code equations were established to yield to exteremely over-conservative and non-economical results in all types of FRP bars with different surface textures.

Introduction

The flexural behavior of RC beams is greatly influenced by the adequacy and degree of the bond between concrete and reinforcement. The tensile force carried by the reinforcement, which counterbalances the total compression force in concrete and compression reinforcement, can only be achieved in the presence of strain compatibility between tension bars and the surrounding concrete layer. The interfacial stresses between concrete and reinforcement enables the transfer of tension forces to the reinforcing bars (rebars). The full tensile capacity of a rebar can only be developed in the presence of sufficient bond strength and development length of the bar.

The bond behavior of FRP rebars have various similarities to the bond behavior of conventional steel bars. But, the number of parameters affecting the FRP-concrete bond is much greater than the number of parameters influencing the steel–concrete bond. The bond strength and development length of FRP reinforcement in concrete depends on many factors. FRP reinforcement type (AFRP, BFRP, CFRP, GFRP), bar surface finish (wound, ribbed, sand-coated, wrapped, braided etc.), reinforcement diameter, embedment length, concrete cover, concrete compressive strength, transverse reinforcement, environmental conditions can be counted among these factors. Certain international FRP-reinforced concrete codes, guides and specifications, such as ACI 440.1R-15 [1], CNR [2], CSA S6-14 [3], CSA S806-12 [4] and JSCE 1997 [5], also incorporated one or more of these factors into their development length equations. However, some researchers stated that the bond strength and development length equations in the codes give very conservative estimates according to the experimental results [6], [7], [8], [9], [10], [11].

In the past, many researchers have investigated the factors affecting the bond strength and development length values of FRP bars through various test methods and presented bond stress and development length equations for these bars [9], [12], [13], [14], [15], [16]. However, the equations presented in the codes and proposed by previous researchers do not take all of the factors affecting the FRP-concrete bond, into account. The developed equations include solely one or more of the FRP reinforcement types (BFRP, CFRP and GFRP) and reinforcement surface types (sand-coated, wound, wrapped, ribbed and combinations of these, etc.) that have a significant effect on the development length. Since the development length depends on many parameters and only some of these parameters were regarded and reported in the previous studies, the results of these experiments cannot be considered in specifying the effect of a certain parameter on FRP-concrete bond.

In a great majority of experimental studies in the literature, the pull-out test method and its databases were employed to determine the development lengths of FRP bars. Since the stress and strain conditions of a bar in this test method differ significantly from the actual conditions, to which the tensile bars in a flexural member are exposed, this method cannot be relied upon when developing bond stress and development length equations for tension bars [17]. Consequently, a number of researchers used the beam-based methods to examine the bond behavior of FRP rebars. The beam-based methods simulate the actual conditions of tension bars in flexural reinforced concrete members by allowing the redistribution of stresses among various fibers in the beam and putting the rebar in an indirect tensile loading condition, i.e. tension from flexure.

Some of the studies on FRP bar-concrete bond via beam-based methods are summarized herein. Saleh et al. [18] examined the bond strength values of wrapped and sand-coated or only sand-coated GFRP reinforcement in high strength concrete through 28 hinged beam tests. In this study, the location of bars in concrete, reinforcement embedment length and bar diameter were used as test variables. The study indicated that the equations in the international regulations give very conservative values. In another study, Mazaheripour et al. [19] examined the bond behavior between steel fiber reinforced self-compacting concrete (SFRSCC) and GFRP reinforcement with the help of 36 hinged beam experiments. Concrete cover thickness, surface texture of the bar (ribbed and sand coated), reinforcement diameter and embedment length were adopted as test parameters. GFRP rebars with a 20d_b (d_b = bar diameter) embedment length in SFRSCC was stated to generally undergo pullout failure. Seis ve Beycioğlu [20] conducted 16 hinged beam experiments using BFRP reinforcement with various diameters and embedment lengths in normal-strength concrete. 20d_b embedment length was found to be critical in providing thin BFRP bars with sufficient adherence to concrete with C30 or higher grades. Based on 144 hinged beam tests with various embedment lengths, Hossain et al. [21] examined the bonding behavior of sand-coated GFRP rebars with low and high modulus of elasticity and diameters ranging between 15.9 and 19.1 mm in high and ultra high strength concrete. The experimental values indicated that the estimates from the equations in international regulations are over-conservative. Tighiouart et al. [22] tested 64 hinged beams to examine the bond behavior of two types of GFRP reinforcement with various embedment lengths and diameters in normal strength concrete. The bond strength values of GFRP rebars were observed to range from 5.1 to 12.3 MPa.

The beam-based experimental studies in the literature are far from considering all of the factors affecting the FRP-concrete bond. Therefore, there is a clear need for new experimental studies, which include all of the factors, all reinforcement types and surface textures, for developing realistic bond stress and development length equations. In this respect, a detailed experimental study, taking all of the parameters into account, was realized in the present study. To investigate the effects of all parameters, the conventional hinged beam method was modified by changing the beam dimensions and reinforcement details. Next, a hinged beam database was established from 51 modified beam experiments, carried out in the present study, and 134 conventional hinged beam experiments, compiled from different studies in the literature. This database was used to develop bond strength and development length equations for different FRP rebars with different surface finishes with the help of linear regression analyses. The main factors affecting the FRP-concrete bond strength, namely reinforcement diameter, concrete cover, concrete compressive strength, modulus of elasticity and tensile strength of reinforcement, were also incorporated into the formulae. The proposed bond strength and development length equations were compared to the bond strength and development length equations of the international codes [1], [2], [3], [4], [5]. Several statistical evaluation criteria, including the Coefficient of Determination (r), Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE), were used in this comparison.