Statistical analysis of existing models for flexural strengthening of concrete bridge beams using FRP sheets

Abstract

This paper performs a statistical analysis of previously proposed models for resisting the debonding of FRP sheets used in strengthening reinforced and prestressed concrete beams. End debonding and intermediate crack-induced debonding modes of failure are studied for beams in flexure. Two different databases are assembled from published experimental debonding tests on concrete beams of different span lengths. The first database contains the results of four point bending tests performed to study the behavior of the FRP-concrete bond at the end of the FRP sheet. The second database which includes four point bending tests, three point bending tests and one point loading tests, has been created to examine intermediate crack-induced debonding. These two databases are significantly larger than those used in developing any of the existing debonding strength models and provide a solid basis for assessing the performance of such models. A regression analysis reviews the relationship between the experimentally measured loads that caused debonding to the model predicted values as well as the bias and the variability in the prediction models. This regression analysis allows for drawing conclusions on the most appropriate and accurate models, from a statistical point of view, that may be used in a follow up reliability-based calibration of partial safety factors. The applicability of such information for the development of design specifications for strengthening of deteriorated concrete bridges is highlighted. This will be implemented in a forthcoming companion paper.

Introduction

Bonding of Fiber-Reinforced Polymer (FRP) to the tension face of concrete beams has become a frequent strengthening method over the last decade. The application of FRP to the tension face of a concrete beam or slab has multiple benefits, including: increased ultimate flexural strength capacity, increased post-cracking stiffness, as well as concrete crack control whereby the bonding of FRP sheets to concrete beams results in finer and more evenly distributed cracks when compared to the cracks that develop in unstrengthened beams. Because of these benefits, it is clear that flexural strengthening of reinforced concrete beams with FRP has a great potential for becoming a primary strengthening scheme for deteriorated infrastructure systems. However, because of the relative novelty of this technology, a more complete understanding of the behavior of FRP-strengthened beams and their failure mechanisms need to be gained before the wide spread adoption of this technology in engineering practice. As a minimum, the confidence levels in the safety margins of existing and proposed design criteria should be ascertained. This would require an objective estimation of the biases implied in existing and recently proposed design criteria and an analysis of the variability of the expected loads that cause failure from the predicted loads.

The fibers used in common FRP strengthening schemes are usually made of glass, carbon or aramid. To bond the fibers together and to the substrate surface on which they are being applied, a resin matrix is used. Two methods of application are frequently used. In situ installations require placing the fibers in an open mold, attaching the assembly to the surface and then saturating the assembly with resin. More commonly, the fibers may be first saturated with epoxy and then bonded to the prepared surface of concrete. In situ assemblies of the fibers are usually referred to as wet lay-up. Preimpregnated plates or sheets of fibers (prepreg) can also be installed by applying resin to bond the sheets to the concrete surface.

Hollaway and Teng [1] recognized six main failure mechanisms for reinforced concrete beams flexurally strengthened with FRP. These are represented in Fig. 1 as: (a) FRP rupture, (b) crushing of concrete, (c) intermediate crack-induced interfacial debonding, (d) concrete cover separation, (e) plate end interfacial debonding, (f) concrete shear failure and (g) critical diagonal cracking. Modes (a), (b) and (f) are classical concrete beam failure mechanisms and have been analyzed to a great extent in the past [2], [3], [4]. The remaining failure mechanisms are specific to FRP strengthened beams and are characterized as premature failure modes because they take place before realizing the full potential of the strengthening scheme. Modes (d), (e) and (g) are often indistinguishable and in fact, Smith and Teng [5], [6] identified a mixed failure mode where the failure occurs at the same time by the concrete cover separation and the plate end interfacial debonding mode. In this paper, modes (d), (e) and the combined mode will be grouped under the label end debonding failure mode. Yao et al. [7] explain that intermediate crack induced debonding, identified as mode (c), normally initiates in the high moment region due to a flexural or flexural-shear crack. On the other hand, end debonding is initiated by high interfacial stresses at the plate end as explained by Yao et al. [7].

Failures of FRP strengthened beams due to concrete crushing are easily predicted and this mode of failure would allow for the most efficient use of the materials while preserving an acceptable level of ductility. FRP rupture is also a mode failure that can be easily determined. Although, the FRP rupture mode is permitted in most existing guidelines, it would be preferable to avoid it as it may lead to brittle failures.

When designing an FRP strengthening scheme, it is generally most difficult to predict and control the debonding modes of failure. In fact, a large number of experimental studies reported premature failures by debonding rather than concrete crushing or FRP rupture. For this reason, considerable research effort has been expended on understanding the underlying factors that cause FRP debonding, to develop models for predicting debonding, and to propose design guidelines to minimize the risk of its occurrence under design loading conditions [2], [8], [9], [10].

Most analytical and experimental studies have focused on studying the end debonding mode of failure, while intermediate crack induced debonding has received much less attention and few models have been developed for predicting its occurrence. Nevertheless, the debonding failure mechanisms are still found to be complicated processes that are not fully understood, making it difficult for engineers to estimate the actual capacity of FRP-strengthened concrete beams and thus making them reluctant to use this new technology on a wide scale.

Over the last decade, several guidelines for use of FRP in construction have been developed [11], [12], [13], [14], [15]. Many of these guidelines are under constant refinement as more information is gathered on the behavior of structural components strengthened using FRP. In particular, the American Concrete Institute (ACI) published the first version of its guidelines in 2002 and released a revised version in 2008. Most of these and other proposed design criteria have used equations that provide lower bounds for the beam’s capacity based on limited sets of experimental data or else developed advanced fracture mechanics models without following modern methods for developing reliability-based design codes and specifications that would take into consideration the uncertainties associated with the input parameters as well as the modeling assumptions. Triantafillou in 1992 [16] was the first to propose reliability-based sets of design equations for FRP-strengthened beams but only looked at the concrete crushing and FRP rupture modes. A recent study by Atadero and Karbhari [17], [18] developed reliability-based criteria for debonding using fracture mechanics models but the approach considered only randomness in the input parameters and did not account for the modeling uncertainties, also known as systemic uncertainties, which in many cases may be more significant than the parametric uncertainties. The implementation of reliability-based design specifications is extremely important for FRP-strengthened concrete beams due to the large level of variability observed in experimental tests results and the uncertainties in determining the material properties.

The objective of a study currently underway at the Technical University of Catalonia (UPC), in Barcelona is to propose appropriate reliability-based design equations with properly calibrated safety factors that can be used during the design of a strengthening scheme to enhance the flexural capacity of existing concrete bridge beams. In a first step of this study, a statistical analysis of available models is performed and presented in this paper. The goal of this analysis is to study the systemic uncertainties associated with existing models. To this end, experimental results on strengthened concrete beams that failed due to either end debonding or intermediate crack induced debonding are compared to several available proposed predictive and design models to determine the most appropriate ones for implementation in design codes. The experimental database was carefully constructed from an extensive survey of the published literature, and presented in Appendix A Database of beams failed by end debonding, Appendix B Database of beams failed by intermediate crack induced debonding. The statistical analysis of the selected existing debonding models will provide the necessary information to calibrate appropriate safety factors that should be applied in conjunction with the selected models so that future design codes would provide the engineers with the tools necessary to use FRP-based concrete beam strengthening schemes that would lead to uniform and consistent reliability levels.