# Development of Analytical Model for Bonding of CFRP Rod in Concrete Subjected to Cyclic Loads
## 1 Introduction
The intricacies of CFRP's bonding with concrete also manifest in the load-slip relationship, a paramount factor in structure longevity. For instance, the pull-out behaviour of CFRP and AFRP reinforced rods is governed by distinct load-slip profiles. The AFRP rod exhibits a linear relationship until a certain slip threshold, after which yield occurs. Contrastingly, CFRP demonstrates a non-linear frequency under loading with higher robustness, supporting loads up until similar slips, presenting a more resilient pull-out behaviour [9]. [PERSON] et al. embarked on a comprehensive investigation into the bond performance of CFRP bars, blending experimental and theoretical approaches. Their study, encompassing the stress-slip behaviour under monotonic and reversed cyclic loading, unveiled a direct link between elevated concrete compressive strengths and enhanced maximum bond stresses. Furthermore, the diameter of CFRP bars and embedment length significantly influenced the regulation of this maximum stress. Notably, the study revealed that under reversed cyclic loading, the maximum bond stresses were diminished compared to monotonic loading under identical conditions, emphasising the susceptibility of CFRP bond to load variations [10]. While much progress has been made, the application of CFRP under the arduous conditions of cyclic loading continues to present a challenge; one that extends beyond traditional means of steel-concrete bonding. The anisotropic behaviour of CFRP, driven by fibre orientation and adhesive matrix properties, demands specialised consideration. This is of particular importance as it governs the primary failure mechanisms--ranging from concrete crushing to FRP rupture--each influenced to varying degrees by the manner of CFRP application [11]. An exploration into the failure modes of CFRP-concrete interfaces under cyclic fatigue provides further perspective. [PERSON], [PERSON], and [PERSON], through intensive experimental studies, recognised the onset of damage at the precise point where interfacial shear stress surpassed 80% of its ultimate strength. Various failure modes surfaced, such as cohesion failures within the concrete, adhesive failures, and interlaminar failures within the CFRP itself [12]. Yet, these investigations have stopped short of effectively simulating concrete sections embedded with CFRP rods, owing mainly to limited comprehension of the bond characteristics between the CFRP and concrete elements. Such information is pivotal for accurate simulations that could, in turn, guide thoughtful design and implementation practices. Currently, most models are constrained by a \"Tie\" constraint, a rudimentary and not entirely accurate representation of the complex CFRP-concrete interface--especially under the force of cyclic \"push-pull\" conditions that accentuate fatigue failures [12]. Despite the volume of studies dedicated to unveiling the mechanical and physical traits of CFRP rods for rehabilitation and enhancement applications, significant gaps linger. The influence of variables like embedment length, ambient conditions (temperature and humidity), and various binders utilised has been well-studied [13]. Yet, the understanding of bonding behaviours between CFRP and concrete, specifically under cyclic load conditions that reflect real-world structural pressures, remains a conspicuous lacuna in current research, limiting the simulation's accuracy for concrete embedded with CFRP rods using finite element methods [8]. It is this knowledge gap that this study seeks to bridge. The primary goal is to elucidate the bonding dynamics between CFRP rods and conventional G40 concrete as well as UHPFRC under the specific stresses of cyclic loads. To extend the practical application of this research, a robust analytical model has been developed to accurately simulate and predict the bonding characteristics of CFRP rods embedded in UHPFRC under cyclic loading conditions.