# Development of Analytical Model for Bonding of CFRP Rod in Concrete Subjected to Cyclic Loads
## 1 Introduction  
Concrete, which has been fundamentally used in the realm of construction, owes its enhanced properties to the advent of reinforced concrete. This significant advancement, credited to [PERSON] in 1849, marries the flexural strength of metal with concrete's inherent compressive resilience, enabling structures to withstand formidable loads [1]. Superstructures--encompassing bridges, transportation corridors, and skyscrapers--are often plagued by fatigue failures arising from the relentless imposition of cyclic loads. Bridges epitomise vulnerability in this context, with cyclic loading precipitating fatigue failure, environmental degradation, and thus potential collapse. The material sciences field has witnessed considerable strides, particularly with the advent of High-Performance Concrete (HPC) and Ultra-High-Performance Concrete (UHPC), which have found favour in modern construction practices [2]. Investigations by [PERSON] and [PERSON] into UHPC overlays for bridge decks have underscored the material's exceptionally low permeability, directly contributing to an extension of the structure's service life. Theduo undertook both cyclic and static loading tests on traditional concrete substrates augmented by UHPC overlays. Their findings elucidate the reinforcement potential of UHPC overlays in sustaining bridge deck integrity, with a pressing emphasis on the precision of joint detailing [3]. Parallel research efforts by [PERSON] et al. have explored the potential of using recycled macrofibres from discarded Glass-Fibre-Reinforced Polymer (GFRP) composites to reinforce UHPC, aiming to mitigate costs and environmental repercussions. Despite observing a reduction in workability and compressive strength--up to 21.8%--the studies revealed significant gains in flexural strength and toughness, suggesting a sustainable and economically viable path forward for the UHPC domain [4]. In a similar vein, [PERSON] and [PERSON]'s engagement with numerical simulations via finite element modelling elucidated the bonding dynamics at UHPC interfaces. Their research unravelled strategies to augment the bonding strength in precast UHPC elements, evidenced by alignment between their model outcomes and empirical data [5]. Now, modern imbroglios demand that the quest for reliability, efficiency, and sustainable innovation in construction never ceases. One such innovation has been the integration of Fibre-Reinforced Polymer (FRP) sheets, which has proven pivotal for the refurbishment and repair of enfeebled structures. The substantive contribution of FRPs in extending the service life of existing buildings through novel applications--from cloaking cracks and improving thermal insulation to bolstering the shear and flexural integrity of concrete elements--cannot be overstated. However, the tale of FRP extends beyond mere structural rehabilitation; it includes preventive applications in otherwise robust structures to enhance their resilience against future uncertainties [6]. The advent of Carbon-Fibre-Reinforced Polymer (CFRP) marked a milestone in this narrative, touted for its superior corrosion resistance to traditional steel reinforcements. The implementation of CFRP as a substitute for steel bars has been largely driven by its remarkable durability in hostile environmental conditions. The pursuit of understanding the full potential of CFRP has spanned various methodologies of application, including the Embedded Through Section (ETS), which has been proven to enhance shear capacity commendably compared to its counterparts--Externally Bonded (EB) and Near Surface Method (NSM). These methods, EB and NSM, themselves have shown shear capacity increases of 23% and 31%, respectively. However, these innovations also delineated the challenges of bonding CFRP with UHPRRC, notably the reductions in bond strength observed when increasing the embedment length, a phenomenon exacerbated by the nature of the composite materials [7; 8].