# Development of Analytical Model for Bonding of CFRP Rod in Concrete Subjected to Cyclic Loads
## 9 Discussion  
The study aimed to enhance understanding of the relationship between Carbon-Fibre-Reinforced Polymer (CFRP) rods and both conventional Grade 40 concrete and Ultra-High-Performance Fibre-Reinforced Concrete (UHPFRC) under the demanding conditions of cyclic loading. Experimental and analytical findings revealed that the CFRP-UHPFRC bond exhibits significantly higher strength and displacement than the CFRP-concrete bond. Figure 26: Numerical Force–Displacement with Interface Element for UHPFRC. Figure 24: Damage Propagation and Bonding/Debonding Area by CFRP Rod under cyclic Pull-Out excitation in: (**a**) G40 Concrete; (**b**) UHPFRC. Figure 25: Numerical Force–Displacement with Interface Element for G40 concrete. This remarkable performance stems from several factors: the superior tensile strength and stiffness of UHPFRC compared to concrete; the enhanced interfacial bonding between the CFRP rod and UHPFRC, attributable to the denser microstructure of UHPFRC; and the reduced cracking tendency of UHPFRC, resulting in more ductile bond behaviour. Deliberate development and integration of an analytical interface element into a finite element model addressed the previously recognised gap in these models' ability to accurately replicate empirical data. The introduction of this interface element proved crucial, aligning computational predictions more closely with experimental results, thereby laying a foundation for the construction or rehabilitation of more reliable and robust infrastructure. The FEM model developed in this study demonstrated accurate predictions of load-bearing capacity, displacement at peak force, bond strength, and average shear stress along the CFRP rod for the CFRP-UHPFRC bond. Discrepancies between experimental and analytical results were within 10% for all parameters. The enhanced Finite Element Method (FEM) centres around the incorporation of the interface element. Data presented in Table 15 highlight that initial simulations without the interface element exhibited significant deviations from experimental data. Notably, the maximum pull-out force was overestimated by a substantial 51.12%. The incorporation of the newly developed interface element effectively mitigated this difference, bringing the force prediction to a much-improved accuracy level of 8.38%. Additionally, the disparity in the critical parameter of displacement at peak forces was dramatically reduced from 12.89% without the interface element to an impressive 2.84% once the element was introduced into the model. The efficacy of implementing the interface element is further emphasised by the improvement in bond strength predictions--a parameter of paramount importance for structural integrity where inaccuracies can lead to catastrophic miscalculations. The initial model projected bond strength at an overestimated figure that was 51.23% higher than the experimental observation. With the inclusion of the interface element, this figure was \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Parameters** & **UHPFRC** & **Discrepancy** & **Improvement*** \\ \hline \multirow{4}{*}{Maximum Pull-out Force (kN)} & Numerical w/o Interface & 70.00 & 51.12\% & \\  & Experimental & 41.50 & & 42.74\% \\  & Data & & & \\  & Numerical with & 45.13 & 8.38\% & \\ \hline \multirow{4}{*}{Displacement at Peak Force (mm)} & Numerical w/o Interface & 9.14 & 12.89\% & \\  & Experimental & 10.4 & & 10.05\% \\  & Data & & & \\  & Numerical with & 10.7 & 2.84\% & \\  & Interface & & & \\ \hline \multirow{4}{*}{Bond Strength (MPa)} & Numerical w/o Interface & 7.65 & 51.23\% & \\  & Intermediate & 4.53 & & 43.39\% \\ \cline{1-1}  & Numerical with & 4.9 & 7.84\% & \\ \hline \multirow{4}{*}{Average Shear Stress along CFRP Rod (Pa)} & Numerical w/o Interface & 5.17 & 51.27\% & \\  & Experimental & & & \\ \cline{1-1}  & Data & 3.06 & & 42.82\% \\ \cline{1-1}  & Numerical with & 3.33 & 8.45\% & \\ \hline \hline \end{tabular}  
* Improvement in accuracy of predictive simulations.  
\end{table} 
Table 15: Comparison of data.