# Analytical Method and Analysis of Cold-Joint Interface
## 6 Conclusions  
1. This article presents a novel analytical model for the calculation of layered concrete interface behaviour. Two shear stress-shear slippage relationship curves (for interfaces with connectors and without connectors) were developed. The proposed analytical model could be employed up to the point when the layers severely slipped. Cold-joint interface behaviour analysis was performed by predicting the shear stress and slippage values using the proposed analytical method, by building a numerical model and employing finite element analysis. It appears that the analytical values were similar to the experimental values, especially at the point of highest interface shear stress. The numerical analysis shear stress results were lower than the experimental results up to the point of highest experimental shear stress and then, in some cases, surpassed the experimental results at the stage of friction and connector action. 2. The comparison of the experimental results, numerical analysis results and the results acquired by the analytical method led to the conclusion that the proposed analytical method is suitable for the analysis of a concrete interface with layers cast at different times. 3. The numerical parametric analysis led to the conclusion that, by increasing the interface friction magnitude, a higher interface shear resistance could be achieved. The interface behaved more rigidly in the earlier behaviour stages. Gradually, at a certain friction angle (coefficient), the cold-joint interface started to behave like a monolithic interface. 4. The parametric analysis of the influence of connector diameter led to the conclusion that a higher interface shear capacity can be obtained by choosing a larger connector diameter. As with higher friction, an interface with a larger connector bar starts to behave more rigidly. However, by increasing the diameter of the bar, the interface might fail earlier due to the crushing of the interface's concrete. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\mathcal{O}\) = 6 mm} & \multicolumn{2}{c}{\(\mathcal{O}\) = 8 mm} & \multicolumn{2}{c}{\(\mathcal{O}\) = 10 mm} & \multicolumn{2}{c}{\(\mathcal{O}\) = 12 mm} \\ \hline
**Point** & \(\boldsymbol{\tau}\)**, MPa** & \(\boldsymbol{s}\)**, mm** & \(\boldsymbol{\tau}\)**, MPa** & \(\boldsymbol{s}\)**, mm** & \(\boldsymbol{\tau}\)**, MPa** & \(\boldsymbol{s}\)**, mm** & \(\boldsymbol{\tau}\)**, MPa** & \(\boldsymbol{s}\)**, mm** \\ \hline A & 2.27 & 0.26 & 3.23 & 0.39 & 4.36 & 0.49 & 5.57 & 0.61 \\ B & 1.92 & 6.00 & 3.17 & 6.00 & 4.58 & 6.00 & 6.07 & 1.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Shear stress and slip values of interfaces with different connector diameters. * (23) [PERSON]; [PERSON] Interface shear strength of concrete-to-concrete bond with and without projecting steel reinforcement. _[PERSON]_**2015**, _75_, 169-172. [CrossRef]
* (24) [PERSON] _Shear and Shear Friction of Ultra-High Performance Concrete Bridge Girders_; Georgia Institute of Technology: Atlanta, GA, USA, 2010. * (25) Longitudinal Shear Strength between Two Concrete Layers with Added. Available online: [[https://www.researchgate.net/publication/268817880_Longitudinal_Shear_Strength_between_Two_Concrete_Layers_with_Added_Reinforcement_Crossing_the_Interface](https://www.researchgate.net/publication/268817880_Longitudinal_Shear_Strength_between_Two_Concrete_Layers_with_Added_Reinforcement_Crossing_the_Interface)]([https://www.researchgate.net/publication/268817880_Longitudinal_Shear_Strength_between_Two_Concrete_Layers_with_Added_Reinforcement_Crossing_the_Interface](https://www.researchgate.net/publication/268817880_Longitudinal_Shear_Strength_between_Two_Concrete_Layers_with_Added_Reinforcement_Crossing_the_Interface)) (accessed on 7 August 2022). * (26) [PERSON]; [PERSON] Influence of Fibers on Interface Shear strength of Cement Concrete Overlays. _Int. J. Sci. Eng. Res._**2017**, \(8\), 11.