# Analytical Method and Analysis of Cold-Joint Interface
## 5 Numerical Parametric Interface Analysis  
A parametric analysis was performed by using the numerical model of specimen S-C65L40-6D10-Ba. The purpose of the parametric analysis was to find out how the interface friction angle and connector bar diameter influenced the interface behaviour. In Figure 11, four stress-slip curves are displayed. Table 3 shows the values of shear stress and slippage. Each curve was acquired with a different value for the interface friction angle, which is used in the Coulomb friction model [36]. As seen in the legend of the figure, each friction angle value corresponds to a certain friction coefficient value, as the friction coefficient is a tangential value of the friction angle. By changing the value of the friction angle \(\varphi\), the value of interface clamping stress also changes, which was considered when the analysis was performed. Four different values of friction were used \(\varphi=10^{\circ}\), \(20^{\circ}\), \(30^{\circ}\) and \(40^{\circ}\). Different values of friction resulted in different shear stresses at point A. Comparing the results with the lowest shear stress of \(\varphi=10^{\circ}\), it appears that, when the friction was \(\varphi=20^{\circ}\), the shear stress value increased by 31.8%; when \(\varphi=30^{\circ}\), it increased by 82.4%; when \(\varphi=40^{\circ}\), it increased by 125.5%. Comparing the slip values, it can be also seen that the increase in friction caused a larger slip at this point. When the friction was \(\varphi=10^{\circ}\) the lowest value was determined; when the friction was \(\varphi=20^{\circ}\), the value increased by 100.0%; when \(\varphi=30^{\circ}\), the value increased by 172.2%; when \(\varphi=40^{\circ}\), the value increased by 227.8%. From this point, with the different values of friction angle, different interface behaviours were determined. The shear stress value for \(\varphi=10^{\circ}\) kept decreasing until the end of the test, which was at point B. The shear stress value was 69.5% lower than the value at point A. When the friction was \(\varphi=20^{\circ}\), the shear stress value decreased and at the end of the test, it reached a value that was 22.1% lower than the value at point A. When the friction was \(\varphi=30^{\circ}\), the shear stress increased by 5.3%. When the friction was \(\varphi=40^{\circ}\), the determined increase in shear stress was 16.0%. The difference here was that, at the end of the test, the interface failed. By increasing the friction angle, the interface became stiffer. It started to behave like a monolithic joint. Interface failure became more sudden and occurred at a relatively lower layer slippage. Comparing the shear stress values at the end of test (B) with the lowest value of \(\varphi=10^{\circ}\), the shear stress value when the friction was \(\varphi=20^{\circ}\) increased by 83.0%; when \(\varphi=30^{\circ}\) the shear stress increased by 225.5%; when \(\varphi=40^{\circ}\), the shear stress value increased by 343.3%. After completing the parametric analysis with friction being a variable, a few patterns became noticeable. By increasing the interface friction value, higher interface shear resistance was achieved. Additionally, with a larger value of interface friction, a larger layer slip was needed for the interface to fully crack. Lastly, with the increase in friction, a higher shear stress was achieved in the further stages of interface performance, after the interface cracked and cohesive bond was lost. In Figure 12, the variation in the interface connector diameter is presented. Four curves display the shear stress-layer slippage relationships based on different interface connector diameters. By changing the value of the bar diameter, the value of interface clamping stress also changed, which was considered when the analysis was performed. Figure 11: Shear stress–layer slip relationship depending on the value of the friction angle.