# Analytical Method and Analysis of Cold-Joint Interface
## 4 Validation of Analytical Method  
Validation of the proposed analytical method was carried out by comparing the analytical calculations to experimental results and by performing a numerical simulation of the experimental test in the FEA software DIANA (Figure 5). The experimental results and data for the push-off tests were taken from the study of [PERSON] et al. (2020) [33]. Three different experimental specimens were chosen as a reference: S-C65L30-6D8-Ba, S-C65L40-6D10-Ba and S-C65L50-6D12-Ba. The numerical model for S-C65L30-6D8-Ba was assigned the following physical parameters: for an older concrete layer, the elastic modulus was \(E_{c}=38.57\) GPa and Poisson's ratio \(\
u=0.2\); for compressive concrete behaviour, a parabolic compression curve based on fracture energy was applied [34]. Concrete's compressive strength was \(f_{c}=65\) MPa and the fracture energy was \(G_{F}=27.74\) N/mm. The compressive fracture energy was calculated according to the study by [PERSON] (1996) [35]. Concrete's tension is described by an exponential curve that depends on the concrete's tensile fracture energy [36]. The tensile strength was equal to \(f_{t}=4.272\) MPa; the fracture energy was determined according to Model Code 1990 [37] and was equal to \(G_{F}=0.111\) N/mm. The properties for a younger concrete layer were as follows: elastic modulus \(E_{c}=30.59\)\(GPa\); Poisson's ratio \(\
u=0.2\); compressive strength \(f_{c}=30\) MPa; compressive fracture energy \(G_{F}=24.66\) N/mm; tensile strength \(f_{t}=2.355\) MPa; tensile fracture energy \(G_{F}=0.065\) N/mm. The connector yield stress was \(f_{y}=285.13\) MPa, ultimate tensile strength \(f_{u}=429.41\) MPa and the connector's elastic modulus \(E_{s}=197\) GPa. The [PERSON] plasticity model was assigned for the connectors. The number of shear connector bars crossing the interface was 6 bars, diameter of connector bars \(\varnothing=8\) mm and concrete interface area \(A_{c}=0.0375\) m\({}^{2}\). The 3D model was meshed into 15 mm quadrilateral finite elements. The interface between the layers was modelled by applying specific parameters. It was assumed that the interface properties were mainly influenced by the properties of the weaker concrete layer because that is where the first cracks were most likely to appear. Therefore, interface characteristics were calculated in reference to a weaker concrete layer. The interface's linear parameters were a normal stiffness modulus, which was equal to concrete elastic modulus \(E_{c}=30.59\) GPa, and shear stiffness modulus, which was equal to \(K_{s}=0.4\cdot E_{c}=12.24\) GPa. Interface plasticity is governed by the Coulomb friction model [38] (Figure 6). Figure 5: Interface push-off test: (**a**) structural model of the push-off test; (**b**) numerical model of the push-off test. The friction model requires the values of concrete cohesion, friction angle and dilation angle. Cohesion stress was determined according to Eurocode 2 [39]. For a smooth-surface interface, the suggested cohesion coefficient was \(c=0.35\). The cohesion stress was equal to \(C=c\cdot f_{t}=0.82\) MPa. The interface friction angle was taken as \(\varphi=30^{\circ}\), which is a recommended value for a smooth interface [40]. The dilation angle, which determines the width of an interface crack in the perpendicular direction, was assumed to be equal to \(\psi=0\). By choosing this value, it was considered that the surface was smooth enough that layers slipped without significant displacement in the perpendicular direction. Additionally, the interface model was supplemented by a curve, which, in the model, was called \"cohesion hardening\". This indicates the magnitude of the concrete layer bonding stress. However, in this case, the first stress value represented a value of cohesion stress, which was already presented, and the second value specified a value of the concrete layer clamping stress, which was caused by tensioned connectors (after the loss of a cohesive bond) (Figure 7).