# Analytical Method and Analysis of Cold-Joint Interface
## 1 Introduction  
Layered reinforced concrete structures are widely used in modern construction. This might include a precast, hollow core slab with a layer of concrete topping [1], a semi-precast (filigree) slab which incorporates void-forming inserts [2], a precast concrete girder and cast-in-place concrete bridge deck [3] or simply two concrete layers that are cast at different times and many others. Layered concrete structures provide a great many advantages. During the installation of a filigree slab, the precast concrete layer acts as a residual formwork, which increases the construction rate [4]. Additionally, the usage of filigree slabs provides flexibility in the choice of structural systems. By reinforcing the cast-in-place layer, a balcony slab might be installed more conveniently and, by reinforcing the layer over the supports, a continuous slab can be constructed. A layered concrete construction can be chosen for repairing and strengthening existing concrete members [5], which is also a suitable option for a voided slab, which can reduce material quantities, reduce weight and provide openings for the installation of different building services [6]. The major characteristic which determines the advantages of layered concrete structures is the mutual performance of concrete layers. The behaviour and properties of a layered concrete member subjected to bending can be considered to be equivalent to the behaviour and properties of a monolithic concrete member, as long as the interface between the layers is completely stiff. However, in the case of a partially stiff layer interface, the advantage of mutual layer performance is lost and each layer behaves, performing individually. In this situation, the properties and behaviour of the individual layers must be considered [7; 8]. Layered slab behaviour is shown in Figure 1.  
In the case of insufficient interface stiffness and large shear stress, an interface might be damaged and layers might slip relative to each other [9; 10; 11; 12; 13; 14]. The performance of a concrete interface which is crossed by connectors is a complex process that depends on many different parameters. The foundation for the study of shear interface behaviour was first established by [PERSON] (1966) [15], which was named the \"shear friction theory\". Nowadays, most design norms base their models on this theory to describe shear interface behaviour. As significant as it was, some assumptions made by the theory, such as the reinforcement being the main contributor to the total shear capacity of the interface, might not be true in all cases. Studies by other authors have found that the calculation methods presented in the design norms are not fully accurate and the different assumptions adopted by the calculations are not correct in all cases [16; 17; 18]. [PERSON] et al. (2021) [19] found out that, in their case, concrete was the most important contributor to the ultimate interface shear capacity, whereas the influence of the connectors was less noticeable. The goal of this research was to further extend the knowledge of shear interface behaviour and the influence of different contributors to interface shear resistance. A statistical analysis of the experimental shear tests performed by other authors [16; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28] was carried out and curves of the shear stress-slippage relationship at different stages were proposed. This analytical model can be employed not only up to the ultimate interface shear capacity (which is the case for most calculation methods in the design norms), but also until the stage of severe layer slippage. This analytical method is mostly suitable for determining the behaviour of the interface between the layers of normal concrete with a smooth interface surface with and without transverse connectors, cast at different times (cold joint interface). The analytical method can also be employed in engineering practice. By using it, it can be determined whether the layers of the structural member are susceptible to separation.