## 2 Background and Design Provisions of Interface Shear  
[PERSON] and [PERSON] [4] were the first authors to propose a shear friction theory, as illustrated in Figure 2, to compute the ultimate shear resistance of concrete interfaces, which can be presented by the following equation:  
\[v_{u}=\rho f_{y}\tan\varphi=\rho f_{y}\mu \tag{1}\]  
where \(v_{u}\) is the ultimate interface shear resistance, \(\rho\) is the interface shear reinforcement ratio, \(f_{y}\) is the reinforcement yield stress, \(\varphi\) is the internal friction angle, \(\mu\) is the friction factor, and \(\rho f_{y}\) is known as the clamping stress. Figure 1: Interfaces of the injection channel connection: (**a**) conventional connection (shear connector and reinforcement intersect) and (**b**) novel connection (shear connector and reinforcement do not intersect). Figure 2: Shear friction theory model [4]. When first suggested by [PERSON] and [PERSON], this equation included the following conditions:  
\(f_{y}\leq 60\) (ksi)  
\(\rho\leq 1.5\%\)  
\(v_{u}\leq 800\) and \(f_{c}^{\prime}\geq 4000\) (psi)  
The shear friction theory assumes that when shear and compression forces act on concrete-to-concrete interfaces, the main load transfer mechanism is friction. The shear resistance is generated by surface roughness and a relative slippage between two concrete surfaces. A normal displacement and tensile stresses in the reinforcement crossing the interface are generated which grow clamping stress and lead to slippage resistance. From Figure 2, the normal displacement grows with the increase in slippage, and this displacement causes the yield tension of the reinforcement, which corresponds to shear resistance. After the shear friction theory was proposed, many researchers introduced different terms to develop the shear friction theory. In 1972, an equation named \"modified shear friction theory\" was proposed by [PERSON] and [PERSON] [5; 6]. In this equation, besides the friction mechanism related to surface roughness and clamping stress, the cohesion mechanism was also considered for the first time. [PERSON] et al. carried out many studies on interface shear resistance [7; 8; 9; 10]. Then, equations were attempted to be adopted by many researchers. In 1997, a remarkable development in the design equations for shear resistance of concrete interfaces was proposed by [PERSON] [11]. [PERSON] considered the interface shear resistance including three load transfer mechanisms: (1) cohesion related to adhesion and aggregate interlock, (2) friction caused by surface roughness and clamping stress and/or externally applied loads, and (3) dowel action due to the deformation of the shear reinforcement. Then, to simplify [PERSON]'s equation, other researchers suggested an equation neglecting the dowel action and considering the dowel action influence as a portion of the clamping stress [12]. In 2000, [PERSON] and [PERSON] [13] analyzed the three different load transfer mechanisms in more detail by establishing the relationship between slippage and interface shear resistance, as indicated in Figure 3. First, cohesion activates after small interface slippage caused by the loss of adhesion; then, it declines quickly with the increase in slippage. Second, friction is related to external loads perpendicular to the interface and clamping influence due to tension force when using shear reinforcement. Lastly, dowel action occurs after cohesion is broken. In 2003, surface roughness was considered directly for the first time in the equation proposed by [PERSON] [14]. To emphasize the importance of surface roughness, [PERSON] and [PERSON] [15] suggested an equation for interfaces with different surface roughness preparations. Figure 3: Three load transfer mechanisms are based on slippage [13]. Based on a great amount of past research, the codes suggest equations for predicting the interface shear resistance of concrete-to-concrete interfaces.