## 4 Calculation of the Interface Resistance  
[PERSON] et al. [32] developed a model able to numerically reproduce the behavior of RC interfaces under monotonic and cyclic shear slips. This model was used for the development of an equation allowing the interface resistance to be calculated. The validity of the equation was checked against numerous experimental results from the literature, compiled in a database ([PERSON] et al. [21]). Following this work, the interface resistance is calculated according to Equation (1) as the sum of the contributions of friction \(\tau_{f}\) due to the clamping effect and the externally acting normal stress, if applicable, and the dowel action, \(\tau_{d}\), of the transverse reinforcement crossing the interface:  
\[\tau_{u}=\beta_{d}\cdot\tau_{d}+\beta_{f}\cdot\tau_{f}=\beta_{d}\cdot\frac{(1.3\cdot n\cdot d_{b}^{2}\sqrt{f_{c}\cdot f_{y}})}{\Delta_{c}}+\beta_{f}\cdot 0.33\cdot(f_{c}^{2}\cdot\sigma_{c})\ \ \ \text{(N,mm or psi)} \tag{1}\]  
\(\beta_{f}\) and \(\beta_{d}\) are contribution factors accounting for (a) the fact that the maxima of the two mechanisms do not occur for the same shear slip value and (b) the interaction of the two mechanisms. A set of values for the contribution factors was proposed by [PERSON] et al. [21], depending on the interface roughness, the embedment length of the reinforcement, etc. In Equation (1), the interface resistance due to friction is calculated for normal compressive stress on the interface, \(\sigma_{c}\), due both to clamping effects, \(\rho\sigma_{s}\), and external (compressive or tensile) stress, \(\sigma_{N,ext}\):  
\[\sigma_{c}=\rho\cdot\sigma_{s}+\sigma_{N,ext} \tag{2}\]  
Figure 14: Effect of cycling on the shear resistance of interfaces (a) under zero normal stress and (b) subjected to external compression. where \(\rho\) denotes the reinforcing percentage (area of steel to the interface area), \(\sigma_{s}\) is the tensile stress in the reinforcement due to clamping effects, and \(\sigma_{N,ext}\) denotes the external normal stress (positive for compression). With the purpose of validating the above model for the case of interfaces under external compression, Equation (1) was applied to the experimental results obtained within this work, as well as to the relevant results of the literature, shown in Table 1. Figure 15a shows the comparison between experimental and calculated interface resistances for 119 specimens in total. The mean value of the ratio \(\tau_{u,calc}\)/\(\tau_{u,exp}\) is equal to 0.834, while the coefficient of variation is equal to 41.7%. As shown in Figure 15a, the experimental values of interface resistance measured by [PERSON] et al. [4] and [PERSON] [5] are significantly larger than the predicted ones. [PERSON] and [PERSON] [5] tested interfaces between two concretes significantly different in compressive strength (42.5 MPa vs. lightweight concrete of 10.0-13.7 Mpa). Thus, as shown in the photographs included in their publication, and as commented by the authors, in several cases, when the interface was smooth, there was no clear crack formation along the interface; the crack deviated into the weaker concrete to a path longer than a clear plane interface crack. This might explain the higher interface resistances obtained. In the tests by [PERSON] et al. [4], the external compression was of very high value (\(\sim\)29% to 57% of the compressive strength of the weaker concrete), and the authors commented that, in this case, the failure was \"aggregate interlock failure\". The photos provided in the relevant paper indicated a compressive failure, with pronounced crushing of concrete. By excluding the specimens that did not fail due to interface failure, as well as the specimens with interfaces of very limited length, the revised plot of Figure 15b presents a better comparison between experimental and calculated interface resistances. In this case, the mean value of the ratio \(\tau_{u,calc}\)/\(\tau_{u,exp}\) is equal to 0.895, with a coefficient of variation equal to 37.8%.