## 3 Numerical Simulation of Direct Shear Test of Bonded and Naturally Rough Concrete-Rock Interfaces
### Performance of the Calibrated Model  
The calibrated model was used to simulate the direct shear tests of bonded and naturally rough concrete-granite interfaces using the explicit geometrical representation of the macro-roughness at the interfaces.  
Figures 24-36 and Table 7 show a comparison of the results of the simulations with the experimental results presented in the first part of this paper, and some observations are made hereafter.  
First, the results of the numerical simulations of all the naturally rough concrete-granite interfaces carried out, reproduce: the first phase of the model (Figure 15, between A and B), by showing the linear increase in the shear stress with shear displacement; the second phase of the model (Figure 15, between B and C), by presenting the decrease in the shear stress with shear displacement, and, the third phase of the model (Figure 15, between C and D), by displaying the evolution of the shear displacement with insignificant change in the shear stress. This is good evidence that the simplifications made during the conception of the model are satisfactory and properly reproduced.  
Second, the model, independently if calibrated for the first type of failure or the second type of failure (see the experimental part), yields a good prediction of the peak shear strength, with the approximation error varying from 1% to 19% (see Table 7). This range of variation of the approximation error is very satisfactory given the complexities and challenges associated with the experimental and numerical modelling of the shear behavior of rough concrete-rock interfaces. Overall, the results of these simulations are good evidence that the model is able to capture the influence of the micro-roughness and therefore the bond strength and also the successful incorporation of the influence of the failure of the tips of concrete (second type of failure) in the shear stress evolution.  
Third, the model can reproduce the influence of the normal stress on the shear stress evolution; this can be observed in the comparison of the results of the simulations with 1 and 1.5 MPa of confinement stress for the bush-hammered interface, noting that the only parameter separating these simulations is the normal stress (see, for example, Figures 22 and 23).  
Fourth, the model, specifically its frictional part, can incorporate the influence of macro-roughness in the shear stress evolution; this is evident because the only parameter separating all the simulations within a group of simulations with the same confinement level is their respective macro-roughness (see Figures 24-36 and Table 7).  
Fifth, the comparison of the results numerical--experimental for all the blocks--is not equally impressive (see, for example, Figures 30 and 32). This was expected for two reasons: the experimental campaign is not always perfect and can affect the results of the tests, and the state of the surface is not equal in all the samples. There could be more weathering in some samples than in others, and these peculiarities are not considered in the model.  
Figure 24: Shear stress evolution with displacement Exp–Num (Block 1).  
Overall, the cohesive frictional model can capture well the main mechanisms and trends of the shear stress evolution of rough and bonded concrete-rock interfaces and present good prediction capability in terms of the peak shear strength with the coefficient of correlation between the peak shear strength obtained experimentally and the peak shear strength obtained numerically above 93% (see Figure 37).