# Numerical Simulation of Anchor Pullout and Shear Tests Using a Regularized Damage Model
## 4 Simulation of Tests with Complete Anchoring System  
### Simulation of Anchoring System Under Tension  
The tests conducted by INSA [2] are now used to evaluate the robustness of the model in the case of a complete anchoring system. No parameters are changed for the steel and concrete model compared to the single-stud configuration because the experimental conditions remain unchanged. The simulated anchorage is depicted in [2], with four studs welded to a plate of equal strength. The mesh, including the plate, is depicted in Figure 12. The base plate and the studs are made of the same steel and are therefore modeled in the same way. The geometry of the studs is strictly identical to those in Section 3.1. The properties of the concrete are the same as in Section 3.1, Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **E (GPa)** & **Yield Strength (MPa)** & **Ultimate Strength (MPa)** \\ \hline Rigid stud & 210 & 900 & 1000 \\ \hline Flexible stud & 198 & 365 & 510 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Summary of steel parameters.  
Figure 11: Impact of \(G_{fc}\) depending on the stiffness of the stud.  
Figure 10: Damage tension/compression, h\({}_{\text{ef}}\) = 80 mm, \(G_{fc}\) = 60,000 N/m, flexible stud.  
The links between the different materials are the same as for the single-stud test and include a perfect bond between the stud and the base plate. Furthermore, the interaction between the anchorage (plate and rod) and the concrete is considered frictionless.  
The simulation only represents a quarter of the experiment (green zone) due to symmetry conditions (Figure 13).  
Figure 13 shows the experimental setup that the simulation aims to reproduce. Several experiments have been carried out to determine the impact of the embedment length. The simulations show similar trends as the experimental results (Figure 14). The critical embedment length at which failure transitions from concrete failure to steel failure is between 120 and 130 mm (both experimentally and numerically).  
The group effect is also investigated. According to [3], in the case of concrete failure, the group effect experimentally reduces the anchorage capacity of four studs by approximately 30% compared to the four studs taken separately. In the case of stud failure, no group effect is observed. The anchoring strength, thus, corresponds to the number of studs multiplied by the strength of a single stud. This same phenomenon is observed numerically with the same orders of magnitude (Table 5).  
Figure 14: Summary of tests and simulations.  
Figure 12: Mesh for full anchoring with 4 bolts.  
Figure 13: Experimental setup.  
Finally, the influence of reinforcements within the concrete is studied. Simulations without reinforcements are proposed. In the studied configuration, the presence of reinforcements does not change the force-displacement curve (Figure 15). It can be explained by the high strength of the concrete and the relatively high deformation of the stud. Indeed, for small embedded lengths (less than 100 mm), the reinforcements are too deep in the concrete to have any effect; the reinforcements are not within the influence zone (Figure 16) during a pullout test. For higher embedment lengths, the concrete is rigid enough not to deform; so, it is the stud that deforms, as observed in [2].