## 4 Anchor Bolt Pull-Out Analysis
### Influence of the the Distance from Free Edge  
The influence of distance between the edge of the concrete block and the anchor bolt is investigated. The analysis model is shown in Figure 25. The embedment depth \(l_{e}\) is 48 mm, and distance \(s\) between the edge of the concrete and the anchor bolts varies from 100 mm to 17 mm. As a boundary condition, the vertical displacement of the black color area (along 3 sides) in the upper surface are fixed, and the other side is not fixed. Figure 26 show the principal strain distribution in half the region of the analysis model in consideration of mechanical symmetry under the 0.45 mm pull-out displacement level.  
From the final crack pattern, it was found that, when there is enough distance from the edge of concrete block, a cone-shaped crack pattern can be observed. However, the cone-shaped crack pattern is not observed in the bulk of the concrete block.  
Figure 23: Load-displacement relationships with different spacing.  
Figure 24: Pull-out strength influenced by input parameters. (**a**) Effect of bolt spacing on pull-out strength (compared to the strength of a single bolt). (**b**) Effect of embedded depth on pull-out strength (compared to the strength of a single bolt).  
shaped crack becomes incomplete with the decrease of distance \(s\). In particular, the crack at the bottom of the anchor bolt extended to the lateral surface of the concrete without changing direction in the case of \(s/l_{e}=0.4\), while, in other cases, the cracks turned. From the load-displacement relationship shown in Figure 27 and the relationship between the maximum load and the ratio of distance to free edge and embedment depth \(s/l_{e}\) shown in Figure 28, it can be recognized that the maximum pull-out strength decreased when \(s/l_{e}\) is lower than 1.0, and the maximum pull-out strength in case of \(s/l_{e}=0.4\) decreased around 40% compared with other cases. As a reference, about 50% of the maximum load drop can be found in the experiment [8; 16]. Compared to the existing studies [8] that showed the influence of the anchor bolt diameter under sufficient embedment depth, we investigated the minimum distance from the free end to keep the pull-out strength of the anchor bolt, and it has been found that maintaining proper pull-out strength requires a distance from the free end that is greater than 1.0 times the anchor bolt embedding depth. This is also shown by the tendency of the experiments conducted in Reference [16]. Thus, it indicates that \(s/l_{e}=1.0\) should be guaranteed when installing anchor bolts at the edges of the concrete structures. In addition, compared to the analysis results in the previous section, it can be found that the analysis model with insufficient distance between the anchor bolt and the free edge is similar to a half model of cases with insufficient intervals between anchor bolts considering symmetricity. When sufficient valid base concrete around a single anchor bolt is not guaranteed, the pull-out performance of this single anchor bolt is limited. When installing anchor bolts under these conditions, it is necessary to avoid densely placed rebar areas to ensure sufficient embedding depth for the bolts and the surrounding concrete area. In the next section, we will consider an example of countermeasures when a sufficient concrete area cannot be secured around the anchor bolt.  
Figure 25: Analysis model with one side free.  
Figure 26: Crack patterns with different distance between the free edge and the anchor bolt.