## 4 Anchor Bolt Pull-Out Analysis
### Influence of the Spacing between Anchor Bolts  
Then, the influence of spacing between anchor bolts to the load capacity of the anchor bolt is investigated. The analysis model is shown in Figure 19, with different spacing between anchor bolts \(s\), from 234 mm to 25 mm. The sides of the upper surface of the concrete block are fixed, and the material parameters are the same with previous analysis. The development process of the cracks during the pull-out process is shown in Figures 20-22. Figure 19: Analysis model with different spacing. Figure 20: Crack development when the spacing \(s\) is 234 mm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{\begin{tabular}{c} **Maximum Bond** \\ **Stress (MPa)** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Anchor Bolt** \\ **Diameter** \\ **(mm)** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Anchor Bolt** \\ **Embedment** \\ **Depth (mm)** \\ \end{tabular} } & \multirow{2}{*}{**Final Crack Pattern**} \\ \cline{1-1}  & & & & \\ \hline
2 & 12 & 16 & 48 & Bond-cone complex fracture \\
4 & 12 & 8 & 48 & Bond fracture \\
5 & 12 & 24 & 48 & Cone fracture \\
6 & 12 & 16 & 32 & Cone fracture \\
7 & 12 & 16 & 64 & Bond fracture \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Analysis cases and final crack pattern. Figure 18: Classification of the pull-out fracture pattern of an anchor bolt. In the case where the spacing is 234 mm, the development process is similar to the case with a single anchor bolt. Inclined cracks generate from the bottom of the anchor bolt and, finally, reach the surface of the concrete block. Two separate cone areas are formed. When the spacing \(s\) is 150 mm, the inclined cracks also generate at the bottom of the anchor bolt. When the pull-out displacement \(x=225\) um, the cracks located between the two anchor bolts joint with each other, forming a long crack connecting the two anchor bolts. When \(x=300\) um and \(x=450\) um, the cracks reach the surface of the concrete, and a complicated double-cone fracture surface is obtained. When the spacing \(s\) is 25 mm, cracks generate from the bottom of the anchor bolt. The cracks outside the anchor bolts are long and inclined, and the cracks between the anchor bolts are short and horizontal. When \(x=225\) um and \(x=300\) um, the inclined cracks reach the surface of the concrete block. The shape and the area of the emerged cone shape becomes more like the cone shape of a single anchor bolt. The load-displacement curves are shown in Figure 23. In the case where the spacing \(s\) is 150 mm, the total area of the emerged cone shape changed little compared to the two separate cone shapes, and the maximum load remains same for spacing of 200 mm and 150 mm. When the spacing \(s\) is 25 mm, the two anchor bolts just behave as a single anchor bolt, and the maximum load is about half of the previous cases. To make the tendency more clear, relationship between the ratio between the total maximum load and the maximum load of a single anchor bolt \(P_{total}/P_{single}\) and the spacing \(s\) is shown in Figure 24a, and the relationship between the ratio between the total maximum load and the maximum load of a single anchor bolt \(P_{total}/P_{single}\) and the ratio between spacing and embedment depth \(s/l_{e}\) is shown in Figure 24b. In Figure 24a, it is found that the maximum load remains unchanged when the spacing \(s\) is larger than a certain value in different case, which is also described in Reference [28]. In Figure 24b, it is clear that the load decrease is not noticeable until \(s/l_{e}\) reaches 2.0. Compared to existing studies that considered the effect of anchor bolt diameter on sufficient embedment depth [28], this study investigated the effect on pull strength of adjacent bolt spacing at relatively shallow embedding depths. As a result, it is confirmed that an interval of 2.0 times of the embedment depth is needed as a minimum distance of adjacent bolt spacing to keep the pull-out strength.