## 5 Conclusions  
In this study, an analysis method that can accurately evaluate the pull-out strength of anchor bolts embedded in concrete using the SPH method is presented and considered the ultimate pull-out strength under various conditions (bolt diameter, embedded depth, adjacent bolt spacing, etc.). The results obtained in this study are summarized as follows.  
1. As a result of comparison with the existing experimental values, it was confirmed that the crack growth analysis using the SPH method proposed in this study was very effective on the accurate estimation of ultimate pull-out strength of anchor bolt.
2. When changing the parameters of the analysis cases, concrete base fractures are likely to occur with lower embedding depth and higher bond stress, and bond fractures are likely to occur with deeper embedding depth and lower bond stress.
3. It was found that, if the distance between two adjacent bolts was shortened under the installation conditions where cone fracture occurred, the cone fracture regions of the individual bolts overlapped, and the total pull-out strength of the two bolts decreased. According to the analysis results, if the distance between two adjacent bolts was smaller than embedded depth, the total pull-out strength decreases around 50% compared to the sufficient distance condition.
4. It was also recognized that, when the distance from the edge was larger than the embedment depth, the pull-out strength could maintain the certain level. However, if the distance from the edge becomes smaller than embedded depth, the pull-out strength decreases with the distance.
5. This research simulation shows that, when the distance from the anchor bolt to the edge is about half the embedding depth, the pull-out strength drops to about 50% of the original strength. However, even in such a case, it was confirmed from the analysis results that it is possible to prevent a decrease in the pull-out strength of the anchor bolt by using a PCM material.  
In this study, it was shown that the pull-out strength of anchor bolts embedded in concrete could be accurately evaluated by the proposed SPH method. By using this method, it is possible not only to predict the pull-out strength and fracture mode under various installing conditions of anchor bolts in the structure but also to quantify the effect of the reinforcement method, such as the PCM method.  
Conceptualization, Y.S.; methodology, C.L. and Y.S.; software, C.L. and Y.S.; validation, C.L.; formal analysis, C.L.; investigation, C.L. and Y.S.; resources, C.L. and Y.S.; data curation, C.L.; writing original draft preparation, C.L.; writing review and editing, Y.S.; visualization, C.L.; supervision, Y.S.; project administration, Y.S. Both authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author, upon reasonable request.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Compressive** & **Tensile** & **Poisson’s Ratio** & **Density (kg/m\({}^{3}\))** & **Young’s** \\
**Strength (MPa)** & **Strength (MPa)** & **Poisson’s Ratio** & **Density (kg/m\({}^{3}\))** & **Modulus (MPa)** \\ \hline
60.0 & 6.0 & 0.2 & 2300 & 27,000 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Material parameter of PCM.