## 6 Conclusions  
In this paper, the effect of the addition of rubber particles on the mechanical properties of concrete under fatigue load was investigated. The RC and OC with optimal rubber particle size acquired from the experiment were used as backfill materials for numerical simulation and comparative analysis. Thus, the following conclusions could be drawn:  
1. The purpose of the test was to analyze the effect of adding different-sized rubber particles on concrete material via the stress-strain curve of materials under cyclic loading and observe microcracks on the concrete specimens before and after fatigue loading. The outcome demonstrated that the compressive strength of concrete material decreased with the addition of rubber particles, but the surface crack propagation was inhibited and the deformation resistance was improved. With the increase in rubber particle size, the crack resistance and deformation resistance of rubber concrete decreased. Therefore, 0.85 mm rubber particles resulted in better stability. 2. The elastic modulus and toughness indices of concrete materials with different mixing quantities of rubber particles before and after fatigue load were measured and calculated, and the energy dissipation of the specimens was analyzed. The result revealed that, after fatigue loading, the incorporation of rubber particles significantly alleviated the decrease in elastic modulus and toughness index of concrete materials, and RC-1 showed better resistance to elastic deformation, toughness, and ductility. At the same time, the energy dissipation method acquired the loss variables of each cycle accurately. The constant amplitude cyclic loading made the loss accumulate slowly, but it could be found that the damage variable of RC was in a narrow range and resulted in remarkable crack resistance and fatigue resistance. 3. Tunnel-surrounding rock deformation and the stress of lining structure using two kinds of backfill concrete were calculated by the finite element method, and the safety and stability of the tunnel structure are contrasted and analyzed. The outcome shows that the deformation and stress of the surrounding rock are lower than those of plain concrete when rubber concrete is used as backfill material. The vault settlement and arch bottom settlement are reduced by 0.4 mm and 0.6 mm, respectively, and the maximum principal stress is increased by 11.5%. Therefore, the stability of the tunnel structure is enhanced by employing rubber concrete backfill. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Evaluating Indicator** & **OC** & **RC-1** \\ \hline Crown settlement (mm) & 29.1 & 28.7 \\ Bottom settlement (mm) & \(-\)26.4 & \(-\)27.0 \\ Horizontal displacement of left arch waist (mm) & 8.58 & 7.61 \\ Horizontal displacement of right arch waist (mm) & \(-\)8.39 & \(-\)7.40 \\ Maximum principal stress (MPa) & 0.96 & 1.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Computing result. **Author Contributions:** All authors contributed to the study's conception and design. Conceptualization was performed by [PERSON] and [PERSON]. Data collection was performed by [PERSON] Formal analysis was performed by [PERSON] Investigation was performed by [PERSON] and [PERSON]. Methodology was performed by [PERSON] Writing--original draft was performed by [PERSON] Project administration was performed by [PERSON] All authors have read and agreed to the published version of the manuscript. **Funding:** This APC was funded by the Natural Science Foundation of China (Grant Numbers: 52168055 and 52278397), the Natural Science Foundation of Jiangxi Province (Grant Number: 20212 ACB204001), \"Double Thousand Plan\" Innovation Leading Talent Project of Jiangxi Province (Grant Number: jysq2020101001).