## 4 Conclusions  
This study employed FLAC3D to meticulously simulate the pull-out tests of conventional bolts and previously developed yielding bolts. The axial force distribution and its dynamic evolution under pull-out conditions for both bolt types was investigated. Additionally, a comprehensive analysis of the shear resistance of the bolts was conducted. A comparative study, within the context of a soft rock tunnel environment, was undertaken to evaluate the support efficacy of conventional bolts against yielding bolts. The findings elucidate the mechanical behavior of yielding bolts under combined loading regimes. In addition, this work bridges critical gaps in the understanding of energy-absorbing support systems. Furthermore, the developed FLAC3D modeling approach provides a versatile tool for future research on advanced reinforcement strategies in geotechnically complex environments. The key conclusions are the following:  
1. The feasibility of simulating the pull-out tests, shear tests, and support effects of yielding bolts using FLAC3D was verified. The simulation results align with the working mechanism and stress characteristics of yielding bolts, establishing a basis for subsequent numerical simulation research. 2. When subjected to pull-out forces, the maximum axial force at the bolt head decreased gradually toward the inner end of the bolt, with the reduction in the yielding bolts being greater than that of the conventional bolts. As the pull-out force increased, the axial force of the bolt correspondingly increased, with the rate of increase in yielding bolts significantly slower than that of conventional bolts, confirming the high extension rate of yielding bolts. 3. In the support of a soft rock tunnel, compared to conventional bolts, yielding bolts exhibit a slower rate of reaching yield strength and a longer duration of maintaining yield strength. The central position of the maximum load-bearing capacity of the conventional bolts breaks under tension, resulting in an hourglass-shaped distribution of axial force, whereas yielding bolts can sustain yield strength for an extended period after reaching yield strength, with the axial force displaying a spindle-shapeddistribution. The elastic and plastic yielding distance of the yielding bolts are 70.54 mm and 130.65 mm, respectively. The axial force distribution law and yielding distances can provide a theoretical reference basis for engineering applications. 4. Bolt spacing exerts a greater influence on support effectiveness in soft rock tunnels than bolt length. It was determined that a yielding bolt length of 5 m and a spacing of 1 m \(\times\) 1 m are the optimal support configuration under the geological conditions discussed in this paper. This optimal support configuration and its determination method can provide a theoretical basis for more complex engineering applications. Overall, this study addresses critical knowledge gaps regarding yielding bolt behavior under combined loading and provides a validated framework for optimizing energy-absorbing support systems in soft rock tunnels. Conceptualization, Y.Z. ([PERSON]) and E.Z. ; Methodology, M.C. and E.Z. ; Software, E.Z. and Y.Z. ([PERSON]); Validation, M.C. ; Formal Analysis, Y.Z. ([PERSON]); Investigation, Y.Z. ([PERSON]) and Y.T. ; Resources, M.C. ; Data Curation, Y.T. and Y.Z. ([PERSON]); Writing--Original Draft, Y.Z. ([PERSON]); Writing--Review and Editing, M.C. ; Visualization, Y.T. and E.Z. ; Funding Acquisition, Y.Z. ([PERSON]). All authors have read and agreed to the published version of the manuscript. This research was funded by the Deep Earth Probe and Mineral Resources Exploration-National Science and Technology Major Project [Grant No. 2024 ZD1004502], the National Natural Science Foundation of China [Grant No. 52404101], and Fundamental Research Funds for China Academy of Safety Science and Technology [Grant No. 2024 JBKY14]. Not applicable. The original contributions of the study are included in the article, and further inquiries can be directed to the corresponding author.