## 3 Results and Discussion
### Comparative Analysis of the Bolts' Mechanical Behavior During Pull-Out Simulation  
To analyze and compare the support effects and load characteristics of the yielding bolts and conventional bolts, models, as depicted in Figure 4, were established for the pull-out simulations. The axial forces experienced at various locations along the bolt reflected the propagation of tensile forces within the bolt, providing a direct response to the loading conditions of the bolt. The distribution of the axial forces at different positions along the two types of bolts is illustrated in Figure 12.  
Figure 11: Results of the pull-out tests in the engineering field [13]. Figure 12: Axial force distribution of the different positions of the bolt. Figure 10: Comparison of the indoor pull-out test and numerical simulation results of the yielding bolt [13]. It is evident that, under the same pull-out force, the tension borne by the bolt at different locations varies, with the axial forces experienced by the bolt gradually decreasing with increasing depth. The curve exhibits a concave shape, indicating a decreasing rate of axial force reduction along the bolt, thus approaching a plateau. As the depth increased, the yielding bolts experienced a faster decrease in axial forces compared to conventional bolts, particularly at the bolt head where higher axial forces are applied and are closer to reaching the yield strength, indicating a stronger adaptability of yielding bolts to resist larger pull-out forces. Furthermore, under the same pull-out load, the yielding bolts exhibited lower axial forces than conventional bolts at equivalent positions, suggesting that yielding bolts can withstand greater tensile forces. The simulated pull-out involved applying a constant velocity at the bolt head, causing the pull-out force to increase incrementally until yielding. Figure 13 illustrates the variation of axial forces at different positions along the conventional and yielding bolts as the axial strain increased during the simulation process. Positions at 0.125 m, 1.125 m, 2.125 m, 3.125 m, 4.125 m, and 5.125 m from the bolt head were chosen for clarity. Figure 13 shows that--before reaching yield, as the pull-out force and axial strain increase--the axial tensile forces increased at all sections, with the greatest increase being recorded near the head and there was also decreasing toward the inner end. Once the maximum axial force reached yield strength, its forces ceased, and this increased with further strain. Continued loading beyond yield led to brittle failure, analogous to necking in steel, and this caused rapid anchorage force decline and eventual failure. Figure 14 depicts the axial forces at 0.125 m (head), 3.125 m (middle), and 5.125 m (end) for both bolt types. Prior to reaching the yield strength of the bolt, the bolt underwent elastic deformation, with the curve showing a significantly higher rate of axial force increase for conventional bolts compared to yielding bolts, highlighting the high elongation capacity of yielding bolts. According to the axial strain variation laws at the three positions of the two types of bolts, as shown in Figure 14, it is obvious that the elastic strains at which the conventional and yielding bolts reach yield strength were 0.08% and 1.26%, respectively, with the corresponding allowable elastic deformations of 4.92 mm and 75.46 mm, indicating elastic yielding distance of 70.54 mm for the yielding bolts. Figure 13: The axial force change process of the bolts: (**a**) conventional bolt; (**b**) yielding bolt. The six curves correspond, respectively, to the distances of 0.125 m, 1.125 m, 2.125 m, 3.125 m, 4.125 m, and 5.125 m from the bolt head. After reaching yield strength, the bolt underwent plastic deformation. The plastic phase duration was longer for yielding bolts, again demonstrating their high elongation capacity.