## 3 Analysis of the Results
### Axial Deformation Behavior of the Tunnel under the Two Support Schemes  
In Section 3.1, the support effect was analyzed at a two-dimensional level under the 3 m support spacing condition. However, at the three-dimensional level, the performance of the support schemes was unknown, i.e., we did not know whether the performance of the radial support was still better than that of the non-radial support, and this advantage remained unchanged when the support spacing was changed. Moreover, how the support affects tunnel deformation in the axial direction is also our concern. Therefore, to further evaluate the performance of the support schemes, it is necessary to study the influence of the support schemes in the third direction. Figure 13 shows the tunnel support effect of the support face of the two support schemes. Apparently, the deformation reduction increased with the decrease in the support spacing, which demonstrates that the better supporting effect was correlated with the more intensive blot installation. On the other hand, under any of the same support spacings, the displacement reduction of the non-radial support was always less than that of the radial support, which illustrates that the radial support maintained a better effect than the non-radial support when the support spacing changed. To further compare this advantage, the support effect ratio of the support face (the sum of roof and lateral displacement of the non-radial support/that of the radial support) was defined to measure the variation between the effect of the two support schemes with the support spacing, and the results are  
Figure 11: Failure zone distributions of the rock mass around the roadway of the support face: (a) unsupported, (b) radial support, and (c) non-radial support. Figure 12: Bolt force distributions of the support face: (a) radial support and (b) non-radial support. given in Figure 14. The support effect ratio did not change much and was close to constant when the support spacing was larger than 3 m, and in a range of smaller than 3 m, the effect ratio continued increasing with the decrease in the support spacing. This reveals that the ratio of the effect of the non-radial support to that of the radial support was not fixed, particularly in the support spacing of smaller than 3 m, the effect of the non-radial support became better and better relative to the radial support. Figure 15 presents the growth rate of the support effect of the support face--the support spacing curve. The support effect growth rate is the change rate of the displacement reduction (the sum of the roof and lateral) as the support spacing decreases, which represents the growth of the support effect caused by each support spacing reduction. Note that, in general, the curve was rising with the decrease in the support spacing, and no matter what kind of support scheme, the support effect growth rate increased suddenly in the sections of 6 m to 5 m, 3.5 m to 2.5 m, and 2 m to 0.5 m, which demonstrates that in these sections, the decrease in the support spacing could bring more benefits to the support effect. This point was unexpected. To further to analyze this phenomenon, the growth rate of the support effect of the middle face (similar to that of the support face) was defined. Thus, under the assumption that the tunnel axial deformation was continuous, the overall tunnel behavior was clearly characterized. The result is shown in Figure 16. In contrast with Figure 15, the curve of Figure 16 moved down with the smaller support spacing, and there  
Figure 14: Support effect ratio of the non-radial support to radial support. Figure 13: Support effect of the support face under the two support schemes: (**a**) roof and (**b**) lateral. higher and higher. It was obvious that the length of the support influence domain was about 6 m, as shown in Figure 15. Then, the second increase was at about 3 m and the third was 1.5 m, which is in accordance with the conjecture.