## 3 Results
### Effect of Rock-Bolt Length  
As discussed in Section 2.1, empirical classification systems propose rock-bolt lengths that depend upon the tunnel size and rock-mass quality. During rock-bolting, the load from the unstable rocks around the tunnel perimeter is transferred to stable rock through the bolt. Therefore, the length of the rock bolt should be sufficiently in excess of the thickness of the plastic zone around the tunnel, for stability [33]. Laboratory test results show that the maximum load-carrying capacity increases with the grouted length of the bolt [34; 35; 36], as shown in the Figure 3a. This laboratory test results are for the 12 mm diameter rock bolt grouted in the 22 mm drilled hole. The water-cement ratio is 40%, and the annulus size is 5 mm. The bolt pull-out force increases linearly with the length. The load-carrying capacity of the rock bolt should not be increased up to the ultimate tensile strength of the anchor, and the corresponding length is called the critical anchor length. The effect of rock bolt length was determined for the three rock-mass types (moderate, soft, and weathered rock) during pull-out tests for 3, 4, and 5 m long bolts. As shown in Figure 3b, the average pull-out displacement decreases with the increase in rock-bolt length. In the field test, 25 mm diameter rock bolts were tested in a 38 mm diameter drilled hole in three different rock-mass classes. The water-cement ratio was kept constant in dry rock-mass condition. The length effect is dominant for moderate rock and negligible for weathered rock (Figure 4).  
Figure 3: (**a**) Rock-bolt length effect on pull-out load (laboratory test) [36] and (**b**) pull-out displacement in different rock units (field test).  
Effect of Bolt and Hole Diameter  
Empirical systems suggest bolt patterns based on 20 mm diameter rock bolts. Critical anchor length of the rock bolt increases with the increase in rock bolt's diameter. In the field tests conducted for this study, 25 mm diameter rock bolts were used in 38 mm diameter drilled holes. The laboratory test conducted on different diameters of rock bolts indicates that the maximum pull-out load of the fully grouted bolts increases linearly with the cross-sectional area of the bolt, while the embedment length was constant, as shown in Figure 5[36]. However, extremely thick bolts are uneconomical and difficult to install. The ratio of the borehole diameter to bolt diameter is a parameter in addition to the variation in the bore hole length and friction of the borehole surface that results in the slippage at the grout-rock interface [37]. The optimum difference between the diameters of the bolt and hole is not greater than 6.4 mm, giving an annulus of approximately 3.2 mm [38] for enhancing the load transfer capability. Large holes can result in poor resin mixing in the case of resin-grouted rock bolt, while smaller holes (annulus \(<\) 3 mm) can cause rock-bolt insertion problems. The annuli fluctuate from 2.5 to 6.4 mm and provide better results in strong rocks [39].  
Figure 4: Effect of rock-bolt length on pull-out strength in different rock-mass units (**a**) moderate rock, (**b**) soft rock, and (**c**) weathered rock.