## 3 Results
### Induced Stresses
#### 3.1.4 Factors Associated with Installation  
Grouted rock bolts are stiffer than others; however, owing to their nature, they allow some deformation to activate the load-transfer mechanism and also require some time for installation. After excavation, the time of fixing bolts has an important effect on the tunnel convergence control. Extremely late installation results in considerable excavation convergence. Moreover, the bolt will probably become overstressed before equilibrium is reached [53]. This clearly shows that the stand-up time has a direct relation with the time of installation of the bolt, and for the same excavation size, the stand-up time is the function of rock-mass quality. The support system should be installed as soon as possible after the excavation in order to prevent the loss of a significant share of the inherent strength of the rock mass.  
Effect of Tension  
The main advantage of the tensioned bolt is that it increases the shear stiffness of the bolted joint as soon as it is installed. The fast-setting resin allows the tensioning of the bolt a few minutes after installation. It should be noted that, when the bolt is pre-tensioned, some elastic deformation of the bar/bolt is utilized, and extra deformation may be induced in the bolt when there is movement in the reinforced joint. Laboratory studies show that pre-tensioning of the bolts produce clamping effect on joint surface; this helps to reduce joint dilation, increases the inherent shear strength of the joint, and reduces the shear displacement [54].  
Rocks surrounding the tunnel have irregular joint patterns. Typically, during rock-bolt installation, the recommended rock bolts are applied perpendicular to the tunnel surface. These rock bolts, perpendicular to the surface, have a variable inclination with the joints. Laboratory investigations show that a fully grouted bolt installed at an inclination to the joint has higher stiffness and contributes more toward the shear strength of the bolted blocks as compared to a perpendicular bolt [54]. The maximum shear resistance of the bolted joints increases with the inclination of the bolt (with respect to normal to the joint surface) provided that there is significant friction in the joint; otherwise, the bolt inclination has no effect on the maximum resistance [55]. The optimum angle of bolt inclination with respect to the joint is from 30\({}^{\circ}\)-60\({}^{\circ}\) and shear displacement at failure is minimal for bolt inclination between 40\({}^{\circ}\)-50\({}^{\circ}\).  
Composite Response  
Empirical classification systems propose compound support systems. If grouted rock bolts are installed with other support systems, like shotcrete and steel sets, then the total stiffness of the support and reinforcement system in the elastic field is given by merely adding the single stiffness by Equation(11). The reaction time of the composite system depends upon the installation time of the individual support/reinforcement and distance from the excavation face (Figure 9) [56].  
\[k_{total}=\sum_{i}k_{i} \tag{11}\]  
where \(K_{total}\) = total stiffness of the composite system, and \(K_{i}\) = individual support/reinforcement stiffness.