*2.4. Empirical Analysis*

The Q-system method was developed by Barton et al. [30] in the Norwegian Geotechnical Institute (NGI) to classify rock masses. The method is based on about 200 case histories of caverns and tunnels. The Q-system has been updated and it is now based on 1260 case records [31]. Barton carried out some changes and adapted it to give support recommendations due to the increasing use of steel fibre reinforced shotcrete (SFR) in underground excavation support [32]. The quality of rock masses (Q) is obtained by applying Equation (1).

$$\mathbf{Q} = \frac{\mathbf{R}QD}{I\_n} \frac{f\_r}{f\_a} \frac{f\_w}{SRF} \tag{1}$$

where *RQD* is the rock quality designation, *J<sup>n</sup>* is the joint set number, *J<sup>r</sup>* is the joint roughness, *J<sup>a</sup>* is the joint alteration, *J<sup>w</sup>* is the water reduction factor and *SRF* is the stress reduction factor. The Q value varies from 0.001 for exceptionally poor quality to 1000 for an exceptionally good quality rock mass. A stress-free form *Q<sup>N</sup>* was defined by Goel et al. [33], which is given by Equation (2).

$$Q\_N = \frac{\text{RQD}}{I\_n} \frac{I\_r}{I\_a} I\_W \tag{2}$$

Barton defined a new parameter *Q<sup>C</sup>* (Equation (3)) to improve the correlation among the engineering parameters, where σ*ci* is the strength of intact rock in MPa [32].

$$\mathbf{Q\_{CN}} = \mathbf{Q} \frac{\sigma\_{ci}}{100} \tag{3}$$

The bolt length (*L<sup>b</sup>* ) may be calculated in terms of the excavation width B, by the Equation (4), proposed by Barton et al. [30].

$$L\_b = 2 + (0.15 \text{ B})\tag{4}$$
