## 2 Research Methodology and Research Materials  
_Determination of GSI and RMR89_  
GSI can be estimated for an exposed rock slope or tunnel face using the standard chart and field observations of rock mass blockiness and surface condition of the discontinuity (see Figure 1). Other charts are available for different rock masses (e.g., flysch, foliated, etc.). Several independent quantitative theories were developed for the estimation of GSI values from drill core data. This has been used in cases when rock exposures, tunnel faces or slopes were not yet available (e.g., initial feasibility studies prior to excavation). Different rock mass classification systems have been utilized in the approach to correlate drill core data to GSI, and include the following:  
* Q-system-based calculation method (e.g., [34; 35])
* RMi-based calculation method (e.g., [36; 37])
* RMR-based calculation method (e.g., [21; 35])  
Several authors [38; 26; 39; 40] have theoretically shown that significant differences in GSI estimation result from applying different calculation methods for different rock types. This paper focuses on calculated estimations of GSI from Rock Mass Rating (RMR) values. Recently, several researchers have investigated the relationship between [PERSON]'s [19] Rock Mass Rating (RMR89) and the GSI. Firstly, [21; 33] suggested the following calculation:  
\[\text{GSI}=\text{RMR}_{89}-5\text{ for RMR}_{89}>23 \tag{1}\]  
In this equation, RMR89 can be calculated from the following parameters:  
\[\text{RMR}_{89}=\text{R1}+\text{R2}+\text{R3}+\text{R4}+\text{R5} \tag{2}\]  
where:  
* R1--uniaxial compressive strength (0-15),
* R2--rock quality designation, RQD (3-20),
* R3--average joint space (5-20),
* R4--joint wall conditions (0-30), and
* R5--water. In the original definition, R5 must be defined as dry (i.e., 15) for assessing drill core. Based on further studies, [PERSON] et al. [35] suggested the following simple formula for GSI calculation:  
\[\text{GSI}=0.5\text{ RQD}+1.5\text{ J}_{\text{c}} \tag{3}\]  
where Jc is the joint wall conditions, according to the definition of [PERSON] [19] and it is equal to the R4 value of the previous equation, thus the rate of it is between 0 and 30. Similarly, [PERSON] et al. [22; 33] and several authors have recommended estimating the GSI value from RMR89 using a linear equation in the form of  
\[\text{GSI}=\text{a RMR}_{89}+\text{b} \tag{4}\]where a and b are different constants, depending on the rock type or geographical location. Table 1 summarizes various constants that have been calculated in previous works. In case of poor and very poor rock mass (i.e., RMR < 30) [PERSON] and [PERSON] [47] suggested an exponential relationship for calculating the GSI value from RMR89:  
\[\text{GSI}=6\text{e}^{0.05\text{RMRR}}89 \tag{5}\]  
The suggested equations (using the constants presented in Table 1) are summarized in graphic form (Figure 2). Reviewing the results, it is evident that the equation of [PERSON] and [PERSON] [47] is the only one focusing on RMR89 below 30. The results also suggest that equations by [PERSON] [41] and [PERSON] and [PERSON] [43] underestimate GSI for RMR89 > 30 when compared to the others. The remaining five formulae converge with similar results between RMR89 values of 60 and 70, while drifting apart above and below. As illustrated in Figure 2, the highest variability between equations occurs when RMR89 < 30, and when RMR89 > 80. These represent rock masses at opposite ends of the spectrum, those of very poor, and very good quality.