## 2 Background
### Cernar Abrasivity Index (CAI)  
Abrasivity is a good indicator of the wear life of cutting tools in any rock excavation operation. CAI is used for estimating the cutting tool life in the TBM performance prediction model of the Colorado School of Mines (CSM). Various rock abrasivity measurements have been introduced throughout the years to allow engineers to estimate cutting tool life. CAI is commonly utilized to characterize the abrasivity of rocks for estimation of cutting tool life and wear in various mining, civil and tunneling applications. The CAI [7] test has been introduced in the 1970s by the Centre d'Etudes et Recherches des Charbonages (CERCHAR) de France for abrasivity testing in coal-bearing rocks in mining industries while gradually being adopted for application in the tunneling industry [15; 25; 26; 27]. Different generations of testing devices and the impact of various testing parameters on the test results have been discussed in the literature [15; 18; 28; 29; 30; 31; 32; 33]. A typical CAI device is given in Figures 3 and 4. A typical rock sample and surface used for CAI is given in Figure 5. \begin{table}
\begin{tabular}{c c} \hline \hline
**Category** & **CLI** \\ \hline Extremely low & \textless{}5 \\ Very low & 5.0–5.9 \\ Low & 6.0–7.9 \\ Medium & 8.0–14.9 \\ High & 15.0–34 \\ Very high & 35–74 \\ Extremely high & \(\geq\)75 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Category of intervals for cutter life index in NTNU Model [24]. Figure 2: Outline of abrasion value (AV) and abrasion value cutter steel (AVS) [24]. The CAI should be calculated as:  
\[\text{CAI}=\text{d}\cdot 10 \tag{3}\]  
where d is the wear tip surface measured to an accuracy of 0.01 mm. The dimensionless CAI value is reported as the arithmetic mean of five or more test replications together with standard deviation as suggested by [9]. While the original formal standard of the test was the French standard NF P 940-430-1 [34], recently an ASTM [8] and ISRM [9] standards  
Figure 4: Setup of a second-generation Cerchar testing device [28]. Figure 5: Example of rock surface conditions with rough surface (left over from BTS test) used for CAI test. Figure 3: Setup of a first-generation Cerchar testing device [7]. (1) Weight, (2) pin chuck, (3) steel pin, (4) specimen, (5) vice, and (6) hand lever [1]. for Cerchar testing were published. An effect of some Cerchar test parameters, including Cerchar pin properties, loading condition, and test length on the rock surface, on the values of CAI are given in Table 3.  
Rock abrasivity could be also examined based on the weighted average abrasivity of the constituent minerals. In this method, the percentage of each mineral in the rock is calculated and multiplied by its hardness or abrasivity, based on different available scales [21]. Abrasive mineral content (AMC), equivalent quartz content (EQC), and Vickers hardness number for rock (VHNR) are the most common methods to compute the abrasivity of rocks. AMC uses Mohs scratch hardness, while EQC uses Rosiwal [46] grinding hardness and VHNR benefits from Vickers indentation hardness (an indentation test in which the ratio of the force to the area of the indentation is considered as an index for abrasivity of the material) [21]. In the EQC method, constituent minerals of the rock would be identified either by microscopic or macroscopic mineral examination. Common methods utilized for abrasion measurement of rocks are given in Table 4.