## 2 Background
### Cernar Abrasivity Index (CAI)
\begin{table}
\begin{tabular}{c c c c c} \hline
**Method** & **Remarks** & **Advantage** & **Disadvantage** & **Ref.** \\ \hline Mohs scale & Mineral comparative scratch test & Simple to use & It is just a qualitative measure & [48] \\ \hline \multirow{4}{*}{Vickers hardness number rock (VHNR)} & Based on indentation hardness (the ratio of force to the area of & Simple method to rate rock & \\  & & & wear capacity based on & \\  & & indentation) using a diamond tipped & available charted mineral & Limited experience for TBM rock cutting & [40] \\  & & micro-indenter (Vickers) & VHNR values & & \\ \hline \multirow{2}{*}{Rock abrasive index (RAI)} & RAI = UCS \(\times\) EQC & Simple method Presence of a & No chart for disc cutter life prediction & [30] \\  & & chart for conical pick life & & \\ \hline Abrasive mineral content & & Uses Mohs scratch hardness & Simple to use & Limited experience for TBM rock cutting & [21] \\ \hline \multirow{2}{*}{Equivalent quartz content} & \multirow{2}{*}{Uses Rosiwal rating} & \multirow{2}{*}{Simple to use} & \multirow{2}{*}{Limited experience for TBM rock cutting} & \multirow{2}{*}{[21]} \\  & & & & & \\ \hline \multirow{4}{*}{Wear index-F} & F = Q \(\times\) D.z.10 = equivalent quartz & & & \\  & percentage, D—mean quartz grain & Is developed for drag & & \\  & size in mm, z=Brazil tensile & & tool cutting & & \\ \cline{1-1}  & & strength in MPa & & & \\ \hline \multirow{4}{*}{Rosiwal mineral abrasivity rating} & Rosiwal = 1000 \(\times\) volume loss & & & \\  & corutanum/volume loss & & & \\ \cline{1-1}  & & mineral specimen & & \\ \hline \multirow{2}{*}{NTNU cutter life index (CLI)} & \multirow{2}{*}{CLI is obtained from AVS and } & Large database and presence & Correct tests can only be performed in SINTEF & \\  & & Siever’s J tests & of disc cutter life & & \\ \cline{1-1}  & & prediction charts & & \\ \hline \multirow{4}{*}{Cerchar abrasive index (CAI)} & Steel pin tip diameter in 1/10 th mm & Widely used test in tunneling, & Good only for rough surfaces, variability in the & \\ \cline{1-1}  & after 1 cm scratch test under 70N & & & test results due to its sensitivity to method of tip & \\ \cline{1-1}  & & normal load & simple, low cost, low & & reading, the rock surface condition, the \\ \cline{1-1}  & & normal load & sample requirement & & non-constant cross-section of pin tip during \\ \hline \end{tabular}
\end{table} 
Table 4: Common methods utilized for abrasion measurement and classification [47]. \begin{table}
\begin{tabular}{c c} \hline
**Testing Factors** & **Effect on CAI Value** \\ \hline Test length & About 70\% of wear occurs in the initial first millimeter of the scratch length, \\  & approximately 85\% of after 2 mm of test slide, and only 15\% of the wear flat is \\  & produced by the remaining 8 mm length [1, 29, 36, 37]. In cases of harder and more \\  & abrasive rocks the CAI value length [38, 39]. \\ \hline Static load & The CAI value increases linearly by changing static loads on the stylus [40, 41]. \\ \hline Testing speed & The testing speed does not affect the CAI values significantly and commonly \\  & higher when conducted with 43 HBC pins at slow testing speeds [2, 41]. The \\  & standardized testing speed is 10 mm/s for articulated hand lever type machine \\  & and 1 mm/s for hand-crank types [7, 9]. \\ \hline Stylus hardness & Higher CAI values are obtained with soft CERCHAR test styli and \\  & vice versa [36, 38, 41, 42, 43, 44, 45]. \\ \hline Stylus metallurgy & No considerable effect on CAI value is observed by changes in the metallurgy of \\  & the stylus keeping regular hardness [43]. \\ \hline \end{tabular}
\end{table} 
Table 3: Effect of some Cerchar test parameters on the measured values of CAI [35].