Investigating the effects of various testing parameters on Cerchar abrasivity index and its repeatability

Wear 418–419 (2019) 61–74

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Investigating the effects of various testing parameters on Cerchar abrasivity index and its repeatability

T

Hamit Aydın Engineering Faculty, Department of Mining Engineering, Zonguldak Bulent Ecevit University, 67100 Zonguldak, Turkey

ARTICLE INFO

ABSTRACT

Keywords: CAI Abrasivity Repeatability Stylus hardness Rough surface West apparatus

Cerchar abrasivity index (CAI) test is widely used to estimate the tool life and wear in various excavation equipment in mining and tunneling projects. The aim of this study is to analyze the effect of various factors related to the CAI testing procedure. Particularly, sensitivity of CAI results is investigated due to variation of certain testing parameters, including the type of apparatus used, wear flat measurement methods, specimen surface conditions and stylus hardness. Relationship between CAI and certain testing parameters, and its repeatability are also investigated through statistical analyses of a series of CAI tests results obtained from twentyone selected rock specimens. Results: show little variation between the type of apparatus used and between the selected wear flat measurement methods. Nevertheless, there is a significant large variation in CAI values according to the changes in specimen surface conditions and the hardness of stylus used. The results show that with an increase in the hardness of the steel stylus the CAI values decrease differently in accordance with the rock type tested.

1. Introduction The production of minerals and construction works in the mining and building industry are commonly carried out either by classical (drilling and blasting) or mechanical excavation methods. These excavation methods use tools that interact with the rock, resulting in wear or deterioration of the tools. Particularly, rapid wear in excavation tools used in mining, drilling, and tunneling applications [1] can result in a significant increase in tool consumption and cost. The wear of equipment has long been known to be a significant factor in the economics of any rock excavation process. Predicting the performance of excavation equipment is an important task in the selection of an appropriate excavation method of a project. In the feasibility phase of a project, engineers are challenged to overcome various geotechnical considerations in order to estimate excavation equipment performance and cost. Over the years, several index methods have been developed to offer a reasonable quantitative measure for rock abrasivity. Among them, the Cerchar Abrasivity Index (CAI) has been accepted internationally in the determination of the abrasiveness of the rock and is considered as a reliable indicator for cutter life and cost estimation in excavation projects [2–9]. The CAI test was developed for the first time by the Laboratoire du Centre d′E’tudes et Recherches des Charbonnages (Cerchar) de France in the 1970s for coal mining applications [10], and the results were

published by Valantin [11]. Then, this test was first standardized by AFNOR-NFP 94–430–1 [12], but later, it was also standardized by ASTM-D7625 [13] and became an ISRM suggested method (SM) in 2013 [9]. Today there are two types of designs (Fig. 1) available for this testing apparatus: the original design by Cerchar and the modified design by West [4]. The Cerchar test principle consists of scratching a steel stylus having a known hardness (HRC55 ± 1) with a 90° conical tip which is slid parallel to the rock sample surface by a distance of 10 mm under a constant force of 70 N. The abrasiveness is depicted by CAI and it corresponds to the wear flat size (unit of 0.01 mm, measured under a microscope) formed by a truncation of the cone tip times 10. According to the ASTM-D7625-10 and ISRM-SM, at least five tests must be performed on each rock specimen to achieve the mean CAI value. The speed of the scratching action varies for the two apparatus accepted by ASTM standards and ISRM-SM. It is 10 mm/s for the original Cerchar apparatus and 1 mm/s for the West model. The CAI classification of rock abrasiveness suggested by ASTM standards and ISRM-SM is given in Table 1. Despite common use of the CAI test, there are some variations in the results which are mainly attributed to differences in the hardness of the stylus used in testing, surface condition of the rock specimens, and wear flat measurement methods [8]. Considerable research has been undertaken to investigate the critical test parameters and to evaluate their

E-mail address: [email protected]. https://doi.org/10.1016/j.wear.2018.11.001 Received 15 February 2018; Received in revised form 2 November 2018; Accepted 2 November 2018 Available online 03 November 2018 0043-1648/ © 2018 Elsevier B.V. All rights reserved.

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Fig. 1. Types of CAI testing apparatus (Working mechanism are depicted on the top [9] and apparatus used in the experiment are on the bottom).

are recalculated with the same functional form. The results of recalculation show that studies of Jacobs and Hagan [21], and Käsling and Thuro [14] give an almost identical linear relation between CAI55 and CAI40. The studies by Jacobs and Hagan [21], and Fowell and Bakar [6] also show similar results between the CAI55 and CAI15. However, findings by Michalakopoulos et al. [19] are different from that of Jacobs and Hagan [21], and Käsling and Thuro [14]. Another test parameter that has had a significant impact on CAI is the surface condition of a rock specimen. Yet, there are some ambiguities regarding the preference of the specimen´s surface condition. The CAI studies carried out on rough and saw-cut surfaces show significant variation in their results [2,7,15,19,20]. Plinninger et al. [17] and Rostami et al. [8] conclude that the lower CAI values on rough and saw-cut surfaces are roughly the same which coincided with the findings of Al-Ameen and Waller [16]. However, on harder rock, the results of CAI testing on a rough specimen surface are higher than those obtained from a saw-cut surface. This is attributed to the fact that on harder rock with a saw-cut surface the stylus tends to slide thus resulting in a low CAI, while on a rough surface the stylus cannot slide, and therefore, results in a higher CAI. Nevertheless, with the softer rocks the stylus tends to indent the rock, and the surface finish of the specimen has little effect on CAI [16]. Plinninger et al. [17] shows that CAI values in hard rocks are about 0.5 unit (0.05 mm) or 14% [14] higher on rough surfaces as compared to saw-cut surfaces. The CAI test standards require a 10-mm scratching length. Studies on testing length reveal that about 85% of stylus wear is achieved during the first two millimeters of testing length. Only 15% of the CAI is attributed to the remaining 8 mm of the testing length [17]. Hamzaban et al. [22] shows that the increased length of the scratch results in

Table 1 CAI abrasivity classification [9,13]. CLASS

Extremely low abrasiveness Very low abrasiveness Low abrasiveness Medium abrasiveness High abrasiveness Very high abrasiveness Extreme(ly high) abrasiveness Quarzitic

ASTM-D7625

ISRM-SM

HRC = 55

HRC = 40

HRC = 55

N/A 0.30–0.50 0.50–1.00 1.00–2.00 2.00–4.00 N/A 4.00–6.00 6.00–7.00

N/A 0.32–0.66 0.66–1.51 1.51–3.22 3.22–6.62 N/A 6.62–10.03 N/A

0.1–0.4 0.5–0.9 1.0–1.9 2.0–2.9 3.0–3.9 4.0–4.9 ≥5 N/A

N/A: not available.

effects on CAI values. Many researchers have investigated the effect of stylus hardness because of its variation in different laboratories [14]. Some laboratories implement the tests with a stylus having a hardness of HRC55, while others use a HRC40 stylus and even softer ones [2,7,15–19]. Stanford and Hagan [21] determined that the grade of steel used for the stylus possess little influence on CAI test results. With respect to hardness of the stylus used in the test, however, they show that CAI linearly decreases with increasing in stylus hardness [21]. Michalakopoulos et al. [18], Käsling and Thuro [14] also express a linear relation between the CAI values of HRC55 and those of HRC40 styli. Table 2 shows the findings of those studies and the relationship between CAI values. As seen from Table 2, there is a linear relation between CAI values of styli having different hardnesses but the results are not readily comparable. For comparability purposes, these relations 62

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Table 2 CAI55 conversion equations from earlier studies. Source

Relation between CAIhigh and CAIlow.

Recalculated relation

2

Lee et al. [37]

N/A (from the data, r =85%) CAI55 range: 0.7–3.1 (n=19) N/A (from the data CAI40, r2=94%) N/A (from the data CAI15, r2=85%) CAI55 range: 0.7–3.6 (n=12) CAI55 = 0.1109+ 0.5874CAI40, r2=74% CAI55 range: 0.64–3.76 (n=68) CAI55 = 0.725CAI40, r2=94% CAI55 range: ~0.6–5.9 (n=30) CAI(V220) = 1.29+1.46CAI(V660), r2=89% CAI55 range: ~0.4–4.7 (n=35) Mean

Jacobs and Hagan [21] Michalakopoulos et al. [18] Käsling and Thuro [14] Fowell and Bakar [6]

CAI55 = 0.768CAI40 CAI55 = 0.732CAI40 CAI55 = 0.537CAI15 CAI55 = 0.621CAI40 CAI55 = 0.725CAI40 CAI55 = 0.479CAI15 CAI55 = 0.712CAI40 CAI55 = 0.508CAI15

N/A: not available, V220=HRC55, V660=HRC15 Table 3 Rock specimens; mean CAI (rough surface, side-view) for the stylus hardness of HRC55 and its corresponding coefficient of variation. Rock type

S. no

Rock sample - location

CAI55 Mean (Sd)

Coefficient of variation Mean (min-max)

Sedimentary rocks

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Shale Limestone Sandstone Dolomitic Limestone Dolomitic Limestone Sandstone Sandstone Quartz Sandstone Quartz Sandstone Andesite Diabase Basalt Andesite Andesite Granite Granite Marble Marble Quartz-Sericite Schist Schist Quartzite

0.65 0.89 1.03 0.97 1.56 1.56 1.89 3.53 4.03 2.34 2.51 2.72 2.83 3.17 3.27 4.09 0.76 0.83 2.57 3.32 4.24

16.09 13.93 25.94 18.12 10.19 27.52 8.97 5.83 10.21 15.57 10.88 9.01 14.21 8.79 8.95 9.94 20.86 22.42 12.79 12.62 9.35

Ingenious rocks

Metamorphic rocks

– Zonguldak – Adana – Fine-grained – Beige marble – Emperador marble – Medium-grained – Medium-grained – Bartın – Zonguldak –Zonguldak – Nigde – Ankara – Zonguldak – Nigde – Karabuk – Pergamon – Marmara – Afyon – Nigde – Malatya – Bartın

substantial wear flat in very abrasive rocks, and conclude that the scratch length should be carefully observed for very abrasive rocks. Yarali and Duru [23] find that about 90% of the wear is achieved after 10 mm and 99% after 15 mm scratching. Their findings regarding the influence of scratching distance coincide with Jacobs and Hagan's [21] findings. Studies on the effects of varying levels of applied loads show a linear increase with applied load [8,21], and conclude that CAI is not overly sensitive to minor errors in the applied load. Studies on geomechanical properties and mineralogical composition of rock show a significant effect on the CAI. McFeat-Smith [24] indicates that, in siliciclastic sedimentary rocks, the abrasivity depends on the cementation degree of rocks. Suana and Peters [2] findings reveal that CAI is mainly determined by the equivalent quartz content of the rock; however, other factors such as grain size and matrix properties are also important for CAI. Lassnig et al. [25] studied the influence of grain size on CAI and finds that there is no grain size dependency on the CAI value. West [4] illustrates that there is a good correlation between CAI and the quartz content of the rock. Plinninger et al. [17] show that the equivalent quartz content alone is not suitable for interpreting the CAI value. Yarali et al. [7] presents that the CAI value has a good linear relationship with the quartz content, degree of cementation, equivalent quartz content, and grain size of quartz of sedimentary rocks. Lee et al.

(0.16) (0.13) (0.30) (0.21) (0.18) (0.50) (0.26) (0.31) (0.46) (0.37) (0.38) (0.33) (0.59) (0.50) (0.35) (0.53) (0.20) (0.22) (0.37) (0.46) (0.86)

(6.41–32.63) (4.41–21.06) (10.49–53.08) (7.25–29.14) (4.93–20.55) (5.55–42.90) (4.86–15.19) (1.88–12.10) (5.74–19.87) (7.29–21.74) (1.45–18.74) (3.91–15.67) (3.61–21.95) (2.88–14.86) (3.01–12.27) (3.99–13.97) (8.05–38.48) (10.76–36.73) (6.62–17.42) (2.05–22.48) (2.8–21.21)

[26] finds that equivalent quartz content affects the CAI value more than the quartz content itself. Yarali [27] states that the influence of rock petrographic parameters on CAI is more than its strength. Nevertheless, recent researches show that there is a strong relation between rock strength and the CAI value [16,28]. Altindag et al. [29] concludes that the CAI value is related to the uniaxial compressive strength and brittleness of rocks. Alber [19] demonstrates that the CAI is stress-dependent. Bakar et al. [30] investigates the influence of water content on CAI values based on a laboratory testing of 33 water saturated sedimentary rock specimens and find that CAI values on a dry specimen are generally higher than those obtained from a water saturated specimen. Statistically, the CAI-dry specimen is roughly 1.25 times higher than that of the CAI-saturated. Considering the questions encountered in the previous studies, it has been decided that some ambiguities should be further investigated. The aim of this study is to analyze the effect of various factors related to the CAI testing procedure. Particularly, sensitivity of CAI resulting from changes in certain testing parameters including the type of apparatus (Type-1 vs. Type-2) used, measurement of wear flat (top-view vs. sideview), specimen surface conditions (rough vs. saw-cut) and stylus hardness. A series of CAI tests are implemented on selected rock samples to evaluate the effects of various factors on CAI and its repeatability.

63

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Fig. 2. Sample view of a disc specimen (Saw-cut surfaces are displayed on the top and rough surfaces on the bottom. From left to right; prepared rock specimen for testing, scratch surface after testing and a close-up view of wear flat respectively).

2. Research methodology

Repeatability of the CAI tests was analyzed using a coefficient of variation (relative variability) of mean CAI, Bland-Altman plot [31], and intra-class correlation coefficient (ICC). The coefficient of variation is a standardized measure of dispersion of data points around the mean. The CV is the ratio of the standard deviation to the corresponding arithmetic mean which was calculated from five test replications on the same rock specimen for this study. The Bland-Altman plot, or difference plot, is a graphical comparison method between two measurements. It is a plot of the difference against the average of the two methods. The Bland-Altman plot is used to investigate any possible relationship (constant or proportional bias) of the differences between the measurements. The presence of proportional bias is an indication of a lack of equal agreement between the measurements over the whole range. Repeatability, as a parametric statistic, is largely known as the ICC [32,33]. That is the proportion of the variation attributed to variation among samples that can be estimated from repeated measurements on a number of samples with analysis of variance (ANOVA), and it is calculated as follows:

Twenty-one sedimentary, metamorphic and igneous rock blocks (Table 3) were collected for the experiment. Core and disc samples (54 mm in diameter with 30 mm height, Fig. 2) were prepared and air dried prior to testing. CAI tests were performed on both rough and sawcut surfaces. The rough surface was the freshly broken rock fracture obtained by Brazilian testing on rock discs. The test apparatus used for the CAI were a replica of original Cerchar (Type-1) and West (Type-2) apparatuses (Fig. 1). The Rockwell Hardness of steel styli (DIN 115CrV3) used in the test were HRC41 ± 1, HRC45 ± 1, HRC49 ± 1, HRC51 ± 1, HRC55 ± 1, and HRC59 ± 1. The hardnesses of the styli were checked with a Rockwell Hardness Tester. Before each test, a worn stylus was re-sharpened to achieve a conical tip angle of 90°, and the tip angle was checked under a microscope. Experiments were repeated on three samples with five scratches for each styli and rock specimen. A total of 72 tests (2 apparatuses × 2 specimen surfaces × 6 styli × 3 samples) were carried out for each rock specimen and 1512 (72 × 21 rock specimens) tests for the whole study. The wear flat on the stylus tip was examined with a digital microscope (35× magnification, Fig. 3) and the wear flat was captured and measured with digital imaging software. Stylus wear flat measurements were taken both vertically (on-top view) and horizontally (side view). Measurement repeatability expresses the closeness of the results obtained. Researchers frequently take repeated measurements of a subject with the goal of quantifying variation among measurements.

ICC =

S2A

S2A + S2w

(1)

where is the variance among groups and is the variance within groups. A two-way repeated-measures ANOVA was undertaken with the aid of R, a statistical software [34,35], to estimate the ICC (i.e., ICC(C,3) and ICC(A,2)). The level of agreement was rated with the implementation of the equal interval ICC classification (5 classes, ICC

SA2

64

Sw2

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Fig. 3. Wear flat measurements (Digital microscope is on the right, styli are in place for side-view and top-view measurement. Captured images are on the left; topview measurement is on the top and side-view measurement is on the bottom).

values from 0 to 1.0) by Landis and Koch [36] as slight, fair, moderate, substantial and almost perfect.

exhibit an unsymmetrical shape with splinters or burrs on the tip of the steel stylus that enlarge beyond the wear flat which makes it difficult to determine the true size of the wear flat by top-view measurements. The vertical (top-view) measurement might result in a significant variation in the CAI values. A summary of stylus wear measurements is presented in Fig. 4. CAI measurements executed by top- and side-view settings exhibit a strong positive linear relationship (Fig. 4a). According to the difference plot (Fig. 4b) the difference (i.e., CAItop-view – CAIside-view) is positive (CAItopview is about 1% higher than CAIside-view – constant biased toward CAItop-view) but insignificant. The box plots in Fig. 4d exhibit the CAI difference between measurement settings with respect to stylus hardness. As seen from Fig. 4d, the mean CAI difference is 0.03 (between −0.1 and 0.2) and decreases with an increase in the stylus hardness. The box plots in Fig. 4c illustrate the CAI variation in relation to stylus hardness and wear flat measurement setting. The CV for all measurements are between 0.5% and 38% (excluding outliers) and measurements from side-view exhibit larger variations. The figure shows that the mean CV of CAI outcomes of the measurement setting are almost identical for the same stylus hardness and increases with an increase in stylus hardness. The limits of agreement (mean difference ± 1.96 SD, Fig. 4b) do not exceed the maximum allowed difference between measurement settings; therefore, the two measurement settings are considered to be in agreement.

3. Results and analyses An overall summary of the results of this study regarding the effects of various testing preferences on CAI value and its repeatability (reliability) is presented in Table 3 and Table 4. CAI55 values in the table ranged from 0.65 to 4.24 with a corresponding ISRM-SM abrasivity classification from “very low” to “very high” for the selected rock sample. CV of the CAI55 exhibited a wide range of variation, ranging from 1.45% to 53%. CAI variation (CV, 5–53%) in sandstones and marbles were high while the variation (CV < 33%) in remaining samples were moderate. ICC statistics for the experiment are illustrated in Table 4. The level of reliability (ICC 95% confidence interval, 0.98–0.99) between the two CAI measurements from side- and top- view, and their averages were almost identical with an “almost perfect” consistency, achieved on both rough and saw-cut surface specimens condition with Type-1 and Type-2 test apparatus. The reliability level between the apparatus (ICC, 0.97–0.98) was “almost perfect” and between the surface conditions of specimens (ICC, 0.74–0.91) was “substantial to almost perfect.” The level of consistency for CAI with the styli having different hardness were “almost perfect” and identical. The detailed results and in-depth analysis of the effects of various testing preferences on CAI value in relation to the testing conditions are presented below.

3.2. CAI testing apparatus There are mainly two types of apparatus (Fig. 1) which exhibit different mechanisms to actuate the relative movement between the stylus and rock surface. These are: (1) the original design (referred as “Type-1”) and (2) the modified apparatus by West [4] (referred as “Type-2”). In Type-1, both the stylus and deadweight are moved across the stationary specimen surface while, in Type-2, the specimen samples

3.1. The methods of wear flat measurements According to the ISRM-SM, the length or diameter of the wear flat may be measured from side- or top-view settings, though side-viewing is strongly recommended. This is because the wear flat can frequently 65

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Table 4 CAI Intra-class reliabilities (ICCs) between measurement methods, specimens surface conditions, type of apparatus and stylus hardness. Reliability

Testing condition

ICC

CAI Measurement

Type-1, saw-cut, mean Type-1, saw-cut, top Type-1, saw-cut, side Type-2, saw-cut, mean Type-2, saw-cut, top Type-2, saw-cut, side Type-1, rough, mean Type-1, rough, top Type-1, rough, side Type-2, rough, mean Type-2, rough, top Type-2, rough, side Type-1, saw-cut Type-2, saw-cut Type-1, rough Type-2, rough Saw-cut surface Rough surface Type-2 apparatus Type-1 apparatus H/A (CAI55 > 3) L/A (CAI55 ≤ 3) HRC41-Saw-cut HRC41-Rough HRC45-Saw-cut HRC45-Rough HRC49-Saw-cut HRC49-Rough HRC51-Saw-cut HRC51-Rough HRC55-Saw-cut HRC55-Rough HRC59-Saw-cut HRC59-Rough CAI41 ( L/A CAI55 ≤ 3) CAI41 (H/A CAI55 > 3) CAI55 ( L/A CAI55 ≤ 3) CAI55 (H/A CAI55 > 3)

ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(A,2) ICC(A,2) ICC(A,2) ICC(A,2) ICC(A,2) ICC(A,2) ICC(A,2) ICC(A,2) ICC(A,2) ICC(A,2) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3) ICC(C,3)

Consistency (Side-view, top-view, mean)

CAI Measurement Agreement (Side and top-view) Apparatus Agreement (Type-1 and Type-2) Specimens Surface Condition Agreement (Rough and saw-cut) Stylus hardness

Consistency

Stylus Hardness Consistency (HRC41 and HRC55)

95% CI 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.98 0.97 0.87 0.85 0.94 0.90 0.98 0.98 0.98 0.99 0.99 0.99 0.99 0.98 0.99 0.99 0.99 0.99 0.98 0.94 0.98 0.97

( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( (

0.987 0.986 0.987 0.986 0.986 0.986 0.983 0.983 0.982 0.985 0.985 0.984 0.995 0.997 0.998 0.999 0.977 0.968 0.815 0.742 0.882 0.831 0.972 0.970 0.972 0.984 0.983 0.975 0.987 0.971 0.989 0.983 0.980 0.980 0.963 0.901 0.953 0.968

-

0.993) 0.993) 0.993) 0.993) 0.993) 0.993) 0.991) 0.991) 0.991) 0.992) 0.992) 0.992) 0.999) 0.999) 0.999) 0.999) 0.985) 0.983) 0.909) 0.905) 0.969) 0.943) 0.991) 0.990) 0.991) 0.995) 0.994) 0.992) 0.996) 0.991) 0.996) 0.995) 0.994) 0.994) 0.985) 0.970) 0.985) 0.987)

ICC(C,3): consistency, ICC(A,2): agreement, H/A: high abrasive rocks, L/A: low abrasive rocks.

are moved under a stationary stylus and deadweight. These fundamentally different mechanisms of relative movement between the stylus and specimen surface might cause a variation in CAI values. The results related to the effects of testing apparatus on CAI are shown in Fig. 5. CAI (side-view measurements) values obtained from Type-1 and Type-2 apparatus reveal a strong positive linear relationship (Fig. 5a). The difference (i.e., CAIType-1 - CAIType-2, Fig. 5b) between CAI values is positive (CAIType-1 is about 2% higher than CAIType-2 – constant biased toward CAIType-1 apparatus) but insignificant. The box plots in Fig. 5d presents the differences between CAI outcomes of two apparatus with respect to stylus hardness. The box plots exhibit a decreasing mean CAI difference (0.05) with respect to stylus hardness, and it is between −0.75 and 0.75. The CV (Fig. 5c) is generally increasing with an increase in stylus hardness, and the Type-2 apparatus exhibits a lower variation for all stylus hardness, except in the case of a stylus with a hardness of HRC59. The limits of agreement (Fig. 5b) exhibit some outliers, but there are no significant differences and proportional bias between the differences of the results of two apparatus. Therefore, the results of two apparatus are considered to be in agreement.

CAI = 1.14CAISaw

Current standards on CAI testing recommend that the specimen test surfaces be fresh, flat, and natural or saw-cut. If a CAI test is carried out on a saw-cut specimen surface, then it is recommended that the CAI values be normalized by using one of the following equations: cut [13]

(3)

The findings of the effects of specimen surface condition on CAI are presented in Fig. 6. Fig. 6a illustrates the relationship between CAI (side-view measurements) outcomes of two surfaces on the same specimens for all the rocks tested. The CAI outcomes on two surfaces exhibit a statistically significant positive linear relation. The CAI test results from rough specimen surface are about 12% higher than those of saw-cut specimen surface for all samples which is coincided with the earlier studies. However, the ICC statistics (Table 4) does not support the argument that “lower CAI values on rough and saw-cut surfaces were roughly the same” which was raised by Rostami et al. [8] and Plinninger et al. [18]. Fig. 7 shows the relationship between the CAI values from a rough-sample surface and those of the saw-cut sample surface in relation to the geological origin. The figure exhibits a positive and statistically significant relationship. It is observed that the CAI values from rough specimen surfaces are 7%, 9%, and 22% larger than those of saw-cut specimen surfaces in sedimentary, igneous, and metamorphic rocks, respectively. The difference (i.e., CAIRough - CAISaw-cut) plot in Fig. 6b exhibits significant proportional bias (upward trend) between the difference from two surfaces. It is also noted that 7% of data points (Fig. 6b) exceed the limits of agreement. The box plots in Fig. 6d present the CAI difference between the outcomes of two specimen surfaces with respect to stylus hardness. The box plots exhibit a decreasing mean CAI difference (0.3) with an increase in stylus hardness, and it is between −1 and 2. The CV of CAI (Fig. 6c, Table 5) is generally increasing with an increase in stylus hardness (from 10% to 18%), and the rough specimen

3.3. Specimen surface condition

CAI = 0.48 + 0.99 CAISaw

cut [9]

(2) 66

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Fig. 4. CAI Stylus Wear Measurement: a) Scatter plot – Top-view vs. Side-view, b) CAI difference against mean CAI of top-view and side-view, c) CV of CAI with respect to stylus hardness and measurements, and d) Box plot of CAI difference with respect to stylus hardness. Box plot illustrates the variation in CAI difference and CV according to stylus hardness. The box indicates the upper and lower quartiles and the median is represented by a horizontal line, and mean values by a small green circle within the box. The vertical lines show the full range of CAI values obtained from the stylus. Small black circles represent outliers.

Fig. 5. CAI Testing Apparatus: a) Scatter plot – Type-1 vs. Type-2 apparatus, b) CAI difference (Type-1 - Type-2) against mean CAI of Type-1 and Type-2 apparatus, c) Box plot of CV with respect to stylus hardness and apparatus type, and d) Box plot of CAI difference with respect to stylus hardness. 67

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Fig. 6. CAI Specimen surface condition: a) Scatter plot – CAIRough Surface vs. CAISaw-cut Surface, b) CAI difference (Rough – Saw-cut surface) against mean CAI of rough and saw-cut specimen surface, c) Box plot of CV with respect to stylus hardness and specimen surface condition, and d) Box plot of CAI difference with respect to stylus hardness.

Fig. 7. The relationship between CAI values from saw-cut surface and those of rough surface in relation to specimen geological origin.

surface mainly generated a higher variation for all stylus hardness values. The mean CV of CAI for a saw-cut surface is 10% while it is 14% for a rough specimen surface. Overall, large CAI variation (CV), large confidence interval (-1 to 1.6CAI, Fig. 6b) of limits of agreement, and a significant proportional bias between the difference of CAI values obtained from rough and saw-cut specimens surfaces conclude that the results from two surfaces are not in agreement.

CAI for all specimens in relation to stylus hardness and specimen geological origin. According to Fig. 8, the CAI values exhibit a wide variation with changes in the stylus hardness, rock type, and geological origin of rock. The mean CAI values are generally decreasing with an increase in stylus hardness for all specimens. Fig. 9 displays CAI for grouped data according to stylus hardness and specimen geological origin to demonstrate a clear pattern between CAI and stylus hardness. Fig. 9a shows that, as the stylus hardness increases from HRC41 to HRC59, the mean CAI values fall from 2.7 to 1.5 in sedimentary rocks, from 4.3 to 2.6 in igneous rocks, and from 3.2 to 2.0 in metamorphic rocks.

3.4. Stylus hardness Test results for all the styli are shown in Fig. 8 which is a box plot of

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Table 5 Coefficient of variation of CAI for all specimens with respect to stylus hardness, specimen surface condition, and apparatus type. HRC

41 45 49 51 55 59

All specimens mean (min-max)

Specimen surface condition Saw-cut mean (min-max)

Rough mean (min-max)

Type-1 mean (min-max)

Type-2 mean (min-max)

12.13 (1.06–35.70) 12.38 (0.71–46.03) 11.44 (1.09–38.23) 13.92 (1.68–42.86) 14.56 (1.64–55.02) 17.35 (2.05–61.11)

10.50 (1.06–35.70) 11.50 (0.71–46.03) 10.62 (1.09–38.23) 13.63 (1.68–42.86) 14.09 (1.64–55.02) 16.97 (2.07–61.11)

13.79 (2.33–35.34) 12.85 (1.95–40.41) 12.27 (1.98–36.83) 14.21 (2.41–40.46) 15.04 (2.47–38.70) 17.73 (2.05–48.13)

12.33 (1.06–35.70) 12.80 (1.95–44.05) 11.49 (1.09–36.83) 14.08 (1.68–42.86) 15.59 (1.64–55.02) 16.52 (2.05–61.11)

11.94 (1.61–33.21) 11.95 (0.71–46.03) 11.39 (1.98–38.23) 13.75 (2.41–37.50) 13.53 (2.20–40.18) 18.17 (2.93–56.35)

The CV of CAI in relation to stylus hardness and specimen geological origin (Fig. 9b) shows significant variation, ranging from 0.7% to 60% (including outliers). While the smallest CVs are observed for igneous rocks, the largest CVs are observed for metamorphic rocks. According to the CV of CAI (Fig. 10 and Table 5), the smallest variations (mean CV 11.44%) in CAI are observed for the stylus having a hardness of HRC49 and the largest variations (mean CV, 17.35%) in CAI are observed for the stylus having a hardness of HRC59. Consistent with the results presented in Fig. 10c, the probability density plots can be categorized into three groups according to stylus HRC hardness and the probability distribution of CVs: 41, 45 and 49 in low variability (90% of CV < 20%), 51 and 55 in medium variability (80% of CV < 20%) and 59 in high variability (70% of CV < 20%). Fig. 11 displays CVs for classified CAI in relation to stylus hardness for all specimens. As seen from the figure as the CAI values (abrasivity) increase while CV decreases. The variability (mean CV) of CAI with values “CAI < 2” are about 20% while the variability of CAI with values “CAI > 3” are about less than 10%. Measurement variability in low CAI values (for all styli hardnesses) is observed as twice the variability of higher values of CAI. This indicates that one should be extra careful when working with low abrasive rocks for reliable results.

Apparatus type

3.5. Case of HRC55 stylus Fig. 12 and Table 3 present the outcomes of the stylus having a hardness of HRC55. The average CAI values in Table 3 are ranging from 0.65 (very low) to 4.24 (very high). The finding for the stylus with HRC55 hardness has a similar pattern with the overall analysis with regard to wear flat measurement setting, testing apparatus used, and specimen surface condition, but the magnitude is different. The CAI differences between wear flat measurement from top-view and sideview settings, and between Type-1 and Type-2 apparatus are less than 1%; however, the CAI difference between outcomes of rough and sawcut surface is significant and CAIRough is about 10% higher for all rock samples. With respect to geological origin, CAIRough values (Fig. 13) are about 8% greater in sedimentary and igneous rocks, and it is about 13% greater in metamorphic rocks. Fig. 14 exhibits a scatter plot and linear regression fit line between CAI55 and CAIX of other styli (HRC; 41, 45, 49, 51, and 59) for rough and saw-cut surface separately. Table 6 shows the regression analysis results of the linear relationship. The results indicate that there are statistically significant, positive linear relationships between CAI55 and CAI of the corresponding stylus hardness. The R2 statistics show that the fitted models explain about 95% of the variability in CAI55, indicating a

Fig. 8. Box Plot of CAI in relation to specimen geological origin and stylus hardness (rock samples ordered according to CAI55 abrasivity classification).

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Fig. 9. Box plot: CAI (side-view measurement) (a) and CV of CAI and (b) in relation to stylus hardness and geological origin.

Fig. 10. CV of mean CAI in relation to stylus hardness: a) Box plot of CV, b) Box plot of CV in relation to abrasiveness (low vs. high abrasive rocks), and c) Cumulative density of CV.

strong relationship between CAI55 and CAI of those corresponding. The findings, for example CAI55 vs. CAI41, (CAI55 = 0.723 CAI41 for saw-cut and CAI55 = 0.689 CAI41 for rough-surface), are consistent with the findings of earlier studies. The data set for each rock sample is also analyzed, and the linear regression coefficients “a” and “b” shown in Eq. (4) are calculated.

CAIx = aX + b

“a” for all rock samples is found to be −0.083 for both surface conditions. Table 7 also includes a column containing the “normalized gradient” which is defined as “a`=a/b” in Jacobs and Hagan's [23] study. Using their substitution, Eq. (4) can be expressed as CAIx = b (1–0.0123×) for a rough-surface and CAIx = b(1–0.0116×) for a sawcut surface. One useful application of this transformation is to estimate the CAI with a different stylus hardness. For example, CAI45 (3.5) for the same rock type measured on a rough-surface can be converted to CAI55 as follows:

(4)

Where, CAIx: CAI for a stylus having hardness of x, X: stylus hardness expressed in terms of HRC Table 7 includes the coefficients “a” and “b,” and the coefficient of determination “R2” in relation to the specimen surface condition (rough and saw-cut surface). According to the Table 7, the mean of the gradient

b = C AI 45 /(1

CAI55 = b(1

70

a X ) = 3.5/(1

0.0123 × 45) = 7.84

0.0123 × 55) = 7.84(1

0.0123 × 55) = 2.54

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Fig. 11. Box plot of CV of mean CAI in relation to stylus hardness and abrasivity (CV ordered and classified according to CAI, x axis labeled with CAI class and corresponding percentage frequency).

If a similar conversion is carried out for a saw-cut surface, then the result will be 2.65. A comparison with an earlier study by Jacobs and Hagan [23] shows that the same conversion with their findings (mean a′ = −0,0107) will result in a value of 2.78. This discrepancy between two estimates indicates that this kind of general (non HRC specific) conversion equation should be used with caution.

4. Conclusion Considering the questions encountered in the previous studies, it has been decided that some ambiguities should be further investigated. This study is evaluated the effect of various factors related to the CAI testing procedure. As a result of this work, the following comments are made.

Fig. 12. CAI55 in relation to stylus wear measurement, testing apparatus, and specimen surface condition: a) CAI55 top vs. side-view, b) CAI55 Type-1 vs. Type-2 apparatus, c) CAI55 rough surface vs. saw-cut surface, d) CAI difference against mean CAI of top and side-view, e) CAI difference against mean CAI of Type-1 and Type-2 apparatus, and f) CAI difference against mean CAI of rough and saw-cut specimen surface.

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Fig. 13. Scatter plot of CAI55 (rough vs. saw-cut surface) in relation to specimen geological origin.

Fig. 14. Scatter plot of CAI55 and CAI of the corresponding stylus hardness with fitted line.

2. Wear flat measurements can be performed either way from top-view vertically or side-view horizontally, (or even the average value of both views) and may be used interchangeably if it is properly measured. 3. It has been observed that the variability of CAI test results is larger in less abrasive rocks; therefore, one should be extra careful when working with such rocks. 4. Specimen surface preference should be saw-cut since the measurement variation on saw-cut specimen surface is generally lower than that of the rough cut specimen surface. However, whenever styli sliding is observed on a saw-cut surface, it is better to use a rough surface. 5. If the test is carried out on a saw-cut surface, CAIsaw-cut should be converted to CAIrough. The CAI conversion from a saw-cut surface to a rough surface should be proportional since the difference between CAIrough and CAIsaw-cut are biased proportionally. 6. The smallest measurement variability (CV) is observed with the

Table 6 Linear regression coefficients between CAI55 and CAIX of the corresponding stylus hardness. Saw-cut surface CAIx CAI55 = (n = 36)

0.723 0.770 0.810 0.875 1.107

CAI41 CAI45 CAI49 CAI51 CAI59

Rough surface R2

CAIx

0.948 0.954 0.969 0.965 0.958

0.689 0.743 0.769 0.859 1.114

R2 CAI41 CAI45 CAI49 CAI51 CAI59

0.946 0.955 0.958 0.955 0.957

1. The Cerchar abrasivity test can be carried out without compromising test results with both apparatuses, as long as it is performed in accordance with the standards.

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Table 7 Linear regression coefficients between CAI and corresponding stylus hardness for each rock sample. Sample

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Mean: Sd: CV (%):

Rough surface

Saw-cut surface 2

a

b

R

-0.025 -0.052 -0.058 -0.077 -0.070 -0.050 -0.075 -0.081 -0.085 -0.080 -0.128 -0.104 -0.106 -0.152 -0.078 -0.069 -0.073 -0.086 -0.116 -0.068 -0.112 − 0.083 0.029 34.7

1.986 3.652 4.227 5.236 5.437 4.427 6.022 8.095 8.679 6.772 9.765 8.504 9.244 11.426 8.540 4.524 4.809 7.219 9.362 6.825 11.129

0.47 0.88 0.75 0.92 0.90 0.55 0.81 0.80 0.71 0.60 0.84 0.60 0.83 0.86 0.65 0.90 0.87 0.61 0.88 0.67 0.66

a′

a

b

R2

a′

-0.013 -0.014 -0.014 -0.015 -0.013 -0.011 -0.012 -0.010 -0.010 -0.012 -0.013 -0.012 -0.012 -0.013 -0.009 -0.015 -0.015 -0.012 -0.012 -0.010 -0.010 − 0.0123 0.0018 14.7

-0.056 -0.061 -0.043 -0.072 -0.067 -0.051 -0.085 -0.051 -0.068 -0.095 -0.114 -0.127 -0.042 -0.092 -0.062 -0.066 -0.078 -0.073 -0.036 -0.075 -0.026 − 0.083 0.029 34.7

3.683 4.208 3.384 4.859 5.138 4.587 6.462 6.058 7.530 7.688 8.666 9.701 5.060 8.297 7.228 4.505 4.987 6.441 4.346 7.280 4.861

0.53 0.91 0.65 0.93 0.91 0.62 0.83 0.88 0.80 0.80 0.88 0.83 0.73 0.81 0.77 0.87 0.90 0.78 0.65 0.71 0.19

-0.015 -0.014 -0.013 -0.015 -0.013 -0.011 -0.013 -0.008 -0.009 -0.012 -0.013 -0.013 -0.008 -0.011 -0.009 -0.015 -0.016 -0.011 -0.008 -0.010 -0.005 − 0.0116 0.0028 24.1

stylus having a hardness of HRC49. However, considering the common use and the small difference between the variability of CAI49 and CAI55, the HRC55 steel stylus still could be a good choice.

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