Abstract
In this article, two rock cuttability parameters, scratching force and specific energy, were determined by means of the Cerchar scratch test, and then in comparison with widely accepted theoretical models of rock cutting. Moreover, a newly proposed parameter called modified scratching force, which is defined as the ratio of scratching force to the scratch depth, showed a good correlation with the theoretical models of rock cutting, and thus can be used to estimate the rock cuttability. In addition, regression analysis method was adopted to relate the cuttability parameters obtained from the Cerchar measurements to the rock mechanical properties. Results indicated that the uniaxial compressive strength shows a good correlation with modified scratching force and specific energy, respectively.
Keywords: Cerchar scratch test, Cuttability, Rock cutting, Scratching force, Specific energy
Subject terms: Civil engineering, Solid Earth sciences
Introduction
Mechanized excavation has widely been used for rock breaking in mining and civil engineering. Compared to the traditional drilling and blasting, it offers significant advantages, including continuous excavation, minimal disturbance to the surrounding rock mass, superior construction quality, and high efficiency1. Excavation tools like chisel and conical pick used for cutting rocks are embedded on the continuous miners, shearers and roadheaders. The estimation of rock cuttability is of vital importance for the feasibility of mechanized excavation in rock engineering. In general, rock cuttability can be expressed by the applied tool force, especially the cutting force (FC) generated on the mechanical tool, as well as by the consumed specific energy (SE) during the cutting process2,3. These two parameters can be regarded as meaningful indicators for evaluating the efficiency of rock cutting, and can be determined theoretically and experimentally.
Over the years, two theoretical models of rock cutting have been developed based on the modes of failure. These are tension-induced failure mode4 and shear-induced failure mode5. The Evans’ theory is described as the penetration of a wedge-shaped tool into the buttock of a coal, while the Nishimatsu’s cutting model is based on the Mohr-Coulomb criterion of failure for the stress condition during formation of a chip. The Evans’ theory4 is the first research on rock cutting in using chisel picks on coal, seen from Fig. 1a, during the cutting process, a circular path starting from the pick tip along the ab-line to the free rock surface is assumed to generate, and the tensile stresses occur predominantly on the interface of ab-path. The rock is then broken off when its tensile strength is exceeded in this path. On the contrary, Nishimatsu5 stated that the cutting path may be a linear, and the shear strength is dominant in rock cutting. The author developed a cutting theory by considering the primary and secondary crush zones beneath the pick, seen from Fig. 1b, the pick cuts the rock piece and generates the shear stresses along the ab-line. As consequence of pick movement, normal stresses are present on the ab-path6. Regarding the specific energy, Hughes7 as well as Mellor8 proposed a theoretical model for predicting the specific energy based on the mechanical properties of rocks (i.e., compressive strength and modulus of elasticity).
Fig. 1.
Illustration of rock cutting theories. (a) Evans’ cutting theory4, (b) Nishimatsu’s cutting theory5.
Besides the theoretical models, empirical models have been developed based on the rock cutting experiments, e.g., in-situ, full-scaled and small-scaled tests, to estimate the rock cuttability. A pioneering work in evaluating the performance of roadheader from specific energy was conducted by Fowell and McFeat-Smith9. The authors measured the in-situ specific energy with the aid of a transducer, and concluded that the cutting rate of roadheader increases with decreasing specific energy. Farmer and Garrity10 as well as Pool11 concluded that, for a given cutting power of roadheader, instantaneous excavation rate can be predicted by using the SE, as formulated by Hughes7 as well as Mellor8. Kahraman et al.12 also proved that the specific energy proposed by Hughes7 as well as Mellor8 can be used as a guide in estimating the penetration rate of percussive drills. The linear cutting machine is the most reliable method to predict the cutting force and specific energy. Bilgin et al.13 compared the theoretical specific energy with experimental one under certain cutting conditions, and concluded that the theoretical predicted model can be used as a guide in evaluating the performance of cutting machines.
In addition, the cutting force and specific energy, respectively, were correlated with physical-mechanical properties of rocks, e.g., uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), Young’s modulus (E), Shore scleroscope and Schmidt hammer hardness index, just to name a few, because different rocks with respect to their physical-mechanical properties can cause the fluctuation of cutting performance, which can significantly affect the excavation time and costs. McFeat-Smith and Fowell14 correlated the properties of intact rocks with specific energy, in which samples of coal measures were subjected to linear cutting in the laboratory, and results demonstrated the importance of rock properties including quartz content, cementation coefficient, UCS and Shore hardness of rocks. Copur et al.15 stated that the optimum specific energy obtained from the full-scaled cutting test can be predicted from the product of compressive and tensile strengths of the rock. Bilgin et al.13 performed the laboratory full-scaled linear cutting tests in using a conical pick for different rock samples with compressive strengths ranging from 6 MPa to 174 MPa, and obtained a good linear relationship between the mean cutting force to cut depth ratio and rock strengths in unrelieved cutting modes. Tiryaki and Dikmen2 studied the correlation of SE with textural, compositional, and geotechnical properties of sandstone through regression analysis method, and found that the Poisson’s ratio exhibits the highest correlation with SE.
Regarding the Cerchar scratch test, it is primarily designed to assess the rock abrasivity16–19, and subsequently to predict the tool wear or lifetime20–22. Recently, with the aid of new test device, the scratching or cutting force applied on the stylus can be recorded during the test23–30. Due to the fact that the actual rock cutting experiments are expensive and time consuming, and sometimes it is not easy to gain a large rock block for the test, the Cerchar scratch test is considered to estimate the rock cuttability. Hamzaban et al.24 proposed a parameter called modified Cerchar abrasivity index (MCAI), which relates the Cerchar abrasivity index (CAI) to the cutting force, and concluded that MCAI exhibits a better correlation with rock mechanical properties than CAI, making it a more promising indicator for estimating tool wear. Zhang and Konietzky (2020) introduced the Cerchar abrasion ratio (CAR) calculated as the ratio of material volume removed from the rock surface to the wear volume abraded on the stylus tip. Accounting for both stylus wear and the associated volumetric removal of material from the rock, information on excavability is added to the Cerchar measurements31. Recently, Kaspar and Latal32 proposed a estimation diagram for classifying the rock excavatability based on three parameters obtained from the Cerchar measurements, namely the CAI reflecting the tool wear during the rock cutting, the material volume (Vm) removed from the rock surface due to the stylus scratching, and the scratch depth (Px) due to the stylus indentation. Seen from Fig. 2 the excavatability is divided into seven classes ranging from highly economical to expensive excavatability. The color regions classify the excavatability based on the Vm and CAI, and Px works as the limitations for distinguishing the excavation economies. The excavation can be economical in terms of time (i.e., high Vm) or in terms of tool wear (i.e., low CAI). Rocks plotting in the same class might exhibit better or poorer values of either Vm or CAI, achieving an economical excavation at the expense of either time or tool wear. Higher excavation volumes within a class are associated with higher rock abrasivity.
Fig. 2.
Estimation diagram for classifying rock excavatability (Kaspar and Latal32, slightly modified).
Since, firstly, the theoretical models in many cases are not in a good agreement with measured values of FC and SE due to the heterogeneous and anisotropic features of the rock, and secondly, experiments like full-scaled tests require a large rock block that is sometimes difficult to gain under certain conditions, it is considered to estimate the rock cuttability by means of the Cerchar scratch test. In this article, under the use of a special designed test device, the applied scratching force was recorded during the scratching process, and the scratch depth produced on the rock surface as well as the rock material removed from the sample surface were measured by using a digital microscope. Based on these raw data, two in the rock cutting meaningful parameters, the scratching force (Fs) and specific energy, were calculated, and then used to express the rock cuttability. In addition, a new parameter called modified scratching force (MoSF), which considers both, the scratching force and scratch depth, was proposed to describe the rock cuttability, which is the novelty of this article. Then, the validity of investigated parameters was examined by relating them to the widely accepted theoretical models of rock cutting. Further on, the cuttability parameters were correlated with mechanical properties of rocks, especially the UCS, to investigate their dependency. Regression analysis method was adopted.
Rock cuttability calculated from theoretical models
Rock properties
In this article, six types of rock including one igneous rock (granite), four sedimentary rocks (dolomite, limestone, greywacke, and sandstone) and one metamorphic rock (gneiss) were chosen for testing. The uniaxial compressive strength test and Brazilian tensile strength (BTS) test were carried out in accordance with ISRM recommendations33,34, respectively, for calculating the rock cuttability parameters (i.e., cutting force) from theoretical models. Moreover, the density (ρ), Young’s modulus35, and P-wave velocity (Vp) were also measured for investigating their correlation with cuttability parameters. Results are summarized in Table 1.
Table 1.
Rock properties.
| Rock |
ρ [kg/m3] |
UCS/σc [MPa] |
BTS/σt [MPa] |
E [GPa] |
Vp [m/s] |
CAI [-] |
|---|---|---|---|---|---|---|
| Granite | 2612.7 | 211.9 | 12.8 | 31.6 | 5226.0 | 3.75 |
| Dolomite | 2561.2 | 113.4 | 6.1 | 19.9 | 4013.7 | 1.54 |
| Limestone | 2568.3 | 188.5 | 10.1 | 45.1 | 5462.7 | 1.81 |
| Greywacke | 2818.2 | 85.5 | 10.4 | 45.7 | 6031.8 | 2.34 |
| Sandstone | 2060.8 | 54.4 | 3.7 | 21.5 | 3145.0 | 2.03 |
| Gneiss *) | 2714.4 | 146.7 | 15.2 | 24.7 | 5089.3 | 2.75 |
*): Loading or scratching direction is perpendicular to the foliated surface of the metamorphic rocks.
Predicted cutting force
The cutting force has the most significant influence on cutting performance, energy consumption, and excavation time and costs. Evans36 proposed the first theory of rock cutting in using conical picks. According to his theory, the compressive and tensile strengths of the rock are of significant importance for determining the cutting force:
 |
1 |
where, FCp [N] represents the peak cutting force, θ [°] is the tip angle of conical pick, dc [m] is the cut depth, and σc [MPa] and σt [MPa] denote the compressive strength and tensile strength of the rock, respectively.
However, there are two deficiencies in this theory. Firstly, the influence of friction angle between the rock and tool was ignored. Secondly, the cutting force doses not decrease to zero when tip angle is equal to zero. Due to this, Roxborough and Liu37 modified the Evans’ theory by taking into account friction angle between the rock and tool:
 |
2 |
where, φ [°] is the friction angle between the rock and tool, and other symbols are identical as given in the Evans’ equation.
Further on, Goktan38 modified the Evans’ theory by taking into account friction between the rock and tool, and by removing the compressive strength:
 |
3 |
where, all of symbols are identical as given in the Evans’ and Roxborough and Liu’s equations.
Predicted specific energy
Besides the cutting force, the specific energy is another meaningful parameter for estimating the rock cuttability, and for evaluating the efficiency of rock cutting. Hughes7 as well as Mellor8 proposed a theoretical model to predict the specific energy in excavating rocks:
 |
4 |
where, SE [mJ/mm3] represents the specific energy, σc [MPa] is the compressive strength of the rock, and E [GPa] is originally defined as the secant modulus of elasticity, which is equivalent to the Young’s modulus of the rock.
In this article, for the calculation of peak cutting force and specific energy, the compressive and tensile strengths were taken from Table 1, and the depth values were taken from Table 4. The friction angle was assumed to be 25° for the tested rocks. Results of cuttability parameters calculated from theoretical models are summarized in Table 2.
Table 4.
Cuttability parameters obtained from Cerchar measurements.
| Rock |
ASFCerchar [N] |
ASD [mm] |
Vm [mm3] |
MoSFCerchar [N/mm] |
SECerchar [mJ/mm3] |
|---|---|---|---|---|---|
| Granite | 47.41 | 0.11 | 0.15 | 431.00 | 3162.67 |
| Dolomite | 56.06 | 0.15 | 1.32 | 374.40 | 424.68 |
| Limestone | 49.40 | 0.12 | 0.59 | 411.67 | 837.15 |
| Greywacke | 49.06 | 0.20 | 0.92 | 245.30 | 533.46 |
| Sandstone | 72.64 | 0.34 | 4.33 | 213.65 | 167.99 |
| Gneiss *) | 40.06 | 0.12 | 0.26 | 333.83 | 1540.58 |
*): Scratching direction is perpendicular to the foliated surface of the metamorphic rocks.
Table 2.
Cuttability parameters calculated from theoretical models.
| Rock |
FCp (Evans) [N] |
FCp (Roxborough and Liu) [N] |
FCp (Goktan) [N] |
SE (Hughes/Mellor) [mJ/mm3] |
|---|---|---|---|---|
| Granite | 0.94 | 1.29 | 5.02 | 710.47 |
| Dolomite | 0.74 | 1.07 | 4.45 | 323.10 |
| Limestone | 0.78 | 1.13 | 4.72 | 393.93 |
| Greywacke | 5.09 | 4.83 | 13.50 | 79.98 |
| Sandstone | 2.92 | 3.83 | 13.88 | 68.82 |
| Gneiss | 2.28 | 2.40 | 7.10 | 435.65 |
Rock cuttability obtained from Cerchar measurements
Cerchar scratch test
Figure 3a illustrates the geometry of steel stylus as well as the associated tip wear before and after Cerchar rock scratching. Fig. 3b indicates that the mineralogic-lithologic factors can truly affect the excavatability of rocks (i.e., cuttability). The type, quantity and grain size of constituent minerals (e.g., quartz, feldspar, mica, etc.) and their spatial orientation, and the type of grain contacts (e.g., siliceous, carbonate, ferritic or clayey) and their cement degree, together with the presence of voids (porosity) and interlocking, control how abrasive the material is, and how efficiently it can be excavated from the intact rock. The stress-strain curve represents the mechanical differences between the various mineral species within the rock.
Fig. 3.
Principle of the Cerchar scratch test in comparison with rock excavation (i.e., granite) (Kaspar and Latal32, slightly modified).
In this article, the Cerchar tests were carried out by using a new test device designed by He et al.39. Fig. 4 illustrates a West apparatus40 mounted with a horizontal displacement sensor used to record the horizontal scratching force generated on the stylus during the test. A computer program controls specified testing distance and velocity. It also records the force-displacement data from the sensors, and displays them on the monitor. The technical data of this device is given in Table 3. The steel stylus applied for testing is made of 115CrV3 tool steel, and heat-treated to the Rockwell hardness number of HRC 54−56. The surface condition of rock samples is sawn cut to exclude the influence of surface roughness on the test result. The test setup and procedure are in accordance with Alber et al.16: under a normal load of 70 N, and at a velocity of 1 mm/s, a rock sample is moved orthogonal under a static stylus with a 90° conical tip angle for a sliding distance of 10 mm. Then, the Cerchar abrasivity index (CAI) is calculated by multiplying the wear flat (d [mm]) on the stylus tip, measured by an optical binocular, with 10. Results of CAI values for the tested rocks are summarized in Table 1.
 |
5 |
Fig. 4.
Instrumented West apparatus for the Cerchar measurements (Zhang et al.29, slightly modified).
Table 3.
Technical data of Cerchar test device
| Item | Value |
|---|---|
| Applied load [N] | 70 |
| Horizontal force measurement range [N] | 0.4–200 |
| Horizontal force measurement accuracy [%] | ±1 |
| Horizontal velocity range [mm/min] | 1–100 |
| Maximum horizontal displacement [mm] | 300 |
| Maximum vertical displacement [mm] | 300 |
| Displacement accuracy [%] | ±1 |
| Sampling rate [ms] | 1 |
Figure 4a illustrates a digital microscope (see Fig. 5a) used to measure the depth profile of scratch with stylus displacement (see Fig. 5b and c) as well as the material volume removed in the scratch groove (see Fig. 5d). Compared to a traditional optical microscope, the lenses, camera, and graphics engine of a digital microscope are designed to optimize the relationship between the depth of field, resolution, and brightness. Due to the high frame rate of camera, this microscope can quickly scan through the focal range of a sample, and recognize areas of focus to build a fully-focused image. Even when a target’s surface has significant variation in height, a fully-focused image can be obtained instantly by compiling images at different focal planes. After creating the composite image, the focal position data can be used to construct a 3D model. Once a 3D image has been created, the data can be collected to calculate profile, height, and volume for any area within the field of view29.
Fig. 5.
Digital microscope for determining scratch depth and material removal volume.
Measured scratching force
The blue solid lines in Fig. 6a to f indicate the scratching force evolved during the rock scratching. As can be seen, the curves of scratching force for different types of rock exhibit in a similar way. As the stylus advances, the fluctuation of scratching force keeps proceeding periodically. As soon as the stylus and rock interact with each other, the force begins to increase from the minimum to the maximum values. When the scratching force reaches its peak value, a major crack occurs, and a large rock ship forms. A slight decrease of force is the result of micro-crack formation due to the failure of cement between mineral gains.
Fig. 6.
Measurement of scratching force for (a) Granite; (b) Dolomite; (c) Limestone; (d) Greywacke; (e) Sandstone; (f) Gneiss.
The averaged scratching force (ASF) is defined as the average force acting on the stylus for the sliding distance of 10 mm, which is visible as red dash lines in the figures for each tested rock. It is reasonable that rocks with higher strength (i.e., UCS) cause the stylus moving gradually towards the sample surface, which means that the magnitude of force is reduced during the scratching process. Among the tested rocks, the highest scratching force is required to fracture the sandstone due to its lowest strength, while the lowest force value is measured in scratching hard crystalline rocks like granite and gneiss.
Measured specific energy
Figure 7a to f represent the variety of groove shapes for the tested rocks, which can be attributed to the rock types with respect to their fabrics (i.e., texture and structure), and mechanical properties (i.e., strength and abrasivity). The surface damage due to the stylus scratching for dolomite and limestone shows a clear V-shaped groove. The groove shape for greywacke and sandstone exhibits in a similar way, the groove becomes irregular and chaotic due to the pore structure of the rock. The groove shape for crystalline rocks like granite and gneiss is similar to each other. A wide groove is formed due to less resistance of soft mica minerals against the stylus action, whereas a narrow groove indicates the existence of quartz or feldspar minerals with a higher hardness. Moreover, the shadow area in Fig. 7a to f gives a measure of rock material removed from the scratch groove for each tested rock. As can be seen, the most material is removed from sandstone sample due to its lowest strength, and the highest porosity among all the tested rocks, whereas the least material is peeled off from the hard and compact gneiss and granite.
Fig. 7.
Measurement of material removal volume for (a) Granite; (b) Dolomite; (c) Limestone; (d) Greywacke; (e) Sandstone; (f) Gneiss.
Since the cutting work or energy can be defined as the area under the force-displacement curve, the scratching energy can be calculated by integrating the scratching force with the corresponding sliding distance. Moreover, in the rock cutting, the specific energy is defined as the amount of work or energy required to break the unit volume of the rock. Then, the specific energy can be calculated by dividing the cutting energy with the material removal volume (see. Eq. 6), where SE [mJ/mm3] represents the specific energy, Fs [N] and Ls [mm] denote the recorded scratching force and corresponding sliding distance, respectively, and Vm [mm3] is the material removal volume in the scratch groove.
 |
6 |
Modified scratching force
The blue solid lines in Fig. 8a to f show the scratch depth (dc) evolved during the stylus displacement, and the red dash lines indicate the averaged scratch depth (ASD) for the sliding distance of 10 mm. It is also found that the largest scratch depth occurs in weak sandstone, whereas the lowest depth in stronger granite and gneiss. The reason is the same as explained for the scratching force and material removal volume that the fluctuation of depth value within a rock can be related to the rock fabrics (i.e., texture and structure).
Fig. 8.
Measurement of scratch depth for (a) Granite; (b) Dolomite; (c) Limestone; (d) Greywacke; (e) Sandstone; (f) Gneiss.
Due to the fact that the scratch depth varies in different types of rock, a new parameter called modified scratching force (MoSF), which is defined as the ratio of scratching force to the scratch depth, is proposed to describe the rock cuttability, where MoSFCerchar [N/mm] represents the modified scratching force, and ASFCerchar [N] and ASD [mm] denote the averaged scratching force and averaged scratch depth, respectively. Fig. 9 shows the ASFCerchar plotted against the ASD based on the tested rocks. Results show that the scratching force increases linearly with increasing scratch depth, and a linear relationship (R2 = 0.78) is obtained.
 |
7 |
Fig. 9.
Relationship between averaged scratching force and averaged scratch depth.
Results and discussion
Estimation of rock cuttability
Results of cuttability parameters for the tested rocks obtained from the Cerchar measurements are summarized in Table 4. Regarding the modified scratching force, the highest MoSF value was found for granite (MoSF = 431.00 N/m), followed by the limestone (MoSF = 411.67 N/m) and dolomite (MoSF = 374.40 N/m), and the lowest value was measured at greywacke (MoSF = 245.30 N/m) and sandstone (MoSF = 213.65 N/m). This finding is reasonable that, according to the definition of MoSF, the scratch depth due to tool action varies in a wide range for different types of rock, the largest scratch depth was measured at sandstone with an average value of approximately 0.34 mm, whereas the lowest one for granite with an average value of approximately 0.11 mm. The variety of scratch depth can be attributed to the strength properties of the rock globally as well as to the hardness of composed minerals within the rock locally. In addition, rock porosity plays also a certain role affecting the scratch depth that its value on compact rock like granite is relative lower than that on porous rock like sandstone. More interesting to see is that the MoSF value for gneiss is not very high, and this can be related to the compositions of this rock, compared to hard quartz minerals, soft mica minerals cannot resist the tool indentation, and an enhancement of scratch depth occurs. Similar results were observed for the Cerchar specific energy based on the tested rocks. The highest SE value was also found for granite (SECerchar = 3162.67 mJ/mm3), while the lowest one for sandstone (SECerchar=167.99 mJ/mm3).
Relationship of rock cuttability between Cerchar measurements and theoretical models
The rock cuttability parameters, namely the scratching force and specific energy, obtained from the Cerchar measurements are related to those calculated by the theoretical models. In Fig. 10a, b and c, the ASF values are plotted against the force values calculated by the Evans’, Roxborough and Liu’s, and Goktan’s models, respectively. However, no meaningful correlation can be obtained according to the available data. In contrast, inverse relationships are found between the newly proposed force parameter, MoSF, and theoretical results. The linear relationship in terms of Evans36 is shown in Fig. 10d, and the R2 is about 0.70. By using the concept given by Roxborough and Liu37, the linear relationship is improved with a R2 value of about 0.85 (see Fig. 10e). By using the concept of Goktan38, the R2 is about 0.92 (see Fig. 10f). Moreover, Fig. 10g shows the Cerchar specific energy correlated with the theoretical specific energy calculated after Hughes7 as well as Mellor8, and an exponential relationship (R2 = 0.81) is obtained.
Fig. 10.
Relationship of cuttability parameters between Cerchar measurements and theoretical models: (a) ASF versus FCp (Evans); (b) ASF versus FCp (Roxborough and Liu); (c) ASF versus FCp (Goktan); (d) MoSF versus FCp (Evans); (e) MoSF versus FCp (Roxborough and Liu); (f) MoSF versus FCp (Goktan); (g) SE versus SE (Hughes/Mellor).
In statistical analysis, adjusted R2 is often adopted to deal with additional independent variables, namely to see how newly added independent variable influences dependent variable. If the R2 and adjusted R2 are close to each other, the R2 is accurate. When the R2 is much higher than the adjusted R2, it means that there are no enough data points to calculate the regression accurately. In addition, since the rock cuttability parameters are found to have linear or exponential relationships between the experimental and theoretical results, F-test or analysis of variance (ANOVA) is adopted to determine the significance of regression fit, or in other words, to examine whether the equation between the two correlated variables is statistically significant or not. In this article, theoretical results were selected as independent variables, and experimental results as dependent variable. The confidence level was set to 0.95. If the probability (P) is smaller than 0.05, the linear regression is considered to be significant, otherwise it is not significant41. Table 5 summarizes the statistical results of adjusted R2, and Fisher index (F) and its significance (Sig.). For both MoSF and SE, all regression curves are found to be significant. This means that the relationships are correct and reliable.
Table 5.
Statistical results of R2-statistic and ANOVA (F-test) analysis.
| Variable (dependent ~ independent) | r | R2 | Adjusted R2 | F | Sig. |
|---|---|---|---|---|---|
| ASF (Cerchar) ~ FCp (Evans) | 0.096 | 0.009 | -0.238 | 0.037 | 0.856 |
| ASF (Cerchar) ~ FCp (Roxborough and Liu) | 0.287 | 0.082 | -0.147 | 0.358 | 0.582 |
| ASF (Cerchar) ~ FCp (Goktan) | 0.501 | 0.251 | 0.064 | 1.341 | 0.311 |
| MoSF (Cerchar) ~ FCp (Evans) | 0.836 | 0.700 | 0.624 | 9.314 | 0.038 |
| MoSF (Cerchar) ~ FCp (Roxborough and Liu) | 0.921 | 0.848 | 0.810 | 22.256 | 0.009 |
| MoSF (Cerchar) ~ FCp (Goktan) | 0.959 | 0.920 | 0.900 | 45.957 | 0.002 |
| SE (Cerchar) ~ SE (Hughes/Mellor) | 0.897 | 0.805 | 0.757 | 16.546 | 0.015 |
By comparing the three theoretical models, the Goktan’s equation shows the best correlation with the new proposed parameter, MoSF, followed by the Roxborough and Liu’s, and then the Evans’. Firstly, the Evans’ theory is developed based on an indentation process, not on a cutting process. Secondly, the Evans’ model is a two-dimensional model, and it is based on the assumption of tensile failure of the rock. Thirdly, the Evans’ model ignores the friction angle between the rock and pick, while the other two models consider this factor. It should be noticed that the cuttability parameters are not a function of rock properties only, they are also related to the operational parameters, such as the power of cutting machine, cutting velocity, and tool geometry. For example, the theoretical models do not consider the tool wear during the rock cutting process, and this factor can truly affect the applied cutting force. Generally speaking, the higher the tool wears, the higher the cutting force required. Wang et al.42 emphasized that the rock failure is a very complex process in terms of the rock cutting, and compressive, tensile, shear or mixed failure modes may be dominant, depending on the rock properties, cutting-related parameters, and pick parameters.
Correlation of Cerchar cuttability parameters with rock mechanical properties
In rock engineering, another approach for predicting the rock cuttability is based on the mechanical properties of the rock. Among these, the UCS has been proven as one of the major factors affecting the rock cuttability, and cutting efficiency, because the most cutting energy is consumed in beating the UCS of a rock to induce cracks at the early beginning of the cutting process2.
Therefore, in this article, the investigated rock cuttability parameters were related to the rock mechanical properties, especially to the UCS, to make a reasonable estimation of rock cuttability. Both R2-statistic and ANOVA analysis were conducted for the ASF, MoSF, and SE, respectively, to examine the accuracy of the regression. Results of statistical analysis are summarized in Table 6. Seen from Fig. 11, although no meaningful correlation is found between the ASF and UCS (R2 = 0.44, P = 0.152 > 0.05), the MoSF shows an increased trend with the UCS. The linear regression (R2 = 0.86, P = 0.008 << 0.05) is significant. This finding confirms the conclusion in the rock cutting that the higher the rock strength, the more force is required to cut or excavate it43. Compared to the linear regression, an exponential regression can better describe the relationship (R2 = 0.78, P = 0.02 < 0.05) between the SE and UCS. The consumed specific energy increases with increasing rock strength. It should be noticed that a certain correlation (R2 = 0.61, P = 0.067 > 0.05) could exist between the SE and abrasive property of the rock, which is characterized by the CAI. This reveals that the cutting energy is also dependent on the rock abrasivity.
Table 6.
Regression and related ANOVA analysis.
| Regression | r | R2 | Adjusted R2 | F | Sig. |
|---|---|---|---|---|---|
| ASF (Cerchar) ~ UCS | 0.662 | 0.439 | 0.299 | 3.131 | 0.152 |
| ASF (Cerchar) ~ BTS | 0.940 | 0.884 | 0.855 | 30.458 | 0.005 |
| ASF (Cerchar) ~ E | 0.388 | 0.151 | -0.062 | 0.709 | 0.447 |
| ASF (Cerchar) ~ Vp | 0.819 | 0.671 | 0.589 | 8.167 | 0.046 |
| ASF (Cerchar) ~ CAI | 0.445 | 0.198 | -0.003 | 0.986 | 0.377 |
| MoSF (Cerchar) ~ UCS | 0.925 | 0.855 | 0.819 | 23.559 | 0.008 |
| MoSF (Cerchar) ~ BTS | 0.450 | 0.203 | 0.003 | 1.016 | 0.370 |
| MoSF (Cerchar) ~ E | 0.106 | 0.011 | -0.236 | 0.045 | 0.842 |
| MoSF (Cerchar) ~ Vp | 0.322 | 0.103 | -0.121 | 0.461 | 0.534 |
| MoSF (Cerchar) ~ CAI | 0.284 | 0.081 | -0.149 | 0.351 | 0.585 |
| SE (Cerchar) ~ UCS | 0.883 | 0.780 | 0.725 | 14.173 | 0.020 |
| SE (Cerchar) ~ BTS | 0.886 | 0.785 | 0.732 | 14.623 | 0.019 |
| SE (Cerchar) ~ E | 0.227 | 0.051 | -0.186 | 0.217 | 0.666 |
| SE (Cerchar) ~ Vp | 0.627 | 0.393 | 0.242 | 2.595 | 0.183 |
| SE (Cerchar) ~ CAI | 0.780 | 0.608 | 0.511 | 6.215 | 0.067 |
Fig. 11.
Relationship between Cerchar cuttability parameters and rock mechanical properties: (a) ASF versus UCS; (b) MoSF versus UCS; (c) SE versus UCS; (d) SE versus CAI.
Summary and conclusions
Rock cuttability can be expressed by the cutting force acting on the excavation tools as well as the specific energy consumed during the cutting process. These two parameters can be determined theoretically and experimentally. Since in-situ and full-scaled experiments are time and cost expensive, small-scaled or model tests is often taken into account. Due to the testing principle, and with the aid of a new designed test device, the Cerchar scratch test is considered to determine the cuttability parameters, such as the scratching force, scratch depth and the modified scratching force, and the material removal volume and specific energy.
Looking at the scratching process taking place in the Cerchar test, it is identified that the scratch of stylus over the rock surface is accomplished with its penetration into the rock. This behavior can more precise reflect the actual feed process occurring in the rock cutting, in which the cutting (caused by cutting force) and indenting (caused by normal force) march in parallel, but it is quite different from that conducting for the rock cutting experiments in the laboratory, in which the cut depth is usually kept constant during the cutting process. For this reason, the newly proposed force parameter, MoSF, which relates the scratching force generated on the stylus, and the scratch depth produced beneath the sample surface, is more reasonable for estimating the rock cuttability. ANOVA results show that the relationship between the MoSF and widely accepted theoretical models of rock cutting is significant.
In addition, the Cerchar specific energy, SE, which is similar to the specific energy in rock engineering, is determined by dividing the scratching energy consumed on the stylus by the material volume removed from the rock surface. An exponential regression is found between the SEs obtained from the Cerchar measurements and theoretical calculations. This means that the Cerchar specific energy can also be used to estimate the rock cuttability, and to evaluate the efficiency of rock cutting.
By relating the investigated cuttability parameters to the mechanical properties of rocks, it is found that – based on the tested rocks – the UCS has a better correlation with the MoSF and SE in linear and exponential models, respectively. This indicates that the UCS is the best factor for predicting the rock cuttability. It is also found that the rock abrasivity expressed by the CAI can be related to the specific energy. It should be noticed that further studies are needed to examine the validity of correlations through testing more rock materials, and the validation of cutting force via in-situ measurements is necessary.
Acknowledgments
Many thanks to Prof. Shouding Li from the Institute of Geology and Geophysics at the Chinese Academy of Sciences, and Dr. Patrick Gehre from the Institute of Ceramics at the TU Bergakademie Freiberg for providing useful testing apparatuses. Special thanks to Prof. Heinz Konietzky from the Institute of Geotechnics at the TU Bergakademie Freiberg for discussing.
Abbreviations
- ANOVA
Analysis of variation
- ASD
Averaged scratch depth
- ASF
Averaged scratching force
- BTS/σt
Brazilian tensile strength
- CAI
Cerchar abrasivity index
- CAR
Cerchar abrasion ratio
- d
Wear flat on the stylus tip
- dc/Px
Scratch/Cut depth
- E
Young’s modulus
- F
Fisher index
- FC
Cutting force
- FCp
Peak cutting force
- Fs
Scratching force
- Ls
Sliding/Testing distance
- MCAI
Modified Cerchar abrasivity index
- MoSF
Modified scratching force
- P
Probability
- r
Coefficient of correlation
- R2
Coefficient of determination
- SE
Specific energy
- UCS/σc
Uniaxial compressive strength
- Vm
Material removal volume
- Vp
P-wave velocity
- θ
Tip angle
- ρ
Density
- φ
Friction angle
Author contributions
Conceptualization, methodology, investigation, formal analysis, data curation, writing-original draft, visualization, Writing –review & editing.
Funding
This article is funded by the Institute of Foundation Engineering at the China Academy of Building Research (Grant No.: 20241602341030006).
Data availability
All data, models, and codes generated or used during the study are available from the corresponding author upon reasonable request.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Data Availability Statement
All data, models, and codes generated or used during the study are available from the corresponding author upon reasonable request.