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Engineering Geology
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Rock strength determination from scratch tests
Thomas Richard a,b, Fabrice Dagrain c, Edmond Poyol d, Emmanuel Detournay b,e,⁎a Epslog, Belgiumb Earth Science and Resource Engineering, CSIRO, Australiac Département de Génie Civil et Mécanique des Structures de la Faculté Polytechnique de Mons, Université de Mons-Hainaut, Belgiumd Rock Mechanics Laboratory, Total, Francee Department of Civil Engineering, University of Minnesota, USA
⁎ Corresponding author at: Department of Civil EnginMinneapolis, MN 55455, USA.
This paper provides compelling experimental evidence that the unconfined compressive strength of rockscan be reliably assessed from scratch tests performed with a sharp cutter, and at depth of cut small enoughto prevent any significant chipping of the rock. The paper describes the model used to interpret the experi-mental results, the test methodology, and the Rock Strength Device that was developed to perform scratchtests under kinematically controlled conditions. It concludes with a summary of an extensive experimentalcampaign involving the testing of several hundred rocks to compare strength data from conventional uniaxialcompression experiments and from scratch tests.
The uniaxial compressive strength (UCS) is the most common mea-sure of strength used in civil, mining, and petroleum engineering, withapplications ranging from the design of underground structures in rocksto the selection of tools formechanical excavation. The procedure to de-termine the UCS has been standardized by the ASTM (2010) and theISRM(Ulusay andHudson, 2007), and the test itself has been the subjectof numerous publications (Bieniawski, 1968; Hawkes andMellor, 1970;Wawersik and Fairhurst, 1970; Broch and Franklin, 1972; Hudson et al.,1972; Jaeger et al., 1976; Pells, 1993).
The uniaxial compression test used to determine the UCS suffersfrom several drawbacks, however. It requires not only cores of intactrock but also precise and time consuming sample preparation, in partic-ular the rectification and the polishing of the sample ends. The magni-tude of the axial stress at which the rock fails depends on the aspectratio of the core, one of the reasons why the procedure for determiningthe UCS has been standardized. The moisture content and the irregularends are also known to affect the test outcome (Bieniawski, 1968;Hawkes and Mellor, 1970; Broch and Franklin, 1972; Hudson et al.,1972; Hoek and Brown, 1980; Dey and Halleck, 1981; Farmer, 1992).Moreover, the test is not well suited for heterogeneous, damaged,layered or fractured rocks. In such materials, failure is often controlledby the weakest plane, joint or a pre-existing crack present in the coresample. Finally, the requirements in terms of power and size for the
eering, 500 Pillsbury Drive SE,
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equipments used for sample preparation and testing have restrictedthe test to a laboratory environment.
Alternative indirect methods to estimate the UCS, such as the pointload test, the indentation test, or the Schmidt hammer test, have beendeveloped over the years (Broch and Franklin, 1972; Bieniawski, 1974,1975; Chau and Wong, 1996; Szwedzicki, 1998; Rusnak and Mark,1999; Aydin and Basu, 2005). Limited sample preparation, light equip-ment, the partial or non-destructive nature of the testing are some ofthe benefits that these methods have over the uniaxial compressiontest. The main advantage of both the point load and indentation testsis actually their ability to assess strength with very small size samples(about 3–5 cm3), while the main benefit of the Schmidt hammer testis that it allows for direct testing on outcrops in the field.
These indirect methods are not without problems, however. First,there is documented subjectivity in the correlation between the pointload index or the Schmidt rebound number and the UCS (Kahraman,2001; Fener et al., 2005). Second, both test results are affected by theelastic properties of thematerial, the sample size and themoisture con-tent (Bieniawski, 1975; Tsur-Lavie and Denekamp, 1982; Kahraman,2001; Thuro et al., 2001; Tsiambaos and Sabatakakis, 2004; Aydin andBasu, 2005). There are other issues, such as the point load testing of ir-regular shapedmaterial (Broch and Franklin, 1972), or the roughness ordegree of polishing of the surface on which the impact occurs, whichalso affect the rebound values (Hucka, 1965).
The scope of this paper stems from an effort initiated at the Uni-versity of Minnesota (UMN) in the mid-nineties to build a scientificapparatus to study the cutting action of a single cutter (Detournayet al., 1997) in order to assess the dependence of the cutting force onthe rock mechanical properties and on the UCS, in particular (Almenara
92 T. Richard et al. / Engineering Geology 147–148 (2012) 91–100
and Detournay, 1992; Detournay et al., 1995; Adachi et al., 1996; Richardet al., 1998). Comparable efforts by other researchers aiming at using re-sults of both cutting and drilling tests to estimate rock strength have alsobeen recently documented (Reddish and Yassar, 1996; Perrier, 1997;Tiano, 2001; Balci et al., 2004; Stavropoulou, 2006; Pamplona et al., 2007).
In this paper, we first review basic aspects of the mechanics of rockcutting, with considerations given to the ductile and the brittle regimes,and to the influence of a wear flat on themagnitude of the cutting force.We then describe the Rock Strength Device, as well as the test method-ology. Finally, we produce compelling evidence that under conditionsreferred to as the ductile regime, the specific energy of cutting is wellcorrelated with the UCS.
2. Mechanics of rock cutting
A scratch test involves tracing a groove on the surface of a specimenwith a cutting tool. The test has been widely used (Nishimatsu, 1972;Duc, 1974; Deliac, 1986; Glowka, 1989b) to study the cutting processand to assess the effect of rock properties and tool characteristics onthe performance of drilling or excavation tools.
The scratch test is typically conducted under kinematic control: thedepth of the cut d (or depth of the groove) and the cutter velocity v(tangential to the sample surface) are imposed and maintained con-stant along the entire cut, while the magnitude and orientation of theforce acting on the cutter are measured, see Figure 1.
The cutter–rock interaction is generally characterized by the coexis-tence of two processes, namely rock fragmentation in front of the cut-ting face of the tool and frictional contact along the wear flat/rockinterface (Fairhurst and Lacabanne, 1957; Duc, 1974; Glowka, 1989a;Detournay and Defourny, 1992). Moreover, there exist two differentcuttingmechanisms, ductile and brittle, whose occurrence is controlledby themagnitude of the depth of cut (Chaput, 1992; Richard et al., 1998;Richard, 1999; Huang and Detournay, 2008; Huang et al., 2012).
At shallow depth of cut (typically less than 1 mm for a mediumstrength sandstone), the rock is intensively sheared ahead of the cut-ter; this cutting regime is mainly characterized by a de-cohesion ofthe constitutive matrix and grains, with grains and powder accumu-lating progressively in front of the cutter (Figure 2).
At larger depth of cut, brittle failure occurs, with macroscopiccracks initiating from the tool tip and propagating unstably ahead ofthe cutter; chips, fragments of rock are created and removed by thecutter (Figure 2).
As expected, experimental results indicate that different materialproperties control the magnitude of the cutting force in the twomodes of failure (Richard et al., 1998): fracture toughness KIc in thebrittle regime and the uniaxial compressive strength, q in the ductileregime. The depth of cut characterizing the transition between ductileand brittle regime scales by the rock intrinsic length scale (KIc/q)2
(Huang and Detournay, 2008; Huang et al., 2012). These twomechan-ical properties reflect different modes of energy dissipation: alongcreated macroscopic discontinuity surfaces in the brittle regime andwithin the volume of the failed material in the ductile regime.
A phenomenological model of cutter/rock interaction in the ductileregime was proposed by Detournay and Defourny (1992). This model
Fc
Ff
v
d
sn
Fig. 1. Cutting configuration. Forces acting on a blunt cutter.
is based on three key assumptions applicable to a particular cutter–rock combination, irrespective of the cutter wear, namely (i) the forceson the cutting face, suitably averaged over a distance large compared tothe depth of cut, is proportional to the cross-sectional area Ac of thegroove traced by the cutter; (ii) the inclination of the average force onthe cutting face is constant; and (iii) there is frictional contact at thewear-flat rock interface. Such a model is characterized by three param-eters: the intrinsic specific energy ε associated with the cutting process,the number ζ giving the inclination of the force acting on the cuttingface, and the friction coefficient μ mobilized across the wear flat.
The force F acting on a blunt cutter results therefore from the super-position of two forces Fc and Ff, acting on the cutting face and on thewear flat, respectively. The components of these two forces in a direc-tion parallel (subscript s) and perpendicular (subscript n) to the cuttermotion can thus be expressed as (Figure 1)
Fcs ¼ εwd; Fcn ¼ ζεwd; ð1Þ
where a rectangular cutter has been assumed, i.e., Ac=wd, while thecomponents of the force Ff acting on the wear flat are constrained by
F fn ¼ μF fs: ð2Þ
The intrinsic specific energy ε represents the energy required to cuta unit volume of rock. The word “intrinsic” emphasizes that this energyis strictly used to cut the rock; in other words, ε does not take into ac-count frictional dissipation associated with cutter bluntness. Thus, “in-trinsic” does not imply that ε is independent of the cutter geometry(shape and back-rake angle) or even the depth of cut. However, thephenomenological model, on which the interpretation of scratch datais based, assumes that ε is indeed independent of the depth of cut andit is a constant quantity characterizing a particular combination of cut-ter geometry and rock. The intrinsic specific energy is expressed hereas a stress (e.g., in unit MPa), rather than as an energy per volume(e.g., in unit J/cm3, which is numerically equivalent toMPa), on accountof the expected relation between ε and the UCS q.
The number ζ can be expressed as tan(θ+ψ) with ψ the inclinationangle of the force to the normal to the cutting face, see Richard (1999);Huang et al. (1999); Coudyzer and Richard (2005) for more details onthe meaning of this angle. For a given back-rake angle, the angle ψ isfound to be independent of the depth of cut.
Finally, μ is the coefficient of friction on the wear flat/rock interface,which can also be expressed as μ=tanϕ where ϕ is the angle betweenthe frictional force Ff and the normal to the wear flat.
Combining the two processes (pure cutting and frictional contact)leads to a relationship between the cutting Fs and normal Fn compo-nents of the total force
Fs ¼ ε 1−μζð Þwdþ Fn; ð3Þ
which scaled by the cross-section area Ac=wd yields a constraint onthe cutter response
E ¼ Eo þ μS; ð4Þ
where E and S are the specific energy and the drilling strength respec-tively defined as
E ¼ Fswd
; S ¼ Fnwd
; ð5Þ
and Eo=ε(1−μζ). Accordingly, points pertaining to tests performedwith a blunt cutter define the friction line in the ES diagram. The posi-tion along the friction line is controlled by the cutter state ofwear (mea-sured as the length ℓ of the wear flat in the case of rectangular cutter),the depth of cut, as well as the normal stress σ on the wear flat. A syn-thetic ES diagram is shown in Figure 3.
0
160
80 300
600
00 20 40
s (mm) s (mm)60 0 20 40 60
a bFs (N)Fs (N)
Fig. 2. Schematic of the ductile and brittle regimes. Examples of force signal (tangential component Fs) in the ductile (d=0.6 mm) and brittle regime (d=3 mm). Tests conducted in aspecimen of Vosges sandstone.
93T. Richard et al. / Engineering Geology 147–148 (2012) 91–100
It is important to reiterate the difference between the intrinsic spe-cific energy ε and the specific energy E. The latter quantity, E, accountsfor both the energy expended in cutting the rock and the energy dissi-pated at the frictional contact between the wear flat and the rock,while the former one, ε, only characterizes the energy used to fragmentthe rock ahead of the cutter.
Figure 4 shows evidence of the proportionality between the magni-tude of the cutting force and the depth of cut, for scratch testsconducted in the ductile regime with a sharp cutter. The rocks used inthe tests have been selected for their high degree of homogeneity;they consist of two sandstones (Vosges and Rhune), three limestones(Anstrude, Buxy, Fontenoille) and one chalk (Harmignies). For eachrock, a best linear fit is conducted on the set of data points (Fs, d).Using Eq. (1), the intrinsic specific energy is then simply inferred asthe estimated slope divided by the cutter width, w. Tables A1–A3 inAppendix A list the UCS q and the intrinsic specific energy ε for the sixrocks of Figure 4, as well as for many others.
An example of a ES diagramwith points pertaining to tests performedwith a blunt cutter on four rocks (shale, coal, sandstone, and limestone) isshown in Figure 5. The friction coefficient μ can be inferred as theslope of the friction line (estimated from best linear fits conductedon the data set). The estimated values of μ and ϕ for the four rocksare listed in Table 1. These results are consistent with previous ob-servations that the friction angle ϕ characterizing the cutter wearflat/rock contact is often reminiscent of the internal friction angleof the rock (Almenara and Detournay, 1992; Detournay andDefourny, 1992; Dagrain and Richard, 2006).
µζ
1
1
E
S
ε
cutting point
friction line
Eo
Fig. 3. Synthetic ES diagram (Detournay and Defourny, 1992). The position of the statepoint on the friction line depends on the cutter bluntness and depth of cut. For a per-fectly sharp cutter operating in the ductile regime, E=ε. The cutting efficiency ε/E de-creases with depth of cut d and/or with increasing wear flat length ℓ.
The above experimental evidence supports the assumptions behindthemodel of rock cutting in the ductile regime, namely that the param-eters ε, μ, and ζ are constant for a particular rock/cutter pair, irrespectiveof the cutter wear. However, the inclination of the cutting force appearsto beweakly dependent on the rock and to only vary in a narrow range.Indeed, the histogram of ζ, measured in scratch tests conducted onabout 375 rocks (Appendix A), using a cutter with a back-rake angleof 15°, shows that ζ is distributed normally with a mean of 0.6 and astandard deviation of 0.16. This relative invariance of ζ can actually beused for monitoring the wear state of the cutter, as values of ζ largerthan 0.9 suggests the existence of a force on thewearflat that is not neg-ligible compared to the cutting force (Figure 6). Although nothing hasbeen said on themagnitude of the force Ff at the wear flat/rock contact,there is evidence that the mean normal contact stress Ffn/Afn, where Afnis the nominal wear flat area, although sensitive to the relative inclina-tion of the cutter velocity on the wear surface, is bounded by the UCS(Almenara and Detournay, 1992; Adachi et al., 1996).
3. Rock Strength Device
The Rock Strength Device (RSD) is a testing apparatus that was de-veloped at the University of Minnesota in the late 1990's (Detournayet al., 1997). The RSD scratches the surface of rock samples under pre-cise kinematic control, while enabling accurate measurements of theforce acting on the cutter. The main components of the frame (seeFigure 7) are: a traverse with a sample holder (indexed 1 on Figure 7),
Fig. 4. Variation of the tangential component of the measured force with the depth ofcut d. Tests performed with a sharp rectangular cutter of width of w=10 mm.
0 100 200 300 4000
100
200
300
400
S (MPa)
E (
MPa
)Boom shaleCoalVosges sandstoneLens limestone
Fig. 5. ES diagram for four different rock materials. Tests conducted with a blunt cutter.
0.0 0.2 0.4 0.6 0.8 1.00
20
40
60
ζ
Fig. 6. Histogram of ζ measured for about 300 rocks, see Appendix A.
94 T. Richard et al. / Engineering Geology 147–148 (2012) 91–100
a moving cart (2) housing the vertical positioning system (3), the loadcell (4), and the cutting element (5). The horizontal movement of thecart is operated by a computer controlled stepper-motor (6) drivingan horizontal ball screw (7) via a gearbox (8). The depth of cut is adjust-ed manually with the vertical positioning system (9) and a micrometer(10). A locking system (11) secures the vertical traveling mechanismagainst the frame, in order to maintain a constant depth of cut whilecutting.
A load sensor measures the tangential and normal components (Fs,Fn) of the force F acting on the cutter. The complete system (sensor,data acquisition) achieves about 1 N of precision and resolution overthe entiremeasurement range [0–4000 N]. The scanning rate is typical-ly set at 25 samples per millimeter travelled by the cutter.
Two types of cutting tools are used: sharp and blunt cutters. Sharptools present only one contact surface with the rock, the cutting face,which is inclined forward by the back-rake angle θ, here set to 15°. Inaddition to the cutting face, blunt cutters possess a machined “wearflat,” moving parallel to the cutting direction against the bottom of thegroove. The flat surface is inclined forward by a small angle (β~2°) toensure conforming contact with the rock (Detournay et al., 1997). Forrectangular shaped cutters, the geometry chosen for the tests, descrip-tion of the cutter geometry reduces to the width w (w=10 mm) andthe wear flat length ℓ (varying from a fraction of mm to a couple ofmm). The cutting face of the cutters commonly used are made of athin layer of polycrystalline diamond compact (PDC) laid down on acarbide tungsten base.
A campaign of scratch tests have confirmed that the intrinsic specificenergy is indeed relatively insensitive to the cutter width w and thedepth of cut d for width around w=10 mm and beyond, if cuttingtakes place in the ductile regime. Figure 8 shows results of testsconducted using five cutter widths (w=2.56,5,10,15, and 50 mm) inVosges sandstone at depths of cut ranging from 0.2 to 1.8 mm(Richard, 1999; Dagrain, 2006). The figure reveals that (i) the specificenergy forw=10, 15, and 50 mm indeed does not depend on d, unlike
Table 1Friction coefficient μ and friction angle ϕ.
the results forw=2.5 mm and 5 mm, where ε is seen to increases withd; (ii) the intrinsic specific energy ε hardly varies when comparing theresults for w=10, 15, and 50 mm.
The variation of ε with w and d that is observed for w=2.56 and5 mm is thought to be related to the existence of another lengthscale, the grain size, and to the dilatant nature of shear failure. In nar-row grooves, the shear-dilatant behavior of the rock could lead to atransverse normal stress (perpendicular to the cutting direction) asthe chain of grains are short enough to offer some resistance to“buckling.” (Vosges sandstone, the average grain diameter is about0.15 μm, meaning that only 10 to 20 grains fill the groove width forw=2.56 mm.) Furthermore, it is also expected that the stability ofthe granular chains increases with the depth of cut. The frictionalstrengthening associated with the transverse normal stress is thentranslated into an increase of the specific energy.
The depth of cut (ranging typically between 0.1 and 1 mm) is theonly parameter controlling the magnitude of the force acting on a cut-ter, given its geometry and the rock being scratched. As the test isperformed under imposed depth of cut, precise adjustment of thedepth of cut and minimal compliance of the frame are thus critical.The vertical compliance of the frame/sensor assembly was estimatedby measuring the vertical displacement of the cutter tip under an im-posed axial force; it was found equal to about 0.038 mm/kN for theRock Strength Device depicted in Figure 7.
An experiment was designed to assess the reliability of the depth ofcut adjustment; the nominal depth of cut dn set prior to the testwith themicrometer, was compared to the mean effective depth of cut de mea-sured with a laser as the thickness of material removed during thetest. The vertical distance between the centre line of the groove bottomsurface and the same absolute reference point is logged using a laser,before and after the cut, thus providing the variation of the effectivedepth of cut along the test. The results for a medium strength rock(q~50 MPa) show that the absolute difference between dn and de fallswithin the precision of the micrometer, see Figure 9.
In addition, the overall stiffness of the assembly (frame and sensor)is sufficiently large to ensure that its dominant natural frequencies(around 600–700 Hz for the sensor) are far outside the bandwidth ofthe cutting force signal (about 98% of the energy associated to the signalsits between 0 and 10 Hz).
4. Test methodology
The testing procedure consists in performing successive scratchtests along the same groove on the surface of a rock specimen, whilemeasuring the force components Fs and Fn, which are respectively par-allel and normal to the cutter velocity. Each test is conducted along theentire specimen length under constant depth of cut d and constant cut-ting velocity v. The tests reported in this paper were carried out withcutters characterized by a width w=10 mm and a back rake angle
Fig. 7. Sketch of the Rock Strength Device (front and side view).
95T. Richard et al. / Engineering Geology 147–148 (2012) 91–100
θ=15° and with the cutter velocity set to v=4 mm/s. The depth of cutd typically ranged between 0.1 and 1 mm,with increment varying from0.05 to 0.3 mm between successive cuts. The force components aremeasured at a sampling rate of 100 Hz, meaning 25 measurements offorce per mm of cut.
The tests can be carried out using either sharp or blunt cutters, asdiscussed below. For testswith sharp cutters, the sharpness of the cutterneeds to be constantly monitored. Besides visual inspection of the cut-ter tip between each test series, the sharpness is most easily monitoredby tracking the evolution of the number ρ=Fn/Fs between each cut. Theforce inclination is indeed a useful indicator for evaluating the cuttersharpness, aswear causes an increase of the ratio ρ of the normal to tan-gential component of the total force acting on the cutter (ρ=ζ for anideally sharp cutter). For tests with blunt cutters, consideration mustbe given to the wear flat size, so as to limit the forces mobilized by theblunt tool to levels acceptable for the sensor.
In order to estimate the rock strength q from cutting tests, the testshave to be conductedwithin the ductile regime. Various indicators, suchas mechanical vibrations, noise, and size of debris, exist to ascertainwhether cutting takes place within the ductile or the brittle regime. Inaddition, the force signal itself can be used for the purpose, as its prop-erties differ in the ductile and in the brittle regime. In the ductile regime,the force signal may be viewed as a white noise, whereas the signal inthe chipping mode presents a marked sawtooth pattern (Figure 2).The coefficient of variation γ, the ratio of the standard deviation to themean, was found to be a good indicator of the difference between thetwo types of signals. Indeed, γ is almost independent of the depth ofcut within the ductile regime, but increases with d in the brittle regime
40 80 1200
20
40
60
80
100
w/d
ε (M
Pa)
w = 2.56 mm5.05 mm10 mm15 mm50 mm
Fig. 8. Variation of intrinsic specific energy ε with w/d for tests conducted on Vosgessandstones with rectangular cutters with various widths (w=2.5, 5, 10, 15, and50 mm). The depth of cut varies as follows: w=2.56 mm, d=[0.2,1] mm; w=5 mm,d=[0.3,1.5] mm; w=10 mm, d=[0.2,1.8] mm; w=15 mm, d=[0.3,1.4] mm; w=50 mm, d=[0.5,0.8] mm (Richard, 1999; Dagrain, 2006).
(Figure 10). This result also suggests that within the ductile regime, themean force is the only relevant quantity.
The question of the appropriate length scale overwhich the signal canbemeaningfully observed (i.e., averaged) is important for interpreting theforce results. One simple criteria concerns the reproducibility of the testresults. The relevant and reproducible information, in terms of mechani-cal properties, is evidently associated with the background trend of theforce signal, at “low” spatial frequencies, while the “high” frequenciesevents are not reproducible because they are associated with stochasticevents such as dislodgement of individual grains. Experience suggeststhat the force signal should be averaged over a length scale of a fewmillimeters to provide repeatable mean value of the force signal inhomogeneous sections. Fig. 11 illustrates the variation of the cuttingforce recorded while scratching the surface of a heterogeneous shalesample (d=0.4 mm); it shows the existence of four distinct regions,each characterized by an approximate “stationary response” andthus by different mean strength properties.
5. Strength determination
An extensive campaign of testing to compare results from uniaxialcompression tests and scratch tests has been ongoing since 1995 in sev-eral rockmechanics laboratories (University of Minnesota, USA; FacultéPolytechnique de Mons, Belgium; Total, France). Results for 376 differ-ent rocks are reported in this paper (Appendix A); these rocks consistof 130 quarry materials (96 limestones, 25 sandstones, 2 chalks, 2shales, 3 granites and 2 schistes) and 246 non referenced rocks, mainly
0 0.25 0.5 0.75 10
0.25
0.5
0.75
1
dn (mm)
d e (
mm
)
Fig. 9. Comparison between the nominal dn and effective de depths of cut.
0 0.5 1 1.5 20
0.2
0.4
0.6
d (mm)
γ
Fig. 10. Evolution of the coefficient of variation γ of the tangential force componentwith the depth of cut d.
0 50 100 150 200 2500
50
100
150
200
250
q (MPa)
limestones sandstonesothers
ε (M
Pa)
Fig. 12. Correlation between the intrinsic specific energy ε and the uniaxial compres-sive strength q. The data of Appendix A have been grouped into limestones, sandstones,and others.
96 T. Richard et al. / Engineering Geology 147–148 (2012) 91–100
core samples from oil or gas reservoirs (310 sandstones, 10 limestonesor dolomites and 24 shales or pelites, 2 granites).
The correlation between the intrinsic specific energy ε and theUCS q isshown in Figure 12. The data pertaining to the quarry materials are sum-marized by rock type in Tables A1–A3, which are given in Appendix A.
A few points have been eliminated from the correlation plot becausethe results of the uniaxial compression were considered as not beingrepresentative of the material strength. As an example, samples of ashale provided scattered results for q varying from 2 to 26 MPa as thesamples were failing along fractures present in the specimen. Cuttingtests performed on the same samples were not affected by the fractureplanes or de-lamination planes (ε=71 MPa).
6. Benefits of the test
One essential feature of the scratch test is its high degree of repeat-ability. Results of tests carried out on an homogeneous rock sampledisplay little dispersion, as illustrated in Figure 13. For this example, acoefficient of variation of about 4% is obtained for the two force compo-nents from 30 similar scratch tests conducted with a sharp cutter on asample of Indiana limestone at constant depth of cut (d=0.2 mm)over a distance of 130 mm.
Scratch as well as compression tests were performed on samples ofVosges sandstone to compare the dispersion of the strength measuredfrom these two tests. A rectangular block (200×200×100 mm) ofVosges sandstone was prepared and scratch tests performed at 10 dif-ferent locations on one outer surface of the sample; all the cuts werein the same direction. For each location, five scratches were carriedout at depth of cut ranging from 0.1 to 0.5 mm and the intrinsic specific
0 20 40 60 800
150
300
450
600
s (mm)
Fs
(N)
Fig. 11. Example of a force signal (tangential component) characterized by 4 distinctregions. Tests performed at d=0.4 mm. A low-pass filter with a cut-off frequency cor-responding to 0.25 mm has been applied to the raw force signal.
energy estimated at each location. Eight sampleswere then cored out ofthe block with the axis of the cores parallel to the cutting direction, andsubjected to uniaxial compression.
The results, shown in Table 2, highlight a dispersion among the com-pression test results that is about one order of magnitude higher thanfor the scratch results; i.e. a coefficient of variation (standard deviationto mean) of 1.3% for the scratch test against 13% for the uniaxial com-pression test. Furthermore, tests carried out on core samples of Lenslimestonewith diameters ranging from 19 to 69 mm show a dispersionin the force measurement comparable to the dispersion observed in re-sults of tests conducted on the same sample (Figure 14). The inferredvalues of the intrinsic specific energy have a mean of 23.4 MPa withstandard deviation of 0.8 MPa, corresponding therefore to a coefficientof variation of about 3%. Similar results are summarized in Table 3 fortests performed on blocks of Vosges sandstone with thickness varyingfrom 100 mm down to 6 mm.
It is also interesting to note that results of tests conducted on a saturat-ed sample sit within the error margin of the results obtained on dry sam-ples (Figure 14), suggesting that themoisture content has negligible effecton the test outcome, at least for rocks whose structure is not altered bythe degree of saturation. For example, there is evidence that the intrinsicspecific energy on some shales is affected by hydro-chemical interactions.
The above results indicate that the intrinsic specific energy can beestimatedwith confidence from the result of a single scratch performed
0 8 16 24 320
50
100
150
200
Test Number
Fs
, Fn
(N)
Fs
Fn
Fig. 13. Averaged force components (Fs, Fn) for a series of 30 scratch tests performed ona sample of Indiana limestone (at d=0.2 mm) over a length of 130 mm.
Table 2Dispersion in the results of uniaxial compressive and scratch tests, performed on samplesof Vosges sandstone. (For the UCS tests: coefficient of variation γ(q)=13%, correspondingto a standard deviation of 6 MPa and amean of 45.7 MPa. For the scratch tests: coefficientof variation γ(ε)=1.3%, corresponding to a standard deviation of 0.7 MPa and a mean of50.3 MPa.)
Table 3Dispersion in the results of scratch tests performed on samples of Vosgessandstone characterized by different thickness. (Coefficient of variationγ(ε)=2.7%, corresponding to a standard deviation of 1.2 MPa and a meanof 45.6 MPa.)
97T. Richard et al. / Engineering Geology 147–148 (2012) 91–100
at a depth of cut small enough to ensure dominance of the ductile re-gime and large enough to neglect the effect of the cutter bluntness (de-fects along the cutting edge). Although E=Fs/wd≃ε for very sharp tools(ℓb0.05 mm), it is preferred, however, to perform additional scratchesat different depths of cut and extract ε from the slope of the linear re-gression line calculated from the pairs (Fs, d).
In summary, the intrinsic specific energy appears to be unaffected bythe sample dimensions as long as a few criteria are satisfied. First, thescratch length should be equal to at least a few millimeters. Second,the sample width should be sufficient to accommodate a cutter of10 mm width. Finally, the sample thickness should be larger than thedepth of cut by a few millimeters.
The continuous nature of the scratch test associated to a spatial res-olution of order of millimeters naturally yields a log of the materialstrength. This strength log can be approximated by the log of the intrin-sic specific energy E by simply dividing the filtered force signal by theproduct wd (Detournay et al., 1995; Dagrain et al., 2004). Practically,the method allows capturing variations of the order of a few MPa overa distance of a fewmillimeters along the sample surface. Logs of the spe-cific energy E measured at different depth of cut from tests performedon the surface of an heterogeneous reservoir rock are shown in Figure15, and show evidence of the reproducibility and resolution of thescratch technique.
7. Conclusions
This paper has provided compelling experimental evidence that theunconfined compressive strength of rocks can be reliably assessed fromscratch tests performed under controlled conditions, namely with asharp cutter and at depth of cut small enough to guarantee that cuttingtakes place in the ductile regime.
0 3 6 9 120
75
150
225
300
wd (mm2)
Fs
(N)
D = 19.4 mm24.5 mm33.5 mm39.6 mm60.2 mm69.1 mm24.8 mm - saturated
Fig. 14. Effect of size and moisture on the response of a sharp cutter, tests performed oncores of Lens limestone characterized by different diameters D.
The scratch test offers several advantages over conventional tests.First, the results are not affected by the sample dimension, and thusonly a small volume of intact rock (10 to 20 mm thick, wide andlong) is required to assess its strength. Second, the sample prepara-tion is limited as it only requires performing a pre-cut on the samplesurface to obtain a flat reference surface that ensures a constant depthof cut along the groove; no additional equipment is thus needed forsample preparation. Third, the test offers a high degree of repeatabil-ity quite uncommon in strength testing of geomaterials. Fourth, thesemi-destructive nature of the test is an interesting asset, as it allowsadditional group of tests to be conducted on the same sample (poros-ity, permeability, sound velocity, uniaxial compression, triaxial test,etc…). Fifth, the scratch technique naturally yields a log of the rockstrength, in contrast to the direct and indirect methods which onlyyield punctual measurements of the strength; the information aboutthe spatial variation of the strength provides not only invaluable in-sights on the inhomogeneity of the rock but also a context to the con-ventional meaning of the UCS. Finally, the equipment is portable, canbe manipulated on site, and the test procedure is quick as parametersare obtained within a few minutes. The scratch test is thus an attrac-tive and elegant alternative to conventional uniaxial compressiontests and to indirect methods such as the point load test and theSchmidt hammer test.
Acknowledgment
Many people have contributed to the development of the scratchtest to measure the strength of rocks and to the design of the RSD.Their contributions are gratefully acknowledged, with the authorsbeing particularly indebted towards Robert Delwiche, AndrewDrescher, Erling Fjaer, David Hultman, Cécile Lasserre, and TanguyLhomme for their help. The research was funded by grants from theSota Tec Fund, Elf Aquitaine, Total, and DBS.
0 100 200 3000
20
40
60
s (mm)
E (
MPa
)
d = 0.3 mmd = 0.4 mmd = 0.5 mm
Fig. 15. Log of the specific energy measured at different depth of cut on the surface ofheterogeneous limestone.
(continued)
Rock q (MPa) ε (MPa)
Rouge des Flandres 108.6 88.0Balzac Fleuri 90.0 90.5
Table A.1 (continued)
98 T. Richard et al. / Engineering Geology 147–148 (2012) 91–100
Appendix A. Compilation of measured specific energy and strengthdata
Intrinsic specific energy ε and uniaxial compressive strength q of quarry limestonematerials.
99T. Richard et al. / Engineering Geology 147–148 (2012) 91–100
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