Estimating rock compressive strength from RockAbrasion Tool (RAT) grinds

B. J. Thomson,1 N. T. Bridges,2 J. Cohen,3 J. A. Hurowitz,4 A. Lennon,2 G. Paulsen,3 andK. Zacny3

Received 11 August 2012; revised 14 December 2012; accepted 8 February 2013; published 7 June 2013.

[1] Each Mars Exploration Rover carries a Rock Abrasion Tool (RAT) whose intendeduse was to abrade the outer surfaces of rocks to expose more pristine material. Motorcurrents drawn by the RAT motors are related to the strength and hardness of rock surfacesundergoing abrasion, and these data can be used to infer more about a target rock’s physicalproperties. However, no calibration of the RAT exists. Here, we attempt to derive anempirical correlation using an assemblage of terrestrial rocks and apply this correlation todata returned by the rover Spirit. The results demonstrate a positive correlation betweenrock strength and RAT grind energy for rocks with compressive strengths less than about150MPa, a category that includes all but the strongest intact rocks. Applying thiscorrelation to rocks abraded by Spirit’s RAT, the results indicate a large divide in strengthbetween more competent basaltic rocks encountered in the plains of Gusev crater(Adirondack-class rocks) and the weaker variety of rock types measured in the ColumbiaHills. Adirondack-class rocks have estimated compressive strengths in the range of70–130MPa and are significantly less strong than fresh terrestrial basalts; this may beindicative of a degree of weathering-induced weakening. Rock types in the Columbia Hills(Wishstone, Watchtower, Clovis, and Peace class) all have compressive strengths<50MPa and are consistent with impactites or volcanoclastic materials. In general, whenconsidered alongside chemical, spectral, and rock textural data, these inferred compressivestrength results help inform our understanding of rock origins and modification history.

Citation: Thomson, B. J., N. T. Bridges, J. Cohen, J. A. Hurowitz, A. Lennon, G. Paulsen, and K. Zacny (2013),Estimating rock compressive strength from Rock Abrasion Tool (RAT) grinds, J. Geophys. Res. Planets, 118, 1233–1244,doi:10.1002/jgre.20061.

1. Introduction

[2] A fundamental goal of geologic exploration on anyplanetary body is to determine the origin and evolution ofrocks and outcrop materials. Chemistry and mineralogy arethe principal means of inferring the nature of rocks, but theirphysical properties provide an additional rich source ofinformation. These include compressive strength, mechanicalbehavior, density, hardness, and texture, which are reflectiveof formation conditions and weathering and alterationprocesses. When analyzed in concert with other data, physicalproperties measurements provide a fuller picture of the natureof surface and subsurface materials (e.g., alteration rinds andfresh, unweathered materials).

[3] The Rock Abrasion Tool (RAT) that is carriedonboard both of the Mars Exploration Rovers [Gorevanet al., 2003; Squyres et al., 2003] can be used in this wayto improve in situ compositional analysis of Martian rocks.Just as a field geologist would use a rock hammer to cleaveopen rocks to expose fresh surfaces for examination, the ro-vers use the RAT to grind off the outer surface layers of rockand outcrop targets to expose fresher interior surfaces. Anal-yses of surfaces before and after RAT brushes and grinds re-veal the near-ubiquitous presence of surface coatings and al-teration rinds on exposed surfaces on Mars [e.g., Herkenhoffet al., 2004; Arvidson et al., 2006; Hurowitz et al., 2006].[4] In addition to providing access to fresher interior

surfaces for other instruments to analyze, the RAT itself pro-vides a wealth of information about the physical properties ofthe target being abraded. Motor currents consumed duringRAT grinding operations provide an indication of the amountof energy required to abrade a given volume of rock, a quan-tity encapsulated as specific grind energy (expressed in unitsof J/mm3, equivalent to 109 Pa). The specific grind energyis related to bulk physical properties of the rock, i.e., the com-pressive strength, mechanical behavior, hardness, and density.Despite the utility of this parameter, it remains difficult to in-fer much about a rock’s formation and evolution from this pa-rameter alone. To date, the RAT team has provided data

1Boston University Center for Remote Sensing, Boston, Massachusetts,USA.

2Johns Hopkins Applied Physics Laboratory, Laurel, Maryland, USA.3Honeybee Robotics, Pasadena, California, USA.4Jet Propulsion Laboratory, California Institute of Technology,

Pasadena, California, USA.

Corresponding author: Bradley J. Thomson, Boston University Centerfor Remote Sensing, 725 Commonwealth Ave. Rm. 433, Boston, MA02215. (bjt@bu.edu)

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JOURNAL OF GEOPHYSICAL RESEARCH: PLANETS, VOL. 118, 1233–1244, doi:10.1002/jgre.20061, 2013

showing the specific grind energy of a few terrestrial testrocks that allow for general comparison with the Mars results[e.g., Myrick et al., 2004; Wang et al., 2006]. But despiteextensive pre- and postflight RAT testing, no data catalogexists that is necessary to create an empirical correlationbetween grind energy and more typical rock strength parame-ters. Because of this fundamental gap in knowledge, the goalof this paper is to experimentally establish a direct, empiricalcorrelation between the specific grind energy measurementrecorded by the RAT and the more traditional, lab-measuredrock strength parameter of compressive strength. Using afully characterized suite of terrestrial rocks will benefit currentand future missions by providing a calibration data set thatcan be used to infer rock strength properties, thereby provid-ing additional information on the formation and modificationof Mars surface materials.

1.1. Rock Abrasion Tool Instrument Description

[5] A detailed description of the RAT is given in Gorevanet al. [2003] and is summarized here. Mounted on the rover’srobotic arm, or IDD (Instrument Deployment Device), theRAT instrument is composed of three separate motors in acylindrical housing 8.5 cm in diameter and 12.8 cm in length(Figure 1). The cutting surfaces of the RAT grinding bit con-sist of two diamond-impregnated phenolic resin pads attachedto either end of a “paddle wheel.” This grinding bit ismounted off the RAT’s central axis and rotates up to3000 rpm about its own axis via one motor (“grind motor”)and 0–2 rpm about the central axis via a second motor(“revolve motor”). The RAT grinding routine is a closed-loopprocedure whereby the speed of the revolve motor variesbased on the current reading from the grind motor; on a

harder rock, the grind motor draws more current, andthe revolve motor slows down, whereas on a softer rock,the grind motor current approaches its no-load value, andthe revolve motor speeds up. A third motor controls thegrinding depth, which is increased in small, quantized stepsafter each revolution (nominally 0.05mm per step). Asuccessful grind produces an abraded circular area that is4.5 cm in diameter and nominally 0.5 cm deep. Each mo-tor’s power consumption is recorded at a nominal rate of2 Hz (i.e., 0.5 s per sample interval). Other ancillary datacaptured include motor positions, contact switch states,temperature sensor values, bus voltage, and various soft-ware states. Both the grind current (rotation motor current)and voltage (rover bus voltage) are encoded as 64 bit binarynumbers, i.e., double-precision floating-point numbers.[6] The grinding bits of the RAT were designed such that

the resin matrix slowly wears away, and the microdiamondsat the surface fall out as the resin around them loses its grip.This continually exposes new microdiamonds from deeperwithin the bit, so there are always fresh diamonds at the bitsurface. This refreshment mechanism ensures that the abilityto grind does not degrade over time, but it also means the bitgets slowly consumed, and the RAT’s grind capabilityceases abruptly once the bits have worn away.

2. Experimental Methods

[7] We assembled a suite of terrestrial rocks for testing.This assemblage was selected to span a wide range of rockstrengths that, although not necessarily matching Martianrock chemistry or mineralogy, spans the range of phys-ical properties expected on the planet. Samples included

Figure 1. Rock Abrasion Tool (RAT) overview. (a) Side view of RAT housing. (b) End-on view of RATshowing cutting heads on grinding “paddle wheel.” Outer butterfly ring (diameter 8.5 cm) aids RAT place-ment against target rock. (c) Schematic diagram indicating paddle wheel motion through abraded region(from Myrick et al. [2004]).

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sandstone, limestone, kaolinite, and three varieties of basalt(Table 1). Major and trace element data were determinedfor each sample by crushing and analyzing via X-rayfluorescence (XRF) and inductively coupled plasma massspectrometry (ICP-MS); chemical data are given in Table 2.Compression tests and RAT grinding tests were conductedon each sample.

2.1. Compressive Strength Test Procedure

[8] The most widely quoted index mechanical property ofrock is the uniaxial compressive strength of an unconfined

cylindrical test specimen [e.g., Attewell and Farmer,1976]. We performed compressive strength tests on the sam-ples listed in Table 1 using an Instron 8502 mechanical loadframe (with 8800R control electronics) at Johns HopkinsUniversity’s Applied Physics Laboratory equipped with a250 kN load cell. Samples were prepared for testing byextracting cylindrical cores using a diamond-tipped rotarydrill bit on a Bridgeport drill press. These cores were24mm in diameter and ideally 48mm in length, althoughlengths varied (Table 3). The core ends were trimmed andprecision ground to create two parallel surfaces. Each test

Table 1. Terrestrial Rock Samples Used in This Study

Sample ID Rock type Source region Texture

bas-01 basalt, aphanitic Prescott, AZ glassy texturebas-02 vesicular basalt Keeler, CA glassy texture with abundant irregular vesiclesss-01 sandstone St. George, UT quartz arenite, no obvious bandingbas-03 basalt Mojave Desert, CA dull glassy texturekal-01 kaolinite Mammoth Mountain, CA very fine-grained texturels-01,02 limestone Santa Barbara, CA fine-grained texture

Table 2. XRF-derived Chemistry of Rock Sample Suite

Sample ID bas-01 bas-02 bas-03 kal-01 ls-01 ss-01

Unnormalized Major Elements (wt%)SiO2 50.92 55.87 49.29 66.99 0.78 89.54TiO2 2.337 1.180 1.146 0.151 0.036 0.294Al2O3 14.28 17.85 17.41 19.90 0.24 4.99FeO* 12.06 6.05 8.88 0.07 0.30 0.72MnO 0.235 0.095 0.166 0.001 0.011 0.033MgO 4.72 3.87 5.72 0.00 0.48 0.08CaO 8.07 6.81 11.28 0.08 54.39 0.19Na2O 3.33 4.06 3.11 0.06 0.05 0.04K2O 1.71 2.21 0.36 0.32 0.03 0.73P2O5 1.093 0.390 0.134 0.026 0.028 0.057Sum 98.77 98.37 97.49 87.61 56.34 96.68LOI (%) 0.37 1.00 1.98 10.41 43.15 2.27SO3 >/= 0.00 0.00 0.00 0.41 0.02 0.00

Normalized Major Elements (wt%)SiO2 51.56 56.79 50.56 76.47 1.38 92.62TiO2 2.366 1.199 1.176 0.172 0.063 0.304Al2O3 14.46 18.14 17.85 22.71 0.42 5.16FeO* 12.21 6.15 9.11 0.08 0.54 0.74MnO 0.238 0.096 0.171 0.001 0.020 0.035MgO 4.78 3.94 5.86 0.00 0.84 0.08CaO 8.17 6.92 11.57 0.10 96.54 0.20Na2O 3.37 4.13 3.19 0.07 0.09 0.04K2O 1.73 2.25 0.37 0.36 0.05 0.76P2O5 1.107 0.396 0.137 0.030 0.050 0.059

Unnormalized Trace Elements (ppm)Ni 24 22 42 0 5 0Cr 32 18 421 7 10 17Sc 36 15 30 3 0 3V 318 142 189 26 12 21Ba 1889 1072 505 1492 8 414Rb 39 37 7 2 2 23Sr 414 971 299 86 393 41Zr 141 165 95 143 4 278Y 46 16 23 11 4 16Nb 8.4 12.8 5.6 10.2 0.7 6.0Ga 19 21 17 14 1 5Cu 41 26 52 1 7 4Zn 125 77 73 3 1 7Pb 7 11 4 15 0 8La 25 34 7 24 5 25Ce 51 60 13 37 5 52Th 2 3 1 25 0 6Nd 35 30 11 9 0 22

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was run by loading the rock core in the Instron until brittlefailure occurred, and the mode of failure (e.g., axial splitting,shear failure, etc.) was noted in Table 3. All specimens wererun at a strain rate of 10�4 s�1 (0.0001mm/mm/s). Thedisplacement rate in microns/s was therefore the length in mil-limeters divided by 10 (e.g., 51.25mm ⇒ 5.125mm/s).The peak force withstood by the sample divided by its cross-sectional area yields the unconfined compressive strength(UCS) in units of MPa (1Pa=1Nm�2 = 1 kgm�1 s�2).[9] A constant strain rate of 10�4s�1 was chosen based on

the requirements of the industry standard test protocol thatstates that a constant strain rate (or stress rate) should be cho-sen such that the specimen will fail in unconfined compres-sion in a time between 2 and 15min [ASTM, 2010]. Basedon that protocol, we selected a strain rate such that the

sample with the shortest anticipated failure time (based ona combination of the expected fracture strength and elasticmodulus) would be slightly greater than 120 s.[10] An example of a displacement versus calculated

stress curve is given in Figure 2a, and correspondingstress-strain curve is given in Figure 2b. Here, displacementrefers to the progressive upward advance of the mobileplaten as referenced to its starting position. These data havebeen corrected for machine compliance by subtracting outthe displacement of the instrument assemblage under load.

2.2. RAT Grinding Test Procedure

[11] An engineering flight spare of the RAT is kept atHoneybee’s facility in New York. The RAT is mounted ina vertical position along a linear stage and can be raised or

Figure 2. An example of results from a compressive strength test (sample bas-03-001). (a) Plot of dis-placement of lower platen of the Instron instrument versus stress (MPa) calculated as force per unit area ofthe sample. (b) Stress versus strain curve for same test given in Figure 2a. Strain is displacement dividedby sample starting length. Red data points are the same as the black points but have been “slackcorrected,” i.e., they have been shifted such that the average linear elastic region passes through the origin.The peak compressive stress withstood by this sample was 128.14MPa (Table 3).

Table 3. Compressive Strength Test Results

Sample ID Length (mm) Diameter (mm) Peak Load (kN) Stress area (mm2) Peak Stress (MPa) Failure Mode

kal-01-001 39.61 22.27 8.57 389.52 22.0 axial splittingkal-01-002 34.41 23.65 9.04 439.29 20.9 axial splittingkal-01-003 31.05 23.60 7.52 437.44 17.5 axial splittingkal-01-004 28.75 24.05 7.60 454.28 17.0 axial splittingkal-01-005 24.53 24.09 6.40 455.79 14.5 axial splittingls-01-001 35.05 23.70 9.26 441.15 21.0 axial splittingls-01-002 28.75 24.03 9.23 453.52 20.6 axial splittingls-01-003 25.05 24.05 10.99 454.28 24.4 axial splittingss-01-001 42.58 23.40 13.59 430.05 31.6 axial splittingss-01-002 50.65 23.71 16.43 441.52 37.2 shear failuress-01-003 49.56 23.80 14.87 444.88 33.4 shear failuress-01-004 30.53 23.71 18.11 441.52 41.5 shear failuress-01-005 25.02 23.60 16.65 437.44 38.8 shear failuress-01-006 23.19 24.00 19.17 452.39 43.7 shear failurebas-01-001 51.25 24.06 193.16 454.65 424.9 total destructiona

bas-01-002 49.08 24.13 200.31 457.30 438.0 total destructiona

bas-01-003 35.88 24.12 193.23 456.92 422.9 total destructiona

bas-02-001 46.90 24.13 45.37 457.30 99.2 axial splittingbas-02-002 45.57 24.11 34.58 456.55 75.7 axial splittingbas-03-001 54.40 24.13 58.60 457.30 128.1 axial splittingbas-03-002 52.43 24.14 57.00 457.68 124.5 shear failurebas-03-003 51.48 24.13 59.74 457.30 130.6 axial splittingbas-03-004 50.56 24.06 57.20 454.65 125.8 shear failure

aBy “total destruction,” what is meant is that the sample completely (and violently) disaggregated along multiple shear planes.

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lowered to preload its contact switches onto a planar facet ofa rock sample. Natural rock surfaces were ground in order tobetter replicate field conditions for the RAT. Each grindbegan with a calibration routine used to assess the no-loadcurrent of the grind motor, followed by a standard “seek-scan” preprogrammed routine that was designed for autono-mous operation on Mars. This routine locates the highestpoint of the rock surface within the grind area and ensuresthat the grind starts just above this point. Due to the irregulartexture of natural samples, the surface area ground tended toincrease with depth into the rock as the paddle wheelattained full contact with the rock surface. Therefore, motorcurrents were averaged over the last 0.25mm depth of theRAT grind to determine the specific grind energy (SGE,units J/mm3), which is a measure of the work done per unitvolume of abraded material:

SGE ¼ V�A� ANL

1000

� �s � vol�1 (1)

[12] Here, V is the voltage (in volts), �A is the mean grindcurrent (in mA), ANL is the no-load current (in mA), s isthe grind duration (of the last 0.25mm in seconds), and volis the grind volume (in mm3). The target depth of each grindranged from 2 to 5mm, depending on the estimated depth re-quired to penetrate the uneven top surface. Where possible,multiple grinds were performed in the same spot on a rockto obtain additional SGE data points.[13] Motor currents versus time for a grind test (on sample

ls-02a) are given in Figure 3. Note that the grind currentrises rapidly over the first 2000 s (~33min) to a value>200mA as the grinding bit fully engages with the targetsubstrate. Following the convention established previously,SGE was obtained using equation (1) from the last0.25mm of the grind where the mean grind current was271mA. The mean grind voltage was 25.6V, the no-load

current was 51.5mA, and the last 0.25mm took 1329 s togrind. The energy expended was therefore 7456 J, andwith a grind volume of 397.6mm3, the SGE was18.7� 2.3 J/mm3. A discussion of how the uncertainty inthe SGE value was estimated is given in section A1.

2.3. Chemical Analytical Procedure

[14] Small pieces (total ~50 g) of each sample wereprovided to the Washington State University GeoAnalyticalLaboratory (WSU) in sealed glass containers for analysis ofmajor and trace elements by combined X-ray fluorescence(XRF) and inductively couple plasma mass spectroscopy(ICP-MS), in addition to loss on ignition (LOI) analysis.These samples were ground to a fine powder by WSU in atungsten carbide ring mill. The major and trace elementsSi, Al, Ti, Fe, Mn, Ca, Mg, K, Na, P, Sc, V, Ni, Cr, Ba,Sr, Zr, Y, Rb, Nb, Ga, Cu, Zn, Pb, La, Ce, Th, Nd, and Uwere analyzed by XRF on glass fusion beads of samplepowder using a ThermoARL Advant’XP+ sequential XRF.Details of the analytical procedures and precision and accuracyof analyses can be found in Johnson et al. [1999] and http://www.sees.wsu.edu/Geolab/note/xrf.html. The trace elementsBa, Th, Nb, Y, Hf, Ta, U, Pb, Rb, Cs, Sr, Sc, Zr, and the rareearth elements were determined on acid digested powdersamples using an Agilent 7700 ICP-MS; details of the ana-lytical procedures and precision and accuracy of analysescan be found at http://www.sees.wsu.edu/Geolab/note/icpms.html. Chemical data will be used in an upcomingmanuscript that is currently in preparation; they areincluded here for completeness.

3. Results

[15] Compressive strength test results are given in Table 3and plotted in Figure 4. Despite the variability inherent innatural rock samples, the results show a high degree ofself-consistency (average departure from the mean value is10.2%). With the exception of the vesicular basalt (samplebas-02), the standard deviation of the mean was less than afew MPa. The mean peak stress withstood by the samplesranged from a high of 429MPa for the aphanitic basalt

Figure 3. Example plot of results from RAT grind testls-02a. Grind depth (blue curve) and motor current (red line)versus time are given; black line is grind current smoothed with1-D median filter to better resolve the overall trend. A z-valueof 0 is the starting position of the RAT; the drop-off to negativez-values at ~12,000 s is due to the commanded retraction of theRAT after completion of a successful grind.

Figure 4. Unconfined compressive strength (UCS) testresults with each rock sample represented by a different coloredsymbol. Horizontal green bars represent mean stress values inMPa. Sample identifications are given in Table 1.

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to a low of 18MPa for the kaolinite. The samples thatexhibited the greatest range of UCS values were the vesicu-lar basalt samples. Void spaces in the vesicular basalt have aheterogeneous distribution, and the measured strengthvalues are likely sensitive to their specific distribution andorientation within a given sample core.[16] RAT grinding test results are compiled in Table 4 and

Figure 5. Green horizontal lines are mean SGE (specificgrind energy) values as given in Figure 4; individualmeasurements are indicated by multiple symbols per sampletype. The results are more scattered than the compressiontests and have an average departure from the mean valueof about 43%. Measured SGE values ranged from 1.1 to82 J/mm3. As with the compressive strength tests, thevesicular basalt sample (bas-02) displays the largest rangeof measured values. For reference, these values are two tothree orders of magnitude greater than the specific cuttingstrength for water ice drilled at 140K, which was found tobe 60MJ/m3 (or 0.06 J/mm3) using a metal-toothed coringtool [Garry and Wright, 2004]. Such a difference is consis-tent with the operational dissimilarities between the grindingaction of the RAT versus the coring action of a drill.[17] A comparison of UCS versus SGE is given in

Figures 6a and 6b. As expected, more competent samplesthat withstood greater compressive force required moreenergy to grind with the RAT. However, the results indicate

that there are two distinct regimes of rock strength as sam-pled by the RAT. In the lower strength regime (less thanabout 150MPa), an approximate linear correlation can bedetermined between specific grind energy as recorded bythe RAT and lab-measured compressive strength values(R2 values of linear and power-law fits are 0.914 and 0.952,

Table 4. RAT Grinding Test Results

Target IDTarget

Depth (mm)No-Load

Current (mA) Duration (min)Actual

Depth (mm)Material

Removeda (mm3)Specific GrindEnergy (J/mm3) Notes

kal-01-a 5 42.56 n/a n/a n/a n/a lost preload after ~1.8mm due torock shifting

kal-01-b 5 47.97 140 3.032 397.6 5.1kal-01-b 6 38.17 n/a n/a n/a n/a lost preload on second grind

attemptls-02-a 4 51.45 191 3.258 397.6 18.8ls-02-a 4 44.39 89 0.986 397.6 3.2 seek/scan “found” top of rim so

higher grind depth commanded tocompensate

ss-01-a-1 5 49.48 107 3.506 366.6 1.5ss-01-a-2 4.5 55.05 98 1.546 392.0 1.8 seek/scan “found” top of rim so

higher grind depth commanded tocompensate

bas-02-a-1 5 42.13 n/a n/a 120.9 23.2 stalled at ~3.4mm due to rockshift

bas-02-a-2 5 41.02 93 n/a 168.2 4.4 one switch “chattered” causing Zstep backwards; bit did not removefull 0.25mm

bas-02-b-1 5 36.12 144 n/a 222.7 65.2 revolve timeout after 3.20mmbas-02-b-2 2.5 59.82 77 n/a 230.2 38.6 revolve timeout after 2.03mmbas-02-b-3 2.5 42.57 81 n/a 397.6 25.1 revolve timeout after 2.39mmbas-03-a-1 5 36.39 216 0.778 397.6 71.4 revolve timeout after 2.80mmbas-03-a-2 2 44.92 96 0.515 397.6 62.0 revolve timeout after 0.71mmbas-03-a-3 2 47.04 89 0.441 397.6 75.0 revolve timeout after 0.71mmbas-01-a-1 4 46.06 97 0.176 191.2 66.9 revolve timeout after 2.13mm, but

grind recoveredbas-01-a-2 3 56.20 72 0.387 260.0 82.0 revolve timeout after 0.76mmkal-01-c-1 5 42.50 110 2.091 215.9 3.9kal-01-c-2 3 46.77 84 2.651 397.6 5.8ss-01-b-1 7 54.75 150 3.610 324.4 1.5 large grind depth used due to

uneven surfacels-01-a-1 1.25 43.60 26 1.134 397.6 n/a grind failed to achieve contact

over full areals-01-a-1 1 47.89 22 0.000 397.6 1.2ls-01-a-2 3 55.16 63 0.000 393.6 1.5 end of grind broke through thin

edge of rock

aMaterial removed determined over last 0.25mm of grind.

Figure 5. Compilation of RAT grinding tests of rock sam-ples. Green horizontal lines are mean values; individualmeasurements are indicated by multiple symbols per sampletype. Sample identifications are given in Table 1.

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respectively). Above this lower strength regime, the SGEvalues appear to reach a “plateau point”: a strength abovewhich RAT grinding operates with reduced effectiveness.Grinding still continues but at a very small rate ofadvancement into the rock. This is due in part to the softwarecontrol law in place that establishes an upper limit on theRAT’s motor current draw (thus limiting the maximumenergy available per unit time or per unit volume of targetrock). As a result, the compressive strength-SGE relationshipsestablished in Figures 6a and 6b for materials with strengthvalues less than ~150MPa are not applicable to strongermaterials.[18] Within the lower strength regime, some complica-

tions are evident even in this limited sample set. The sand-stone sample (ss-01), which is composed of medium-sized,rounded quartz grains held by a diagenetic cement, fallsbelow the trend line. Although resistive to compression(as compared to the kaolinite sample, for example), it maybe that the grinding action of the RAT dislodges orplucks individual quartz grains more efficiently than for anon-granular target, thus lowering the amount of energynecessary to grind such a sample.

4. Discussion and Application to MER SpiritResults

[19] Our study indicates that an approximate correlationcan be determined between specific grind energy as recordedby the RAT and lab-measured compressive strength values.As expected, more competent samples tend to require moreenergy to grind. However, extremely competent rocks(>150MPa) are ground progressively less efficiently bythe RAT (requiring long grind times to achieve minimaldepth into the target substrate). Given that the original designobjective of the RAT was to grind away and remove the outerweathered rinds of Martian rocks, this objective is expected tobe satisfied as it is unlikely that weathering products willexceed the strength of intact, hard rock. In other words,whereas some range of intact rocks strength may exceed thecapabilities of the RAT to efficiently grind it, the RAT shouldbe able to remove any weathering rinds during nominalgrinding activity. A notable exception to the general trend ofweakening with increased weathering is the formation of moreresilient, thin surface crusts (such as case hardening or rock var-nish [e.g., Conca and Rossman, 1982]). On Earth, such crustsare often mediated by an active biologic component [e.g.,Dornand Oberlander, 1981; Kurtz and Netoff, 2001] that is likelyabsent on exposed surfaces on Mars. Therefore, martian rockvarnish may be weaker than its terrestrial counterpart.[20] A potential source of variability in both grind and

compressive strength measurements is sample anisotrophy,e.g., rock texture and fabric. Texture is more relevant tothe RAT grinds as natural surfaces were used for grind tests,although this is partially mitigated by focusing on the last0.25mm of the grind for the SGE calculation. The originalsurface textures were not preserved in the cores preparedfor compression tests, so texture is not a critical factor inthese measurements. Rock fabric effects, however, arerelevant to both test methods. Aligned grains, phenocrysts,microcrysts, vesicles, bedding plains, laminae, or otherbanding or grading could affect the results by artificiallyweakening (or in a few cases, strengthening) the materialrelative to a bulk isotropic medium. However, no macro-scopic anisotropies were observed in the samples prior totesting. Indeed, the absence of foliation and other visibleplanar fabrics was a criterion for sample selection.

4.1. Estimated Strength Values for Spirit RAT GrindTargets

[21] A general question is how relatable are the compres-sive strength results to the grind results—what are the differ-ences and similarities between them in terms of the modes offailure, and how much can the results from one set of testsinform us about the other? In the compressive strength tests,the samples are compressed along a vertical axis and experi-ence a tensional force that is orthogonal to the direction ofcompression. The ends of the cylindrical samples are notfixed to the spherical platens, and the sample responds tocompression in part by expansion in the orthogonal direc-tion. Many of the samples failed by axial splitting, i.e., oneor more longitudinal cracks propagating parallel to the direc-tion of the load (see Table 3). These are Mode I cracks thatare due to tensile stress normal to the plane of the crack.Another common failure mode was along one or moreinclined planes, labeled here as shear planes to distinguish

Figure 6. (a) Unconfined Compressive strength (UCS,units J/mm3) plotted against specific grind energy (SGE,units MPa). Horizontal and vertical error bars are standarddeviation from the mean values based on multiple measure-ments (given individually in Figures 4 and 5). Solid blue lineis linear fit to data points with UCS values < 150 MPa.Dashed blue lines are 95% confidence intervals around fittedtrend. R2 value of linear fit is 0.914. (b) Same as Figure 6abut with power law fit to data points with UCS values< 150 MPa. R2 value of power law fit is 0.952.

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them from the more simple geometry of the axial fracturefailure mode. But whether or not all of these inclined frac-tures are true shear features is debatable [e.g., Slate andHover, 1984; Yang and Jing, 2011]. Since friction restrictslateral expansion near the ends of the specimens, theresulting stress distribution in the specimen may be neitheruniform nor uniaxial [e.g., Wang and Shrive, 1995]. There-fore, while some of these inclined fracture planes may haveincluded a shearing component, others may be only apparentshear displacements that occurred after vertical crackingparallel to the direction of uniaxial compressive load hadtaken place.[22] The RAT grinds are a combination of fracture and

frictional sliding. As tensional force is required to breakinteratomic bonds, the specific mechanism of materialremoval in RAT grinds must be compression-induced ten-sion, and in that respect it is broadly similar to the uniaxial

compression case. Microdiamond particles embedded inthe RAT cutting heads are compressed against small surfaceasperities in the target material due to the rotary action of thecutting heads, akin to the action of a blunt, chisel-like tool.Given the geometry of this cutting action, the role of shearmay be more important here than in uniaxial compression.The situation where strong particles are plucked froma weakly bonded matrix (e.g., in a coarse sandstone) is aseparate case—here the RAT grinding action attains a spe-cial efficiency relative to a more uniform target medium. Insummary, while the failure mechanism in each strength testis distinctive, they share the basic commonality of compres-sion-induced tensional failure.[23] An additional consideration is loading (or strain) rate

sensitivity. As noted previously, the compression tests wereconducted at a strain rate of 10�4s�1. The characteristicstrain rate of the RAT is less straightforward to determine,

Figure 7. Estimated compressive strength values (inMPa) inferred from Spirit’s Rock Abrasion Tool (RAT)grinding energy (in J/mm3). Blue and red points give linear and power-law fits to calibration data fromFigure 6,respectively. Light gray boxes enclose range of strengths of different rock classes identified at the Spirit site(rock classes from Squyres et al. [2006]). Vertical column at left gives rock mechanical strength classificationfrom Hoek and Brown [1997].

THOMSON ET AL.: ROCK STRENGTH FROM RAT GRINDS

1240

Tab

le5.

Sum

maryof

SpiritRATGrindingActivity

Sol

Feature

(Rock)

Nam

eTargetS

urface

Nam

eGrind

Current

(A)

No-Load

Current

(A)

Motor

Voltage

(V)

Tim

e(sec)

Vol.

(mm

3)

Z-end

(mm)

SGE

(J/m

m3)

Prev.

reported

SGEa-d(J/m

m3)

TargetType(Float,

Outcrop,Soil)

34Adirondack

Prospect

0.362

0.177

24.1

2727

298.2

max

40.7

51b,5

3.2c,6

4a,5

0-60

dfloat

58Hum

phrey

Heyworth1

0.304

0.175

24.1

568

263.5

max

6.7e

49c ,83

b,94

a ,50-60d

float

59Hum

phrey

Heyworth2

0.308

0.184

24.2

2568

253.5

max

30.4

-float

81Mazatzal

New

York

0.352

0.185

23.1

1704

180.7

max

36.4

50-60d

float

83Mazatzal

Brooklyn

0.392

0.173

23.4

2853

326.6

13.07

44.8

49.7c ,61

a ,65

b,5

0-60

dfloat

195

Wooly-Patch

Sabre

0.339

0.186

23.1

358

397.6

max

3.2

5.15

c ,4-9d

displacedslab

198

Wooly-Patch

Mastadon

0.313

0.180

23.7

320

397.6

max

2.5

4.11

c ,4-9d

displacedslab

216

Clovis

Plano

0.414

0.162

22.4

367

397.6

max

5.2

8.26

c ,4-9d

outcrop

231

Ebenezer

Cratchit2

0.401

0.166

23.7

455

397.6

max

6.4

8.9c,4-9d

float

285

Uchben

Koolik

0.409

0.174

22.3

347

357.8

max

5.1

7.3c,4-9d

outcrop

334

Wishstone

Chisel

0.447

0.165

23.2

822

397.6

max

13.5

24d

float

355

Champagne

Bubbles

0.434

0.147

23.3

658

397.6

12.81

11.1

15d

float

374

Peace

Justice

0.182

0.164

24.9

159

397.6

11.2

0.2f

-outcrop

377

Peace

Justice

0.274

0.161

24.5

203

397.6

19.5

1.4

2doutcrop

416

Watchtower

Joker

0.431

0.144

23.1

528

318.1

15.8*

11.0

12.6d

outcrop

a Value

reported

byMcSweenet

al.[2006].

bValue

reported

byArvidsonet

al.[2004].

c Value

reported

byWanget

al.[2006].

dValue

reported

bySquyreset

al.,[2006].

e RATslid

offrock

after~2

0min.

f Pow

er-lim

itedgrinddueto

duststorm.

THOMSON ET AL.: ROCK STRENGTH FROM RAT GRINDS

1241

but it can be constrained by the maximum linear velocity ofthe grind heads. Based on a grind bit diameter of 23.3mmand a maximum rotational rate of 3000 rpm, the maximumlinear velocity is about 3.7m/s. While this value is higherthan for the compression tests, in general, brittle materialsare relatively rate insensitive until the loading rate becomesvery high, i.e., on the same order of magnitude as a crackpropagation speed (see Figure 12 of Bhat et al. [2012]).While some supersonic shear crack speeds have been mea-sured [Rosakis et al., 1999], the upper limit of crack propa-gation is typically considered to be roughly equal to the Ray-leigh (elastic) wave speed. For basalt, assuming conservativevalues for Poisson’s ratio of 0.1 and an elastic modulus of50GPa, the Rayleigh wave speed is roughly 2400m/s. Asthis value is several orders of magnitude lower than thelikely RAT strain rate, we do not consider the difference instrain rates between the compression tests and the RATgrinds to be a factor that precludes their comparison.[24] Using our experimentally determined correlation given

in Figure 6, we provide a first-order estimate of the compres-sive strength values for target surfaces ground by the MarsExploration Rover (MER) Spirit (Figure 7). The rocks inves-tigated by the Spirit rover span a greater range of apparentstrengths than targets probed by the Opportunity rover; hence,we focus our attention on the former. Table 5 provides a sum-mary of RAT grinding activity on Spirit through Sol 416. Af-ter this point, due to wear of the grinding bits of Spirit’s RATpaddle wheel, further grind operations of rock targets werenot attempted. A full list of RAT-related activity is given inthe general mission timeline summary tables of Arvidsonet al. [2006, Sols 1–512, 2008, Sols 513–1476].[25] Rock and outcrop targets encountered by Spirit were

classified according to their geochemical, spectral, and physi-cal properties [Ming et al., 2006; Morris et al., 2006; Squyreset al., 2006; McCoy et al., 2008; Crumpler et al., 2011]. Thelargest division in inferred strength between rock types is be-tween Adirondack-class rocks (including Adirondack,Mazatzal, and Humphrey) and rock and outcrop materialsfound in the Columbia Hills, a distinction noted previously[e.g., Squyres et al., 2006]. Adirondack-class rocks are thestrongest rocks measured by Spirit and have inferred com-pressive strength values in the range of 70–130MPa.

Although this falls within the “strong” to “very strong” fieldsof the rock hardness classification scheme (Table 6), it issignificantly weaker than the strength of intact, fresh basalt.No in-place outcrops of Adirondack material were observedby the rover—all contact and remote measurements wereconducted on float (i.e., isolated, displaced rock fragments).Ruff et al. [2006] identified numerous examples of rocks oflikely Adirondack class in the Columbia Hills, although nonewere investigated by RAT grinds. As these pieces of floatwere likely ballistically emplaced during impact events [e.g.,Grant et al., 2006], some weakening during the impactprocess coupled with pre- or post-impact weathering likelyaccounts for their relative weakness compared to their freshterrestrial counterparts.[26] The second strongest class of rocks is Wishstone class

(i.e., Wishstone and Champagne); inferred compressivestrengths range from 40 to 55MPa, straddling the classifica-tion division between medium strong to strong materials(Table 6). Their relative strength compared to Clovis,Watchtower, and Peace-class rocks is consistent with theirlow inferred degree of alteration based on their low ferriciron content (Fe3+/Fetotal [Morris et al., 2006]) and alsolow S, Cl, and Br [Ming et al., 2006; Squyres et al., 2006].Although only pieces of float were abraded by the RAT,clasts of Wishstone-class materials were identified in theVoltaire outcrop [Arvidson et al., 2008; Ming et al., 2008].Given the observed textural characteristics, which includean absence of layering and 1–2mm angular clasts in a fine-grained matrix, an origin as impact ejecta or volcanic ashflow (e.g., an ignimbrite) is inferred [Squyres et al., 2006;Crumpler et al., 2011].[27] Clovis-class material was abraded at the outcrops

Clovis, Wooly Patch, and Uchben and the float sampleEbenezer. These materials are massive to layered poorlysorted clastic rocks of basaltic bulk composition [Squyreset al., 2006] with elevated Ni concentrations [Yen et al.,2006]. Inferred compressive strengths for this material arein the range of 15–30MPa (weak/medium strong). Asignificant percentage of phyllosilicate minerals (14–17%)is inferred in Wooly Patch [Wang et al., 2006], which liesat the lower end of the range of strengths exhibited byClovis-class material and is broadly consistent with the

Table 6. Classification of Rock Strength After Hoek and Brown [1997]

Strength ClassUniaxial Comp.Strength (MPa) Field Characteristics Terrestrial Examples

Extremely strong >250 Specimen can only be chipped with a geologichammer

Dense fine-grained igneous rocks (fresh basalt,chert, diabase, gneiss, granite); quartzite

Very strong 100–250 Specimen requires many blows of a geologichammer to fracture

Competent igneous, metaphorphic rocks(amphibole, basalt, gabbro, gneiss, granodiorite,marble, rhyolite); some fine-grained sandstones,limestones

Strong 50–100 Specimen requires more than one blow of ageologic hammer to fracture

Limestone, marble, phyllite, sandstone, schist,shale; some low-density, coarse igneous rocks

Medium strong 25–50 Cannot be scraped or peeled with a pocket knifebut can be fractured with a single blow from ageologic hammer

Competent sedimentary rocks (claystone, coal,concrete, schist, shale, siltstone)

Weak 5–25 Can be peeled with a pocket knife with difficulty,shallow indentation made by firm blow withpoint of geologic hammer

Weakly cemented sedimentary rocks (chalk,rocksalt, potash)

Very weak 1–5 Crumbles under firm blows with point of geologichammer, can be peeled with a pocket knife

Highly weathered or altered rock

Extremely weak 0.25–1 Indented by thumbnail Stiff fault gouge

THOMSON ET AL.: ROCK STRENGTH FROM RAT GRINDS

1242

strength of pure kaolinite (terrestrial sample kal-01).Overlapping the strength regime of Wishstone-class rocksis Watchtower class, of which only a single example(Watchtower itself) was abraded by the RAT. The inferredstrength, 39� 9MPa to 47� 11MPa, nominally falls inthe “medium strong” category (Figure 7; Table 6). Theinferred strength of Watchtower is subject to higheruncertainty because the RAT’s progress stalled whilegrinding, likely due to a combination of bit wear andclogging by cuttings.[28] Weaker still are the inferred strengths of Peace-class

material, which is the weakest non-soil material investigatedat the Spirit site. Compressive strengths of Peace-class materialis ~1–10MPa, in the “weak” to “extremely weak” strengthclassification. These low strength values are consistent with apoorly consolidated sandstone [Squyres et al., 2006], one withultramafic grains weakly bound by sulfate minerals.[29] The rock types abraded by the RAT in the Columbia

Hills share many common elements. They are all relativelyweak compared to the more competent Adirondack-classbasalts (UCS< 50MPa) and, with the exception ofPeace-class rocks, have been inferred to be impactites orvolcanoclastic in nature. In terrestrial samples of tuffs, rockstrength varies with factors such as welding intensity, whichis the sintering and compaction of glassy pyroclasts undercompressive load at temperatures above the glass transitiontemperature [e.g., Ross and Smith, 1980]. The reportedstrengths of tuffs and similar material also vary widelydue to differences in density, porosity, fabric, and watercontent, among other factors. But with inferred compres-sive strengths of ~40–55MPa, Wishstone-class materialslie at the higher end of this range, consistent with a morecompetent or welded tuff-like material, while Clovis-classmaterials lie at the lower, weaker end [e.g., Quane andRussell, 2003].[30] In summary, these data provide an approximate

estimate of the compressive strength of rocks on Mars.When considered alongside chemical, spectral, and rocktextural data, these results help inform our understandingof rock origins and modification history. Future work on thistopic includes an attempt to better constrain the linkedeffects that weathering has on the chemistry and strengthof basalt with the goal of better constraining Martianweathering processes. In addition, a similar approach to thatdeveloped here could be applied to future surface studies, forexample using the rotary-percussive drill on the Mars Sci-ence Laboratory rover Curiosity [Anderson et al., 2012].

Appendix A: Specific Grind Energy Error Analysis

[31] To assess the level of uncertainty in the specific grindenergy (SGE) determinations, we perform a basic error anal-ysis. SGE values are determined by five factors in equation(A1).

SGE ¼ V �A� ANLð Þs1000 vol

(A1)

[32] Here, V is the voltage (in volts), �A is the mean grindcurrent (in mA), ANL is the no-load current (in mA), s isthe grind duration (of the last 0.25mm in seconds), and vol

is the grind volume (in mm3). The relative uncertainty inSGE is the sum of the squares of the relative errors of theindividual factors.

dSGESGE

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidVV

� �2

þ d�A�A

� �2

þ dANL

ANL

� �2

þ dss

� �2

þ dvolvol

� �2s

(A2)

[33] The factor with the lowest uncertainty is the grindvoltage V; values in the lab-based RAT grind tests variedfrom 25.5 to 27.2V, with an uncertainty level <0.1V (arelative error of less than 0.4%). The no-load current valuesANL were determined by rotating the grinding paddle wheelin free space prior to grinding and ranged from 36.1 to58.9mA. The level of variability within a given test waslow, and the uncertainty level is <0.5mA (equivalent to arelative error of less than 1.4%).[34] Variation in the mean grind voltage �A is also relatively

low. As indicated in the example grind current versus timerecord given in Figure 3, the current level exhibits apseudoperiodic variation. In this example, the current spikescorrespond to instances where the Z axis incrementally ad-vances. The median value, however, remains relatively con-stant (black curve in Figure 3), and the relative uncertainty inthe mean value is <5%.[35] Since the SGE is calculated over the last 0.25mm of

the grind, the volume ground is defined as

vol mm3� � ¼ 0:25p 45=2ð Þ2 1� fð Þ; (A3)

[36] which is the grind surface area multiplied by depthtimes 1 minus the pore space f. Pore space is determinedusing post-RAT images of the abraded area, and the uncer-tainty in the volume ground is dominated by the pore spaceestimate. For the lab measurements, the post-RAT surfaceswere cleared of cuttings using compressed air, and the porespace estimate is fairly straightforward (this factor has a typicaluncertainty �2–3% based on repeated measurements). Theuncertainty will be slightly higher in situations where the cut-tings are not cleared after grinding is completed; if the cut-tings partially fill the pore space, the uncertainty level risesto ~5%. This uncertainty is partially mitigated by the fact thatonMars, post-RAT brushing is part of the standard commandsequence to help clear out cuttings from the abraded hole.[37] Perhaps non-intuitively, the overall uncertainty in

SGE is dominated by the uncertainty in the final term s.Although the number of seconds during which the last0.25mm is ground is readily determined with millisecondprecision from the test telemetry, the real uncertainty isdriven by the inherent uncertainty of the Z axis position.Grind depth measurements (Z axis) are determined fromreadings of the Z axis motor. While the precision of thismeasurement is high, its accuracy is lessened due to the un-known amount of strain accommodated by the RAT instru-ment itself (as well as mounting assembly in the lab versionor, on Mars, by the rover’s arm and chassis). Consequently,the actual grind depth achieved is typically less than that in-dicated via the Z axis position. A plausible fractional error of�10% of the grind duration was used to calculate the uncer-tainty in the specific grind energy. Using equation (A2) and

THOMSON ET AL.: ROCK STRENGTH FROM RAT GRINDS

1243

the values given above, the relative uncertainty in SGE is12.3%. For reference, if each factor in equation (A1) has arelative error of 5%, the SGE uncertainty would be 11.2%.[38] In the future, the overall accuracy of the specific grind

energy determination could be improved if more precisedepth measurements were available. For a few targetsinvestigated by at the MER landing sites, post-RAT DigitalTerrain Models were painstakingly constructed from sets ofstereo pairs of Microscopic Imager frames [e.g., Herkenhoffet al., 2006]. However, practical considerations precluded thisfrom being done for all abraded surfaces. Yet even this method-ology produces only a single post-activity volume estimate.More precise depth measurements, preferably made whilegrinding was being conducted, would permit greater insightinto the nature of abrasive wear of the target surfaces.

[39] Acknowledgments. This project has benefitted from helpful dis-cussions with current and former Honeybee Robotics engineers; insightfuland constructive reviews from Ralph Lorenz and an anonymous revieweralso improved the manuscript. Support for this research was provided by aNASA Mars Fundamental Research Program grant to BJT. The authors alsogratefully acknowledge Robert Anderson and Gregory Peters from JPL forhelp with rock sample procurement.

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