The drop weight test is a common laboratory measurement used to determine the comminution characteristics of rock samples. A common metric derived from a drop weight test is a value “A×b”. Another common metric that is derived from the SMC Test™ variant of a drop weight test is a “Drop Weight Index”, abbreviated as DWi. This work looks at a public database of test results to determine a relationship for DWi as a function of A×b.

by Alex Doll @ SAGMilling.com

Method

A database of publicly published grindability test results has been collected by the Author. This database includes just over two hundred instances of a DWi and A×b being published for the same rock sample. A series of equations were fitted to this database with the goal of finding the best fitting equation.

An equation published by Lane et al. (2015) gives a relationship, equation

[1], that includes the density of the coarse particles (ρ, or SG for “specific gravity”) and two fitted constants, c and d.

Drop_Weight_Index

As the database contains the values for DWi, ρ, and (A×b), the constants c and d can be determined with some algebraic rearranging and linear regression.DWi

Equation [4] is in a form suitable for plotting and determining a linear regression. The regression of the database of test results using this equation is given in Figure 1.drop_weight

The fit of this data is not particularly good, and there is quite a bit of scatter that, upon interrogation, is due to high density samples being significantly offset versus the body of the data points.

A different equation

Variations from Equation [1] were tried to see if any gave a better fit. Inverting the density value (equation [5]) was found to improve the data fit dramatically, as given in Figure 2.

dwi_equation

drop_weight_test_results_for_various_minerals

There is still some scatter about the body of the test results. Interrogation shows that these samples are identified as “averages” or “percentiles” of much larger data sets, and are not single drop weight tests where both of the parameters are reported from a single determination.

Data filtering

It is known that not all grindability parameters are “additive”, and the additivity of the A×b parameter is particularly poor. This means that arithmetic averages of a mixture of A×b test results will not give the same value as if you performed a single test on the mixture of the rocks whose individual results were averaged.

It is reasonable to exclude these samples identified as “averages” or “percentiles” from the analysis so that only the parameters determined from the same, discrete drop weight tests are compared. This dramatically reduces the scatter, resulting in the regression in Figure 3.

The regression equation is determined to be:

Equation 6                              [6]

Figure 3 Filtered database regression for Equation [5].

Figure 3: Filtered database regression for Equation [5].

Result

The fitted equation for DWi, given a rock density ρ (kg/L) and a A×b value is:

Equation 7                                         [7]

References

Grindability database collected from public sources such as conference proceedings and NI43-101 reports.

This database includes references for each result and is freely available to the public by contacting the Author at SAGMilling.com

For an updated Database, please contact Alex.

Hardness Data Table 1

IdNameProgramWiBMWiRMWiCDensityAxbMiaCISGIAi
1902Cadia East u/g crushCadia21.531.12.727
1609Cadia EastCadia20.3293029.70.2
12Boddington PipelineBoddington16.3528.350.49
11Boddington Pit A brecciaBoddington20.728.10.78
1901Cadia East u/g May 08Cadia21.426.52.727
230Kanowna Belle 4Kanowna Belle19.726.51
228Kanowna Belle 2Kanowna Belle19.4526.4230.69
9Boddington Pit F zone 4Boddington17260.35
2023Turnagain 102Turnagain23.224.92.9520.20.29
260LB maximumLos Bronces2224.62.6422.830.55.2424.2
927Boddington N. volcBoddington15.624.528.50.54
505St IvesOther16.524.5
499Three Mile HillOther16.424.55227
231Kanowna Belle 5Kanowna Belle15.924.3290.45
15Wandoo NorthBoddington16.624.28.425.50.52
986White Foil- Nov1997Other18.624.138.43.110.67
991White Foil- actualOther18.624.12.826.6
13Boddington Pit DBoddington17.823.9
205Cadia VolcCadia22.323.821.32.632.1
1502granite/MVol wasteYaramoko18.423.58.333.90.27
331Prominent Hill 7Prominent Hill19.823.53.235.1
1432Boddington designBoddington15.623.43027.30.5
1042Blackwater maximumBlackwater22.123.215.882.742330.1
928Boddington S. volcBoddington14.523.1270.45
990White Foil- Mar1999 maxOther17.6422.9316.22.828.20.62
1465Krumovgrad WallOther2022.816.12.5329.20.6
14Wandoo SouthBoddington15.122.88.427.90.45
929Boddington Mine N.Boddington1622.80.51
227Kanowna Belle 1Kanowna Belle16.122.726.7270.49
2284Detour Lake maxDetour Lake20.122.725.622.50.55
1499FW wasteYaramoko1922.710.90.35
1510Sabodala composite 1Sabodala17.722.42.8230.90.19
1515Sabodala composite 7Sabodala1822.32.828.80.15
2002DDH 93-16Huckleberry18.722.2
300WBX-IMount Milligan20.3522.150.22
1511Sabodala composite 2Sabodala18.122.12.8234.90.16
462Geita mill designOther16.822.1303.1
1514Sabodala composite 6Sabodala16.821.92.833.90.12
1517Sabodala composite 13Sabodala17.421.62.8234.40.17
989White Foil- Mar1999 minOther17.4621.5142.836.40.46
1516Sabodala composite 12Sabodala17.321.52.8235.60.14
2380Fekola var maxFekola Gold19.721.515.82.8526.60.88
2004Granby composite 2Huckleberry19.6221.49
930Boddington S. dioriteBoddington14.921.40.27
988White Foil- Dec1997 maxOther16.0921.38
926Boddington dioriteBoddington15.221.33030.10.49
1512Sabodala composite 4Sabodala17.721.22.8240.40.19
267Mastabe Sample 3Mastabe20.321.22.4942
486Mt Milligan sample 2Other19.921.12.7521.330.31
303Mt Milligan Sample 2Mount Milligan19.921.12.7521.330.31
297SIX-IMount Milligan20.421.050.27
1608RidgewayCadia18.72130420.43
2382Fekola var 85th percentileFekola Gold18.4212.7827.650.7
1497MVOLYaramoko16.820.911.30.13
1855Cadia Round Robin P lab ACadia17.120.921.32.640.49
1498HW wasteYaramoko17.920.810.50.37
1475Comp PAPXPlatreef22.320.7329.90.34
2377Fekola shallow HG compFekola Gold16.520.7142.827.60.38
294MBX-IMount Milligan19.8520.70.24
330Prominent Hill 6Prominent Hill17.820.73.258.4
299STR-SMount Milligan1920.70.23
298SIX-SMount Milligan20.4520.70.2
1858Cadia Round Robin P lab DCadia17.620.60.31
2025Turnagain 104BTurnagain20.220.63.02240.4
2265Nico P5Nico14.320.622
271Mastabe Sample 7Mastabe19.520.62.5847.8
301WBX-SMount Milligan20.120.520.26
2022Cadia 1999 surveyCadia1720.528.52.6
2376Fekola deep HG compFekola Gold18.820.515.82.7928.150.53
292Maxi-Q/1Mount Milligan19.5520.450.25
305Maxi-Q/3Mount Milligan19.720.40.28
293MBX-DMount Milligan19.420.40.2
2381Fekola var medianFekola Gold17.220.3142.7828.40.51
304Maxi-Q/2Mount Milligan19.320.30.33
1513Sabodala composite 5Sabodala1720.32.8232.30.13
209Pit 3Copper Mountain22.220.22.8720.1
473Copper Mtn Pit 3Other22.220.22.8720.1
472Copper Mtn Pit 2Other22.320.12.7522.9
229Kanowna Belle 3Kanowna Belle15.520.126.4280.43
208Pit 2Copper Mountain22.320.12.7522.9
2264Nico P2Nico14.820.1
274Mastabe Sample 10Mastabe19202.644.4
1433Boddington Apr 2010 surveyBoddington14.42027.7300.52
1607Cadia HillCadia17.52030350.33
278Mastabe Sample 14Mastabe23.6202.6341.9
2419BCOC‐004Buriticá22.5919.942.7226.810.1
2283Detour Lake 90thDetour Lake16.519.919.723.40.54
1856Cadia Round Robin P lab BCadia19.2819.6312.43.170.68
296SIX-DMount Milligan20.3519.60.36
2378Fekola low grade compFekola Gold16.919.6142.7427.550.27
2024Turnagain 104ATurnagain17.919.63.11250.3
276Mastabe Sample 12Mastabe19.719.52.6144.9
1041Blackwater 75 percentileBlackwater19.719.514.92.7427.526.5
295MBX-SMount Milligan19.419.50.14
2416BCOC‐001Buriticá22.0219.412.79230.18
328Prominent Hill 4Prominent Hill15.419.43.243.3
302Mt Milligan Sample 1Mount Milligan19.919.42.7524.20.24
481KCGM designOther14.619.4402.931.2
306Maxi-Q/4Mount Milligan18.119.40.31
236KCGM designKCGM14.619.4402.931.2
485Mt Milligan sample 1Other19.919.42.7524.20.24
269Mastabe Sample 5Mastabe19.719.32.6535
1500mineralized graniteYaramoko1819.37.244.10.21
235Kanowna Pilot PlantKanowna Belle18.319.30.37
2003Granby composite 1Huckleberry17.4219.29
312Footwall sedimentsPalmarejo19.419.28.62.5244.2
2263Nico P1Nico14.219.1
1463Duparquet pilot sampleOther18.519.17.52.73280.55
1903Cadia 1998 surveyCadia17.11916.52.736
234Kanowna Belle 8Kanowna Belle18190.58
1700US21_AMalartic16.118.9814.32.7225.93144.690.43
1681US08_12Malartic17.1618.9312.42.7420.56151.960.29
2369Moose River ArgilliteMoose River8.818.90.03
2282Detour Lake 75thDetour Lake15.518.917.52.9424.40.54
339Selbaie Welded acid tuffSelbaie13.1518.817.42.850.52
1000Snelgrove Lake IronOther17.718.617.73.48312.5194
992Snelgrove LakeOther18.617.73.443122.89.3184
2417BCOC‐002Buriticá21.9218.62.4936.890.17
202Cadia M-PrCadia20.1518.5521.052.820.46
259LB 75th percentileLos Bronces17.418.52.6427.126.710.1163.4
1603New Gold HypogeneOther21.818.582.70.16
272Mastabe Sample 8Mastabe18.618.52.5954
277Mastabe Sample 13Mastabe16.518.42.5746.5
1604New Gold MesogeneOther19.818.382.770.07
2001DDH 93-18+93-21Huckleberry15.818.3
1501mineralized MVolYaramoko17.718.35.544.80.05
952Cerro Verde BPSCerro Verde1618.315.5
873K491New Liberty20.9518.3327.4
242Pit 3Kubaka15.518.2
326Prominent Hill 2Prominent Hill1618.23.245.3
1863Cadia Round Robin G lab BCadia17.618.29.062.710.43
39607-RN-47-GR027Dumont21.218.22.5944.30.01
2379Fekola var minFekola Gold14.118142.73310.21
243Comp 123Kubaka1518
311AmygdaloidalPalmarejo1918152.6533.8
2391Grassy Mountain zone 2Other21.3183.62.440.78
2281Detour Lake 50thDetour Lake14.31814.82.925.80.48
1680US08_11Malartic16.8417.9216.092.7520.94163.270.22
1865Cadia Round Robin R lab ACadia15.517.925.62.670.64
1862Cadia Round Robin G lab ACadia16.417.98.12.740.25
934Brucejack VOK Ore 3Brucejack15.417.910.42.753920.20.09
1679US07A_12Malartic16.0317.8515.322.7227.24143.310.84
872K492New Liberty17.517.8321.3
1496GRYaramoko16.617.870.25
1040Blackwater averageBlackwater18.317.813.512.7430.424.2
22661999 sampleNico16.117.8
493Rainy River Zone-433Other16.9517.72.8310.18
948Cerro Verde GKPCerro Verde15.717.723.8
2293Zone 704-2Meadowbank14.517.72.7829.80.24
503Teck-CoronaOther22.117.617.6
2393Grassy Mountain compositeOther20.217.63.622.440.71
501Santa Rita designOther21.817.6163.2441.3
500Santa Rita averageOther19.117.6163.2446.20.28
207Cadia M compCadia19.417.624.82.637.80.5
1692US15_12Malartic13.9417.5213.092.7523.98156.620.23
203Cadia M-RCadia18.117.530.52.60.56
354SM 11Spanish Mountain16.717.50.28
2370Moose River GreywackeMoose River10.217.50.17
1861Cadia Round Robin P lab GCadia17.8617.4915.72.64
318Phu Kham most competentPhu Kham13.617.43.131.540.41
461Asarco RayOther14.717.426
484Lone TreeOther19.217.42.8744.80.64
1866Cadia Round Robin R lab BCadia16.1817.3412.072.640.64
308MMZ softNkomati18.317.348
307MMZ hardNkomati2117.330
1472Comp FPXPlatreef19.8517.33.19350.36
201Cadia MCadia19.117.322.82.60.52
981Quimsacocha comp 2Quimsacocha17.317.32.6540.719.31.27
2418BCOC‐003Buriticá20.9617.222.6932.110.1
487Phoenix Des CritOther15.517.217.637.50.46
2392Grassy Mountain zone 3Other17.717.23.642.440.53
38607-RN-20-GR11Dumont21.717.22.5540.60.01
1013Duncan Lake 3 SEDDuncan Lake1417.22.8133.622.1
314blended orePalmarejo18.217.210.82.6
2280Detour Lake 25thDetour Lake12.717.211.927.50.36
244Comp 5Kubaka15.517.1
1696US19Malartic16.2217.118.122.7225.58159.670.4
240UG 1Kubaka15.117.1
942Brucejack WZ Ore 4Brucejack15.5179.52.7543.318.30.25
310Quartz brecciaPalmarejo18.9178.62.6341.1
251UG 12Kubaka171792
358SM 15Spanish Mountain16170.19
1450SGS 2012 Composite 9Volta Grande14.21725.62.5199.80.28
1864Cadia Round Robin G lab GCadia17.2816.917.22.69
1688US12_11Malartic15.7716.8919.392.6921.64143.50.28
38407-RN-16-GR054Dumont2216.82.5336.20.01
2424Composite 1Buriticá16.316.813.622.7336.20.35
372Stronsay SiltstoneStronsay16.816.8
44410-RN-216D01Dumont21.416.8182.5644.50.01
275Mastabe Sample 11Mastabe15.616.72.6367.8
40408-RN-109-GR049Dumont20.216.72.6339.20.03
881Metates intrusiveOther13.316.713.22.7667.30.04
258LB medianLos Bronces16.516.72.643024.813130
355SM 12Spanish Mountain15.716.70.27
273Mastabe Sample 9Mastabe17.316.72.5859.4
2292Porphyry 2014Meadowbank16.716.72.6235.90.61
261LB averageLos Bronces16.516.72.6432.323.913.8137.9
980Quimsacocha comp 1Quimsacocha16.716.72.8936.3211.37
939Brucejack WZ Ore 1Brucejack16.716.711.80.31
983Quimsacocha comp 4Quimsacocha16.616.62.7339.919.61.26
1447SGS 2012 Composite 4-6Volta Grande14.816.6241.7206.20.44
474Hidden ValleyOther16.616.6152.761.60.3
43508-RN-83-GR04Dumont19.916.62.641.60.03
950Cerro Verde PPPCerro Verde14.916.521.7
984Quimsacocha comp 5Quimsacocha16.516.52.743.418.31.28
343Selbaie Nov 1988 compositeSelbaie12.716.515.82.97
2289FS Vault avgMeadowbank13.816.52.8140.50.23
44710-RN-217EG01Dumont20.5516.516.42.5839.30.02
1468Lucky Friday, wallOther13.416.55.20.09
1689US12_12Malartic14.0116.452.7423.780.24
1676US05_11Malartic14.2816.4313.712.7519.9163.870.2
1702US22Malartic16.5816.4216.042.726.24133.230.39
39908-RN-101-GR05Dumont22.216.42.5153.90
954Los Helados intermediateLos Helados17.116.42.8229.11500.16
880Metates sedimentaryOther12.316.415.70.05
268Mastabe Sample 4Mastabe16.716.42.6541.5
39407-RN-45-GR035Dumont20.316.32.6138.50.02
38307-RN-14-GR043Dumont2216.32.547.8
237MLWKCGM15.316.3402.87
170809-21-CV1A-8h_12Malartic16.316.318.522.7424.1115.270.35
953Los Helados upperLos Helados16.0316.32.7831.91800.08
1707Super BlastMalartic14.8516.316.872.7224.220.32
359SM 16Spanish Mountain15.116.32.828.70.21
1673US03_11Malartic14.9816.2714.442.7625.02125.120.55
170910-31-CV1A-11h_12Malartic14.2616.2617.92.7225.71131.60.32
1448SGS 2012 Composite 5-7Volta Grande15.516.2263.8173.90.46
1697US20_AMalartic16.2716.213.062.6925.05118.10.38
951Cerro Verde PKPCerro Verde15.116.232.2
245Comp 7-11Kubaka16.216.2
982Quimsacocha comp 3Quimsacocha16.116.12.740.519.41.23
348SM 5Spanish Mountain14.716.10.26
43408-RN-83-GR03Dumont20.516.12.4447.6
1672US02_12Malartic14.3416.114.842.7425.37111.20.42
1471T2LPlatreef21.816.13.0844.5
200Cadia M-CCadia19.216.123.22.60.4
1693US16_12Malartic13.9616.0514.892.7337.39109.620.18
199Cadia M-BCadia17.41624.12.60.53
1464Krumovgrad UpperOther171612.52.5361.40.28
20051995 compositeHuckleberry1416
5Sulfide PhylliteBibiani16.31692.7237.640.09
342Selbaie CompositeSelbaie12.61614.92.970.4
1524Lik composite 2Lik16.3166.654.30.23
40308-RN-109-GR048Dumont21.6162.4647
360SM 17Spanish Mountain14.5160.3
40208-RN-105-GR12Dumont20.5162.5446.90.01
1446SGS 2012 Composite 2-3Volta Grande16.51630.60.9133.20.29
1685US10_12Malartic13.8315.9613.782.7226.58132.540.41
1684US10_11Malartic14.7515.9512.492.7521.39134.180.36
2290Vault drill coreMeadowbank13.915.92.8140.986.4
2279Detour Lake 10thDetour Lake11.215.99.930.20.24
193BH 2004 medium gradeBatu Hijau11.815.96.50.12
871K490New Liberty18.8515.9329.7
1474Comp OLOPX-OPXPlatreef20.415.93.1732.80.3
1857Cadia Round Robin P lab CCadia18.315.90.31
171002-12-CV1A-8h_13Malartic14.215.917.542.7226.23
1867Cadia Round Robin R lab GCadia15.815.8314.82.58
923Maracás 32Maracás14.615.8
955Los Helados deepLos Helados16.1215.82.8328.11360.18
44810-RN-217H01Dumont21.115.815.62.5349.10.01
40808-RN-126-GR08Dumont20.415.82.5354.70
2291Stockpile 2013Meadowbank1415.82.73390.24
1705Conv No. 1Malartic13.6415.7317.462.7227.410.22
41708-RN-37-GR060Dumont20.115.72.6256.60
43008-RN-79-GR01Dumont22.415.72.5955.40
40008-RN-101-GR06Dumont18.215.62.7332.90.09
1449SGS 2012 Composite 8Volta Grande15.515.629.62.1147.80.5
932Brucejack VOK Ore 1Brucejack14.415.611.42.7943.618.10.21
39307-RN-45-GR034Dumont2215.62.4548.8
38207-RN-14-GR042Dumont21.515.62.4751.10
870K489New Liberty20.3515.6328.5
1503GR QZYaramoko13.215.6
334HuacajchiSan Bartolome18.615.613.81.960.8
945Cerro Verde PKGCerro Verde13.815.621.8
944Cerro Verde PPGCerro Verde16.715.518.2
43108-RN-79-GR02Dumont20.115.52.6256.6
875Aurora Gold Rory KnollOther14.615.515.52.8131.20.22
874Cameron GoldOther12.415.52.87310.33
941Brucejack WZ Ore 3Brucejack15.815.510.30.66
2426Albany Graphite WPOther1715.411.32.6540.40.61
315Phu Kham 80th percentilePhu Kham14.715.43.290.720.29
869K487New Liberty14.6515.4322.4
2425Albany Graphite EPOther1815.411.42.6335.60.68
1675US04_11Malartic12.0415.352.7119.280.47
1703US23Malartic14.115.3314.432.6624.15127.20.58
350SM 7Spanish Mountain13.515.30.2
496Rainy River ODM-4Other13.7515.32.8339.20.1
2018Pebble west 2004Pebble1415.32.6142.6
43909-RN-169-GR15Dumont19.815.32.5547.60
1677US06_12Malartic16.3415.242.728.580.66
1674US03_12Malartic15.1115.2213.032.7228.04119.230.57
1706Conv No. 3Malartic14.3815.2116.892.7126.570.23
459EHM Primary MaxErnest Henry15.115.23.4241
41608-RN-37-GR059Dumont20.915.22.647.80
327Prominent Hill 3Prominent Hill12.715.23.271.1
38107-RN-10-GR041Dumont21.315.22.5457.90
1504VOL QZYaramoko13.215.2
935Brucejack VOK Ore 4Brucejack14.215.29.30.38
44510-RN-216E01Dumont20.115.214.82.5454.30.01
266Mastabe Sample 2Mastabe14.715.22.4765.1
1704High gradeMalartic14.7615.1817.532.7234.790.27
351SM 8Spanish Mountain13.515.10.22
38707-RN-35-GR063Dumont22.615.12.644.50
2287FS North Portage avgMeadowbank10.715.117.53.2440.70.54
940Brucejack WZ Ore 2Brucejack15.315.110.72.7639.419.90.35
40108-RN-103-GR031Dumont2315.12.4858.10
347SM 4Spanish Mountain13.315.10.25
1698US20_BMalartic15.5415.0914.32.6829.67106.560.44
1678US07A_11Malartic12.0415.0214.042.7524.42101.640.34
42208-RN-58-GR032Dumont22.1152.5155.60.01
194BH 2004 low gradeBatu Hijau12.1156.20.17
41008-RN-129-GR025Dumont21.2152.5550.10
337Diablo NorteSan Bartolome14.115
336Diablo EastSan Bartolome15.4150.21
1523Lik composite 1Lik16.31510.3480.1
191BH 2008 low gradeBatu Hijau15.1156.20.17
1527Lik composite 5Lik13.5159.346.70.16
39007-RN-43-GR018Dumont20.7152.651.3
1682US09_11Malartic16.114.912.6725.60.93
43308-RN-82-GR021Dumont20.514.92.6454.50
867K485-1New Liberty16.614.9329.4
1882004 Life of MineBatu Hijau11.214.98.1550.24
198BH VolcanicBatu Hijau1114.97.40.18
947Cerro Verde GPPCerro Verde15.514.921.6
1528Lik composite 6Lik15.114.914460.17
987White Foil- Dec1997 minOther13.8314.89
44309-RN-196-GR045Dumont2014.82.6351.80.01
38007-RN-10-GR040Dumont22.4514.82.4752.40
353SM 10Spanish Mountain13.814.82.7947.80.3
38507-RN-20-GR10Dumont21.214.82.4465.5
1470T2UPlatreef19.2514.73.1839.5
42608-RN-63-GR039Dumont2114.72.6449.40
39207-RN-45-GR033Dumont21.814.72.550.80.01
257LB 25th percentileLos Bronces15.614.72.6435.721.616.5106.7
946Cerro Verde GPSCerro Verde13.814.76.7
868K485-2New Liberty15.7514.7330.5
1671US02_11Malartic12.9814.692.7227.520.42
44910-RN-218AC01Dumont20.1514.613.92.5554.2
38907-RN-39-GR030Dumont20.714.62.6460.10.01
933Brucejack VOK Ore 2Brucejack14.414.611.10.14
40508-RN-111-GR09Dumont19.514.62.6561.50
454RNC-V130HQ-GR017Dumont2114.62.646.90
322Phu Kham SWD primaryPhu Kham14.614.62.881.370.2
1701US21_BMalartic15.314.615.962.6830.79102.560.71
39107-RN-43-GR019Dumont20.314.62.6157.1
42708-RN-73-GR016Dumont20.614.52.651.70.01
338Selbaie Rhyodacite BrecciaSelbaie11.6514.514.13.080.3
1469T1MPlatreef19.7514.53.1943.6
45310-RN-222G01Dumont19.7514.513.12.6156.20
2026Turnagain 106ATurnagain16.414.52.9235.10.08
1458SGS 2013 Composite 8Volta Grande14.914.527.60.43
241UG 2Kubaka13.814.5
325Prominent Hill 1Prominent Hill14.814.53.276.1
495Rainy River ODM-3Other13.2514.52.8339.80.1
494Rainy River ODM-1Other13.614.52.8336.10.08
1694US17_12Malartic14.3614.4114.292.73