v081n05p117 south african mining and metallurgy journal

7/27/2019 v081n05p117 South African Mining and Metallurgy Journal

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G o ld -m in e p r o d u c t i v i t y a s a f f e c t e d b y t h ea v e r a g e w e t - b u lb t e m p e r a t u r e o f t h eu n d e r g r o u n d w o r k in g p la c e sby D. G. K RIGE*. Pr. Eng.. D.Se.. (Eng.). F.S.S.A.. F.S.A .I.M .M .. and

c. P. S. BARNARDt. F.S.S.SYNOPSISO bjec tive ju stification o n e co nomic g ro un ds fo r ex pen diture aim ed at im prov in g the q uality o f th e u nd erg rou ndw orking environm ent requires a suitable m easure of any im provem ent in productivity that would result underro utine w orking co ndition s. F or th is pu rpo se, a co mp osite p ro du ctio n criterio n is su gge sted , as w ell a s its co rrelationunder actual operating conditions w ith various factors directly affecting productivity and the environm ent. O f thee nviro nm enta l facto rs, w et-b ulb tem peratu re ap pe ars to b e th e m ajo r fac to r affe ctin g pro du ctivity. T he pro du ctiondata given indicate that a decrease in the wet-bulb temperature of I QC can be expected to result, on average, insome 3 to


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rground labourersxcluding novices for periods

o f (mont hs ):---2t 3 3t

-1339 11 217 11 0980947 10 732 107560706 10545 106270486 10279 10 2419853 9439 94239690 9305 93680496 10233 100821073 10791 102450968 10624 10 1970732 10 263 102050656 10400 1009108.52 10774 10 1640802 10431 98631049 10 451 105372064 11 8 68 11 9 082679 12493 11 9373490 13 2 77 122943596 13 397 13 2043491. 13 232 13 1183063 12816 12 6 372197 12 197 11 7981757 11 4 60 11 2 390941 10584 104479705 9551 97058939 8018 83441 217 10 993 105032926 12924 12 6174440 14422 12 5 984458 14280 140094644 14622 146404321 14 125 142854405 14204 140483536 13 387 134913380 13 246 12 9873199 13010 12 7962654 12 6 03 12 3 552400 12 2 92 12 1313716 13 658 133374096 14014 13993

AverageMonth Rock wet-bulb Equiva- ----No. breakers tem- lent m"perature broken TotalC

1 14 2 30,2 105854 11 7322 138 30,5 101 709 11 4863 13 5 30,6 100583 11 5 424 13 4 29,5 94660 11 445[i 13 3 29,0 91 490 11 0036 13 0 28,7 98 118 11 3 187 12 8 28,4 102444 12 359 18 13 2 28,2 105452 12 6.54 19 12 9 29,0 106 833 12 4 04 110 12 9 29,0 101 787 12 4 55 111 13 2 29,6 96 404 12539 112 134 29,9 94 487 12381 113 132 30,4 91 883 11 8 41 114 13 3 30,6 90419 12 545 115 139 30,8 93 785 14 198 116 142 29,9 95 905 14454 117 141 29,4 101 372 14468 118 145 28,9 109628 14595 119 145 28,2 112 239 14575 120 150 28,3 III 407 14227 121 15 1 28,6 109345 13 209 122 15 0 29,4 101 383 12549 123 146 29,1 91 728 11 893 124 141 30,0 81 450 11 16925 136 30,3 74 194 1088326 129 31,0 79 164 13 593 127 132 30,4 86631 15 219 128 133 29,8 93 410 14911 129 135 29,1 99012 14677 130 135 28,3 101343 15 060 131 14 4 28,9 108485 14 920 132 145 29,4 110574 15045 133 143 29,9 104706 14482 134 141 30,2 104481 14217 13.5 14 3 30,0 102552 13957 136 139 30,6 92374 13354 137 135 30,6 86 092 12990 138 138 31,1 88913 14093 139 136 30,6 93991 14511 1

11 8 May 1981

VariancesCool-Wet W et Wet Air mgkata kata bulb velocity powerin sto pe sm( s W(m"

---- -- ---- -- -11,1 1,l.5 31 711,1 1,17 30 510,1 1,13 29 711,4 1,19 35 112,8 1,30 38 313,5 1,40 40 513,9 1,19 39 913,3 1,06 39 512,5 0,99 35 412,6 1,02 35 711,3 1,09 33 810,9 1,08 32 410,6 1,14 30 710,6 1,18 30 110,0 1,06 28 310,9 1,08 32 411,0 0,85 32 312,0 0,89 34 812,5 0,95 38 212,7 0,93 37 612,2 0,87 35 711,2 0,99 33 811,8 1,15 36 610,7 1,06 31 810,9 12,7 2,6 0,94 29 59,1 8,4 2,0 0,94 26 410,4 8,3 2,1 1,05 30 011,0 11,0 2,5 1,04 32 512,1 9,5 3,6 1,06 35 712,2 8,9 3,7 0,97 38 111,8 8,6 3,9 0,94 35 311,4 9,4 3,9 0,99 33 89,6 9,3 4,0 0,91 30 99,8 10,1 3,9 1,00 30 410,9 8,6 2,9 1,09 32 110,5 6,6 2,4 1,03 28 99,6 9,2 2,4 0,90 27 89,3 10,0 3,0 0,95 26 09,8 10,3 2,2 1,32 31 0

The addition of the three above amounts provides thetotal equivalent square metres broken as a singlemeasure of the effective level of production. The factorsused in (2) and (3) will not be entirely objective but,provided the relative levels of the square metres forsweepings, development, and stoping do not vary dras-tically over the period studied, and provided the m easureis not used for comparisons between different mines,changes to these factors within realistic ranges shouldnot have a significant effect on the total equivalentsquare metres as a relative production measure for thesame m ine from month to month.

Factors Affecting ProductionApart from the average wet-bulb temperature of the

working places in a m ine (stopes and development ends),the quality of the environment can also be monitored bythe w et kata-tem perature and air velocity. Furtherm ore,a table recently published by Steward and W hillierl canbe used to derive the composite measure of 'coolingpower' of the air. Apart from the quality of the environ-ment, production levels should naturally also be well

correlated w ith the n um bers of prod uctive w orkers under-ground. The novices have been accepted as effectivelyunproductive for a lim ited period and have been excludedfor periods ranging from 2t to 3t months. The produc-tion teams comprising the rock breakers as teamleaders and the underground labourers as team membersare directly involved in the activities of breaking stopesquare metres, sweeping stoped areas, and advancingdevelopm ent ends. All the other underground and surfaceemployees can be viewed as an 'overhead' work forcerequired to provide the production teams with therequired supervisory, back-up, and follow-throughfacilities.If data are collected over a long period and for different

m ines or mine sections, a number of factors w ill alsoaffect production levels, e.g., depth and spread of w orkingplaces, degree of mechanization, widths and dips of ore-bodies mined, hangingwall conditions, etc. In theshorter term , the effects of these factors on the samem ine should be small, and probably time-dependent; ifso, this cJ,n be catered for, at least partly, by the incor-poration of any trend in productivity linked to time. If

TABLE IBASIC DATA FOR HARTEBEESTFONTEIN GOLD MINE, JANUARY 197.5 TO MARCH 1978

UncleE

JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY


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Corr. Regres- Standardcoeff. sion error of regr.with m" coeff. coeff. Mean-~----(I) Averag e w et-bulb tem p., C - 0,624 -4010,1 970,0 29,65( 2) Under gr oundlabourers excl.novices for 3t ..months 0,426 4,151 0,684 11 623(3) Month no. -0,170 ~523,8 97,5 20( 4) Rockbre ake rs 0,435 359,4 134,1 137,8I

I AverageMonth Rock-

I

wet-bulbno . breakers temperatureC

1 2395 29,22 2365 29,43 2325 29,44 2377 28,95 2362 28,76 2357 28,17 2341 28,08 2369 28,19 2336 28,410 2369 28,411 2355 28,712 2331 29,113 2323 29,214 2335 29,315 2388 29,216 2367 28,917 2373 28,618 2406 28,219 2425 2.7,920 2460 28,021 2444 28,122 2444 28,623 2421 28,924 2376 28,825 2336 29,0

26 2340 29,527 2378 29,328 2444 29,129 2447 28,730 2454 28,031 2477 28,332 2491 28,333 2478 28,834 2502 29,135 2492 29,336 2473 29,437 2435 29,638 2456 29,939 2518 29,5

Equivalent Underground labourers excluding M onthly turnovm" novices for (months): for undergrounbroken labourers

2t 3 3t %1 435 126 162 0 49 158 8 89 158 787 11,131 426 697 162467 159 072 158 8 62 11,611 440 691 161 909 158 368 159 716 10,951 458 149 163 315 159175 156 981 12,82I 499 182 165 817 161 858 159 015 11,41I 558 513 172 003 169 044 164 908 8,521 5 80 54 4 178471 175 633 170 181 7,631 5 66 43 5 178 5 32 175 041 170 603 9,43I 539 327 174 145 169 981 168 216 10,23I 511 149 169 5 74 165 392 163 881 II,40I 446 629 16.5 617 161 989 158 619 10,61I 385 693 160718 158 5 43 152 378 7,82I 376 827 158 4 89 151 893 150 108 17,01I 408 000 169 4 82 162 2 43 162 215 16,18I 445 926 175 4 II 170 572 171 0 50 12,34I 455 822 181 242 177 846 168 033 9,69I 487 722 189 979 186 723 175490 8,60I 537 973 192 007 188 160 182 319 9,III 545 004 191 8 21 188 153 185 0 11 8,61I 527 558 184 8 08 180 667 178 286 9,75I 516 966 181 726 181 726 174 0 20 0,411 472091 178 934 175377 171585 10,231 375 456 173 0 93 169 116 164 799 12,47I 283 042 158 379 156 138 158 379 10,451 260 136 156 761 146 964 149 634 21,90I 326 078 183 320 177 4 26 175 356 13,73I 404 591 187 192 184 150 182 6 99 8,871 449 898 196 596 192 105 176 994 12,551 497 385 209712 207 165 197 906 7,661 532 443 206 966 204 515 200 867 8,901 572 741 213 314 210 772 204 321 8,85I 597 348 212 398 208 733 207 294 12,191 584 750 214 966 212 996 210 051 9,831 586 513 211 813 209 538 206 717 10,391 526 133 206 714 204 173 199 3 72 12,291 422 131 196 862 194 9 02 192 9 08 10,70I 419449 197 755 193 8 57 193 194 16,06I 478 218 212 996 211 940

I

207 904 8,65I 500 545 223 226 221 794 219 292 9,19

TABLE IlANALYSIS OF DATA GIVEN IN TABLE I

the months covered by the data used are numberedconsecutively, and the month number as a furtherindependent variable is correlated with the dependentvariable of production, any net trend in productivitywith tim e should becom e evident.

M ultiple correlation coefficient - 0,878Y -intercept for regression form ula - 129448,5 mo /mont hMean of m" distribution - 97 853 m O/m onthR egression form ula:

m" broken = 129448,5-4010,1 (temp. C)+4,151 (U/Glabourers less novices)-523,8 (month no.) +359, 4 ( rockbre ake rs ).Standard error of regression estimate = 4606,0= 4,7 % of mean m".Regression coefficients as percentages of the mean m":

A verage w et-bulb tem perature - 4, 1 % (standard error1,0%)M onth num ber = -0,54%

Data and AnalysisThe main data on the quality of the undergroundenvironment available on a regular basis for m ines cover

the average wet-bulb temperature of the working places,the wet kata-thermometer readings, and the air velocityalong stope faces; more recently, data on the spread ofwet-bulb and wet-kata readings across the individualworking places have been recorded monthly. From thewet- bulb and air-velocity figures, the correspondingmonthly cooling power of the air in watts per squaremetre can be derived.1 The monthly temperature andother data figures for the Hartebeestfontein M ine for theperiod January 1975 to March 1978 are recorded inTable I. The data were subjected to a stepwise multiple-regression analysis with square metres broken as thedependent variable and all the other data listed for theperiod of 39 months as independent variables without

BASIC DATA FOR A GROVP ,OF 27 .LARGE GOLD M INES, JANUARY 1975 TO MARCH 1978TABLE III

erd

~-

May 1981 11 tOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY


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( 1) Ave ragewe t-b ulb te mp .,DC -0,567 - 48 526 9 982,2 28,82

(2 ) Underg roundlabourerse xc l. n ov ic esfor 3 m onths 0,575 4,663 0,517 180 580(3) Month no. 0,045 -6738,3 804,7 20(4) R oc k-breakers 0,466 277,6 172,1 2 4 04 ,2

any transform ations. T he follow ing independent variableswere selected in the sequence listed in Table II, and theremaining variables were rejected on the basis of a mini-mum F value of 4 for acceptance of a variable and amaximum F value of 3,9 for removal of a variable.

The data for a second analysis covered only the last 15months for the above 4 variables plus the variance inwet-bulb temperature across the individual workingplaces, but was too lim ited; in fact, only the independentvariables nos. (2), (3), and (4) in Table II were accepted.Thus, the only environmental factor selected as signifi-cant w as w et-bulb tem perature.Follow ing the analysis for the H artebeestfontein M ine,a sim ilar analysis was done by the Chamber of Mines ofSouth Africa over the same period for a group of 27 largegold mines but accepting only wet-bulb temperature asthe main measure of the quality of the environment. Anadditional variable of m onthly turnover of undergroundlabourers w as included.However, this new variable was rejected as contribu-ting no significant additional information towards theexplanation of variations in production levels. In thiscase, for the number of underground labourers, theexclusion of novices was selected on a 3 months' basis.The basic data are recorded in Table Ill, and the resultsof the analysis in Table IV. The high multiple-correla-tion coefficient indicates that the four independentvariables explain almost 90 per cent (r2 = 0,89) of thetotal variability in the monthly production levels.

The close agreement for the group of 27 mines betweenthe actual number of square metres broken and thatestimated from the above regression formula is evidentfrom Fig. 1.

The analysis was also done for the individual mines(excluding turnover rate) and resulted in the skewdistribution shown below for the tem perature regression

TABLE IVANALYSIS OF DATA GIVEN IN TABLE III

Corr.coeff.w ith m2Standard Ierror ofregr. Meancoeff.

Regres-sioncoeff.--

Mu ltip le c or re la tio n c oe ffic ie nt - 0,941Y-intercept for regression formula = 1496571 m 2/m onth.M ean of m2 distribution - 1472789 m 2/m onth.R egression form ula:m 2 b ro ke n = 1496571-48526 (temp. C)+4,663 (U /Glabourers- 6738,3 (month no.) +277,6 (rockbreakers)-Standard error of regression estimate = 29514,6= 2, 0 % of mean m2.Regression coefficients as percentages of the mean m2:A verage w et-bulb tem perature - - 3, 2 % (standard error0,7%)

= -0,45%.onth number

TABLE VSUMMARY OF REGRESSION FORMULAE

Hartebeest-fontein 27 m inesMean of m2 brokenY-interceptTemperature, CMonth no.RockbreakersUnderground labourers

(C )(T )(M )(R )(B )

97 8531 32 ,3 %C-4,1 %C.T- 0 ,5 4 %C .M+ 359,4R+4,15lB

14727898 4,5 %C- 3 ,3 %C .T-0,45%C.M+277,6R+4,663B

coefficient expressed as a percentage of the average totalof monthly square metres:C ate go ry lim its, % 1 2 3 4 5 6 7Frequency 5 5 4 8 3 2

The regression formulae for the HartebeestfonteinMine and for the group of 27 mines are sum-marized in Table V. It should be noted that the numberof underground labourers excluded novices for 3t m onthsfor Hartebeestfontein and 3 months for the 27 mines.Furtherm ore, the conversion factors from sweepings anddevelopment to equivalent centares broken varied fromm ine to m ine. T he regression coefficients for tem peratureand month, expressed as percentages of the averagesquare metres broken, are nevertheless of the same orderfor Hartebeestfontein and the group of 27 mines; fortemperature, the category 1 to 5 per cent included 20 ofthe 27 individual m ines.

If a new ventilation project concerns a specific m inesection, conditions could differ from those for the mineas a whole and, if at all possible, a sim ilar regressionanalysis should be conducted on specific data from thatsection. W here feasible, the possibility should also beinvestigated of a nonlinear regression of production ontemperature; it seems obvious that the slope (estimatedat above 3 to 4 per cent) for wet- bulb temperatures in therange from say 28 to 31C should steepen at the upperend of the temperature range, and should approach zeroat some temperature below the ranges analysed forHartebeestfontein and for the group of 27 mines.This was confirmed by work2 conducted by theResearch Laboratories of the Chamber of M ines; thiswork indicated a zero slope at 28C and a slope of 3t to4 per cent at 31C . A non-linear approach was attem ptedfor the data of the 27 mines by transforming tempera-ture (T ) to eT /1012; the m ultiple correlation coefficientw as only slightly reduced from 0,942to 0,929,and theregression coefficient for tem perature as transform ed w as-13226,7, indicating a slope of 1,3 per cent at 28Cand 9,6 per cent at 30C. The regression coefficients forthe individual 27 mines also show som e positive correla-tion with the corresponding 27 average wet-bulb tem-peratures; however, in view of the lim ited data thetrend is not significant (r = 0,25).

ConclusionsThe above analyses indicate that, within the ranges

and the limitations of the available data, wet-bulb tem-perature is the m ost significant m easure of environm entalquality. They also indicate that a change of 1C inaverage wet-bulb temperature affects productivity by

12 0 May 1981 JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY


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1 ,6A C T U A L S . M E T R E SE S T IM A T E B Y R E G R E S IO N - - - - -/\

If)

.~ 1 , 5~IIfi }e x :I-w~c jC l); : J , 1 , 4t- .0I-

1 ,3

J A N . 1 9 7 S5 1 0 1 5

~\\

M A A . 1 9 7 8

2 0M O N T H S

4 05 3 0 3 5

F i g . I-Total equivalent square metres broken for a group of 27 gold m ines

an estimated average extent of some 3 per cent. Theextent, if any, to which the percentage for a m ine or sec-tion w ill vary within and outside the temperature rangesobserved cannot be stated with confidence on the basisof the available data, although it seems logical that,at temperatures of 30C and higher, the percentageshould be higher. A quantitative approach based onproduction data is thus suggested for the economicanalysis of any new ventilation or refrigeration project.A lso, from this analysis it seems that, on balance,

(a ) productivity declined over the period studied bysome t per cent per month;(b ) the marginal productivity of one additional under-ground labourer is small (4 to 5 m2 per month)whereas that of an additional rockbreaker is large(some 300 m2 per month).

The indicated decline in productivity is serious, andwarrants continued study and analysis. The marginalproductivities of underground workers should not beaccepted at their relative levels without qualification.

The rockbreaker and his team should be seen as aworkers' unit, and the combined figure of additionalcentares produced by an additional team then becom esmeaningful, Le., the number of rockbreakers shouldrather be seen as the num ber of production team s.

There appears to be considerable scope for furtheranalyses along these lines.

AcknowledgementThis paper is published by kind permission of the

Anglo-Transvaal Consolidated Investment CompanyLim ited and the Chamber of M ines of South Africa.

References1. STEW ARD, J. M ., and W HILLIER, A. A guide to the measure-ment and assessment of heat stress in gold m ines. J. M ineV en t. S oc . S .A Jr ., voL 32, no. 9, Sep. 1979. pp. 169-178.2. COOKE, H. M ., e t a l. The effects of heat on the performance ofwor k u nd er gr ou nd . J. M ine Vent. Soc. S.AJr., Oct. 1961.pp . 17 7-19 6.

JOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY May 1981 12 1

v081n05p117 south african mining and metallurgy journal

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