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J S Afr Inst Min Metal/ vo . 84, no. 11.N ov . 1 98 4. p p. 3 65 -3 68 .

The design of pillars in the shrinkage stopingof a outh frican gold m ine by R .W .O . K ER STE N*

SYNOPSIST his pa pe r d e scrib e s the m eth od use d at A g ne s G o ld M ine in th e ca lcu latio n of p illar stre ng th s, w hich in vo lvesa b a ck-an alysis typ e of ap p ro a ch . Th e re sults o b tain ed the re a re co m pa ra b le w ith th ose o bta ine d b y a ccep ted fo r-m ula e for pilla r s tren gth .It w a s fo u nd tha t a stre ss le vel o f 7 0 M P a fo r th e w id th of co m b ine d p illa rs L e. cro w n an d sill p illa rs) ca u se sfailure of the re ef d rive s as w e ll a s the to p s an d bo ttom s of the sto pe sid e w alls. A s sh rin ka g e sto pin g to de p th s o fm ore tha n 65 0 m w o u ld resu lt in ve ry Iow p ercen tag e extra ctio n s, alte rn a tive m e tho d s o f stop ing w ill h ave to bein ves tig ated fo r th es e d ep th s.S A M E V A T T I N GH ie rdie refe raa t be skryf die m eto de w a t by A gn e s-g ou dm yn vir die b e re ken ing van p ila a rsterktes g eb ruik w o rdw a t n teru go ntle din gsb en a de rin g b eh e ls. D ie re sulta te w at d a ar ve rkry is, ve rg e lyk g oa d m et d ie w at volg en s dieaa n va ard e fo rm ula s vir pilaa rste rkte verkry is.D aa r is ge vind d at n spa nn ing svla k va n 7 0 M P a vir d ie b ree d te van ge ko m b ine e rd e pila re d .w .s. kru in e ndru m p elp ila re) sw ig ting va n die rifstre kga ng e en d ie bo - e n o nd e rka nte van die syw a n de va n afb ou p le kkeve roo rsa ak. A a n ge sie n krim pa fbo u in g tot d iep tes va n m eer a s 6 50 m to t ba ie la e e kstraksies sa lle i, sa l alte rn a tie w eafb ou m etod e s vir h ie rdie d iep tes o n de rso ek m oat w ord .

IntroductionThe shrinkage method of stoping with pillar support has

been used at Agnes Gold M ine since mining started there.U ntil recently, rock in stability did no t h ave any detrim entaleffect on safety or production, but now sill pillars are fail-ing, not only on the current production levels, but also inshallow er w orked -o ut areas. T he inciden ce offailu re raisesquestions as to whether the dimensions of the pillars areadequate at the current working depths and what their sizeshould be at greater depths.A lthough formulae for pillar design have beendeveloped for South African coal m ines by Salamon andOraveczl, little work has been done on this subject forhard-rock mining. Coates2 gives formulae for pillarstrengths that are being used in Canadian mines, and them atter has been investigated in South Africa by D e 10ngh3.

The applicability of the form ulae to mines such as AgnesGold Mine was investigated by means of a back-analysistype of approach. The application of the method is illus-trated here by the calculation of future pillar sizes forAgnes Gold M ine.

D escription o f A gnes G old M in eAgnes Gold M ine is situated in the Swaziland Super-group in the eastern Transvaal, Republic of South Africa.This Supergroup, approximately 3,5 billion years old,consists in the main of argillaceous and arenaceous sedi-ments together w ith a volcanic sequence, which has beenintruded by a basic to ultrabasic suite. The Agnes depositcomprises large low-grade reserves of consistent value,which are found in the shales of the Clutha Formation. Thereef is situated in steeply dipping (85 to 90), intensivelylam inated m etam orph osed sh ale.* Group Rock Mechanics Engineer, Anglovaal Limited, P.D. Box62379, Marshall town, 2 1 0 7 Transvaal.@ The South A frican Institute of M ining and M etallurgy, 1984.SA ISSN 0038-223 X / 3.00 + 0.00.

Sulphide mineralization occurs in strata-bound zonesthat are 1 to 2 m wide, these being the economic goldhorizons. Tw o of these 'shoots' are being m ined at present:the W oodbine and the Giles. The extent on strike is shownin Fig. 1; they are open-ended at depth.The uniaxial compressive strength of the rock in thehangingwall and footwall, as well as that in the reefhorizon, is 80 to 100 MPa at right-angles to the beddingplanes. Horizontal joints spaced approximately 1 m apartare found on most levels. These joints are tightly closed,but form preferential planes of failure when subjected tohigher levels of stress. There being no evidence to thecontrary, the vertical primitive stress is assumed to be afunction of the depth of overburden, while the horizontalvirgin stress at right-angles to the orebody, as determ inedby the hydro-fracturing technique, is 0,85 of the verticalp rimi ti ve s tre ss .

The vertical projection in Fig. 1 shows the extent ofm ining on the Giles and Woodbine shoots to date. Fig. 2 isa generalized section of these two shoots showing theirspatial relationsip, and Fig. 3 gives the standard layout forsill a nd crown p illa rs.

Back Analys isCalculations of the stress level at which pillar failure

occurs gives som e m easure of pillar strength. This im pliesthat there is a reliable m ethod for the calculation of stress.

From the geom etry of the M ine (Fig. 1) it was concludedthat a two-dimensional approximation can be madew ithou t the introd uctio n of a sig nificant error. It w as th ere-fore d ecided that the b oundary-elem en t m eth od develo pedby Crouch4 should be used. The M insim program me, w hichincorporates the influence of the third dim ension, was usedas a check on this assumption. The M insim resultscom pared w ell w ith those obtained by the tw o-dim ensionalapproximation.

In the calculation of the regional intluence of m ining, theJOURNAL OF THE SOUTH AFRICAN INSTITUTE OF MINING AND METALLURGY N O VE M BE R 1 98 4 36 5

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S U R F A C E-----------/ /~ G I L E S S TE 2 2 2 3 W O O B IN E S H O O T

1 1 0 ~ oS c a l e ? O m

F i g . 1 V e r t i c a l p r o j e c t i o n o f A g n e s G o l d M in e l o o k i n g s o u t h

crow n and sill pillars w ere treated as com bined pillars .T he m ining levels w here pillars had failed w ere selected,and stress levels w ere calculated for the com bined pillars.V isible signs of instability in sill pillars are apparent at70 M Pa, and at 120 M P a the reef drive becom es inaccess-ib le o wing to to ta l p illar fa ilu re .

P ill ar D e si gnIn the past, pillar sizes at A gnes G old M ine w ere based

largely on the experience of line staff. H ow ever, w ith theonset of failure of som e of the pillars, it becam e apparentthat a m ore sophisticated approacb w as required. T he w orkalready m entioned m akes it possible for procedures to bedeveloped by w hich pillar sizes can be calculated. U se ism ade of the concept of a safety factor, defined as the calcu-lated pillar strength divided by the calculated stressim posed on the pillar.

For stable situations, the factor can vary betw een 1 and 6,the m agnitude depending on the reliability of the tw ovalues; the higher the m agnitude, the less reliable the calcu-lation. In the present pillar design, a safety factor of 1,5 w asaccepted. T his value has been used by other authors3, avalue of 1,65 being used for coal m ines in South A frica.

P il la r S tr en g thT he strength of a pillar depends on the follow ing: a) geom etrical param eters the w idth-to-height ratio and

the shape of the pillar),

b) the strength of the rock m ass, and c) the presence and orientation of joints and other w eakzones.

GeometryT he effect of w idth-to-height ratio on the strength of coal

pillars as determ ined by Salam on and O raveczl is expressedb y the fo llo win g form ula :

P i ll a r s tr e ng t h = Kw 46 ho 66kPa, ... . .. 1 )w h er e K = stren gth of 1 m 3 of coal as m eas-u re d i n th e l ab or ato ryw = p illar w id th in m etre sh = p illar he ig ht in m etre s.

T h e s up er sc rip ts 0 ,4 6 a nd 0 ,6 6 a re a pp lic ab le to c oa l m in es .O th er a uth ors h av e a sc rib ed v alu es o f 0 ,5 a nd 0 ,7 5 a s b e in ga pp lic ab le to h ard -ro ck m in es3 . T he la tte r v alu es a re u se di n t hi s p a pe r.T his fo rm ula is ap plicab le on ly to sq uare p illars, an d, ifre cta ng ula r p illa rs su ch a s th e c ro wn p illa rs sh ow n in F ig . 3are used , the fo rm ula h as to b e m odified. T h e effectivew id th is th en u se d in ste ad o fth e a ctu al w id th :E ff ec tiv e w id th = 4 AIC . . . . . . .where A - p i ll ar a r ea

C = p i ll a r c i rc u m f e re n c e .Strength of Rock M ass

T he strength of test specim ens is generally accepted as

2)

36 6 N O V E M B E R 1984 JO UR N AL O F T H E SO UT H A FR IC A N IN STITU TE O F M IN IN G N MET LLURGY

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ACE

z~

~ D EP TH m

- 200m

~8 18 LEVEL~ ~zIf

I~i ~ 1 8 L EV ~

~ ~ItLmL

~2 0 L EV EL

r

2

4 0 L I4 5 0 m )3 5 L 1 2 5 0 m )

3 0 L 9 5 0 m )5 0

I 2 3 4 5 1 0 1 5 2 0C O M B IN E D P I L L A R W ID T H - metre. 25

Fig. 4--Expected stress levels and pillar strengths for variouslev els an d p illa r sizes (distances refer to depths below surface)

the maximum value obtained in the test, but the actualstrength of a rock mass is lower owing to the presence ofgeological discontinuities. This can be allow ed for in theformula by modification of the equation as suggested byWagne~:

P illa r s tr en gth = [ c ; 2 0, 5 / 0,75] oc kPa,. (3)where w = pil la r wid th

wo - specimen widthh = pi llar he igh t

ho = sp ec im en h eig htoc = unia xia l c ompre ss iv e s tre ng th .

Equation (3) was used for the calculation of the curvesgiven in Fig. 4, a value of 80 M Pa being used for the uniaxialcompressive strength of the shale. The difference in thestrength values for crown and sill pillars should be noted.The reason for the greater strength of the crown pillars isth at th e effec tiv e w id th w as u sed .

The formula for pillar strength given above generallygives reasonable results w here the w idth-to-height ratio isl es s t han 5. W hen this ratio is higher, the strength values areu nd er-estim ated an d th e re su lts are c on serv ativ e.

P il la r L oa dThe calculation of the stress levels on the com bined pillarwidths at various levels was based on the tributary areatheory. This theory states that, if the extent of mining issuch that the edge effects of the unm ined solid areexcluded, the pillars support the overburden load evenly.The magnitudes of the stress levels calculated in thismanner are initially over-estimates but, as mining pro-g resses in ex tent, they are a fair app roxim atio n.

Since the orebody under consideration is vertical, thehorizontal stress at right-angles to the ore body w as used,the values being adjusted incrementally w ith increasingdepth. The magnitude of the horizontal component of theprim itive stress field at right-angles to the ore body wasfound to be 0,85 of that of the vertical prim itive stress.

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Width o f W id th o f Size ofLevel combined pillar crown pillar sill pillar Extractionm m m 25 11 4 7x 7 7830 15 5 lOxlO 7035 17 6 11 x 11 6640 20 7 13x13 60

The stress values given in Fig. 4 were calculated for thev ariou s lev els w ith d iffe ren t c ombin ed p illar w id ths.

P ill ar S izesThe safety factor, as defined previously, is a useful

m easure of relative pillar stability. A s an illustration, use ism ade of the graphical representation for level 20 in Fig. 4.The stress acting on the pillars on that level for a

combined pillar width of 6 m is 90 M Pa (i). The strength ofa 3 m crown pillar and a 3 m sill pillar is given as 70 M Pa (ii)and 95 M Pa (iii) respectively. Therefore, the safety factorfor the sill pillar is

70/90 = 0,78;a nd , fo r th e c rown p illa r,95/90 = 1,06.

Compa riso n of R esu ltsThe stress levels at w hich failure occurs as determ ined by

the back analysis varied between 70 and 120 M Pa. Failurestarts at 70 MPa, and a progressive deterioration takesplace until total failure occurs at 120 M Pa. As depicted inFig. 4, 3 m sill pillars on level 20 should start to fail at astress level of 60 to 70 M Pa, and crown pillars at 90 M Pa.A s the back-analysis and pillar design form ula both indi-

cate that pillar failure starts at about 70 M Pa, a m easure ofconfidence can be placed in the use of the latter method inthe prediction of pillar failure at greater depths.

C alc ulation of P illa r S iz es fo r V ario us L ev elsThe stress levels of combined pillars of various sizes at

various depths can be determ ined from the curves in Fig. 4.T he dim ensions of individual crow n and sill pillars can thenbe calculated, the ratio of sill-pillar width to com bined-pillar w idth being kept constant at 0,55.W ith a safety factor of 1,5 for design purposes, the values

given in Table I were obtained for pillar dimensions andth eo re tic al o re-e xtra ctio n pe rc entag es a t de pth in creme ntsof 50 m . The stress levels for com bined pillars of differentsizes on the various levels were read off from Fig. 5. Thesize of the crown and sill pillars was then determ ined, andthe safety factor calculated for these widths for the givens tr ess l eve ls .

T LE IPILLA R SIZES FO R V AR IO US LEV ELS

illar sizes rounded off to practical dim ensions.

DiscussionIt is obvious that the percentage extraction decreasessubstantially with increase in depth, and the economic

significance (\f this w ould be severe. In addition, it m ust be

4,020 L e v e l

3 0Cl :0t;~ 2,0 40Level

t- SF 1,5011 I~...~cCl) 1,0

5 10 15 20COMBIN ED PIL LA R W ID TH - METRESFig. 5-Safety factor for the widths of the combined columnsrem em bered that the square configuration required for sillpillars lengthens the distance between draw points to up to13 m, which in turn results in a loss of the broken ore thatcollects on top of these pillars.Pillars of adequate size to prevent collapse of the work-

ings do not represent the only criterion since dilution alsoincreases w ith depth. T his aspect is not discussed in detailhere, but is a major factor in a consideration of thecontinued use of shrinkage stoping at depth.In addition to the above, unless adequately designed

pillars are left, the stress level on the reef drive itselfincreases substantially and side wall scaling occurs,re su ltin g in u ns ta ble c on ditio ns .

ConclusionsFrom the back analysis it was concluded that the stress

level of 70 MPa for the width of combined pillars causesfailure of the reef drives, as well as the tops and bottom s ofthe stope side w alls. The use of standard form ulae for pillardesign gave sim ilar values to those obtained by the backa na ly sis, ind ic atin g tha t th is d esign pro ced ure is a pplica bleto Agnes Mine. The introduction of relevant strengthvalues would make this procedure applicable to otherm in es in a sim ilar se ttin g.As shrinkage stoping to depths of m ore than 650 m would

result in very Iow percentage extractions, alternativemethods of stoping will have to be investigated for thesedepths.

AcknowledgementThe author thanks the management of Anglovaal forperm ission to publish this paper.

References1. SALAMON, M.D.G., and ORAVECZ, K.I. Rock mechanics in coal

mining. Johannesburg, Chamber of Mines of South Africa, 1976.p.29.

2. C OA TES. D .G . R oc k m ec ha nic s p rin cip le s.3. DE JONGII, CL. The design parameters used and the materials

selected for a new base metal mine in the Republic of South Africa.Conference on Application of Rock M echanics to Cut and fillM i ni ng L u le a 1st to 3r d J un. 1980 . Vo\. 1, p. 227.

4. CROUCH, S. M ining applications of the boundary elementmethods. Johannesburg, University of the Witwatersland, Wmk.shop 14th to 17th Aug., 1978.

5. WA(;NER, H., and SAIAMON, M.D.G. Pillal design, Seri,~s (;(lectures given at Sappers Rust, Pretoria, Aug. 1979.

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