An Emperical Relacionship for Trona Mine Design

7/29/2019 An Emperical Relacionship for Trona Mine Design

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CALLER NO. D, LITTLETON, COLORADO 80127

W i l l i a m G. Fi sche rE'MC W y o m i n g C o r p o r a t i o n

G r e e n R i v e r , W y o mi ng

AN E WIRIC .4L RE L A T IONSH IP FOR T RONA MINE DE SIGN

Permission is hereby given to publish with appropriate acknowiedgrnenls,excerpts or summaries not to exceed one-fourth of the entire text of the paper.Permission to print in more extended form subsequent to publication by the Institutemust be obtained from the Executive Director of the Society of Mining Engineersof AlME.I f and when this paper is published by the Society of Mining Engineers of AIME, itmay embody certain changes mads by agreement between the Technical PublicationsCommittee and the author, so that the form in which i t appears here is not necassariiythat in which it may be published later.These preprints are available for sale. Mail orders to PREPRINTS, Society of MiningEngineers, Caller No. D, Littleton, Colorado 80127.

PREPWINT AVAILABILITY LIST IS PUBLlSHED PERIODICALLY INMININGENG1NEERING


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M B i P IR ICAL XLATIOI?SHIP FOR T3OTIA DESIGI7 re su lt in g from hi gh ex tra ct io n. Tn is- ~o rkwa s donei n conjunction w ith t he Sureau of Mines overAbstrac t . This pper a tt em pt s t o c l o s e t h egap between extens ive rock te s t in g wi th f i e ldmeasurements and t h e mine oper ato r's need fo rsa fe mine layo-&s and a l te r na t i ve s .I t ves fcundt h a t mmy of t h e va r i a b l e s t h a t i n f l uenc e minegeometry and worker saf e t y ar e re l a t iv e l y unim-portan t while oth ers a re c r i t ica l .T he Zevelopmento f m p i r i c a l r e la t i o n s h i p v h ich t i e t h e c r i t i c a lv a r i ab l e s t o t h e " s af e u s ef u l l i f e " o f a t r o namine lay out and ob serv atio ns made i n 140 produc-t i on a rea s where th e va r iab le s were r esea rchedover a f i f te en year per iod ar e discussed.Theconcepts presented may bave ap pl ic abi l i ty i nmine des ign fo r othe r bedded de ws i t s .

In t roduc t ionLong before th e te rm "Rock ~e ch an ic s" wascoined mine operators were observing workingcondi t ions i n th e i r mines and a t t empting t o

m r o v e th e i r de s igns arrd l ayouts .Success fu ldes igns depended heavi ly on ex ~e r i en ce andkeenness of observation.The a r t of mine designthen gave way t o . a new breed of sc ie nt i f ic a l ly* ori ent ed people who assenbled equations,developedins trumentat ion,and conducted f i e l d t e s t s lNyexper ience has genera l ly been rha t th e ves tedinteres t of these "rock mechanics" i s best'serv ed by con tinu ing t o conduct more and moreexpensive f i e l d and labora tory t e s t in g .whiledelayi ng mine design decisi ons needed ky th emine operator.The science of mine design thusf a l l s e qual l y s ho r t o f i t s intended goal---quan-t i ~ f y t he de si gn - m a m et e rs u se d i n c he arti n s uc h a m nne r a s t o p r ov ide s a f e and e f f i c i e n tn i n e b y o u t s .

A framework of s c i e n t i f i c 'knowledge i s cer-t a i n l y o f g r e a t i m yr t a n c e t o t he mine des i gne r;bu t i n t he f i n a l a s se s s se n t e ac h ope r a to r mustknow hi s mine and under stan d i t s ind iv idua lp e c u l ia r i t ie s . T hi s p p e r i s the re fore an a t t -t o de sc r ib e some of ngr observat ions end re la tedf s t s tha t have t aken p lace ove r the p s t twentyy ea rs a t t h e IXC trona mine near Green River,Wy.General ized ni ne des ign e-tions were' developedbas ed u p n t he s e obs er vat i ons a s e a l y a s 1969and f i f teen years of cont inued observat ionshows th a t th es e equat ions a re h e lp ful whenplanning new working sec tio ns and de ve lo pe ntnetworks .A minimum aocount of underground t e s t i n gi s needed t o develop new generalize d equati onsfo r s imi la r mines .

PART 1Discussion of Mine Design Variables

The mj o r v a r iab le s inf luenc ing mine des igna t t he 9 l C t ro na mine ar e given in Table 1.Thefo llowing l imi te d d i scuss ion of t he i t ems i nTable 1 is intended t o he13 descr ibe t h e GreenRiver mine and th e app l ic ab i l i ty o f geners l izedequa t ions presented l a t e r .he-mining ground load i s not under theope r a t o r ' s c o n t r o l but it i s one of t h e mosti p r t a n t of t h e ve-iab les he must understand.:.la-; or e f f o r t was m d e i n t he l a t e 1950' s andear ly 1960's t o def in e th e pre-mining loadc ond i ti ons a t t h e B l C mine and develop effectivemeans of counter ing t e r r ib le nining condi t ions

a se r iod of years:h!oren,Fischer,ecd S t u r g i s(1965 ) W.G.Fischer(1965) ,W.Fischer and S.F eld e(1966).The conclusion of this e f f o r t was t h a tt h e r e g i ona l ba s i n c on t e in i ng n?any bur ied l aye r sof t ron a was e s s ent ia l l y gravi ty loaded v i tha t endency toward s l i gh t l y h ighe r hor izo nta lforces than would be e~ p ec te d ased on an averagePois son ' s Ra t io of 0.25 i n th e ea r th ' s c rus t.Thismeans t liat s tr es s chenges due t o mining canbe r e l a t e d t o t h e de ns i t y o f t h e ove rbu rden , thedepth of th e seam,and th e e-xtrac tion r a t i ov i a t h e f a m i l i a r e quat ion :

where S i s t h e av er ag e p i l l a r s t r e s s , P i s t h eun i t d ens i ty of th e overburden (p s i per footof depth or kPa/m), d i s th e depth of t he Sean( f e e t o r n e t e r s ) , an d R i s the ex t rac t ion ex-pressed es a dec imel less then one .A t Green River th e overburden d e ~ s i t y isone psi pe r foot of d e s h (22.62 kPa/m) v i t ha r e g i ona l - a r i a t i o n o f a bou t t h r e e pe r ce n t.The depth o f th e seam being nined i s ekout1550 fee t (473 meters) vi t h a range f rom lh50fe e t (451 meters) to 1700 fee t (516 ine ters) .S l i ght changes i n sur f ace topgraph y and seend e ~ t h occur over th e 23 square miies (59.6

hZ) overed by t h e e-xtensive ~i i n e corirings.The e s sen t ia l ly f l a t ly ing t rone Sean be ingnined (des ignated as bed #17 by t h e IISCS) islo ca l ly d i s turbed by a d i scontincous h igh-mglereve rse fa ul t loca ted severa l hundred Zeet( n e t e r s ) below t a e t rona d ew s i t i n geoloqical lS.old er sediments of t he Te r t ia ry ; iesa tch Form-t ion .T he e f f e c t s o f z h i s de e o l y i ng f au l t systemrem ined unexpec tedly n i n im l whi le miningi n t h e r eg ion and the pre sumpt ion of gravi tyload condi t ions cont inued t o r e su l t in somdmining layou ts.This may not rerrain >r ue through-ou t t he t m n a ba si n.S t rength and o the r phys ica l prope r t i e s oft h e r oo f, se sn , an d f l o o r z t e r i a l s iias inves t iga-t e d by T.Morgen (1965) and ( l $ 7 3 ) . ~ h ee l a s t i cYoung's modulus va r ie s *om 2.0 e v 6 pi (13.79~ ? a ) o 4 .5 ex? i; (31.03 ~ ? a ) 3th regionso f r e l a t i v e l y s t i f f t r o r a g r ad in g i n t o re gi on sof le ss -s ti ff tror?a.T;?ese tre nds ;-ere reg io na liydetermined us in g dynamic phys i ce 1 cro pert ytechnicues i n sur face boreholes .?h in sec t ion sa l s o showed a ni s ot r ophy i n t he m l c r o c ~ j s t a i l i nem s s i - r e apz ea r ing t r ona s i n i i e r t o t he p r e f e r r eddi rec tio ns of mtrcro-orientations deserminedv ie th e regi one l surf ace borehole tec 'r .niques. :' srsof :o int s and 2e c t ur e s ve re :,eg.n i n 1950and t he ov era l l gec tech nicz l Frogram was repor te di n l imi ted c ir c l es by Fischer and &zzu


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s t i f f r e g i o n s , p r t i c u l a r l y w here t h e o r e i sthi n. Wona and th e surrounding shal es exh ibi ta high degree of creep and this probably tendst o be a normalizing factor.0bviousl.y an averageYoung's modulus canno t be used t o dete rmi nes t r e s s l eve l s from s t r a in da t a ob t a ined v i aovercoring techniques and ther efo re t h e varyingphysical propert ies and apparent load condit ionst end to genera te a g r ea t dea l o f s tudy .Geometry of t h e mine openings and pane lsi s of grea t importance in mine design sin cechanges in thes e fac to rs a re perhaps th e mostvi ab le means of improving working condi tionsonce t h e equipment and mining method have beenselected.Seam height i s v i r t u a l l y c o n s t a n ta t t he Green River mine. I t averages aboute igh t f ee t (2 .44 mete rs) but ranges from sevenfee t (2.13 me te rs ) t o twe lve f ee t (3.66 meters) .Mining condi t ions i n t he t h inne r seam areasa r e o f t en poor d ue t o t h e e f f e c t s o f a i r andmoisture on elcposed roof sh al es and th e weakernature of th e sha les.Mining condi t ions i n th ethi cke r seam areas a re ge neral ly good but rooffa l l s sometimes occur wi th l i t t l e pr io r warnings ince t he so f t e r roo f sha l e s tend t o l oad th estr ong er tr ona roof beam without caus ing muchobvious damage t o warra nt a tt en ti on . The geometryfac to r s a r e t h e p rimary sub jec t o f t h i s paper .Paother ext reme ly i mp r t an t f a c to r i n t ronamine des ign i s t h e r a t e o f mining. A l l o f t h em. ter ia l s involved exhibi t ' a creep phenomenat i h i ch is highly s t re ss dependent, o r shouldI s~y -ex tra cti on dependent. The mining r a t edepends upon tho se sub-facto rs given i n TableE . & % si ca ll y, a h ig h e x t ra c t io n p e l musthe adned quick ly before t h e f l oo r heave androof de f lec t ion begin t o e a t away a t product iv i -t y , s e t t i n g up an eve r sp i r a l i ng wor seningof condi t ions which u l t imate ly re su l t s i n aban-donment of th e working area. Operations resea rchthus en ters t he design pictur e. The mine designermust t he re fo re r ecognize t h e capab i l i t y o ft h e o v e r a l l sy st em o f ~ e o p l eand mchines inadd it i on t o t he phys i ca l parame te r s o f t h erock and i t s geologic se t t ing .Woof s-upport a t t h e Green River mine hase-rolv.ved from timber and s h e l l b ol ts i n t h e1950 ' s and 60's t o various combinations ofshell bo l t s and ewxy bo l t s i n t h e 1970 's and8 0 ' s . Roof-truss work i s l im it ed t o c r i t i c a ldevelopment ar ea s where th e added cos t canbe j u s t i f i ed . I t has been ny expe r i ence t ha tth e use of epoxy bolting has made a significantimprovement i n working con dit ion s and t h e lati-tuUc for fu rt h er mine desig n improvement hasbeen iridened accordingly. Rusting of s h e l l' ~? l t s , e s pe c i a l l y he t h inne r ones made o f h ighst re ng th stee1 ,ha s been a problem which weh ~ v e ot ye t exper ienced wi th th e l a rg er epoxykobts,The gene raliz ed mine desi gn equationshwre therefore been modif ied t o ta ke roof suppor tinto account,al though t h e method o f doing t h i sis subjec t ive .Provided the equipment i s proper ly appl iedin a productive system, t h e type of miningbeing used seems t o have l i t t l e eff ec t uponth e overa l l design. Boring typ e continuousminers a r e used f or long term development wherecorner cut t ing i s mi ni ml . These machines havea l s o been e f f e c t i v e l y a p p l ie d i n p i l l a rextra ct ion work i n a patented mining layout,Fischer (1969).

Although th e shape of t he continuous mineropening l ends i t s e l f t o r educed co rne r s t r e s se s ,t h e i n t e r s e c ti o n s tend t o become wide; of fs e t t i ngt h e i r d e s i r a b i l i t y i n hi gh e x t r a c t i o n p ro d uc t io np e l s . The co nv en ti on al d r i l l i n g and b l a s t in gsyste m which inv olv es peop le and machines movingi n a re la t i ve ly quick success ion f rom one p lacet o a no th er i s i d e a l l y s u i t e d t o h i g h e x t ra c t i o nproduction panel work. Se ver al patented sy st emfo r u se i n heavy ground were developed butit has been r ecen t p r ac t i ce t o avo id s e t t i n gup th e heavy load condi t i ons i n t h e f i r s t place;Love and Bern atis (1963) and Fis che r (1968).Conventional equipment i s equal ly unsui tedt o widely spaced development layouts. The r ipp ertype continuous miners te nd t o f a l l somewherei n between. It i s presumed then, t ha t th e useof an ove r a l l de s ign equa t ion neces s i t a t e st he proper se l ec t ion o f equipment and forc eaccount s chedu ling needed t o e f f i c i en t ly ca r r yout t he p lan f or any given area .

Over t he year s we have found th at t h e direc-t i o n of at ta ck o f new workings upon old workingscan be very impor tant s in ce s t re ss l eve l s a roundpreviously mined a rea s a re gene ral ly much high erthan i n v i rg in ground. High s t r es s loads onol d mining abutm ents o-%en ext end f o r huzzdredaof f ee t (me te r s ) and it i s usua l ly undes i r ab l et o mine p ar a l le l t o o ld mine workings wi thoutl e av i n g some s o r t o f b a r r i e r . P a r t i a l e x t r a c t i o ntechnia-ues (ie. 50 p e r ce n t ) seem t o r e s u l ti n ground load be ing shi f ted fur the r f rom t h eedge of old workings than the y were when f u l lcavin g tec hni que s were used. The magnitudeo f t h e t r a n s f e r r e d l o a d ap pe ar s t o b e l e s sthan it was when f u l l cavin g was pracz iced.A general ized mine design eq wt io n must the re fo reprooide t h e mine o perat or wit h a method o fsub jec t ive ly cons ide r ing v i ab l e des ign a l t e rna -t i v e s wi th f u l l r ea l i z a t i on th a t new workingsmust follow old workings and that developmentheadings w i l l soon be surrounded by higherext rac t ion panels . An exact equat ion for everys i tu a t io n would be ludicrous .Subsidence effects which manifest themselveson th e sur face re su l t f rom phys ica l changeswhich have ta ken p lac e underground. No-extractionre su l t s i n no subsidence and comple te ext ra c t i onre su lt s i n a mxirnun of subsidence. Green Rivermine subsi denc e was rep or te d by Korgan andS t i l l ( 1 9 7 3 ) . I t i s my g e ne ra l op in io n t h a tlayouts which reduce t he r a t e of subsidenceon t h e s u r f a c e t e n d t o r ed uc e t h e r a t e o f c l o s u r eof nearby openings underground. Here aga in,some judgement must be applied when using agenera l ized mine des ign equat ion s inc e the reappears t o be no easy way t o formalize th eground e ff ec ts t o be expected around an ar eawhich has resu l ted i n s ign i f i can t s ur fac e move-ment. We have noted th a t ext r ac t io n beyond55 percent tends t o re su l t i n caving-type loadt r a n s f e r .The point of the foregoing d iscuss ion ofsome of t h e var iab les which appeared i n Table1 i s s imply th a t grea t expense i s involvedi n chas ing down exact re la t ion ship s fo r eachand every one of them. The re la ti on sh ip , whenfound, i s only a small p r t of t h e dec i sionmaking proces s t h e mine op er at or must go throughwhen he makes a se ri ou s e f f o r t t o im$rove hi slayouts and designs. I t i s t h i s gap be tweenex tens ive t e s t i ng and " f ly ing by the s ea t o f


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your pant s" th a t th e au thor wishes t o c lose bypinpoint ing th e re la t ion ship s between keyvar iables and enter ing them into general izedequat ions appl icab le t o t rona mine s i tu at io ns .The methods used a re not en ti re ly subj ecti veand th e basic approach may have app li ca bi li tyi n tho se mines which exp erience si mi la r time-de-pendent lo ad tr an sf er and creep phenomena.PART 2

Design Generalizat ionCharles Holland (1962) published a summaryo f a s e r i e s o f i n t e r e s t i n g t e s t s i n which c ub i cspecimens of co al were loaded t o fa i lu re . Forany given coal he could show that the compressives t reng th o f a cube w a s an inve rse func t ionof t he square roo% of specimen width. Thisimplied that as specimens became larger theya l so became weaker, which was at tr ib ut ed t oth e effe cts of suspected f laws. I r e a l i z e d

that seam height is usua l ly on ly a smal l f r ac t iono f p i l l a r w id th a nd t h e r e fo r e c u b ic p i l l a r sex i s t on ly under very r ar e circumstances .Hol-l a n d ' s b a s i c r e l a t i o n s h i p f o r p i l l a r s w i t hheight d i f fe ren t f rom width i s given by e g a t i o n( 2 ) .

where; CD is the compress ive s t r eng th o f thep i l l a r m a te r ia l ,v i s th e l eas?; w id th o f the p i l l a rh i s th e seam heig ht, andk i s a cons tan t fo r the ma te r ia lcompri sing th e p i l l a r .(Units must be consis tent fo r th e system ofmeasurement being used)

If we assume t h a t a sa fe ty fac to r ,S .F . , r e su l tsvhen the compressive strength i s l a r g e r t h a nth e appl ied s t r es s due t o mining we can subs t i -tu t e the g rav i ty load equa tion (1 ) in t o equa tion(2) with the fo l lowing resu l t :

CP = k;i(-R)S.F. =- SLet G equ al a new term, t h e geometry fa ct or ,which equals &(l-R) . In our case , p is equalt o on e p s i p e r f oo t o f d ep th ,d ;( 22 .6 2 ~ a / m )I tcan be observed from equat ion ( 3) th at t h e

s a f e t y f a c t o r i s a l in ea r func t ion o f G , t h ema t e r i a l pr o pe r ty k , and f o r a l l p r a c t i c a lpurposes ( a t Green ~ i v e r ) a constant inversefunc tion of pdh.This i s shown i n equation( h ) vi a rearrangement o f t he terms i n equat ion(3).

I f it can be presumed that trona materialsare reasonably similar f rom one place t o anotherwithin the same mine,and perhaps similar fornearby mines within t he t r ona ba sin; then th es a f e t y f a c t o r i s a l inea r func t ion o f G; t h eremaining terms being essent ia l ly constantfo r each mine (des p i te the ap pr en t va r ia t io nspreviously disc usse d). The mining load func tiondefined as (1-R) needs %her explanations i n c e it can be determined from local conditions

around a s ingle pi l lar or f rom regional paramet-ers which ta ke i n t o account th e eff ect of nearbyworkings, o r la ck of workings. I t i s t h e a u t h o r sopinion th at use of a semi- i nf ini te area withextract ions generated by one ty pi ca l p i l l aran d i t s surrounding openings represents a propergene rali zati on of t'ne load condition regard lessof t he number of e nt ri es used, and rega rdle ssof th e shape of th e openings being driven.Thisi s no t qu i te t ru e s ince d i f fe ren t shapes genera ted if fe reniz. r i b s t r e ss es and requ i re d i f f e ren troof su p p r t pa t t e rns , due ca re and d i l igencebeing equal. The extr acti on,R , can then bequant i f ied i n a general ized fashion as fol lowsby r e f e r r i n g t o f i g u r e s l ( a ) and 1 ( b ) ;Let X= crosscut spacing, ( f t o r m et er s )

Y= entr y spacing, ( f t or meters )Z= ang le r igh t , en t ry t o c rosscu t , (deg)W= m i n i m p i l l a r wi dt h, !f t o r m et er s)where W i s t h e l e s s e r of(Y-N) o r (XsinZ-W)PI= e n t r j w id th , ( f t or meters )M= crosscut width, (13 r meters )R= d e c ii ml e x t ra c t io n , ( u n i t l e s s ) .

The general izat ion of t he mater ia l c onstant , k,i s no t so s imple a s it might app ear . Roofs h al es i n t h e mC mine were found t o have unia xi-a l unconfined conpress ive s t rengths rangingfrom 2840 t o 4100 p si (19.58 t o 28.27 MPajfor specimens with an i/D of 1.3. The tronai t s e l f ranges f ro n 4120 to 7560 psi (28.41t o 52.12 m a ) and th e f l oor sh2les range f rom2630 t o 3900 ps i (18.13 t o 26.89 ?@a). ikisc ou pl ed w it h a s i mi l a r wide v a r i a t i o n i n Y o ~ ~ g ' smodulus wi th pronounced time and st r e s s dependentbehavior generates a very complex problem forth e rock mechanic with thought s of att em$tinga s c i e n t i f i c a l l y j u s t i f i a b l e ge n e ra l i za t i on .Fortunately weak trona associates with weaksha les and s t rong t rona wi th s t r ong sha les .The author made an ar bi tr ar y assunpiionth a t the s a fe t y ;'ac tor g iven in equa t ion ( h )i s en ample 2.0 when the design lajrout canbe expected so remain sa fe f or 30 years (t=360months) and i s a marginal 1 .0 when th e d e s i gcan be expected t o remain s af e fo r only ',, year(t =6 months ) .From obser-rations as ea rl y as 1960 it becameapcarent t ha t openings dr iven vi t h a bor ing-Type continuous miner c ut ti ng en ocening L3.3fee?; wide (4.2 meters), with crosscuts ande m r i e s s ~ c e d n 100 foot (30.5 Meter) int er-vals and using 90 degree crosscut angles, wouldr e s u l t i n a s a f e u s e f u l l i f e o f 30 y e ar s ( t =? 6 0months 1. ,The geometry function,G, f or t h i slayout is ecu al t o 6. 9. The openings wouidaverage eight feet (2.44 meters) high and besupported using f ive foot long (1 .52 meter)s h e l l bo lt s. Some roof support reglacementcould be expected but t he cos t or' reb olt ingwas cons idered minimal a t t h i s sp acin g 2r.dload condi t ion.Also from observation of numerous closelyspaced workings it became ap p re n t th at openingsformed by convent ional dr i l l in g and bla s t in g


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th at ver e 15.5 fe et (b.72 meters ) wide,vith an 8foot (2.lr4 me ter) mining he igh t, dr ive n on60 foot (18.28 meter) centers a t r i gh t anglest o each othe r, would stand saf el y fo r onljr+ y ear ( t= 6 months). Wooden c r i b s and p s t swould occa ssionall y be used i n addit ion t oth e sh e l l bolt s. The geometry factor,G, i nt h i s c as e would be 3.7.Using t h e s e r e s ~ e c t i v e v al ue s f o r s a f e t yfa ct or and geometry f ac to r with ea_uation ( 4)and calcu l a t ing fo r the mater i a l constan t ,k ,we fi nd ( neglect ing uni t conversion fac tors ) :Long Li fe k = (2 .0 )(1 )(1550)(8 ) = 3594(6.9)

Short Life k = (1 .0 )(1 )(1550)(8 ) = 3351(3 .7)

On t h e pr es um pt io n t h a t observat ions aresubject t o s ubs ta nt ia l judgement and ar e neces-sa r i ly in ex ac t , it can be shown tha t t he sa fe tyfac to r i s approximit ely eq ual t o 0.28G whendimensions ar e i n f e e t and 0.507G when dimensionsar e i n meters .S.F. = 0.280(&)(1-R) f o r U.S. u ni t sS.F. = 0 .5 0 7 (& )(1 -~ ) fo r S I u n i t s ( 8 )I t was realiz ed ea rl y that a c er ta in h u n tof c losu re of mine openings could be to le ra te dand resupported; or removed i n th e ca se offl oo r heave and minor roof f a l l s .In t he mid 1960's it was p o t unusual t o?em ir openings which had closed ve rt ic al lyas much as 25 percent although economic condi-tions and tougher standards would make it d i f f i -cu l t t o work under the se condi tions today.Creep t e s t s showed th a t t h e n t e a t which c lo su recould be exoected t o ta ke p la ce was higihlydependent u p n t h e s t r e s s l ev e l i n th e a rea .T hi swas r e p r t e d by Leonard Obert ( 19641.Since c losure is u l t i n a t e ly th e main f a c to rwhich det er nin es hov long a mining system c mbe used and closure i s a s t r a i n = m e t e r ,it was f e l t t ha t cree p functions could be usedt o generel ize th e t ime a mining system couldbe saf el y used. When plo tt ing on lo ga ri th dccoor dina tes Earron and Toa-s (1963) found t h a tclosure of mine o p en in g in sal t p l o t t e d l i n e a r l ywith time. We had d iscovered th at th is re la t ion-shi p held t ru e fo r trona mine openings as well .noting that the geometry function, G, e s s e n t i a l l ydoubled when going from sh or t l i f e openingst o l on g l i f e o ce ni ngs w h il e t h e l i f e o f t h emining systems increased 60 fold, it wes decidedt o es tab l is h l inear equat ions involv ing G andh ( t ) which could pe solved simultaneous1.yf o r t h e r es p ec t iv e s l o p and i n t er c ep t s. Thisves done as follows ;Short Life: 3.7 = A + ~ s l n ( 6 )b n g Li fe : 6.9 = A + ~ s l n ( 3 6 0 )from which A = 2.3 and B = 0.782 .The I n i t l e i generali zed mine desi,a equationwas therefore:

where ( t ) r e pr e se n ts t h e s a f e u s ef u l l i f e o fa destgned system i n months and G has un i tsof ft*, I n t h e SI system where G would haveu n i t s o f Idi the equation vould be:

This equation, i n i t i a l l y developed i n 1969,was used extensiveigr a s a guide f o r mine layoutand design through th e e ar ly 1970's when t h emine more than doubled i n cap aci ty t o i t s cu r ren tmaximum r a t e o f 5.2 MTPY. This equation hel dreasonably sound u n t i l t he advent of epoxyb o l t in g l a t e r i n th e 1 97 0' s and ea r ly 1 9 80 's .Figure 2 slpm a plot on logarithmic coordinateso f t h i s s a f e u s e f u l l i f e " a ga i n s t d e c i na lext ra ct io n. Actual exp erience with numerouspanel designs i s shown on th i s f i gur e and al sotabu lat ed i n Table 2. The da ta f or designswhich were supported, a l l or i n part, by epoxybol t ing techn iques i s al so indicated. Usingth is general ized equat ion it was p s s i b l e t ocompare the effects of varying crosscut angles,d i f fe re n t opening widths, and d i f fer en t en t ryand crosscut spacings. A s a f e t y f a c t o r l e s sthan 1 .0 does not neces sar i ly represent anu nsa fe d esig n s in ce p i l l ax y ie ld in g i s q u i t erap id fo r sm l l p i l l a r s i z e s . The a r e a must,however, be l a i d out i n such a manner as t opermit rapi d completion of a ct ive mining.S ince th e advent o f epoxy bo l t ing , f i e l dobservati ons showed t h e equat ion w e s too consem-a t i v e a n d i t was la te r modif ied fo r t he newtechniques. A mul ti pli er was added t o th e gener-a l i zed equat ion t o compensate fo r t he imrovedr oo f s u r r t methods. The m u l t ip l i e r f o r s h e l lbol t system was considered t o be 1 .0 and th ee p x y b ~ l t ystem was a ssi gned a va lue of 2.0.S ince nany new workings r e r e dri ven i n th eregi on of old workings which carried su bs ta nt ia labutment loads generated i n t he pa st it becameap p ro p r i at e t o a s s ig n a m u l t ip l i e r o f 0 .5 t odesigns intended f or th es e workirg are as. Theadjusted equation took the folloving form.Dimensions a r e i n f e e t when usin g equation(13) and i n meters when using equat ion ( 14).

Approximately 140 ~ o d u c t i o n areas havebeen mined d u r io g th e p s t 15 years which tendt o demonstrate tha t a generalized mine designequation i s n ot e n t i r e l y r id i cu lo u s as hasbeen suggested by some. I t can be use ful vhense le ct in g t he la;routs fo r uwoming workings.A t t h e very l e a s t , mine management has a reasona-b l e t o o l f o r c o q a r i s o n of a l t e r n a t i v e s . Theequations a re simple enough t o use with wc ke tca lcu la to r s in t h e f i e l d ; b ut k eep i n mindth e u nd erly in g fa c t t h a t t h ey a re o n ly g u id e l inesand e qe r i e n c e coupled wit h sound Judgemenzremain a necessity .


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References TABLE 1 MIHE DESIGS VARIABLFSBarron,K. ,and Toevs,B.A., (1263) "~ ef or ma ti onAround a ?,line Sha ft i n Sa l t. Fro c.l st CanadianQmpsium on Rock Mechanics. Gttawa,Queent sBinter,pp 115-136.Fischer,W.G., (1965)"How Rock Mechanics i s Appl iedt o S pec ifi c Mining Problems a t t h e WestvacoMine. "~-l.ansAIM!3,Vol. 229 ,pp 435-443.Fischer , . G. ,and Felde,S . . , 1966) "4-Nort~Panel, A Eold ExTJeriment i n iloof Def le ct io n.Mining bgineer ing,Vol . 18 ?To. h,Apr il 1966 p ~63-67.Fischer,W. G. , (1968) " ~e th o d For Mining Trona. "U.S.Patent Jo.3402968,Issued Se~t.24~1968.Fischer W. G. ,Norgord,J.D. ,and Wilson, J., (1969"~ont inuousMethod f o r $fining Trona." U.S.PatentXO. 3455606 .Is sue d July 15,1969.Fisch er,W illia m G.,and Sozzuto,Xobert T.,(1976)"Use of 3D-Velocity Lolgs and Seismic Methodsi n Wyoming Trona Mining. Minutes o f t h e Sol ut io nMining ReSearch Institute,Dec. 2,1976.Griggs ,D.T., (1939 ) "cr eep of ROC&" J .ofGeology7~ol.47,?To.3,p 225.Holland,C.T., (1962) " ~ es i gn of Pi l lar s" f orOverburden Support;Part 1." Mining CongressJ. ,bfarch 1962.Eiolland,C.T. ,(1962) " ~ es i gn of P i l la rs fo rOverburden Support ;? ar t 2. " hlining Congressz. , ~p i l962.bve,R .F. ,and B ern ati s ,T.S., (1963) Mining Methodsand Systems i ncl udi ng Caving t o Reli evePressure. " U.S.Patent Ro.3097830 Issued July16,1963.Morgan,T.A. ,Fischer W. G. ,and S t u r g i s, . , (1965 ."Di str ibu tio n of Str;:s i n t h e Westvaco TronaMine,Westvaco,Fyoming. U.S.Bureau of MinesRI 6675.Morgan,Thoinas A. , a n d S t i l l , J a n C. , 1973) "TheEffects of Mining and Subsidenge Rates onTr an sf er of Overburden Weight. U.S . ureauof Mines I C 8630,pp 35-43.Obert ,Leonard, (1964) "Deformational Eehaviorof Model P i l l a r s Vade from Sa lt , Trona, andPotash Ore." Proc. 6t h Sy mp si m on RockMechanics, Uni ver sit y of E.lissouri,Rolla,Oct.l96L, ed. by E.M.Spkes and C.R.C hrist ianse n,pp 539-560.

1. PRE-MINING GRO-JflD LOADa ) Stress Changes Resulting from 14iningb) Regional and Local Effects2. STRMGTH OF THE M A T 3 R W I N 5%

ROOF,SWl,NUI FLOORa ) load ca r ry ing capac i tyb) failure modec ) mo is t u re / a ir e f f e c t sd ) t im e dependent ~ o p e r t i e se ) Jo in t s /Frac tu res /C lea t sf ) S t a t i s t i c a l V a ri at io ns

3. GEOMETRYa ) Panel Widthb) Panel Lengthc ) Bo. of Entr iesd ) Crosscut Anglese ) Spacing of Openingsf ) Width o f Openingsg) Shape of Openingsf?) Sesm Heightg ) P i t ch o f t he Sesn

L. RATZ OF lIIXINGa ) a Function of Product ivi tyb) a Function of Xachinery Usedc ) a -Function of Panel Designd ) a Function of Crew Size/Schedulee ) a Function of Crew Eq er ie nc e5. W E OF ROOF SWPORTa ) S h e l l E o l ts

b) E p x y 31:sc ) m s oltsd ) Timber/Oth.er6. TYPE OF EIINIBGa ) Convent ional Dr i l l ing & Slas t ingb) Continuous Minersc ) Longwall/Short-rlalld ) Caving Techniques7. KETHOD OF ATTACK(new Workings upon Cld Workings)

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An Emperical Relacionship for Trona Mine Design

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Transcript of An Emperical Relacionship for Trona Mine Design