Slope modification of open pit wall using a genetic algorithm case study: southern wall of the 6th Golbini Jajarm bauxite mine

Transcription

1 Sept_83-88:Templte Joul 11/10/08 11:43 AM Pge 651 Syopsis Slope modifictio of ope pit wll usig geetic lgoithm cse study: southe wll of the 6th Golbii Jjm buxite mie by K. Goshtsbi*, M. Atei, d R. Kltehjy I this ppe geetic lgoithm is used i hevily joited ock mss i ode to ivestigte the citicl cicul slip sufce d modifictio of slope sufce. This method ws pplied to the southe wll of the 6th Golbii Jjm buxite mie. The mie is the lgest buxite deposit i I, locted to the othest of the tow of Jjm i the Khos povice. Estimted eseve of buxite i this deposit is bout 160 millio toes. Field d lbotoy ivestigtios wee coducted i ode to detemie ock mss behviou. A geetic lgoithm code tht uses the Simplified Bishop method s objective fuctio ws developed fo fidig the sfety fcto of cicul slip sufces. Sesitivity lysis ws pplied to detemie the optimum vlues of the geetic lgoithm vibles, such s popultio size, selectio method, cossove d muttio tes. Afte fidig the citicl cicul slip sufce, slope modifictio is cied out by emovig ustble sectios fom mked citicl slip sufces, d this pocess is epeted util the lst usfe sectio is emoved. Bsed o this code, modifictio occued duig 7 steps, by echig sfety fcto of 1.3 i the lst step. Filly, the modified slope gle of the southe wll of the 6th Golbii Jjm buxite mie ws detemied to be degees. Keywods: Geetic lgoithm, slope modifictio, cicul slips sufce, 6th Golbii Jjm buxite mie. Itoductio Slope stbility is oe of the most impott issues i stbility lysis i geomechics. Of the vious vilble methods (umeicl d lyticl), the limit equilibium is widely used due to its simplicity d the esults e foud to be close to the igoous methods1. The covetiol limit equilibium method fo slope stbility lysis cosists of two steps: () clcultio of the sfety fcto fo slip sufce d (b) detemitio of the citicl slip sufce with the lowest fcto of sfety. My methods (Bishop, Jumbo, Mogeso d Pice, d Spece) hve bee peseted to compute the fcto of sfety usig limit equilibium with citicl slip sufce2. A simple cicul slip sufce is sufficiet fo slope i homogeous ock msses. But the lysis of slope stbility equies my lyses of diffeet potetil slip sufces i ode to ech the sufce with the lowest fcto of sfety. To void the difficulty i detemiig the globl miim, evolutioy methods such s the geetic lgoithm (GA) e beig used, d e moe obust to chieve the optiml solutio i my complex poblems3. The geetic lgoithm diffes fom othe methods sice it seches mog popultio of poits d woks with codig of pmetes set the th the pmetes themselves. Goh (1999) hs used the GA to wok out the citicl sufce d the fcto of sfety usig the method of wedges4. McCombie d Wilkiso (2002) used Bishop's method to detemie the citicl sufce usig GA5. I the bove studies, GA poved bette solutio comped to othe tditiol ppoches4,5. This ppe pesets method fo detemiig the citicl cicul slip sufce usig GA with objective fuctio bsed o Bishop s simplified method. The modifictio of the slope is cied out by emovig ustble sectios fom mked citicl slip sufces. This pocess is epeted util the lst usfe sectio is emoved. Cosequetly, the lysis c be pefomed though the followig stges: () developmet of objective fuctio d (b) the pplictio of GA to solve the objective fuctio d echig optimum slope gle. Developmet of the objective fuctio Sevel slope stbility lysis methods (e.g. Spece) e moe igoous d should be fvoued fo the detiled evlutio of the fil desigs. Othe methods (e.g., Spece, Modified Swedish, d Wedge) c be used to lyse o-cicul slip sufces. Ceti methods (e.g., Odiy Method of Slices, * Tbit Modes Uivesity, Miig Egieeig Deptmet, Teh, I Shhood Uivesity of Techology, Miig Egieeig Deptmet, Shhood, I Sciece d Resech Cmpus Uivesity, Teh, I The Southe Afic Istitute of Miig d Metllugy, SA ISSN X/ Ppe eceived Oct. 2007; evised ppe eceived July T s c t i o P p e The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER OCTOBER

2 Sept_83-88:Templte Joul 11/10/08 11:43 AM Pge 652 Slope modifictio of ope pit wll usig geetic lgoithm Tble I Compiso of fetues of limit equilibium methods 6 Fetue Odiy Simplified Spece Modified Wedge Ifiite Method Bishop Swedish Slope of Slices Accucy Ple slip sufces Cicul slip sufces Wedge filue mechism No-cicul slip sufce Suitble fo hd clcultio Simplified Bishop, Modified Swedish d Wedge) c be used without compute id d e theefoe coveiet fo idepedetly checkig the esults obtied usig compute pogms. Also, whe these ltte methods e implemeted i the softwe, they execute extemely fst d e useful whee vey lge umbes of til slip sufces e to be lysed. The limit equilibium methods e summized i Tble I6. The geologicl study of the southe wll of the 6th Golbii Jjm buxite mie shows tht the ock mss is homogeous d ude dy coditios7. Cicul slip sufces e widely used i slope stbility lysis of homogeous ock msses s they e fi eflectio of ctul filue mechisms, d c be lysed elibly without the eed to justify the ssumptio mde, o complex testig. Amog the vious methods tht c be used fo lysig cicul slip sufces (e.g., odiy method of slices, Simplified Bishop, modified Swedish d Spece), the Simplified Bishop d the Spece led to moe ccute esults. Also the Simplified Bishop is extemely fst d suitble to use i GA, s the slope stbility comes with lge umbes of til slip sufces to be lysed. Theefoe, the Simplified Bishop Method c be the best objective fuctio to clculte the fcto of sfety i GA. Simplified Bishop method The Simplified Bishop Method ws developed by Bishop6. This method is bsed o the ssumptio tht the ite slice foces e hoizotl (E i = E i+1 ), s show i Figue 1. A cicul slip sufce is ssumed i the Simplified Bishop method. Foces e summed i the veticl diectio. The esultig equilibium equtio is combied with the Moh- Coulomb equtio d the defiitio of the fcto of sfety to detemie the foces o the bse of the slice. Filly, momets e summed bout the cete of the cicul slip sufce to obti the followig expessio fo the fcto of sfety, F,6: slice, M p is the momet ctig o the cete of the cicle iduced by the wte foce ctig o the top of the slice, R is the dius of the slip cicle d m α is defied by the followig Equtio6 : The fcto of sfety clculted fom Equtio [1] stisfies the equilibium of foces i the veticl diectio d ovell equilibium of momets to the cete of the cicle. Sice the vlue of the tem m α depeds o the fcto of sfety, it ppes o both sides of Equtio [1]. Cosequetly, Equtio [1] cot be mipulted i such wy tht explicit expessio is obtied fo the fcto of sfety d itetive, til d eo pocedue is pplied to solve it6. Slice umbe is citicl pmete i the Simplified Bishop Method. Accucy i the fcto of sfety vlues is icesed with highe slice umbes, but icese i slice umbes eeds moe clcultios d moe time. The optimum slice umbe is equied fo fste d ccute vlues. Alysis o slice umbes ws implemeted usig the Simplified Bishop Method fo fou slip sufces d slice umbes fom 10 to 100 with steps of 5. As see fom Figue 2, fte slice umbe 40, thee is o sigifict impovemet i the fcto of sfety, so, slice umbe 40 ws selected s the objective fuctio. Geetic lgoithm The geetic lgoithm, developed by Holld, elies o the piciple of Dwi s theoy of the suvivl of the fittest8. [2] [1] Whee Δx is the width of the slice, W is the weight of the slice, c' d φ' e she stegth pmetes fo the cete of the bse of the slice, α d β e the slice iclitios, u is poe wte pessue t the cete of the bse of the slice, P is the esultt wte foce ctig pepedicul to the top of the Figue 1 Typicl slice d ite slice foces fo Simplified Bishop method OCTOBER 2008 VOLUME 108 REFEREED PAPER The Joul of The Southe Afic Istitute of Miig d Metllugy

3 Sept_83-88:Templte Joul 11/10/08 11:43 AM Pge 653 Slope modifictio of ope pit wll usig geetic lgoithm Fcto of sfety Solutio of the poblem c be obtied though evolutio. The lgoithm is stted with set of possible solutios clled popultio. Ech possible solutio withi the popultio is clled chomosome. Ech chomosome is ssiged fitess vlue bsed o the fitess fuctio tht eches fom the objective fuctio. Solutios fom oe popultio e tke d used to costuct ew popultio clled offspig. So, the offspig will be fitte th the old popultio. This pocess is epeted util temitio citei e met. Fo exmple, the epoductio will stop whe the totl umbe of geetios eches specified mximum umbe o best fitess is costt fo while. The bsics of GA e descibed i the followig sectios. Codig The fist step i the GA is tsltig the el poblem ito biologicl tems. Fo this, ll vibles e epeseted by chomosomes d this pocess is clled codig. Thee e vious codig methods i the GA. The method pplied i this GA is deciml codig tht cosists of stigs of bits, 0 to 9. Selectio Slices umbe Figue 2 Fcto of sfety vs. slices umbe I ode to epoduce offspig, pets eed to be selected. The two most commoly used methods e the oulette wheel d toumet selectios. I the oulette wheel selectio, the chomosomes e ked i scedig ode bsed o thei fitess vlues, F j (j=1, 2, ). Next, pobbility vlue, P j, is ssiged to ech chomosome (j=1, 2, ) tht gives highe pobbility to the chomosome with highe fitess vlue. Afte kig the chomosomes ccodig to thei fitess vlues, the best chomosome is plced fist with the getest pobbility vlue (P 1 ) d the wost chomosome is plced lst with the lest pobbility vlue (P ). The pobbility vlues fo othe chomosomes e liely itepolted s: [3] The othe method is toumet selectio. I this method, smll subset of the chomosomes (two o thee chomosomes) is selected domly d the oe with the best fitess will be cosideed s pet. I some geetic lgoithms, elitism is pplied to keep the best chomosome i the ext geetio. Cossove The cossove sttegy detemies how the pet chomosomes e combied to geete offspig. Cossove is pplied domly to selected pis of pets with pobbility equl to specified cossove te. A sigle-poit cossove is the most popul opeto. Oe cossove poit is domly selected log the pet chomosomes. The coded bits fom the begiig of the fist pet to its cossove poit e copied to the fist offspig i the sme positio. The est of the bits fom the sme cossove poit of the secod pet to its til e copied to the fist offspig i the sme positio. This ctio is the coducted fo the secod offspig (Figue 3). Muttio Afte cossove is pefomed, muttio tkes plce. Muttio is the geetic opeto tht domly chges oe o moe of the chomosome s gees. The pupose of the muttio is to pevet the geetic popultio fom covegig to locl miimum d to itoduce ew possible solutios to the popultio. The muttio is cied out ccodig to the muttio te (Figue 4). Iitilizig GA pmetes A flow cht depictig the mjo opetios of the GA is show i Figue 5. To ehce the pefomce, the lysis is bsed o diffeet combitios of vious pmetes such s popultio size, selectio methods, cossove te d muttio te. T s c t i o P p e Figue 3 Sigle-poit cossove fo 27 gees legth chomosomes Figue 4 Muttio fo 27 gees legth chomosome The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER OCTOBER

4 Sept_83-88:Templte Joul 11/10/08 11:43 AM Pge 654 Slope modifictio of ope pit wll usig geetic lgoithm Figue 5 Mi flow cht of geetic lgoithm cossove te of Note tht the muttio te of cuses the GA to covege to locl optimum poits. Totl geetio Popultio size Figue 6 Totl geetio vs. popultio size Rock mss stegth pmetes The RMR ock mss clssifictio system9 ws utilized fo the ssessmet of dolomite wll stegth pmetes i the 6th Golbii Jjm buxite mie. As fist step, joit study d site ivestigtio wee cied out fo RQD d RMR detemitios. The esults fom these studies show tht thee e fou mjo discotiuities. The secod step ws ivolved i lbotoy tests d detemiig goudwte coditios tht c be used to ssess the RMR. The ucofied compessive stegth of itct dolomite specimes ws detemied i the lbotoy. The fidigs e show i Tble II. With espect to Tble II, the RMR B is clculted s follows: Me fitess Popultio size Figue 7 Me fitess vs. popultio size Geetio o. Popultio size The GA is implemeted fo popultio sizes betwee 10 to 30 chomosomes, with step of 5, d 15 epets fo ech step. As see i Figues 6 d 7, the totl geetio d me fitess vlues chge with popultio size. A popultio of 20 chomosomes c stisfy esoble fitess vlue. Selectio method The GA is executed fo the oulette wheel d the toumet selectio methods with 15 epets fo ech oe. As c be see i Figues 8 d 9, geetio umbe d me fitess vlues chge i ech epet. I geel, the toumet selectio is moe stble. Muttio d cossove tes The GA ws pplied fo muttio d cossove tes with 15 epets fo ech te. As c be see fom Figues 10 13, best esults chieved fo muttio te of d Figue 8 Geetio umbe vs. selectio methods Fitess vlues Figue 9 Fitess vlues vs. selectio methods 654 OCTOBER 2008 VOLUME 108 REFEREED PAPER The Joul of The Southe Afic Istitute of Miig d Metllugy

5 Sept_83-88:Templte Joul 11/10/08 11:43 AM Pge 655 Slope modifictio of ope pit wll usig geetic lgoithm Me geetio Me time Figue 10 Me geetio vs. muttio te Figue 13 Me time vs. cossove te T s c t i o Figue 11 Me time vs. muttio te Me geetio Figue 12 Me geetio vs. cossove te RMR B = = 56 Filly, the equied ock mss stegth pmetes wee clculted usig GSI (Geologicl Stegth Idex) d RocLb softwe10. With this egd, the Moh-Coulomb stegth pmetes, cohesive stegth(c') d fictio gle (φ') of the ock mss wee clculted to be MP d degees, espectively. Applictio of GA to fid the citicl cicul slip sufce To detemie the citicl slip sufce, the objective fuctio must fid the slip sufce with the miimum fcto of sfety. Ech popultio chomosome hs tee sectios: the fist d secod sectios e the X d Y coodites of the slip cicle, d the thid sectio shows the dius of the slip sufce. The GA is implemeted with iitil dom popultio of 20 chomosomes, usig the toumet selectio method, cossove te of 0.70, d muttio te of The citeio fo temitio of the lgoithm is to ech diffeece of 0.01 betwee the best fitess of cuet d pevious popultio chomosomes fo the lst 10 geetios o fo mximum of 50 geetios. The esults show tht the lgoithm coveged fte 21 geetios d ech the citicl slip sufce with fcto of sfety equl to The esults e show i Figues Slope modifictio Thee is sufficiet cotol of optimiztio betwee sfety d ecoomic pmetes i slope modifictio usig the GA. This is becuse most ecoomic svigs will be chieved with miimum emovl of the ustble sectios tht e mked. Slope modifictio uses sevel itetios d the best esult is gied fo 7 slope modifictio steps withi 27 geetios of GA (Tble III). Filly, fcto of sfety of 1.3 is eched fo slope gle of degees (Figue 17). P p e Tble II RMR pmetes d tigs. RMRB= Bsic RMR = Σ tigs 10 Pmete Itevls UCS (MP) > <1 Rtig * RQD (%) <25 Rtig * 8 3 SPACING (mm) > <60 Rtig * Coditio of Vey ough Slightly ough Slightly ough Slicke sided Soft gouge Discotiuities sufces No septio Septio < 1 mm Septio < 1 mm wlls O gouge < 5 mm >5 mm o septio Uwetheedwll ock Slightly wetheed wlls Highly wetheed o septio cotiuous Not cotiuous Not cotiuous Wlls 1 5 mm Rtig (16) * 10 0 Goudwte Completely dy Dmp Wet Dippig Flowig I joits 0 (0 0.1) ( ) ( ) -0.5 Rtig 15 * The Joul of The Southe Afic Istitute of Miig d Metllugy VOLUME 108 REFEREED PAPER OCTOBER

6 Sept_83-88:Templte Joul 11/10/08 11:43 AM Pge 656 Slope modifictio of ope pit wll usig geetic lgoithm Coclusio The peset ppe suggests slope modifictio method bsed o the GA fo loctig the citicl cicul slip sufce d modifictio of ustble mked sectios. The poposed techique hs simple stuctue d is esily pogmmble. I dditio, cse study hs bee peseted to demostte the cpbilities of the poposed ppoch. The esults show tht the GA c be successfully employed to locte the citicl filue sufce i homogeous ock mss slope, d the Simplified Bishop Method c be esily solved with the GA i ode to obti the fcto of sfety. The study o GA pmetes cocluded tht popultio size of 20, toumet selectio method, sigle poit cossove with the te of 0.7 d muttio te of 0.05 c locte the citicl cicul slip sufce. Filly, i cse study, slope modifictio ws implemeted usig the GA. The slope modifictio pocess of the southe wll of the 6th Golbii Jjm buxite mie temited by 7 slope modifictio steps withi 27 geetios. A fcto of sfety of 1.3 is eched fo slope gle of degees. Refeeces 1. BAKER, R. Detemitio of the citicl slip sufce i slope stbility computtio, Itetiol Joul of Numeicl d Alyticl Methods i Geomechics, vol. 4, pp ABRAMSON, L.W., LEE, T.S., SHARMA, S. d BOYCE, G.M. Slope Stbility d Stbiliztio Methods, Joh Wiley & Sos, Ic., New Yok, USA GOLDBERG, D.E. Geetic Algoithm i Sech, Optimiztio, d Mchie Leig, Addiso-Wesley, Msschusetts, USA GOH, A.T.C. Geetic Algoithm Sech fo Citicl Slip Sufce i Multiple- Wedge Stbility Alysis, Cdi Geotechicl Joul, vol. 36, pp MCCOMBIE, P. d Wilkiso, P. The Use of the Simple Geetic lgoithm i Fidig the Citicl Fcto of sfety i Slope Stbility lysis, Compute d Geotechics, vol. 29, pp US ARMY CORPS OF ENGINEERS, Slope Stbility-Egieeig d Desig, Deptmet of the Amy, USA ATAEI, M., GOSHTASBI, K. d KALATEHJARY, R. Assessmet of Dolomite Wll Filues i the 6th GOLBINI Jjm Buxite Mie by Usig SMR Clssifictio System, 7th Itetiol Scietific Cofeece-SGEM 2007, Bulgi HOLLAND, J.H. Adpttio of Ntul d Atificil Systems, the Uivesity of Michig Pess, A Abo, MI BRADY, B.H. d BROWN, E.T. Rock Mechics fo udegoud Miig, Secod Editio HOEK, E. Pcticl Rock Egieeig, 342 pp, Rocsciece Ic Figue 14 Lowest fcto of sfety vs. geetio umbe Figue 16 Citicl slip sufces i cosecutive geetios Figue 15 Best, vege d wost fitess vs. geetio umbe Figue 17 Steps of slope modifictio usig geetic lgoithm Tble III Slope modifictio detils Modifictio step Geetio umbe Sfety fcto of the citicl sufce Totl time (hh:mm:ss) 00:20:32 00:47:10 00:58:54 01:07:22 01:45:12 02:32:18 02:45: OCTOBER 2008 VOLUME 108 REFEREED PAPER The Joul of The Southe Afic Istitute of Miig d Metllugy