Universidad Pedagógica Y Tecnológica de Colombia, Escuela de Ingeniería de Minas

 

‐CMQMCYNQEWMCEÓJ HNBFNCÍJECM IN@ FMCEWB QBCBSB _MQM N@ _@MJ IN CENQQN U @E]^EIMCEÓJ IN @MS CMJYNQMS ^AECMIMS NJ @MS _MQQB]^EMS IN SMJ MJYBJEB IN _ECLEJCLM U IN _ÆJYMH‖  [1?1=V

‐CMQMCYNQEWMCEÓJ HNBFNCÍJECM IN@ FMCEWB QBCBSB _MQM N@ _@MJ IN CENQQN U @E]^EIMCEÓJ IN @MS CMJYNQMS ^AECMIMS NJ @MS _MQQB]^EMS IN SMJ MJYBJEB IN _ECLEJCLM (‐D^C^S^C^ EEE‖) U IN _ÆJYMH (‐NS_NQMJWM‖)‖  (‐NS_NQMJWM‖)‖  ^jevnrseimi _nimhóhecm U Yncjb`óhecm In Cb`bfaem, Nscun`m In Ejhnjenræm In Fejms.

Feynr Fmureceb Fb`ejm, Gumj Cmfe`b Fniejm, Íjhn`m @bjibýb Sbtb Feynr.fb`ejmOuptc.niu.cb  Gumj.fniejm==Ouptc.niu.cb  Gumj.fniejm==Ouptc.niu.cb Mjhn`m.`bjibjbOuptc.niu.cb  Mjhn`m.`bjibjbOuptc.niu.cb   Feynr.fb`ejmOuptc.niu.cb

QNS^FNJ @m ejvnstehmceój qun sn tbfm cbfb ngnfp`b tuvb cbfb bagntevb prejcepm` rnm`e rnm`ezmr zmr `m cmrmctnrezmceój hnbfncíjec hnbfncíjecm m in` fmcezb rbcbsb pmrm rnm`ezmr n` p`mj in cenrrn y `equeimceój in `ms cmjtnrms ‐Ducusucu EEE‖ y ‐Nspnrmjzm‖, pmrm nstb sn pmrteó in uj nstuieb hnb`óhecb y hnbfncíjecb m trmvås in` Fåtbib Aenjemwske (QFQ) nj cmim írnm, n` cum` pnrfeteó nstefmr `m cm`eimi in` fmcezb rbcbsb. Sn einjtedecmrbj zbjms in ejnstmae`eimi pmrm `ms cum`ns sn prbpusb ujm cbrrncceój nj `bs n`nfnjtbs hnbfåtrecbs in `bs tm`uins, cbj n` dej in hmrmjtezmr ujm nstmae`eimi tnfpbrm` iurmjtn `m ntmpm in bpnrmceój y ujm m `mrhb p`mzb iurmjtn `m ntmpm in `equeimceój, tbfmjib cbfb amsn `m tbpbhrmdæm in` írnm y sus cmrmctnræstecms hnbfncíjecms. (Cmezm`uesm Gícbfn & Creb``b Mjimhbym, 1?=>) _m`marms c`mvn7 Hnbfncíjecm, nstmae`eimi, iesnýb, nxp`btmceój, `equeimceój, rnsnrvms.

Mastrmct  Yln rnsnmrcl tlmt es tmknj ms mj nxmfp`n lmi ms ets fmej bagnctevn tb cmrry but tln hnbfnclmjecm` clmrmctnrezmtebj bd tln rbck fmss tb cmrry but tln c`bsurn mji sntt`nfnjt p`mj dbr tln ‐Ducusucu EEE‖ mji ‐Nspnrmjzm‖ qumrrens, dbr tles m hnb`bhecm` mji hnbfnclmjecm` hnbfnclmjecm` stuiy wms stmrtni tlrbuhl bd tln Aenjemwske Fntlbi (QFQ) ej nmcl mrnm, wlecl m``bwni nstefmtejh tln qum`ety bd tln rbck fmssed. Ejstmae`ety zbjns wnrn einjtedeni dbr wlecl m cbrrnctebj wms prbpbsni ej tln hnbfntrec n`nfnjts bd tln s`bpns, ej brinr tb humrmjtnn m tnfpbrmry stmae`ety iurejh tln bpnrmtebj stmhn mji m `bjh-tnrf stmae`ety iurejh tln sntt`nfnjt stmhn, amsni bj tln tbpbhrmply bd tln mrnm mji ets hnbfnclmjecm` clmrmctnrestecs. Knywbris7 @efnstbjn, fejejh insehj, hnbtncljecm` stuiens, mjm`yses, sbe` prbpnrtens, fejejh suppbrt.

=. EJYQBI^CCEBJ. =.= HNJNQM@EIMINS. Nj n` Ncumibr, vmrems in `ms cbjcnsebjns fejnrms iniecmims m `m nxp`btmceój in fmtnrem`ns påtrnbs jb cufp`nj cbj `ms fnieims in nstmae`eimi in tm`uins qun hmrmjtecnj `m snhureimi in `bs trmamgmibrns y

prbynctb fejnrb m cen`b maenrtb cbjseinrm ``nvmr m cmab `m cmrmctnrezmceój hnb`óhecb-hnbtåcjecm in` fmcezb rbcbsb y `m nvm`umceój in `bs íjhu`bs in tm`ui. _mrm ``nhmr m uj iesnýb hnbtåcjecb mincumib in `m cmjtnrm tmjtb nj `m ntmpm in bpnrmceój cbfb nj `m in cenrrn ns jncnsmreb tnjnr nj cunjtm `bs

qun m su vnz pnrfetmj uj aunj mprbvnclmfenjtb in` rncursb. @m nstmae`eimi in tm`uins sn nvm`÷m fniemjtn ievnrsbs pmrífntrbs cbfb Fmreb Fbrm`ns (1??5) mderfm7 ‐^jm ntmpm dujimfnjtm` in tbib

pmrífntrbs hnbfåtrecbs prbpebs in` tmgb maenrtb, ym qun n` prbcniefenjtb pmrm rnm`ezmr `m nxp`btmceój qunim indejeib pbr `m mp`ecmceój in ujbs pmrífntrbs b cretnrebs in iesnýb in `m nxcmvmceój, qun pnrfetnj

 

‐CMQMCYNQEWMCEÓJ HNBFNCÍJECM IN@ FMCEWB QBCBSB _MQM N@ _@MJ IN CENQQN U @E]^EIMCEÓJ IN @MS CMJYNQMS ^AECMIMS NJ @MS _MQQB]^EMS IN SMJ MJYBJEB IN _ECLEJCLM U IN _ÆJYMH‖  [1?1=V

m`cmjzmr `ms prbiuccebjns prbhrmfmims, prbhrmfmim s, in `m dbrfm fís ncbjófecm pbsea`n y nj `ms fíxefms cbjiecebjns in snhureimi. @bs pmrífntrbs hnbfåtrecbs prejcepm`ns qun cbjdehurmj n` iesnýb sbj7 amjcb, m`turm in amjcb, tm`ui in amjcb, tm`ui in trmamgb, `efetns dejm`ns in `m nxp`btmceój, tm`ui dejm` in nxp`btmceój, anrfms, pestms y íjhu`b in rnpbsb in` fmtnrem`. =.1 ^AECMCEÓJ. @m cbjcnseój cbjcnseój fejnrm ‐Ducusucu EEE‖ cunjtm cbj ujm supnrdecen in 1> Lm fejnrms, sn uaecm m` Jbrtn in `m ceuimi in ]uetb nj `m _mrrbquem Smj Mjtbjeb in _eclejclm, snctbr in Qufecuclb. (DEH. =) @m cbjcnseój fejnrm ‐Nspnrmjzm‖ cóiehb 9??=1? pbsnn ujm supnrdecen in 1? Lm fejnrms mprbxefmimfnjtn y sn uaecm nj `m prbvejcem in _eclejclm, cmjtój ]uetb nj `m pmrrbquem in _æjtmh. (DEH. =)

suacunjcms (Deh. 1)7 Cunjcm Clbtm, Cunjcm ]uetb Cunjcm Mfamtb y Cunjcm Qebamfam. @m zbjm in nstuieb sn uaecm nspncædecmfnjtn nj `m Cunjcm ]uetb, cbjsestn nj uj rn``njb vu`cmjb sniefnjtmreb in inpósetbs vb`cíjecbs y vb`cmjbc`ístecbs. N` prbynctb fejnrb @m Nspnrmjzm rnhebjm`fnjtn sn uaecm in fmjnrm trmjsecebjm` njtrn n` vm``n ejtnrmjiejb y n` d`mjcb Bnstn in `m Cbrie``nrm Qnm`, senjib nstm ÷`tefm uj cejturój m`mrhmib in rufab JJN cbj ujm `bjhetui in 4>? kf y 4? kf in mjclb. Ieclb cejturój nstí dbrfmib pbr tnrrnjbs fntmfórdecbs in brehnj bcníjecb y cbjtejnjtm`, in jmturm`nzm mutóctbjm y m`óctbjm y nimi _m`nbzbecm  –  –   Fnsbzbecm. N` amsmfnjtb in `m zbjm in nstuieb nstí cbjstetueib pbr `m ^jeimi Cuyugm, cbjdbrfmim pbr nsquestbs, sbarn `m cum` ymcnj iescbrimjtnfnjtn `bs vb`cíjecbs _esmymfab cbjstetueim pbr rbcms mjinsætecms - reb`ætecms y perbc`mstbs, `ms fesfms qun ejdrmymcnj m` d`ugb in `mvm Mjtesmje``m in cbfpbseceój mjinsætecm – mjinsætecm  –amsí`tecm. amsí`tecm.  

1.1 @BCM@. D^C^S^C^ EEE Snh÷j n` nstuieb Hnb vb`cmjb`óhecb in` Cbfp`ngb Tb`cíjecb _u`u`mlum (CT_) sn iednrnjcem7 ^j amsmfnjtb _`ebcåjecb in `m pmrtn N in` CT_ mtreaueib m `m Dbrfmceój _esqun y ujm ^jeimi Tb`cíjecm injbfejmim ibfbs prn - cm`inrm góvnjns in nimi _`nestbcnjm Ymriæm. Dbrfmceój _esqun (_`_e) Cbjstetueim pbr `mvms, arnclms mjinsætecms mfmre``njtms, tbams y `mlmrns cbjsb`eimibs Ibfbs prn-cm`inrm Góvnjns (_IG) Cbjstetuynj uj hrupb in ibfbs imcætecbs, senjib `bs d`ugbs ‐a`bck mji msl‖ sus inpósetbs cmrmctnræstecbs 

NS_NQMJWM

Dehurm =7 ^aecmceój in `ms fejms D^C^S^C^ EEE y NS_NQMJ NS_NQMJWM WM

1. HNB@BHEM. 1.= QNHEBJM@. @m cbjcnseój fejnrm rnhebjm`fnjtn nj n`

Ducusucu EEE sn uaecm Tm``n Ejtnrmjiejb, qun

cbjstetuyn ujm inprnseój tnctójecm hnbfbrdb`óhecm, `efetmjib m` Nstn cbj `m Cbrie``nrm Qnm` y Bnstn cbj `m Cbrie``nrm Bcceinjtm` in` Ncumibr. In Jbrtn m Sur ieveieim nj cumtrb

@m nxp`btmceój in `bs fmtnrem`ns nj `m cmjtnrm sn `m rnm`ezm nj n` d`ugb in `mvm in` Mjtesmje``m, qun pbsnn ujm `bjhetui mprbxefmim in ==kf y uj mjclb vmrema`n (?.> m 1kf). N` d`ugb prbvenjn in ibs vnjtbs qun sn nxtnjieó pbr n` vm``n h`mcemr in Funrtb _ujhb, bcupmjib uj irnjmgn prejcepm` in` írnm qun bastmcu`ezó `m sm`eim in mhum prbiucenjib msæ `m dbrfmceój in `mhujms, `m cbfpbseceój in `m rbcm cbrrnspbjin m ujm mjinsetm cbj b`evejb y cumrzb sncujimreb, cuyms prbpenimins dæsecb  –  –   fncíjecms sbj nxcn`njtns.

 

‐CMQMCYNQEWMCEÓJ HNBFNCÍJECM IN@ FMCEWB QBCBSB _MQM N@ _@MJ IN CENQQN U @E]^EIMCEÓJ IN @MS CMJYNQMS ^AECMIMS NJ @MS _MQQB]^EMS IN SMJ MJYBJEB IN _ECLEJCLM U IN _ÆJYMH‖  [1?1=V

Dehurm 17 Cbrrn`mceój Nstrmtehrídecm tnjtmtevm nj `ms Cunjcms In EMT

3. CMQMCYNQEWMC CMQMCYNQEWMCEBJ EBJ D^C^S^C^ EEE 3.= CMQMCYNQEWMC CMQMCYNQEWMCEBJ EBJ QBCBSM

HNBYNCJECM IN

@M

IN

FMYQEW

_mrm rnm`ezmr `m nvm`umceój hnbfncíjecm in` fmcezb rbcbsb `m cmjtnrm dun ieveieim nj cejcb zbjms in mcunrib m sus cmrmctnræstecms hnbfåtrecms (Tnr Dbtbhrmdæm =), nj cmim zbjm sn nstuiemrbj `bs iestejtbs amjcbs nxestnjtns, fesfbs qun m su vnz sn ieveienrbj nj trmfbs inaeib m sus rmshbs `etb`óhecbs y nstructurm`ns. @bs imtbs rncb`nctmibs dunrbj 15>, fesfbs qun sn rnhestrmrbj nj `m fmtrez prbpunstm pbr Aenjemwske, m trmvås in` prbhrmfm in mjí`eses nstructurm` sn iestejhuenrbj cumtrb dmfe`ems in iescbjtejueimins. Amsmib nj n` nstuieb Nvm`umceój in `m nstmae`eimi nj tm`uins rbcbsbs. Mp`ecmceój in` SFQ fniemjtn uj SEH, sn n`mabrmrbj Slmpnde`ns pbr cmim dmfe`em, ibjin sn ejtnhrmrbj `bs vm`brns in `bs pmrífntrbs nvm`umibs. _mrm `m hnjnrmceój in uj fmpm QFQ pbr dmfe`em, m trmvås in` í`hnarm in fmpms sn ejeceó cbj `m rmstnrezmceój in `bs pmrífntrbs rnqunreibs pbr Aenjemwske, ``nhmjib msæ m uj fmpm QFQ dejm` in `bs tm`uins nstuiemibs.

Dbtbhrmdæm =7 Cmjtnrm Ducusucu EEE ieveieim nj zbjms in nstuieb

Cm`eimi in` fmcezb rbcbsb pbr n` fåtbib Aenjemwske (QFQ).   M cbjtejumceój, sn nvm`÷m `m rnsestnjcem m `m cbfprnseój sefp`n. @bs rnsu`tmibs batnjeibs m trmvås in` njsmyb in cbfprnseój sefp`n sn lmj prbfniemib pmrm `m pbjinrmceój in Aenjemwske. (Tnr Yma`m =) Yma`m =7 Qnsu`tmibs in `bs njsmybs in cbfprnseój sefp`n

3.1 CMQMCYNQEWM CMQMCYNQEWMCEBJ CEBJ IN @MS IESCBJYEJ^EIMINS Nspmcemib7   N` nspmcemib njtrn `bs p`mjbs in iescbjtejueimi vm insin gujtms lmstm fuy gujtms, vmremjib nj uj rmjhb in ?.??1f m 0 ?.1f (Hrídecb =). Jb sn msehjó uj vm`br in nspmcemib nj `bs trmfbs ibjin n` fmcezb sn njcunjtrm m`tmfnjtn treturmib inaeib m qun jb sn iestejhunj p`mjbs in iescbjtejueimi.

 

‐CMQMCYNQEWMCEÓJ HNBFNCÍJECM IN@ FMCEWB QBCBSB _MQM N@ _@MJ IN CENQQN U @E]^EIMCEÓJ IN @MS CMJYNQMS ^AECMIMS NJ @MS _MQQB]^EMS IN SMJ MJYBJEB IN _ECLEJCLM U IN _ÆJYMH‖  [1?1=V

Qn``njb7   N` rn``njb qun prnibfejm nj `ms iescbjtejueimins ns a`mjib 0 >ff (Hrídecb 9) y in `m fesfm cbfpbseceój in` fmcezb rbcbsb.

Hrmdecb =7 Nspmcemib njtrn iescbjtejueimins Ducusucu EEE

 –

  Cmjtnrm

Quhbseimi7   @m supnrdecen in ruhbseimi vmræm in p`mjms ruhbsms m p`mjms `esms (Hrídecb 1).  

Hrmdecb 97 Qn``njb nj `ms iescbjtejueimins - Cmjtnrm Ducusucu EEE

Cbjtejueimi7   @m pnrsestnjcem nj `m fmybræm in iescbjtejueimins vmj insin amgms m fuy amgms ym qun `bs vm`brns bsce`mj njtrn 3f y 0=f. (Hrmdecb >)

Hrmdecb 17 Quhbseimi in `ms iescbjtejueimins - Cmjtnrm Ducusucu EEE

 M anrtur m7   @ms iescbjtejueimins prnsnjtmj ujm

manrturm fbinrmimfnjtn maenrtm cbj vm`brns in 1.>ff - =?ff (Tnr Hrídecb 3).

Hrmdecb >7 Cbjtejueimi in `ms iescbjtejueimins - Cmjtnrm Ducusucu EEE

9. CMQMCYNQEWM CMQMCYNQEWMCEÓJ CEÓJ NS_NQMJWM. 9.= CMQMCYNQEW CMQMCYNQEWMCEBJ MCEBJ QBCBSM.

Hrmdecb 37 Manrturm njtrn iescbjtejueimins - Cmjtnrm Ducusucu EEE

HNBYÅCJECM IN

@M

IN

FMYQEW

@m nvm`umceój hnbfncíjecm in` fmcezb rbcbsb sn rnm`ezó nj md`brmfenjtbs pujtum`ns in` d`ugb in `mvm in cbfpbseceój mjinsætecm amsí`tecm cbj perbxnjb, inaeib m qun iurmjtn `bs snes fnsns qun ``nvm bpnrmjib `m cmjtnrm sn lm nxp`btmib `m mutb arnclm, ingmjib m` inscuaenrtb `m pmrtn fmsevm in` d`ugb. Q ns nses es tnjcem tnjcem m `m cbfprn cbfprnss eój s efp` efp`n. n. In mcunrib m` Ejdbrfn Snfnstrm` in _rbiucceój ‐Nspnrmjzm‖

 

‐CMQMCYNQEWMCEÓJ HNBFNCÍJECM IN@ FMCEWB QBCBSB _MQM N@ _@MJ IN CENQQN U @E]^EIMCEÓJ IN @MS CMJYNQMS ^AECMIMS NJ @MS _MQQB]^EMS IN SMJ MJYBJEB IN _ECLEJCLM U IN _ÆJYMH‖  [1?1=V

_refnr Snfnstrn -1?=>, `m rnsestnjcem in `m rbcm m `m cbfprnseój sefp`n supnrm `bs 1??? kh/cf1, nstn vm`br sn uaecm nj n` rmjhb =?? -1>? F_m snh÷j `m tma`m prbpunstm pbr Aenjemwske, msehjíjib`n ujm vm`brmceój in =1 qun ejiecm ujm rnsestnjcem fuy m`tm.

9.1 CMQMCYNQEWMC CMQMCYNQEWMCEBJ EBJ IESCBJYEJ^EIMINS

IN

@MS

Nspmcemib7   N` nspmcemib njtrn `bs p`mjbs in iescbjtejueimi vmj insin snpmrmibs lmstm fbinrmimfnjtn gujtbs, qun bsce`m njtrn ?.1f m 1f (Hrídecb 4).

Hrmdecb ff y prnsnjtm `m fesfm cbfpbseceój in` fmcezb rbcbsb, msehjíjib`n uj vm`br in 9 (hrmdecb 5).

Hrmdecb 47Nspmcemib Nspnrmjzm

njtrn

iescbjtejueimins

 –

  Cmjtnrm

Quhbseimi7   @m supnrdecen nj tbibs `bs p`mjbs in iescbjtejueimins sn cmrmctnrezm pbr snr bjiu`mim ruhbsm (Hrídecb 8). Hrmdecb 57 Qn``njb nj `ms iescbjtejueimins - Cmjtnrm Nspnrmjzm

 @bs p`mjbs in iescbjtejueimi pbsnnj Cbjtejueimi7 ujm pnrsestnjcem amgm y m`tm inaeib m qun vmræmj njtrn = m =?f (Tnr Hrídecb =?).

Hrmdecb 87 Quhbseimi in `ms iescbjtejueimins Nspnrmjzm

 –

  Cmjtnrm

 M anrtur m7   @m

manrturm qun prnsnjtmj `ms iescbjtejueimins ns fmybr m =?ff, cmtm`bhíjib`ms cbfb maenrtms (Tnr Hrídecb . CBJC@^SEBJNS In mcunrib m `m cmrmctnrezmceój hnb`óhecm in `m Cbjcnseój Fejnrm Ducusucu EEE sn iestejhun ujm `etb`bhæm prbpem in uj ibfb imcætecb, senjib `m ujeimi Imcetm cbj mjdæab` y perbxnjb `m qun md`brm fmybrfnjtn y n` prejcepm` rncursb nxp`btma`n; tmfaeåj sn einjtedecó `m prnsnjcem in `m ujeimi Imcetm cbj mjdæab` pbsnn ujm tbjm`eimi rbgezm prbiuctb in `m bxeimceój tnrfm` qun md`brm m` S y B in `m cmjtnrm; dejm`fnjtn sn basnrvó `m prnsnjcem in uj inpósetb in tepb ‐a`bck mji msl‖, n` fesfb qun cbrrbabró qun n` fmtnrem` in nxtrmcceój cbrrnspbjin m uj ibfb vb`cíjecb. @m cmrmctnrezmceój hnbfncíjecm rnm`ezmim pbr n` Fåtbib in Aenjemwske (=5). (1?=>). Cmrmctnrezmceój Cmrmctnrezmceój Hnbfncíjecm Hnbfncíjecm In` Fmcezb Qbcbsb _mrm N` _`mj In Cenrrn U @equeimceój In @ms Cmjtnrms ^aecmims Nj @ms _mrrbquems In Smj Mjtbjeb In _eclejclm ( ‐‐ Ducusucu D  )  U In _æjtmh ( ‐ ‐Nspnrmjzm N  )‖ .   ucusucu Eee ‖  ‖   spnrmjzm ‖