Investigating continuous time open pit dynamics

Size: px

Start display at page:

Download "Investigating continuous time open pit dynamics"

Oswald Welch
5 years ago
Views:

1 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 61 Sy Ivgg uu m dym by H. Ak-Nb*, S. Fmg, d J. Szymk* Cu m du lg, hdulg, d ll f u bd mhml gmmg mdl. I, h mzd lu b d whu xmg ll bl mb d mu f h x qu. O h mhd hv lmd l lg-l uf mg bu h umb f vbl bm lg. h my bjv f h udy dvl d mlm hybd mul fmwk f h hdulg blm. h vg h dym f gmy d h ubqu ml mvm uu ym dbd by m-dd dffl qu. h uu mul (COS) mlmd MALAB, bd mdfd lll fuum ud mdl h vlu f gmy m d. D mul (DOS) mm h d x f h lyu. Fu xm f h d muld uh-bk vd h m v h f l dffl qu (DE), ug h dym f lyu, ym f dy dffl qu (ODE). Numl g wh h Rug-Ku hm yld h jy f h gmy v m wh h v vlum f ml d h vlu (NV) f h mg. A udy f m wh blk w d u vfy d vld h mdl. h mzd lm w dgd ug Lh-Gm lghm. h b- ul hdul, gd by h hll d Whl Fu-X yldd NV f $449 mll v 21-y m lf du f 10% um. DOS b u f mul uld NV f $443 mll d COS yldd NV f $440 mll v h m m. h hybd mul mdl h b f fuu h ug fm lg bd gl-dd llg g. Idu h fl lm mz lghm vlly h f ulm u, whh mxmz h l um f h f f ll h blk h u. h ml fl lm m ky f lgm g lg. Cu lghm um h h u dug whu dg h m f h blm. h lg f m d h ml u f h xl dm h qu f blk x d mxmz h gd m hughu h lg d. M lg m x d by glgl, g, hlgl, d ll fld. h m lg mdl uully df d f lg hz. h mdl uully m mxmz h dud vlu f f1 6, mz h l fdg d7 10. Hu mhd, m m ly, h, d g lghm hv b ud fmul d lg blm. O dg, mz, d ubqu ml hdulg gvd by h dym. hu, u lghm lmd h bl dd h blm g fm h dm d dym fld 11,12. I, h mzd mg hdul b d whu xmg ll bl mb d mu f h x qu. hf, lv lg dul blm wh ffy, ul dl wh h lm f mug u, m d. h m u f h udy mdl h dym f gmy d h ml mvm uu ym dbd by m-dd dffl qu. h mul u gml mdl bd mdfd lll fuum13 u h hg f h gmy d h ubqu ml mvm. A f l dffl qu (DE) u h m-ld bhvu f h mg ym. Mly h f f h DE d llw uqu lu h blm, * Shl f Mg d lum Egg, Uvy f Alb, Edm, Alb, Cd. Dm f Mg d Nul Egg, Uvy f Mu-Rll, Rll, USA. h Suh Af Iu f Mg d Mllugy, SA ISSN X/ vd A. 2007; vd vd A h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER FEBRUARY

2 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 62 Ivgg uu m dym bu df gl mu b gd. hf, h d f ddl fm d uxly d b uqu lu. h d h mul mdl14 ud yld h ddl d uxly d dd v h f DE f dy dffl qu (ODE). h d du mul13 (DOS) mm h d x f h lyu. h f h m x mdl (EEM) wh h glgl d m blk mdl u h v mu f, w, kl ml, d h vlu (NV) f h vu. h mul u ud dff wh uff umb f yld h qu f x, whh mxmz h NV, ubj ll h udlyg. Fu xm f h d muld uh-bk vd h fmwk du h umb f dd vbl, d v h f DE ym f ODE. Numl g wh h Rug- Ku15 hm yld h jy f h gmy v m wh h v vlum f ml fd. I f h uu mul (COS) wh EEM u h h flw f h mg hughu h m lf. h du h hl fmwk f h udy bd gml mdl, uu m dym, d h m x mdl. I COS mdl, l m, d mv ly f COS v. DOS hdul. h NV f h b- hdul, gd by m ly ug Whl Fu-X16 fw, md h ul f DOS. Gml mdl f lyu O d w x fm m k l dff lv. h xd hzlly d vlly wd h fl lm. h m lg-m bjv m quy d quly g f du d mxmz h mk vlu f h mg vu. h hf d f mdl h u h vlu f h gmy h xd hugh m d. Fmg l.11 vdd b f ug h ld gmy f lll fuum mdl h x. h um udlyg h lll fuum u dbl vlum mu. du h, m lbl, mdfd lll fuum mdl w d by Ak-Nb l.13. h mdfd gmy f fu qud f lll fuum, whh dd lg h mj d m x f h lld. Fgu 1 llu h mdfd lll fuum, whh dfd by w lld wh A 1 d A 2 d by vl d h. h mdl dvd h fu, h-w, h-, uh-w, d uh-. Eh dfd by h mj d m x f h v lld. h vll bl l θ dfd f h g dg h k l bly d gmhl ud. h vlum f ml h gv by qu f h vlum f Equ [4]. bl I llu vbl dfg qud. h f h d bm lld, dfg h fuum, gv by Equ [1], [2], d [3]. h l vlum f ml h fuum gv by Equ [4]: Fgu 1 Mdfd gml fuum mdl bl I Fuum vbl h g f Rg Mj x (m) M x (m) Sl (dg) A (m 2 ) NW W b N θ NW A NW NE E b N θ NE A NE SW W b S θ SW A SW SE E b S θ SE A SE [1] [2] [3] [4] 62 FEBRUARY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

3 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 63 Ivgg uu m dym Cuu mdllg f dym h mh f lyu x dd h du, whh fu f vl vbl. h vbl lud: () vlum f v v; () v gmy; () d m lf; (v) y f ldg d hulg fl; (v) umb f v ldg qum; (v) umb f v wkg f; (v) mllg d g l y; (v) mll hd gd; d (x) d wkg d. A ufm fd qud m h l ml y dug h m lf. Cuu mdllg f dym vlv hz f h hg md h gmy f h d h vlum f ml mvd by f dffl qu. I gl, h mdl d hv ly lu, d qu ug xm lu mhd uh f lm, f dff, budy lm. Dz f h dym h f fg h uu mdl d qu d u. ylly dz vlv lg h g f f mll lm, dug d xm f h dffl qu h lm, d h lvg ll f h d xm mululy. h l vlum f ml fd hughu h x gv by Equ [4] b d h dffl hg vlum f ml by Equ [5]. h dffl hg vlum, ΔV, fu f h fl z, F ; fl y, F ; vlbly, A; ulz, U; yl m, C ; h l dy f ml, γ l ; d h lll fuum m, φ 2. m f Δ W, Δ E, Δb N, Δb S d Δh. S V wll b fu f fv vbl W, E, b N, b S, d h. V, ( W, E, b N, b S, h) umd ly fu, ll dvv wuld x. A ul, V b d by yl x fv vbl. h glzd fm f yl x f l fu vbl17 gv by: Adgly, h yl x f fu V ( W, E, b N, b S, h) fv vbl gv by Equ [7]: Ug h d d xm Equ [7] yld Equ [8]: [6] [7] [8] [5] h gml mdl u h uh-bk ul f m f h wh gd xm. h mdfd lll fuum wll hv m lm lulg h vlum f ml vy gul hd. Cu h fug dvlg mul mdl f dym f h bh ly. h ul xd b bl vm h u f vy gul h. DOS13, bd M Cl mul mhd, u f qully bbl muld lz f h lg-m m l. O f h lz wuld b h gud f h lg-m l, whh b f h bjv f h mgm. Af h vl f h g l, h x bk g d hvbl g wh h fmwk f l l. COS g hdul bd h m d udlyg h g l. I df d g wh h m fm. h mu f hg vlum gv by Equ [5] dd h du lg d hdulg qum. A h g h gl dg du mk fml hg Equ [5] wh hg m f fu φ 2. h ul wll b qul ΔV wh y hg du m, Δ. Ovll l dff g θ NW, θ NE, θ SW, θ SE, umd b v h g. h hg m f fu θ 1 (F, F C, A, U, C, γ l ) wll hv d ff ΔV, whh dfd Adg Equ [8], h hg vlum f h gmy y f d f m, Δ, uld b ud f l dffl qu. h budy d udlyg Equ [8] h l bx u d h fl lm gmy. h vlum f fu gv by Equ [4]. h f d, d d, d m l dvv Equ [8] dvd fm Equ [4]. h d Δ W, Δ E, Δb N, Δb S, d Δh fu f m. Ful xm f DOS mul ul ud yld h ddl d dd v h f DE ym f ODE. DOS u h fbl mg m Δ W, Δ E, Δb S, Δb N, d Δh h d f h d f du. DOS mul bul d f h m v h m lf. d ly d uv fg ud xm fu f m Δ W, h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER FEBRUARY

4 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 64 Ivgg uu m dym Δ E, Δb S, Δb N, d Δh v h m lf. h m d fu f m. Subu f h xmd ml fu f Δ W, Δ E, Δb S, Δb N, d Δh, Equ [8], d lm f h l dvv dvd fm Equ [4] Equ [8], v h f DE ym f ODE wh m h ly dd vbl. hu, h hg h vlum f h fuum wll h hg dh, mj, d m x f h fuum d fu f m gv by Equ [9] [14]. [9] h uml g f h ym f ODE fd by Equ [15] u h bhvu f hll x v m. h ul l gud f h h-m du lg. h m mmly ud fmly f uml g hm, Rug-Ku15, ud by COS u h dym f h uu-m ym dbd by h f ODE gv by Equ [15]. h hybd mul mdl bv mb f d d uu-m mhml mdl, uml lu, d ly hqu u h dym f d ml mvm vm. [10] [11] [12] [13] [14] Em x mdl A uful lg mdl mu b bl l h dym f h wh h glgl d m blk mdl. Suh mdl mu yld gd f, kl, d m ml. I mu l vd h mu f d w mvd bh-by-bh b, wll, h m f h uh-bk dg f h d f h mg. EEM l h mdfd gml mdl h m blk mdl, d u h my vlu, vg gd f, w, d kl ml y dd d f du. Fgu 2 llu hw EEM f h gml mdl h m blk mdl. h f h h f Equ [9] [14] wh h v budy d d Equ [15] [17]. [15] Wh: [16] Z [17] Fgu 2 Em x mdl 64 FEBRUARY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

5 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 65 Ivgg uu m dym ll ld h xv g. h du hg h m blk mdl lvl by lvl. I h lvl, h d bw h f h ll d h f h u blk dd by Equ [19] md h lgh f h d f h ll gv by Equ [24]. Afwd, d md whh h blk d h fuum. I h fllwg fmul d Fgu 2: C(x 0, y 0 ) = f h ll; (x 0, y 0 ) = g f x; α j = h gl bw h f h ll d h blk (,j ) dd by Equ [18]; k=0,1,,-1, umb f lvl h blk mdl; h = bh hgh; d = h d bw h f h blk d h f h ll dd by Equ [19], = h d bw h f h ll h m h d f d gv by Equ [24]. h qu f h ll fllw: [18] [19] [20] I l d, h gl α j Equ [18] lld h gl. Subug h l qu C d Equ [20] d lvg f wll yld Equ [24]. [21] [22] [23] [24] h du m fm Equ [24] wh d fm Equ [19] dd f h blk h u. h u flly u h vlum f, w, kl ml, d h v gd, d h h flw f h muld uh-bk. Cuu mul COS hybd mul mdl mlmd MALAB, bd h mdfd gml mdl, h ym f DE ug h uu-m dym, d h m x h hm. h f f h uu-m dym ym f DE wh h v budy d gv by Equ [9] [14] d llw uqu lu h lg-m hdulg blm. h bly fly my lu h f DE, h wd h my uhbk dg h dl h bdy fm h l bx u h fl lm. Wh gl ODE hv lu h fml wh h lu hzd by h vlu f m m, f DE h lu f mzd by fu. Ifmlly u, h m h h f lu muh lg. hf, h d f ddl fm d d b uqu lu h uu-m x mdl, whh f h mgm bjv v m. DOS ud yld h ddl d uxly d dd v h f DE f ODE. D mul ud u h lyu vlu ul f ml mvm hughu h m lf. DOS mul h ml mvm mg d d vlu h d f vy d f x. h mul u ud dff wh uff lz yld h qu f x, whh mxmz h NV ubj ll h udlyg. Fgu 3 dm h DOS flw h. h mul g bbly dbu fu f ml uh-bk f Δ E, Δ W, Δb N, Δb S, d Δh. Ug M Cl mhd, h mul ml fm ml uh-bk dbu d wh EEM. Adgly d h d hg h gmy, whh mxmz h NV mg ll h mul lz. h DOS uu h u f COS, wh h f DE vd f ODE d lvd by Rug-Ku g hm. h b um f h d mul ud h u f h uu mul mdl. h b uv f ud xm fu f h ml uh-bk Δ E, Δ W, Δb N, Δb S, d Δh gd by DOS. Numl g f h ym f ODE g h uu jy f hg h gmy, wh v vlum f, w, kl ml d h NV f h vu. h f vgg h dym wh uu-m ym hzd by h f ODE gv by Equ [15] g b j. S m dy dffl qu lubl lylly, uml g h h b fm bu h jy. My dff mhd hv b d d ud lv uly vu y f dy dffl qu. Hwv, h hdful f mhd kw d ud uvlly (.., Rug-Ku, Adm-Bhfh-Mul d Bkwd Dff Fmul mhd). All h mhd dz h dffl ym du dff qu m. h uml mhd hv h m m h h dym f h m huld d lly h dym f h dffl qu15. MALAB u xl Rug-Ku d d45 u, whh ud gg Equ [15] COS. h lu f h uu ym u h j f hg mj d m x f h fuum wll h vlum f ml fd. h, h lu d h EEM. h hm u h blk h uh-bk dg u, vlu f h muld hdul, d h vlum f d w. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER FEBRUARY

6 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 66 Ivgg uu m dym Fgu 3 DOS d COS flwh 66 FEBRUARY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

h fl lm gmy ud by h lll fuum mdl wh m, W, E, b N, b S, d h, h u DOS f mul f h l uh-bk. h NV f h b- d, dgd wh Whl Fu-X md h ul f h b- DOS mul.

7 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 67 Ivgg uu m dym Fgu 4 3D vw f h d Bh # Bh # Fgu 5 g f - bh Numl l f COS A udy f d d u vfy d vld h mdl. h udy ud h fllwg um: () kl ml hdlg w dd; () bldg f ml w dd; () h mll hd gd d h ul mll fd w gd qum. h fl lm dmd ug h LG lghm18, ug Whl Fu-X16 fw. h fl lm gmy ud by h lll fuum mdl wh m, W, E, b N, b S, d h, h u DOS f mul f h l uh-bk. h NV f h b- d, dgd wh Whl Fu-X md h ul f h b- DOS mul. h d xld wh 159 xl dll hl d 113 fll dll hl llg m f dllg. h y f, mg; xd; d bm mg lfd h d. g l bd mg h m d ml fm m h wgh vy. Kgg ud buld h glgl blk mdl19,20. h mll blk vlum f k qul 20 m x 10 m x 15 m. h mdl blk h mk mdl fmwk wh dm f 95 x 80 x 15. Fgu 4 llu mul - f h d lg , h, d lv f m. h blk mdl lm 243 mll f dd u f wh h vg gd f 63%. Fgu 5 llu h vg gd, l mu f, d bh-by-bh b. Sl bly d g-mhl ud mmdd 43 dg vll l ll g. h m blk mdl bd : () mg = $2/; () g = $2/; () llg = $14/ (F); (v) mxmum mg y = 20 M/y; (v) mxmum mllg y = 15 M/y; (v) dy f d w = 4.2 /m3; (v) ul du = 10%. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER FEBRUARY

h mzd fl lm hw h l mu f 343 mll f ml g f 201 mll f d 142 mll f w. h b- lg-m hdul dgd wh m ly Whl Fu-X hw NV f $449 mll f 21-y m lf.

8 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 68 Ivgg uu m dym h dm f h fl lm ud by mdfd lll fuum d dgd wh Whl Fu-X dfd : W = 1 040m; E = 440 m; b N = 260 m; b S = 360 m; d h = 120 m. DOS w ud u h mul wh wh dff f mg g. h b- hd g d h, whh ld d h mll gd by d Whl Fu-X fw. Fgu 6 dm h uh-bk f h b hdul muld by DOS f y h mzd fl lm hw h l mu f 343 mll f ml g f 201 mll f d 142 mll f w. h b- lg-m hdul dgd wh m ly Whl Fu-X hw NV f $449 mll f 21-y m lf. h ul f h DOS hdul ud h m um wh qul m lf, mxmum ul du, d mllg y dm NV f $443 mll. h b- mul ul f DOS, wh h hgh NV ud h u f COS. h ul ml uh-bk gd by DOS h d hg f Δ W, Δ E, Δb N, Δb S, d Δh. COS qu h m b d fu f m. h fu fl ug h dym f x f uu m-dd, dffl qu. Fu xm f DOS mul ul, ud yld h ddl d dd v h f DE ym f ODE. d ly d uv fg ud xm fu f Δ E, Δ W, Δb N, Δb S, d Δh, d m v h m lf. b lbl ul, gd f f f ll h xm vlud by dul. Rdul h dff bw h d d h f h d h d vlu. h um f qu du (SSE)21 vlud, wll, b h b f. Fgu 7 llu h dul f xl, Gu, d lyml fu xm h d lg x, b S. h Gu fu wh SSE = d qu = h b f mg ll h xm. Fgu 8 dm h Gu f h ml hg lg b S wh h d bud. h b f ly mmd Gu fu f Δ W, Δ E, d Δb, d xl fu f Δb N d Δh. h ubu f h xmd fu Equ [8] v h f DE ym f ODE. h COS u MALAB dd lv f dy dffl qu d45 u. h fu mlm h xl Rug- Ku15 mhd wh vbl m f ff mu. Numl g wh h Rug-Ku hm yld h jy f hg gmy d h vlum f ml fd v m lf. h vlum f k h fl lm qul x 107 m3, bu h lu h dffl qu dm vlum f x 107 m3 v h m lf (Fgu 9). h l fm f Fgu 9 dm h h lu f h dffl qu du hdul wh ul k xv. Fgu llu h d gmy uh-bk D d F Rdul Fgu 7 b S fu xm dul b S Ex Gu lyml Ex Gu lyml uh-bk lg b S d h b f Elv bs uh-bk (m) x x Nhg Eg mx_b S_y Gu d bd (Gu) Y Fgu 6 uh-bk y (m) Fgu 8 bs b f d h d bud 68 FEBRUARY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

9 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 69 Ivgg uu m dym E (m) Vlum (m3) Vlum f ml fd Fgu 9 Vlum f k xvd v m lf x m (y) E d v uu mul bn (m) b N d v uu mul D m (y) Fgu 12 Chg bn, COS v. DOS bs (m) b S d v. uu mul Cuu Fgu 10 Chg E, COS v. DOS W (m) m (y) W d v. uu mul D m (y) Fgu 11 Chg W, COS v. DOS Cuu D Cuu 220 Cuu D m (y) Fgu 13 Chg bs, COS v. DOS muld by DOS md h uu lu f h dffl qu ug h dym f h v h m lf. h f h uu hg gmy f h wh EEM u h vlum f, w d h vlu f h mg. h b- ul hdul u f mul, gd by DOS yldd NV f $443.6 mll v 21-y m lf du f 10% um. COS hdul uld NV f $440.2 mll v h m m. Fgu 14 llu h mv ly f DOS v. COS ul. Clu A uu-m du mul, COS, dvld d mlmd MALAB. h gmy ud ug mdfd lll fuum. D du mul, DOS, mm h h dym x f ug d ml uh-bk dff d. h f m x mdl, EEM, wh h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER FEBRUARY

10 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 70 Ivgg uu m dym g (M) Chflw ($M) C (M) g (M) Avg gd (% m) O (M) Fgu 14 D d uu mul ul DOS u h NV fllwg h muld hdul. h mul u f uff fd h l qu f x mg ll lz, whh ul h hgh NV. COS mdl h dym f gmy d h ubqu ml mvm uu ym dbd by m-dd l dffl qu. Fu xm f h d muld uh-bk gd by DOS, vd h m v h f DE ym f ODE. Numl g wh Rug-Ku hm yld h jy f h gmy v m wh h v vlum f ml fd d h NV f h mg. A udy f d wh blk w d u vfy d vld h mdl. h fl lm w dmd ug h LG lghm. Cmv ly f h ul f h x qu gd by m ly ug Whl Fu-X fw, DOS, d COS uld h fllwg lu: () h mzd fl lm hw h l mu f 343 mll f ml g f 201 mll f d 142 mll f w; () Whl Fu-X yldd NV f $449 mll v 21-y f m lf du f 10% um; () DOS yldd NV f $ FEBRUARY 2008 VOLUME 108 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

11 SAIMM_fb_7-17:ml Jul 3/3/08 12:16 M g 71 Ivgg uu m dym mll f mul, d COS gd NV f $440 mll ud h m um v h m m lf. Alhugh mly gud wh h m ly Whl 4X, g l f dfyg hgh gd lu h mdl. h hybd mul mdl vdd h b f fuu h ug fm lg by gl-dd llg g g wh h vm. h llg g fmwk, ju wh h d h mul mdl, vd wful l f mzg h hdulg, whl ddg h dm fld d dym m lg. Rf 1. CHANDA, E.K. d WILKE, F.L. A ED mdl f h m du hdulg mz f fm bd. dg f 23d ACOM Symum, SME (d.), ELVELI, B. O m dg d x qug by u OR d AI. Il Jul f Suf Mg. Rlm d Evm vl. 9, ERARSLAN, K. AND CELEBI, N. A mulv mdl f mum dg. h Cd Mg d Mllugl Bull vl. 94, HALACHEV, R.A. A mdl f dud f v f du qug mz. dg f Al f Cmu d O Rh h Ml Iduy, u, Az. yl & F Gu(d.), Ld, YOUDI, Z., QINGZIANG, C., d LIXIN, W. Cmbd h f uf m h-m lg mz. dg f 23d ACOM Symum, SME (d.), Cld, MANN, C. d WILKE, F.L. O h m m lg f gd l mb f CAD hqu d l gmmg. dg f 23d ACOM Symum, SME (d.), Cld, FRIMONG, S., ASA, E., d SZYMANSKI, J. MULSOS: mulv mzd hll mul f l m lg. Il Jul f Suf Mg, Rlm & Evm vl. 12, FRIMONG, S., ASA, E., d SUGLO, R.S. Numl mul f uf m du ym ug hll mul. Ml Ru Egg vl. 10, ASKARI-NASAB, H. d SZYMANKSI, J. Mdllg dym ug M Cl mul. dg f Cmu Al h Ml Iduy (CAMI), Bff, Alb, Cd. O CD-ROM, h Rdg Mx I., CA, USA, ASKARI-NASAB, H., AWUAH-OFFEI, K., d FRIMONG, S. Sh mul f uhbk wh du mul. dg f CIM Mg Iduy Cf d Exhb, Edm, Alb, Cd CD-ROM 15. CARWRIGH, J.H.E. d IRO, O. h dym f Rug-Ku mhd. I. J. Bfu Ch vl. 2, WHILE ROGRAMMING Y, LD. Whl g m lg fw, Gmm Sfw Il I., ABRAMOWIZ, M. Hdbk f Mhml Fu wh Fmul, Gh, d Mhml bl. Sgu, I.A.E. (d). Nw Yk: Dv, ONUR, A.H. AND DOWD,.A. O mz 2: du hdulg d lu f dwy. f h Iu f Mg d Mllugy vl. 102,. A105 A OLWINSKI, B. d UNDERWOOD, R. A lghm m h ml vlu f m. dg f 23d ACOM Symum, Uvy f Az. SME (d.), Ll, Cld, DOWD,.A. d ELVAN, L. Dym gmmg ld gd l ub-lvl g.. IMM vl. 96,. A171 A CHANDA, E.K. d DAGDELEN, K. Oml bldg f m du ug gl gmmg d v gh ym. Il Jul f Suf Mg Rlm d Evm vl. 9, LERCHS, H. d GROSSMANN, I.F. Omum dg f - m. h Cd Mg d Mllugl Bull, vl. LXVIII, DEUSCH, C.V. d JOURNEL, A.G. (d). GSLIB gl fw lby d u gud. Ald g. Nw Yk, Oxfd Uvy, KRIGE, D.G. A l h m b m vlu d lld blm h Wwd, M h, Uvy f Wwd, Suh Af, MARQUARD, D. A lghm f l qu m f l m. SIAM J. Al. Mh vl. 11, h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 108 REFEREED AER FEBRUARY

Incorporation of ore grade uncertainty into the push back design process

Incorporation of ore grade uncertainty into the push back design process Sy I f gd uy h uh bk dg by J. Ghlmjd*, d M. Ol I m lg d dg, uh bk m qug wdly ud f lg-m du lg. I uh bk dg, f d gd d h dd bl uh bk wh gd h mmum uh bk wdh qum. h d dud by mzg m m lk mmdy, mg g, g,. h m m