Engineering application of thrust block analysis in slope stability problems in open pit mines

Transcription

1 67-85:ml Jul 6/5/09 11:06 AM g 309 Sy Egg l f hu blk ly l bly blm m by K.N. Kv* d M.F. Hdly h ll lm qulbum mhd ud b ffv dg h l f hghwll flu my l m ud h wld. Sl g hv f my y gzd blk hu flu mhm f l flu, bu ll wk hd b d bf 2000 xl h ul mhm whh mu b bl f h flu. h m f h h lm qulbum mhd mlly um gd blk, d h ulg f qu mu b fd vywh mululy f hm hv y mg. h wll hw h h ml vlvd h l flu gd; dd udg dbl m dfm dug flu. h bv llw h uh h blk bud ddly, bu hy d m l lh wh h, umd h mhd. bl ly f h y h uh um h h wgh f h blk vly dbud. h bl, bu h l ml g ugh b lf-ug whu m f, g ugh b bl ly ld h uudg ml. h u f h xd h l l f h lyl mhd dvld fm mhm ud vd bjv m f h k f l flu, d hf gudl f m bl l dg. h wk bd ud d u w flu l m Suh Af, d vd mhdlgy h l f flu m bjvly h bl wh uly d mhd, whl h m m mg uffly ml llw bk f h g bx m by ghl g. Idu Evy k l l u mg ubl bly d vul ll. O l m Suh Af ly d h m, whl xml f mv hyy d uh lbw d h -gld d h Chl Ad my b md fm d h 500 m. h d uh md f f ggd hghwll l kd u h h, muh lk, wh h fl vg bw l kw bh. I my, h hghwll l vl f m d hl. h vll l gl dfd by gh l h j h f uv hghwll l u h d f h. Hghwll flu u wh k l mg h hghwll ll, l, lum, ld u. N ly h dgu, f m fm m u-f-hdul lg u, whh m ff du l, d hf vu, vly. Ulk h g, mg g h h ml, h, hy mu dg d u h l h k d l h h ml u hy wh x. Emlly, bvu h h l gl mu b bl d mv ll vlyg l d k bl, whl h m m h l gl mu b fl ugh du h bly f flu bl mmum. Dgg l d k h bl bw m d fy m lld l gg. h m gl m k l gg lud ly mg l bu l vl gg l, uh d ug hlld. h f h du l bly, d hf h bbly f flu, mg-dud, glgl, d hydlgl g. M l hmgu uu mg ly f l d k hzd by dff ml. I dd h vbly f h f h ul ml, hy vu f dm fm whg d * Agulul Egg Sv, Nl Dm f Agulu. Dm f Mg Egg, Uvy f. h Suh Af Iu f Mg d Mllugy, SA ISSN X/ vd O. 2008; vd vd Fb h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

2 67-85:ml Jul 6/5/09 11:06 AM g 310 Egg l f hu blk ly l bly blm gudw, d hy duu bu f jg, bddg lyg, d h lg-l glgl uu uh gu u, ful, d fld. h m uu f udbl bhvu, g qu bu l h k l h l h b u, d h ff d dfm wh h l. Chg gudw d whg d by h l u l ly m l l flu. Hk d By bk1 k l gg f h m gzd h fld f k l dg, d w f ublhd 33 y g. h m f dg h l d z f uully lld flu k l (wdg, l h, d -wdg mdl) l wll dvld h CANME Sl Mul2. Sm l flu bvd Suh Af d Aul l fld3, vlv ly f wk k h l wh hk xmly ¼ f h l hgh. h wk ly mmly hl, d uully xd h (f) f h l, d uully d wd h. h flu md hzd by gf dwwd mvm f h gud uf bhd h l, md by h hzl hu f h k f f u h, Fgu 1. h hzl hu uully fld by h wk ly dg wd h. h flu mhm kw h blk hu mhm. Sml l flu h blk hu mhm hv l b d lwh4 7. Skm d Huh8 dfd h mj l f l mvm, mly fll, ld, d flw. hy hv dfd umb f hm f lf, bu lud h blk hu mhm fly. Sd d Sbl9 lyd 226 l flu h k l Bh l m, wh hy fud h bu 66% f h flu, h ldg u lg gl-, dubl- mull uf gld wd h ( Fgu 2). Bu f h h u f k l flu, y gz h mhm f flu x h f x hw Fgu 2, whh u f ly 34% f h flu udd. h mg 66% uld ly hv ludd blk hu flu f h. h my mhd h bly f k l. All h mhd b lfd w gu10: Lm qulbum mhd Mhd bd h u d lw bud hm f ly. h d ly h fm, mly lm qulbum mhd, bu l hm -gd bd. Glly, lm qulbum mhd ly h dubg f g umd gd bdy dfd by mgy bud wh vlum f k l, d m h wh h g f. h dubg f wuld u h bdy mv, whl h g f wll k h bdy l. I k, dubg f uully gudw u, h wgh f h bdy ud d, d mm h f lg flu. h g f f, k gh, d blzg mm. I lmg qulbum, h g f h mxmum hy b,.g. h k ldd full gh, d/ h fl f fully mblzd. If h dubg f xly qul h mxmum bl g f, h bdy m wll b qulbum, bu h, lmg qulbum. Lm qulbum mhd hf vlu h mxmum bl g f, d h m h wh h dubg f f h l mud b lg, h ly d l flu. If h d wg, uld b bu f l um, uh k, blk gdy, jd fd glgl uu h l. h lm qulbum mhd b dvdd w ubgu: l d -l mhd, bu h du bdly ml 11. h l mhd f ly, whh m mbl hd lul, h w-dml l ly hqu dg udd h gh, h mhd f l, d wdg flu. h mhd ml u h l qu f h f f fy; f h hy xmly uful. h l lm qulbum mhd ly ffv ly f l, wh h ffv b dmd ud umd flu uf f flu uf d h l. I, h l hvbl by dvdg h ml mg h l umb f mgy l. h blk hu mhm l lm qulbum hqu, bu m mlx h h lg, ldg, ll mhm ldy md. I h, wdg-lk blk wh h h d dw fm h k Fgu 1 Sl d l flu d by Byd 7 Fgu 2 yl flu md, gv g, bd 226 udy l m h Ud Kgdm (f Sd d Sbl 9 ) 310 MAY 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

3 67-85:ml Jul 6/5/09 11:06 AM g 311 Egg l f hu blk ly l bly blm m bhd h hghwll, by fu h u ul f gvy ldg d hzl h hghwll. h wdg, by fm, fm d blk f k bw h hghwll d f h wdg, d h hghwll f lf. If h wdg h hu dwwd ud w wgh, hu h d blk uwd (.. h hghwll f) h ( Fgu 1). h mhm bl ly f bh blk dfmbl. Wgh l.12 udk uvy whh hy ld h h f ll d lm qulbum mhd, ludg h dy mhd f l13, Bh Mdfd Mhd14, f qulbum mhd15, Jbu du f l16, h Mg d mhd17, d S 18 mhd. h m b m u h h Mg-17 mhd f h m lbl f h mhd. h l ll h mhd umd b gd, d h ml f g h b f y l dmd by lvg f ml h b f h l. mk h blm dm, h um md h h ul f h l f g y l lll b. Ufuly, h um bu h l f d fy d d h my ld udm f h f f fy by muh 60%19,20. Blly, h um md bu d f h m f h dguh lm qulbum mhd fm h, d y lf ly fl d11. S ll h mhd vlv mlfyg um f mlx ghl vm, h h f bg h vlu f f f fy wll b dud10. h wk mk ml lm qulbum mhd lbl h bk ly f h bv bvd l flu. h f vw w l flu Suh Af l m, d h db h glgl g d hy whh h l m fmd. h glgl hy vd b f mg h xd h m bf mg, bu mum d dfful d xv b, d hf vy. h h du h hu flu ly hqu w h l bly d m, d l h w flu vwd l. h hu flu ly hqu k ghl d u, ludg h ff f gudw, ml Nw ly f dfmbl blk, whh hv fmd h l ul f fu fm wh h l. h d ml um md h ly h bu h blk dfmbl, h f hy x h muul bud wll b ufm h budy gm, d dd f h h budy gm. h llw dd f lul f h budy gm, d h dd f f fy lul f h gm, h b wghd by h gm lgh fd vll f f fy f h l. W lud h h mhd vd m dbl ul h y f h vlbl l bly mhd uly u, bu fuh wk fu gwh k wh h l dd, bu h wll lud blk fm mhm, blg b flu d. Sl flu Suh Af lly O lly A m h l m wh vg l hk f xmly 16 m. Fgu 3 h lly gh lum21, whl m l ( dud h) hw h udgud mg by vu lly hd lf ll h mddl l m m, h bm l m h, wh h ul h mm h w l ll umd u h h lw d mddl m. h md m dylgh h m, d uld bu l bly. h u l m w v md by h ld udgud lly. w l flu k l dug dff d dff bu bh h dd wd h, d bh, f h l m hd b md vuly. Bh flu k l f h mddl l m hd b xd h fl, bu bf h l hd b md. h f f l flu k l A-1 h bw hl d h mddl l m, bh f whh dd wd h. h l m h w vy h (bu 1 m hk). h flu k l w g: h l flu (vlvg ly h dy vbud) d h mj ll, whh ld lg h bm f h hl ly bv h mddl l m. h l fl22 bf d f flu Fgu 4. h l flu w bbly ul bu ld lm qulbum mhd f ul flu yldd f f fy f 0.72 f h l. h mj ll fllwd h lg f h ul flu, wh h l fl hd fl l gl h hd h ul flu ( Fgu 4). N f h gd-blk lm qulbum mhd md bv dd flu h l f h m ul flu hd ud. h mj flu d mull blky y f flu, bu ld blk- Fgu 3 Rv gh lum f h m (f Muhk 23 ) h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

4 67-85:ml Jul 6/5/09 11:06 AM g 312 Egg l f hu blk ly l bly blm Fgu 4 Sl fl A-1 bf d f ul flu, d f mj ll (f SRK 21 ) fd hqu ud f h l f f fy lul w uful bu w hgh h uy, dg bl l. M l fm h ld udgud m dd hw y udgud mg v h udh h flu, h h w l m blw h l w. Fgu 4 hw h l fl bf h mj flu, d h fl f flu d. h l d h h hl blk, mkd gy d lblld A d f h v d v blk vly, mu hv udg dfm dug flu. h mu hv b dfm h l bf h flu, bu h w uffly bl hv wd m l, bu h flu w vy uxd. h vlum f k h l bulkd fm 1702 m3 m f l m3 m f l, dg bulkg f f 43.6% dug flu. h jud budy bw h v d v blk f flu gv by umg h bh h v d v blk wuld bulk h m mu dug flu, d h fdg h budy f h quvl vlum h fld fl. I w l umd h h w mxg f h ml fm h w blk dug flu. h u l budy f h v blk m m l h m l f flu (hw by dk g dhd l h gh), f umd h h v blk bulk h m dg h v blk. Wh l fm Fgu 4 h h v blk h l gvl l gy, whh wuld hv vdd h hu f h v blk h. h vll l f gvl l gy f h whl l md by g h h f gvy f h ufld l 33 m bv dum (gh-hd d d l Fgu 4), whl h fld l f gvy l 24 m bv dum (lf-hd d d l). Ug h ufld l vlum gv bv d umg u wgh f 25 kn/m3, h l gy hg dug flu md 383 MJ m f l. If h whl l mvd 25 m h lf dug flu (h ud m, bu h f gvy f h fld l 25 m h lf, bu h wdh f h fld ml h d, whl hgh h dmhd), h gy um du f l ug f gl f 10 f h hl-mddl l m bu 187 MJ m f l. h lv ly 200 MJ m f l f bkg h k u d mmug. h lul h ud m, bu hy d h hu mhm bl, l fm gy bl lul. h d l flu k l A-2 f h m lly. Fgu 5 h l fl22 bf d f h flu. M l l bw 20 m d 25 m hgh hd b dumd d f xmly 20 m bhd h l. Ay j h mgh hv b bl f wdg flu w bvd h. Whu y vbl d wg f mdg flu, h l lld, d h flu vlvd h l, vbud, l m, d h bud bw h l m d h mddl l m. h flu l k l bv umd gud, f h mddl l m w xd h bm, bu bf w md. Af h lg, h flu uf, g h bw h hl d h mddl l m, w lly vbl h. A h f h flu, h dd vg gl f 16 wd h. h md f f fy f ul flu f h l vd bw 2.4 d 2.6 ddg h mhd f lul (Fllu Ody Mhd13, Bh Mdfd Mhd14, Jbu du f Sl16, Mg- 17, d S18). Clly, h flu uld hv k l by ul mhm. Ug h bv mhd ly blk-y f flu mhm gv vy lw fy f vlu ( f h Mg-17 mhd). h h mhd, uh h Jbu16 d Bh14 dd lghly hgh fy f ud 0.15, whh ugg h h l wuld hv lld mmdly, v whl w bg u. Fllu Ody Mhd13 yldd f f fy f 1.2, whh uld b dd b h b ul, v hugh dd d flu. Ag h l ug h vlum-gy h bv ml, bu h xm m3 m f l mg, f w um h h l l vlum dug h flu. I uld hv bm md dug ll, bu h wuld u f h dy. I l fm mmu wh h m22 whh y l d dy vbud hd b mvd bf h fld l fl w mud, d h vd h h l l bm md dug flu. Fgu 5 Sl fl A-2 bf d f mj ll (f Cdy 22 ) 312 MAY 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

5 67-85:ml Jul 6/5/09 11:06 AM g 313 Egg l f hu blk ly l bly blm h gmy f h fld l gly ugg hu mhm, d b dld 22 m h d b ( Fgu 5). h fld fl gv 704 m3 m f l d 625 m3 m f ufld l, f h vlum mud whl gg h l l d h dy vbud bhd h ud v blk, Fgu 5. h u f bulkg f f 13%, whh l dbl f h dvdul blk vlvd h flu yd m l. Ah f h uld u f h d fud h dwg uld b h u-f-l v f h l fl, d bl u-f-l ml mvm. I l kw whh h l l fl bf flu w uly d. h lm qulbum mhd fl bu hy um gd, hmgu, d k d l whu l uu. Oh flu mhm uh wdg flu lg flu ld by Sd d Sbl9 d llud Fgu 2, w l. Alhugh h w flu w vy dff h, h bh uld fm h m mhm, h w x fu mm bh: h l fl by hzl mvm wd h by f blk (v blk) whh hw vyg dg f dg h fwd mvm f h v blk dv by h vlly dwwd mvm f h v blk bhd, whh d u wh fl lv gfly lw h h f h gl l fl, d h blk udg gf dg I bh h l ud dg wd h I bh h flu uf h bw h hl d h mddl l m h flu uf dylgh h f h ufld l bh Alm vl l fu w uf bhd h l, uully bv h f h udul h l-bg. h uh lud h m f blk hu mhm bl f bh flu, v hugh h w gd w vy dff l gm, d yldd vy dff ul. I d udd m lly hw h flu uld hv dvld, y vw h glgl hy f h l d, d h lkly - d -mg h m l. Glgl hy f h l d h l d fm f h Vl B, whh ddl h Gug-Og F S budy h uudg Vgg d Slbug. A v gh lum f S M A Fgu 3, whh dud f Muhk23, d hw h v gh lum whh l flu ud. h l læ-fu f h d h uv dlm b, whh h ld dm dd bg uv. h dlm læ-uf w fmd wh dlm blgg h vl Sugu. h l-bg bv ufmly hk lvl, bu udul fllwg h dlm b. h l m, wll h h, h bv læhgh d hk bv læ-lw h dlm. h fu h uld dg u 15 bw hgh d lw h dlm læ-uf. h dlm hgh hmlv dm-hd d m dm, gvg hm hll-lk fm. N h h uduld fm dbd dfly fm, bu h ul f whg d hml, whh uld k ghy h dlm bm24. h k fm h dlm w fllwd by gl, whh mhd h uggd k ghy d fmd ll d h gh lw. C24 h h lg-bg (l lbg) qu umuld h fg f flud-gll u h d f h lz wh h uh f Af w ld h Suh l. h dvlm f lg f gll d h dg mu Af dfd hwd fm xm uh lud. h lg fmd fm vgl m bg whd dw lk. A gdully m m lm llwd h gwh f mly dduu vg wmy -h vm wh v d wkd gll ll ml d l m ubdg b. h lg-bg bbly h gdul fm d fl dwg f gv dl lb, wh flud-gll fu f h Dwyk fm vl by gd dl dm, whh u vl by bh d m d f h w-gzd hd vbud d hd bud h lvl gdully 24 ( h gh lum Fgu 3). A md l, h udulg fl h udlyg dlm læ-uf by hvg ml ghy, h hy xmly ul l wh dm f fw hudd m d hv hll-lk fm. Fuh wdg d jg f h k fu h dlm f h d f h vlyg dm l bud h dg f udul fm h vlyg. Dg d lf f h lg d ud f h f gl x ld h bk-u f Gdw dug h l lz ly, d h dg u f dl dyk25. h glgl hy f h l-bg u h m bg hg h -mg, whh u h flu l bhvu dug mg. S h udul w, mlfd h mdllg bu h uh dd hv m hzl h wuld hv b uff u h udul h, d hf mk um f wh hd h. Ifd m l h Eh u d d h m lm mlly uxld, lly h f h ld u. h bu mum k d l h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

6 67-85:ml Jul 6/5/09 11:06 AM g 314 Egg l f hu blk ly l bly blm uly dfful d xv, d hf d m ( f xml Vgh26, Gy27,28, Sy d Wl29, d Sll l.30). Rk m hf uully bd fudml hy, mll umb f mum, d lg mu f ddu d f. I h f h l bly udy, l m w dff. I h ly f lv h l m qu, V d Mw31,32 m h hzl h uf l m f h d f w h vl. h vl u, mu b qul h vbud wgh fm qulbum d. I h b f y h vg d, h uh um h h hzl h l bf w xvd w f h d f w h vl f h fllwg : V d Mw 31,32 mm Hk d Bw33 d h hzl bw d h m lg h vl hllw dh h udul h l-bg w h ul f dg h v vuly uv h h fldg du hzl mv. Fm h bv, h uh umd vl quvl h vbud wgh, d dlly hzl xly dubl h vl. I dd h bv, h uh umd h h udgud l m wuld hv uld gf hg h gl bf mg h fmd by uml mdllg34, bu hw h. Sl flu k l f h l w u; h w y mu h h l f w u. h w d ug h w-dml f dff hm FLAC35. h FLAC (F Lgg Aly f Cu) mdl dvld h udulg glgl uu dbd bv, d l k u h f h hl bv h mddl l m. h h h mdl h umd b, hmgu, d, v hugh hy d ll hv h m mhl 34. h l whl hf hgu, bu f vl ly, h wh w f. h m l mdl w dvld ug h flu fl hw Fgu 4 d 5 d m h h l ug FLAC35. h md fm h mdl hf ul f h udulg glg uu, xludg h ff f du, hy, d whg, ll f whh b k u h mdl. h ff f gudw wll b dld d dl wh h hu flu ly l. h ul f h f mg Fgu 6. Fgu 6 zm h mdl f h l, h h dbu b m lly. h zm wdw hw by wh qu Fgu 5, d d h b f h wdg. h f dff z g lllgm, d h l h z d by wh lmb lgh l h mgud f h m, d wh d h l d. h h b f h wdg Fgu 4 gfly dff, d hw h. h hw h f uum d hf h h wuld hv xd h l bf h blk hd fmd. h m m fu f h dbu : h fm f l hzl h uf bhd h l ( hw, bu l f h whl l wuld b lud y dl) h f h l lll wh h ld h duu hg ( h lvl f xm) mgud f h m l lll h bw h hl d h d h uy f h h hl-l h ufmy f h h um bu f h k ml dfmbly. h fu l h dvlm f h flu mdl f h l, d hy u u um h h h blk bud wll b ufm, d dd f h h. Blk fm m l Uxd l flu ud w, bh f whh bbl h v d v blk w f fmd by h gwh f flu uf wh h l f hd b u. h flu uf mbd fm dd dfmbl blk, whh w uffly ubl ul h ll f h l h m. Alhugh udgud mg hd k l h mddl d bm l m bf h m mmd, h f h l ll k l v md gud. hf h ff f md gud l bly wll lg b dd h, bu d d ul Kv34 f fuh dl. Fgu 6 l dbu l bf l ll 314 MAY 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

7 67-85:ml Jul 6/5/09 11:06 AM g 315 Egg l f hu blk ly l bly blm Vl fu Vl l fu mmly dvl h gud bhd m l, d h l m qu w x. h mdllg fm h l k huld dvl, hw Fgu 7, whh l f h hzl m lg vl fl l bv h f h udulg fm. h gf h l m gh wh dh f h l z wh l h b u. h gf f h ul h d duv uf l kg gd by mb f mg d h ubuf glgl uu. I f vy dld mdl ud l flu, B36 fud h h k bhd h l w gd by mll mvm wh h k m, d h d f l xv. Alhugh h dvdul mvm w vy mll, h umulv ff w gf dlm f h l uf uff u f ml bhd h l d fm k. h vl v blk bud dfd by vl l k. W hf um h x f h fu bf flu, bu hy fvud h mdl, d hv b bvd h l m qu, bh h l flu, d lwh. Ild h uf fm blk wdg d flu h uh ju h mm f h fm f h l fu, h fu mu hv d dvlg h l df h blk wdg. Whh h k l bf f h fm f h flu uf h hl-mddl l m dbbl, d huld fm h ubj f fuh h. Ev ld k ml (wh jg d h uu gf), h flu m mlx ulg mlx fu uu A yhzd h fu g ll h fu, d bd h wk f Rdl37, Vm d D B40, d Ol41, Fgu 8. A hgh f h fu hd k Fgu 9. h u f g ll h dl gz h h fm f h z h l wll b mlx, ju hy y glgl ml. Alhugh h uu f h fu z mlx, vll ml,.. b umd l lll wh h d f h mxmum h h l. Sh bd fu, hwv, d u ly f gl, bu uld u v g f gl l h mxmum l d Flu uf hl mddl l m Flu k ll ly udd bu f h vy d mlxy f h ld. S-fh- f dff hm uh FLAC35 bl du dbl flu ul f k bu h k m ml h mdl umd b uu, v f hgy d y hv b k u. h mdlld k ml m uu hughu, v f mdlld flu. I, k ml ly wuld h d fu, hby bmg m duu dug h f flu. H mdl ul dvg fm ly h ml bk u. S h mdl h w ubl fm l flu h ghl d dbd bv, vg h mhm hugh whh flu vully ul lg h hl-mddl l m dd, d bfly dud blw. Alhugh l hm h udy, Kv34 vgd hw flu uf uld dvl h hl-mddl l m by u h udy f h f h hl ud h m, fu mh hy, d h mdlld h l f mg, d bf l ll. h wk dd du bl ul, bu d bl mhm by whh flu uf uld lwly dvl lg h hl-mddl l m. h uf lly l h l ll ( Fgu 4 d 5), d bu h llg k m ld, y dl fu h my hv d h mhm f fm hv b bld. Ev hugh h mhm f fm m ufmd, h flu uf d bg l h l ll, w fud h hl-mddl l m bh. Fgu 7 Hzl l bhd l, vl l bv fm Fgu 8 Rdl uu bl ml (f Rdl 37 ) h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

8 67-85:ml Jul 6/5/09 11:06 AM g 316 Egg l f hu blk ly l bly blm Fgu 9 Exml f h fu bl k d lvl gld m hwg Rdl Suu (f Ol41) gh wh h ff f y h hl (.g. Jg d Ck43). N h ly bl Rdl Sh Suu dw g Fgu 8, whh h jud Vm d D B35 dl lu h b ld. h h bl Mh-Culmb lv hw f u f kg h dwg l. Wh f h FLAC lu bf blk fm gv Fgu 6, h uh ju h h h z ld 45 h hzl, d h hy xmd by gh l, lhugh h d b h ly. W ju h h v blk bmg d fm h uudg k m by mll mvm. Sh fu w fm 45 h hzl. h uh ddu fm h mdl, d fm vlbl h hy m lkly dvl dwwd fm h bm f h l fu, h h l m fvubl f h z dvlm h b f h l k bu h hzl h ffvly z. Kv34 f mg h dh, bu fuh h wll b y fm h. h h z dvl xmly 45 h hzl hugh h ubk k bw h l fu d h hl-mddl l m. Dug h h fm h x f h wdg, h k h h z wll dl (xd). h wll g hzl f h v blk, whh wll l h dvlm f h uly fl uf h hlmddl l m. A m (bbly bf h w h z vg), h ml bw h h z wll bg uh ud h wgh f h vlyg ml mg h v blk. h wll l hzl k dl, bh h h z d h uhd k h b f h wdg. h dly f my b uff hu h v blk h, d h h h v blk wll u lum dwwd ud w wgh, fg h v blk fuh u h. h whl d wh h v blk lum dwwd, hby dg h dly f h dvg h v blk h. Dug h bh blk bm mmud, d h v blk h m h h v blk. Fgu gv qu f v h uh hv ddud mu k l dug h l flu. Bd h mhm, h jud v d v blk Fgu 4 d 5 f h w m l flu. O h fu hv fmd, ud l bly b ly qu f h bl f f xg bw h blk h fl, d h h Fgu 10 Mddl Cl Sm bf mg, wh vg hzl fl Cug h v-v blk gmy f h bv ud Wh h fl u md, fu g bu f k lx. A h m, h vl l fu dvl gud uf bhd h l, d h bl l fu h f h l lg h hl-mddl l m uf fm f h d h. 316 MAY 2009 VOLUME 109 REFEREED AER Fgu 11 Sl u x m, wh ul hzl fl h Jul f h Suh Af Iu f Mg d Mllugy

9 67-85:ml Jul 6/18/09 2:58 M g 317 Egg l f hu blk ly l bly blm Fgu 12 Dvlm f l k bhd l Fgu 16 M lumg f v blk bhd l u uh h wdg blw Fgu 13 Cmmm f h fu gwh Fgu 17 Fl l ll lvg vd f b-l mull flu uf dbd by Sd d Sbl 9, d Kv d Fz 44 Fgu 14 Cud h fu gwh wh d dl, d dgd f y h lg l Fgu 15 Av d v blk w fully dfd by fu gwh h l vd m lu f ml - lul h wll b dud l. I m gz h h ly d ly f qulbum d um h ll f hugh h blk d. I h wd, mm qulbum dd h mdl bu bv f h flu h m dd vl y gf l m h flu. Kv34 vd vy dld u f hw ll h f, ludg h dvd fm gudw, mud, d h Adx A. h mu bd Nw Lw f M, whl h blk bly md umg dfmbl v d v blk d f f fy h h l f l flu h blk d d h hlmddl l m h bvd flu dud bv. h mhdlgy huld b fd h dud bv ly; b dd h ghl d y. S h blk dfmbl, h uh um h h lg h blk bud xmly, d dd f h h. h mk bl lul f f fy f h budy, d h fdg wghd vg ug h lgh f h v fu uf h df h v blk d v blk. h dl lghly lud h, ll h fm y fm h ly w dbd Kv34 Adx A fllwg h. Oly h ul fmulæ y f h f f fy lul d blw. h uf f f fy f flu gv by ( Adx A f df f vbl d ll h lul y mu h FS): h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

10 67-85:ml Jul 6/5/09 11:06 AM g 318 Egg l f hu blk ly l bly blm h u uf f f fy gv by: h fy f f h bl uf (hl-mddl l m ) : Flly, h f f fy mbd wghd vg f h l gv by: h uh lld h flu mhm h hu flu mhm, bu l ll u wh h v blk ubd ud w wgh, hug h v blk h. h mhm llud Fgu 1, whl h bw h ufld l fl d fld l fl hw Fgu 4, d 5 gly ugg h mhm. h ulm bjv f Kv 34 h w vd ml lul h uld b ud h bly f l uh h dbd bv. h v mlzd bu f h ghl mlxy h w flu, d h mlxy f h jud flu mhm. h d uh h dd bl f mlfyg h qud lul uffly mk - m bl, bu h bbly fugh wh d uy bu f h um h hv b md. h fllwg gv bf d f uh mhd, bu h mu b wdly d d hw b lbl bf b ud wh fd. Quk ll l lul ug h blk hu mdl Fu ugh d k gh gd, d hf h v d v blk umd hv fmd All h ul wll h blk budy du hv f gl f 37. h um f hg (mly v mly h), d huld b vwd my ghl d bl d vlu h vldy. I d mk quk m, h ghl g huld mu h f h l l fu bhd h l, d h mu h f h l fu fuh fm h l. h dff bw h h v blk wdh ( Fgu 10). h, kwg h hgh f h l, mu k h qu: h > w / 2? (S Fgu 18 f df f h vbl). If, h wh gg hd wh h ml m. h v d v blk vlum m f l gv by ( Fgu 18 f h mg f h vbl): f h v blk, d f h v blk, wh umg h l gmy gv Fgu 18. I g h l f flu ug h vlum qu, l h = w, d = bw. h d d h blzg f : whl h ug f : h f f h ml fld lul h b fmd fm mum f l fu bhd h l, kwg h l hgh, d h vll l gl. h vy ml gudl b fd ly by wdd g. h d f h du h ul f h dld mu hy uld Adx A. Sml f FOS m whl h Bd h bv ju d um, bl kh xm u f h blk fm d h ubqu l flu. F h ml - lul, gl d umd fllw: h bm fmd hzl duy h dylgh h f h l Fgu 18 glzd v d v blk gmy f mlfd fld ly 318 MAY 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

11 67-85:ml Jul 6/5/09 11:06 AM g 319 Egg l f hu blk ly l bly blm Dfg h l bly m f f f fy: f mlf d gm. h bl dw h f h f h vlum f h v blk xd h f h v blk, h h f f fy l h uy. H, f V V, h l dd ubl, d h ghl g huld fm h full ly m f ugy. I ml m dw u f bl ug dh dm f f fy f v h,, d θ. h mlfd mhdlgy vl f f fy f 1.28 f l gl θ f 30, = 1.1, d = 0 h f h f l ll. h ugg h h ghl g huld vw h l bly ug h blk hu mhm bu y f f fy l h 1.3 dd mgl. I h f h d flu, θ = 60, = 1.3, d = 0, whh gv f f fy f 0.59, whh ugg h h l d ug. Dld FOS m ug h hu blk mhdlgy Bd h ju d um dbd l, bl kh xm u f h blk fm d h ubqu l flu. h Adx h full lyl du d by Kv34, whh huld b ud d h l f f fy m uly. h flu mdl, whh w ld h m ll, Fgu 4 d 5. h ul fm h mu, gh wh mbl ul fm d l bly ly bl I, ug k m d bl II. I fm h fy f mu h ul flu ulkly x h f h l flu h vbud A-1. Obv h m fm h bh. Blky flu ul f A-2 w lly mgl x f h ul bd fm h dy mhd, whl h l ul flu A-1 w qully lkly mf blky flu dg h Bh14, Jbu16 d Ody Mhd13, whl h bl I Sl ll fy f, luld f h flu d Fgu 4 d 5 (f Kv 34 ) Alyl hqu hu flu mhm Ody Bh Jbu Mg- Mm F A-2 Cul flu Blky flu U (l) Lw (l) U. ( l) Lw. ( l) A-1 Il flu Cul flu Blky flu A-1 mj ll Cul flu Blky flu U Bm bl II Rk m ud h f f fy lul (f Kv 34 ) Rk Sdy vbud Sd Shl (ml bddg) Shl (lll bddg) Dy, kg/m Sh mdulu, G Bulk mdulu, G l gh, M Ch, k F gl, dg Ly hk*, m *Avg ly hk h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

12 67-85:ml Jul 6/5/09 11:06 AM g 320 Egg l f hu blk ly l bly blm Mg-17 mhd dud mgl ul. A f h mj ll w d A-1, ll d mhd dd h ul flu w ulkly, d h blky flu w xmly ulkly. bl 1 hw h bh, h hu flu mhm h bl h f ug, whl ll h h mhd yldd l ul. Du d lu h hu mhm flu l w ld h w mj ll umg l uf h u hl, d d flu uf h lw hl wh h mddl l m. h u f h w h l f h mhm dff bw l ll flu uf d h. I bh, flu w dd f h u hl, whl ll w dd f h lw hl. h l wh h bv h m. Igly, h l l A-2 hd lgh blzg ff, lhugh h w uff v ll. h hu flu mhm b mg w l bly ly hqu bu lly b ld wd vy f ghl d. I h b d w wll-dumd, d h b hw b uful, h h ly ld mhd. h d m h h mhd fllbl f f u bl ly f h d hqu b hw wk ly vy bl wh h blk hu mhm ud, d wh ll flu wk b hw b h ul f l f h mhd. h uh hv b bl ublh m flu h hv b lyd ug h mhd, bu hv ddd ublh h d mk h mhd kw h h h h wk h fld wll b wllg hl l flu hy hv bvd, d whh vl mhd hv fld d. h bgg umblg blk bg d l flu d wh h m: uully l flu xv d mbg hm h m mgm f hd fm ubl vw. h xl h ymy f h w dud bv. Hwv, h lu vw lly hw h my l flu udbl ug vl mhd, d h, h m f ghl g m mgm, h bbly ld h dg f lly ubl l. h uh hf l h duy f uxld l flu hy hv ud, h h mhdlgy h h f bg d m wdly. h d hu flu ly vl mhd f l bly m mlx ghl d wh h blk hu mhm ud. h mlxy f h ly huld lly fl h mlxy f h ghl d whh l flu my k l. I wll b fllbl h bu f ubjvy h f h g vlvd. Suful l wll dd ful bl bw mly, whh h blk hu mdl lylly bl, d mlxy, wh h l fu f h ghl d h ff l flu l ludd. ylly, m ud m l ufm mg vm, whh h ul f mb f h læ-glgl d h xd h m f h fm f h bdy, d h ubqu glgl hy f h u h m f mg. h glgl hy f h hgg glgl d h h bdy my b ubjd f fm, f xml, d f ul f d lx; f vlyg k d d f w dm; ful, fld, d j fm; hml l by whg gl mmhm; d u by dyk d ll. All bd wll b ubjd mb f m ll f h bv m dug h glgl hy d h wll ul mg vm uqu h bdy. Wh h mg vm h wll b m ghl, f xml fuld gud d ufuld gud. h blk hu flu mhm my h ly b bl fuld gud f xml, whl h l bly blm my b x h ufuld gud. I wll b h duy f h g d glg dfy h d, dm h l f l ll, d h u wh y. h fllwg lu b dw: h ly hqu k u h m lkly vg d ul f h l fl, d h l ff l ll Wh h d f h mhd m l l bly fy f d gl l gl dg bl h mhdlgy lud h ff f -w u l ll h mhd dv fuh, bu h uh hv b bl b d m h h bv-dbd flu A ml quk m mhd glz l d blk gmy, d h l ml mk lmy - l bly m h ublhd h h h h blk hu mhm wll v wd d l h mg duy, bh Suh Af d bd. h uh d h bu vd g wh h l l bly um wh h d mhd kw fl. h uh mmd h h mhd huld b ld my ud fm h wldwd mg duy bl, wh uff dl f h dvdul flu d h glgl d vlbl. Sdly, fu dvlm k wll v b fm vg Rdl wk37, d h huld b ld dg h l f h gwh f h fu, d h ulg l bly, ll ghl d. 320 MAY 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

13 67-85:ml Jul 6/5/09 11:06 AM g 321 Egg l f hu blk ly l bly blm Rf 1. HOEK, E. d BRAY, J.W. Rk l Egg. h Iu f Mg d Mllugy, Ld, CANME. Sl Mul, Mg h Lb, CANME, Cd HARRIES, N. l mmu h Il Symum Sl Sbly, C w, 4 7 Mh SURMAN, J.M. Iflu f l bly m f l mg h d h mdld f Egld. Sd Il Suf Mg d Quyg Symum, 4 6 O. 1983, Bl, UK, SINGH,.N. d SINGH, D.. Ag bly f vd mul m mg. Clly Gud, July 1992, MALGO, J., BALIAK, F., d MAHR,. d f h flu f udgud l mg l bly h Vk mu. Bull f h Il A f Egg Glgy, vl. 33, BOYD, G.L. Gmh h ld l mg Aul. Sd Il Suf Mg d Quyg Symum, 4 6 O. 1983, Bl, UK, SKEMON, A.W. d HUCHINSON, J.N. Sbly f ul l d mbkm fud, S-f-h-, 7h I Cf SMFE, Mx Cy, 2, SEAD, D. d SCOBLE, M.J. Rk l bly m Bh uf l m. Sd Il Suf Mg d Quyg Symum, 4 6 O. 1983, Bl, UK, ANDERSON, M.G. d RICHARDS, K.S. Sl bly ghl gg d gmhlgy. Rd, Jh Wly & S BROMHEAD, E.N. h Sbly f Sl. Suy Uvy, Chm d Hll, Nw Yk, WRIGH, S.K., KULHAWY, F.H., d DUNCAN, J.M. Auy f qulbum l bly ly. J. f h Sl Mh. d Fud. Dv., ASCE, vl. 99,. SM10, FELLENIUS, W. Clul f h bly f h dm.. 2d Cg. Lg Dm, Whg, vl. 4, BISHO, A.W. h u f h l l h bly ly f h l. Ghqu, vl. 5, LOWE J. d KARAFIAH L. Sbly f h dm u dw dw.. 1 -Am. Cf. Sl Mh. Fud. Eg., Mx, vl. 2, JANBU, N. Sbly ly f l wh dml m. Hvd Uvy Sl Mh. S, MORGENSERN, N.R. d RICE, V.A. h ly f h bly f gl l uf. Ghqu, vl. 15, SENCER, E.E. A mhd f h ly f h bly f mbkm umg lll -l f. Ghqu, vl. 17, URNBULL, W.J. d HVORSLEV, M.L. Sl blm l bly, ASCE, J. Sl Mh. Fd. Dv., 93, (SM4), WHIMAN, R.V. d BAILEY, W.A. U f mu f l bly ly, ASCE, J. Sl Mh. Fd. Dv., 93, (SM4), SRK. Flu ly f h Nh Flu, Clly A-1. uublhd l m CANADY, I.I. l mmu. Hd f flu l flg m, MAUSHEK, M. l Cmmu. Dvl Glg, Nw Vl Clly, Suh Af CAIRNCROSS, B. ldl vm d -dmy l f h gll m l, K B, Suh Af. Il Jul f Cl Glgy, vl. 12, SNYMAN C.., d BARCLAY J. h lf f Suh Af Cl. Il Jul f Cl Glgy, vl. 13, VOIGH, B. Bzhug zwh g hzl Sug m Gbg ud d kk ud d Abgug. 1 Cg I. S. Rk Mh., Lb, 1966, vl. 2, GAY, N.C. I u mum Suh Af, hy, vl GAY, N.C. h f lg dyk E.R..M., Bkbug, Suh Af. I. J. Rk Mh. M. S. & Gmh. Ab., vl. 16, SACEY,.R. d WESSELOO, J. I u mg Suh Af. Ju. S. Af. I. M. d Mll. vl. 98,. 7, SELLERS, E.J., COEZER, S.J., d KAMSRA, R. Uddg d Dmg h Vbly f h mv S Evm. SIMRAC Rh j GA707, Dm f Ml d Egy,, Mh VAN DER MERWE, J.N. l mmu, Dm f Mg Egg, Uvy f VAN DER MERWE, J.N. Hzl : h f ll vl?,. 19h Cf. Gud Cl Mg, h, I. 2002b. 33. HOEK, E. d BROWN, E.. Udgud Exv Rk. h Iu f Mg d Mllugy, Ld, KARAROV, KN. Sl Sbly Aly Cmlx Ghl Cd hu Flu Mhm. hd h ubmd f xm h Uvy f,, Suh Af, Augu IASCA CONSULING GROU. FLAC2D: F Lgg Aly f Cu. Ml, M, USA BARON, N.R. A Mdl Sudy f h Bhv f Exvd Sl. h.d. h, Uvy f Ld, Iml Cllg f S d hlgy RIEDEL, W. Zu mhk glgh buhhug. Zlbl fu Mlg, Glg ud llg B, (Abhdlug) LADE,.V., COLE, D.A., d CUMMINGS, D. Mull flu uf v dl ful. Jul f Ghl Egg, vl. 110,. 5, My 1984, SYLVESER, A.G. Sk-l ful. Bull f h Glgl Sy f Am, vl. 100, VERMEER,.A. d DE BORS, R. N-d ly f Sl, C d Rk, H, vl. 29,. 3, Dlf Uvy f hlgy, Dlf, h Nhld ORLE, W.D. Rk Fu d Rkbu: lluv udy. Mgh S M9, Suh Af Iu f Mg d Mllugy, Jhbug GAMMOND, J.F. Dlm fu d wh ful z: m bw bvd xml d xml mdl. Jul f Suul Glgy, vl. 5, JAEGER, J.C. d COOK, N.G.W. Fudml f Rk Mh, 3d Ed. Nw Yk, Chm d Hll KOVARI, K. AND FRIZ,. Sl bu: Sl bly wh l, wdg d lygl ldg uf. Symum Rk Mh Rld Dm Fud, R d J BAER, G. Mhm f dk g lyd k d mv u dmy k. Jul f Ghyl Rh 96, vl. 11, , NARR, W. d SUE, J. J g dmy k. Jul f Suul Glgy, vl. 13, GROSS, M., FISCHER, M., ENGELDER,., d GREENFIELD, R. F llg j g bddd dmy k; gg uml mdl wh fld bv fm h My Fm, USA. Am, M.S. (d.). Fghy. Glgl Sy Sl ubl, Glgl Sy, Ld, BECKER, A. d GROSS, M. Abu h Dugdl k ud mxd md ldg. I J Fu, JI, S. d SARUWAARI, K. A vd mdl f h lh bw j g d ly hk. Jul f Suul Glgy, vl. 20, HELGESON, D.E. d AYDIN, A. Ch f j g ly f dmy k. Jul f Suul Glgy, vl. 13, SANG, Y.W. h ff f uy flud flw hugh gl fu. W Ru Rh, vl. 20, IASCA CONSULING GROU. FLAC2D. F Lgg Aly f Cu, HOEK, E. Sl bly ly. Lu Sg hl Uvy, Ch 7 A: Sl bly blm Hg Kg, h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

14 67-85:ml Jul 6/18/09 2:58 M g 322 Egg l f hu blk ly l bly blm Adx A Mhd f hu flu mhm ly f l bly mlx ghl d Idu h d flu mhm ld h lygl flu uf hy by Kv d Fz44, Byd 7 bv ( Fgu 1), d h wk f Sd d Sbl9. Ad lu hw h ldg uully k l uf h b mdlld by v-u lyglly hd uf. F uh, Jbu16, d Mg d 17 hv uggd l mhd f mu, dg whh h ubl h- km dvdd u vl l. h Kv d Fz44 lygl flu uf hy bd um bu h dbu d l f h l f, wll h hyh f lm qulbum. h mhd bd u h hyl qum h ldg lygl uf ly bl kmlly f uff umb f l h uf dvl. F h k f mlf, ly uu h uf g fm h l f h lyg-ldg uf umd. hu, hw Fgu A.1, h ld f m h uf mu b md by l w l h uf. F xl ldg uf (-1) uh f qud. h h ml h hy d mk kmlly m dfful jufy. h hu blk mhm lv h dlmm by g h mull flu uf, d ubug h w m blk Fgu A.1 wh gl v blk. h v blk quvl h f blk Fgu A.1, lb wh dff gmy. h Kv d Fz44 mhd u h fllwg b um: h blk mg h k m h dd b gd h d f h l h uf kw O h l d xl ldg uf ( h d f lm qulbum), h Mh-Culmb flu l, d l gh md. h gh m my b lld dff vlu h ldg uf. h d f h l h uf h fm bd ful vg f h uu f h lly ldg m. Hwv, f hghly jd k, h d f h l l uf fud by h d f mmum fy f f h ym. h Kv d Fz44 mhd d k u h x f mlx ghl uu wh h l. I l g h fm f l fu bhd h l, whh mm fu m k l. I h mhd, h l flu uf dmd by ful fld bv, whh h lm f ubjvy dud by bv x, bu h h mul-l u f h h uf wll blhd. h d hu flu mhm hf mlf Kv d Fz 44 mhd by ug ly h flu uf bu h vgd l fl dvdd w blk, mly v d v blk ( Fgu 10 m x). h d mhd l k u h l fu bhd h l. Fm f l fu l k fm bhd h l wdly bvd d bly wll udd. I f vy dld mdl ud l flu, B (1971) fud h h k bhd h l w gd by mll mvm wh h k m, d h d f l xv. Alhugh h dvdul mvm w vy mll, h umulv ff w gf dlm f h l uf wd h uff u f ml bhd h l d fm k. Ug FLAC52 mdl, Kv34 md h f h l z h l, hw Fgu A.2. h l h df h vl x f h fu, whh hw blu Fgu A.2. Fm f h fu b f v blk Fu dvlm k mlx d m ly udd. I lyd dmy k, g-md fu hv b bvd bu g bddg (B45, N d Su46, G l.47, Bk d G48, d J d Suw49), hugh Fgu A.1 Km f l flu f lygl ldg uf (f Kv d Fz 44 ) Fgu A.2 Fm f v blk budd by l d h fu 322 MAY 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

15 67-85:ml Jul 6/5/09 11:06 AM g 323 Egg l f hu blk ly l bly blm (Bk d G48), d jg -v bddg (Hlg d Ayd50). Fu m fqu bddg du hghly uu fu h dm (g51). By, fu h g gh hugh bddg vd wlld hwy. A l md fu h jg v fw m bddg (Hlg d Ayd50). Alhugh h h y f fu wh bddg ly gzd h fld, h mhm h l h dg f fu ffg bddg uf y wll udd. Igh llg mhm d m uld d h d f ubuf fu g. I ld k ml wh jg d h uu gf, h flu mlx ulg mlx fu uu. I bk k m u h my k l lg -xg fu, wh h ul h h h fu lkly b ml. A mm mlgy f bl h fu k dud blw (dd fm Rdl37, Sylv39, d Vm d d B40) d hw Fgu 8 d 9 h m x. Rdl 37 vlbl, d h wk mlly ukw ld mh, whl wdly fd uul glgy. h du f h Sylv39 d MK d D l B52 bbly mldg bu h mh d f hw h vu fu dvl. Rdl wk huld b vd fm ld mh f vw, bu vd gd g f h, fm d dfm f vw, f mll d lg ful k m. h b l h l f h fu fm ju blw h mdlld hzl l z, wh h hzl wll b mll. h mh f h bu h h h mxmum ld blk wgh bv (h blk umd b dfd by w m l fu bhd h l ) d h huld b fvubl f h g f hg, wh h hzl lw. h hg fu l umd hv h mlxy f hg ll glgl ml,.. lg ful, m, d h lby. S Rdl37 d h hg mdl, h b wdly d d h dly b dmd b lbl gud f h f h lg ll y f glgl fu. Kv 34 wk m dl Rdl Fu. h u f g ll h dl gz h h fm f h z h l lkly b mlx, ju hy y glgl ml. Hwv, Rdl 37 bv h h h fu uu mlx, wh h ml bv h h h z m lkly l lll wh h d f h lg h h l, whh xmly 45 fm h hzl, gv h FLAC mdl ul34. Lkg h v blk l Kv34 m mlx u, bu b umd h h uf AFE lkg h l d h v blk b Fgu A.2 fl. h uf my hv b hv, d Kv34 udk m ud dm hw h hv bd h uf uld hv b bk. I w ludd h h udy dd du dubl ul, d h m h w dd. Aywy, h uf mu vully bm fl, bu bh flu vgd hwd h b h. O ll h l d h fu hv lkd gh fm h blk gmy hw Fgu A.2, l flu vbl, f h v blk uffly lg hu h v blk h. Aly f u flu mhm I l m gz h h ly d f qulbum, bu dfmbl blk uu. I hf um h ll f huld hugh h blk d, bu h y xl h l u f h flu. I h wd, mm qulbum dd h mdl bu bv f h flu h m dd vl y gf l m h flu. Fgu A.2 d h flu y d lgh ud f h u f h l bly lul. Symbl ud h ly fllw: A, F, C h ld f h v blk d h fl d hv z f h v blk vly I, O h h f h d u d f h v blk vly l I, l O h h flu lgh f h d u d f h v blk vly l F, l C h lgh f h fl gh z d h hv gh z f h v blk flu uf vly l B h lgh f h v blk flu uf d qul h um f h lgh f fl gh d hv gh z (l B = l F + l C ) β I, β O h h flu uf gl h d u d f h v blk vly (umd b 45 ) R h f h v blk ld h v blk f vi, f vo h vg l f gl lg h h flu uf h d u d f h v blk vly w h d gl f h. h vg f gl lg h uf mullyd mdum b xd h wghd vg: [A.2] wh m h ly hk f h h ly d f h fl gl f h h ly. Lk h f bv, h vg h l luld lg h h flu uf f h v blk d h wghd vg: h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

16 67-85:ml Jul 6/5/09 11:06 AM g 324 Egg l f hu blk ly l bly blm [A.3] wh m h flu uf lgh h h ly d C h h f h ly d by h v blk h flu uf. h v blk wgh f u hk luld : [A.4] wh A h ly vlum h v blk fl, ρ h ly dy, d g h l du gvy. h v blk ud h fllwg wy, ug h l fu mud h l : Dw w l fu vlly dwwd fm uf h hy w uf Fd h md f hzl l jg h w fu, d j h vlly dwwd h fl uf l (h uf h v blk wll ld ) j w h flu uf u gl f 45 h hzl fm h h fl uf ul h h v vl l fu. h v blk w dfd ( Fgu A.2, Fgu 10 h m x). h u dd h qu f dvlm f h fu h ll uff vd dm xly hw h flu uf d gw wh h l, v f h gw uffly lk u. O ll h fu dvld d d, h fm f h v blk ml. A w md l, w my hv w z lg h flu uf h v blk b, mly h fl d hv z. h w z hv dff h gh, whh hv b k u wh h f dvld by h v blk mud. h v blk wgh lul h m f h v blk. Rg f h b f h v blk fmd by h fl gh lg h flu uf du h blk wgh d h hv d fl gh f h f h uf h h y yldd h. Dvg f fmd by h gl m f h wgh lg h m uf. H, h f b xd : [A.5] Sml h fl z, ml d gl ld m h hv z f h v blk b luld wh Equ [A.7]. h h g d gl f h flu uf wll hv h fm: d [A.7] [A.7b] vly. Fgu A.2 hw h h k m w l flu uf: h fl uf AFE, d h v blk h flu uf ED. h vy ml h Kv d Fz44 gmy dud l. hu blk flu bl ly f l uf EG Fgu A.2 dvld. h h f g hw Fgu A.3. Fm Fgu A.3 w w [A.8] If w k u h df f fy f h w w d Fm Fgu A.3 d Equ [A.10] w hv [A.9] [A.10] [A.11] [A.12] If w mb Equ [A.11] d [A.12] d FOS = 1, whh m h h l l uf h f lg, h w wll hv [A.13] [A.5b] wh ϖ vg l gl f h flu uf, F h v blk ld bv fl z, N F d F h ml d gl m vly. h g f lg h fl z wll hv h fm: [A.6] wh φ E h fl gl lg h bddg. Fgu A.3 Dl f l 45 h uf 324 MAY 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

17 67-85:ml Jul 6/5/09 11:06 AM g 325 Egg l f hu blk ly l bly blm h gl f l f Equ [A.13] h fy h d Equ [A.14] f hv l lu: [A.14] Fm Equ [A.14] w h ud w- d, φ = 0 f l =, whh bl ly f R = 0, R d bh 0 d l 0. I h f l = 0, w huld hv l fu fm h uf h flu uf. Kv d Fz44 d h w- h lygl mdl, whh gv h gl f f qul h gl f l f (δ = φ). h fllwg qu b ld f h v blk ld dbu lg h w h flu uf h fm h wdg uu: d [A.15] [A.16] f h u d h flu uf vly ( Fgu A.2 f df f u d ), wh A h wgh f h v blk d ϖ A h ly l gl h blk wdg. Fgu A.4 hw h m l fl hw Fgu A.2, wh dfg h blk bud. L u f lul h -w u lg h l CD Fgu A.4. h l luld dud vl l fu dh (z) d h uf, (z W ), bv h l fu dh dd. hf, h -w u D Fgu A.4 qul : [A.17] [A.18] L u lul h -w u lg h l DE. A f, l u df -w u lg h l DA. F h u, w um z -w u D. W l hv z u A h l, f h w flwg u f h l. H, w um h, h mddl f h bw h w ( I), w wll hv h hgh -w u vlu h wll b qul : [A.19] DA wh z w h dff bw dh f D d A. Nw w m dw dgm (ADJ) bw h A d D. Fm Equ [A.17], w hv -w u D. S l u dw h l D, qul h -w u D ml h l AD d dd h m mgud I ddg JK. Nw u dgm k w fm (AJKD), whh ul bu f h AJK. A h I h mddl f AD, h hlf f h JK b ddd h AI d h h hlf h ID. H, w hv w qul [A.20] whh qul h l MN u dgm. h l u mv u mgud MN wd D ul h l K. h hw Fgu A.4. Nw w hv w dgm (AND), whh -w u dbu lg h l AD. L u w lul h -w u E. F h, l u mk hgl j h l AD, whh L, whh h u wh h mgud LR. hf, h u E wll hv h mgud [A.21] wh γ w h u wgh f w d z W h uf l fu dh blw h h uf. h l f g lg h uf vl l fu h v blk u d qul wh z LE ω h dh dff bw h L d E. h u l bu E lghly d h L. fd h wh w hv mxmum -w u lg h u h flu uf w df O, wh hgl j h l AD M. Wh hgh dg f xm, w y h h -w u O qul [A.22] I w y u -w u dgm lg h l f h h flu uf (HE) bu w hv luld h -w u E (Equ [A.21]) d hv umd z w u H. h um bd h l h w f uf AB d BC. -w u F fllw h m d f E (Equ [A.21] d [A.22]): [A.23] Fgu A.4 l f -w u h l wh σ w Q h -w u mgud Q d z w QF h dh dff bw h Q d F. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY

18 67-85:ml Jul 6/5/09 11:06 AM g 326 Egg l f hu blk ly l bly blm Nw w dw h -w u dgm lg h v blk flu uf d h v blk flu uf. Fgu A.5 hw -w u dgm d ul f V CD, U O, U I, U C, d U F g lg h flu uf f h vl l fu, h v blk u d h flu uf, d h hv d fl lgh vly f h v blk b. h fgu l hw h luld -w u D, E, O, d F vly. Adg h -w u dgm, luld ul f hv h fllwg mgud: [A.24] [A.25] [A.26] [A.27] wh l DO, l EO, l EH, l EF, d l AF lgh bw DO, EO, EH, EF d AF vly. Sml w u ly w udk by Hk53. A h h uf, w hv h mbd f w f. h f f k u h um f dvg d g f (wh h g - d + vly) lg h l flu uf f h v blk b, xd [A.28] I h f (Fgu A.6), h ml m h h uf ud h v blk d h dg v blk wgh (R N d AI N ) xmly -dl, whh h dvg f f h v blk u h flu uf d mgh ld flu. H, h v blk flu uf wll hv ly hv gh. I h d (Fgu A.6b), w hv f, g h f f h v blk ld. gl ( h h uf) m f h f d h dg v blk ld d, whh wll d h l dvg ff. Ug h bv du d um h δ = φ lm fl f h flu uf, w u Equ [A.10] df h f h x f h h flu uf, whh h h fm: [A.29] If w k u Equ [A.16] d [A.17] d h lh [A.30] h Equ [A.29] b w [A.31] d, dly, h dg v blk ld. H, w uld hv w d f h v blk f (Equ [A.28]): h f wh h um gv (Fgu A.6) d h d, wh h um v (Fgu A.6b). A f h f l gl (δ = φ), llw u u ly hv gh lg h h flu uf. W f h ml h uf m f h v blk f (R ), h u flu uf wh h dg l gl. Fgu A.5 Shm f -w u lul h v d v blk bud Fgu A.6 -w u dgm h flu uf, Fgu A.6 v blk f R g xmly dl h v blk ld h h flu uf, Fgu A.6b v blk f R g h v blk ld h h flu uf 326 MAY 2009 VOLUME 109 REFEREED AER h Jul f h Suh Af Iu f Mg d Mllugy

19 67-85:ml Jul 6/5/09 11:06 AM g 327 Egg l f hu blk ly l bly blm [A.32] whh f h x f h h flu uf d h uf f f fy. If h h fu (η) fm Equ [A.32] hgh h 1.3, h h flu uf wll fm. hf, w wll hv d f h flu y (uh mul l lygl) bu f hu flu. If h lw h 1.3, w hv h flu h uf d, fm h, blky-y flu. A w dud l, h m ml h flu uf f h dg v blk ld d h v blk f fd h u h uf. h h mbd lg h u uf b xd : hf, h u h flu uf wll hv f f fy qul : [A.33] [A.34] Equ [A.34] b fuh mlfd : [A.35] h bl uf fy f h bl f ldy luld dvg d g f lg h uf h v blk b ( Fgu A.12), d h h fm: [A.36] wh φ B h f gl lg h flu uf d v F d v C h d gl lg h fl z d hv z f h v blk b Fgu A.2). h flu uf lgh (l I, l O, d l B, Fgu A.2) vy, d dd l gl, ly l, ly hk, d k. vd vmg h flu f h h flu uf h l bly, wghd fu f luld fy f huld b ud. H, w hv h fllwg wghd vg qu f lul f h l bly f f fy fm h dvdul flu uf f f fy d h v lgh: [A.37] h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 109 REFEREED AER MAY