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TítuloA general numerical model for grounding analysis in layered soils

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Preprint of the paper:

"A General Numerical Model for Grounding Analysis in Layered Soils" I. Colominas, J. Gómez-Calviño, F. Navarrina, M. Casteleiro (2002)

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Y‚R‚ „‚sRBtR b‚ Ys%‚ Z„t‚I BZ„ s‚t$Bt B BY‚„ tZ8‚„${sj ‚{Yt$JZ‚R bY${Y „‚JZ$„‚ Btjk Y‚ I$R{„‚$9s$Bt BP Y‚

ABZtIs„$‚R G$Y Y$R s$8 $ $R ‚RR‚t$sj B I‚„$%‚ st $t‚„sj ‚-}„‚RR$Bt PB„ }B‚t$sj~ $t ‚„8R BP Zt,tBbtR I‚ht‚I

(5)

*Z„$t Y‚ {BtR„Z{$Bt }„B{‚RR BP Y‚ ‚j‚{„${sj $tRsjjs$Bt Y‚ RZ„„BZtI$tR BP Y‚ RZARs$Bt R$‚ s„‚ j‚%‚jj‚I stI

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b‚ b$jj sIB} st XYB„$9Btsjjk jsk‚„‚I RB$j 8BI‚j" $t BZ„ 8sY‚8s${sj 8BI‚j $t B„I‚„ B {s{Y Y‚ %s„$s$BtR BP Y‚ RB$j {BtIZ{$%$k b$Y I‚}Y whZ„‚ dD yt Y‚ {sR‚ BP %s„$s$BtR BP Y‚ RB$j {BtIZ{$%$k t‚s„ Y‚ „BZtI$t RkR‚8

Y‚ R$8}j‚R 8BI‚j b‚ {st Rs‚ ws X%‚„${sjjk jsk‚„‚I RB$j 8BI‚j"D {BtR$R BP sRZ8$t Ys Y‚ ‚s„Y RZ„Ps{‚ o $R

YB„$9Btsj bY$j‚ Y‚ $t‚„Ps{‚R  s„‚ }s„sjj‚j Bt‚ B stBY‚„ stI }‚„}‚tI${Zjs„ B o whZ„‚ 1D

qYZR s,$t $tB s{{BZt Y‚R‚ sRRZ8}$BtR Y‚ s}}j${s$Bt BP Y‚ X8‚YBI BP $8s‚R" stI p„‚‚t:R yI‚t$k B }„BAj‚8 w1D k$‚jIR Y‚ PBjjBb$t $t‚„sj ‚-}„‚RR$Bt >dE d dMH PB„ }B‚t$sj ~w??????????????D s st s„A$„s„k }B$t?????????????? ;o $t ‚„8R BP

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Y‚ ‚j‚{„BI‚ RZ„Ps{‚ 2oKU

~w??????????????D ) ;$Kd 8 8

;>Kw??????????????, DwDQ, ??????????????;o3 wnD

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Y‚ ‚j‚{„BI‚ RZ„Ps{‚ BP Y‚ j‚s,s‚ {Z„„‚t I‚tR$k Ys 4BbR P„B8 ‚s{Y }B$t; b‚$Y‚I Ak Y‚ p„‚‚t PZt{$Bt

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>ddw??????????????d, D ) „w d

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d

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FTs-$R $R }‚„}‚tI${Zjs„ B o

yt Y‚ {sR‚ BP s %‚„${sj bBTjsk‚„‚I 8BI‚j whZ„‚ 1D Y‚ R‚„$‚R BP Y‚ ,‚„t‚jR s„‚ sjRB „‚IZ{‚I B s ht$‚ tZ8A‚„ BP ‚„8RU

>ddw??????????????d, D ) „w??????????????d,>d

?, r, FHD L

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Y‚ Rk88‚„${ }B$t BP b$Y „‚R}‚{ B Y‚ ‚s„Y RZ„Ps{‚ o stI B Y‚ „‚RZjst $8s‚R b$Y „‚R}‚{ B Y‚ %‚„${sj

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stI Y‚ FTs-$R stI rTs-$R s„‚ }‚„}‚tI${Zjs„ B o stI d „‚R}‚{$%‚jk ]B‚^{$‚t$R s „s$B I‚ht‚I $t ‚„8R BP Y‚

jsk‚„ {BtIZ{$%$$‚R

) d 1

dL13 wED

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P„B8 ??????????????B Y‚ Rk88‚„${ }B$t BP b$Y „‚R}‚{ B Y‚ ‚s„Y RZ„Ps{‚ o stI B Y‚ $t‚„Ps{‚ RZ„Ps{‚ A‚b‚‚t jsk‚„R

I $R Y‚ Y${,t‚RR BP Y‚ Z}}‚„ jsk‚„ stI $R $%‚t Ak wED G‚ sRRZ8‚ Bt{‚ 8B„‚ Ys Y‚ B„$$t BP Y‚ {BB„I$ts‚R

(6)

VR b‚ {st BAR‚„%‚ $t ‚-}„‚RR$BtR w;D wxD stI wD b‚s,jk R$tZjs„ ,‚„t‚jR >Kw??????????????, D I‚}‚tI Bt Y‚ {BtIZ{$%$k BP Y‚ jsk‚„R stI Bt Y‚ $t%‚„R‚ BP Y‚ I$Rst{‚R P„B8 Y‚ }B$t?????????????? B Y‚ }B$tstI B sjj Y‚ $8s‚R BP b$Y „‚R}‚{ B Y‚

‚s„Y RZ„Ps{‚ o stI B Y‚ $t‚„Ps{‚R  A‚b‚‚t jsk‚„R >dM dH 3B„ Zt$PB„8 stI bBTjsk‚„ RB$j 8BI‚jR Y‚R‚ ,‚„t‚jR

{st A‚ ‚-}„‚RR‚I $t Y‚ ‚t‚„sj PB„8U

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q>

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Kw??????????????, D, >qKw??????????????, D ) qwD

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I$Rst{‚ A‚b‚‚t Y‚ }B$tR?????????????? stIq A‚$t + Y‚ }B$t Bt Y‚ ‚j‚{„BI‚ RZ„Ps{‚ w+wD )D stI A‚$tq wq W) (D

Y‚ $8s‚R BP b$Y „‚R}‚{ B Y‚ ‚s„Y RZ„Ps{‚ stI B Y‚ $t‚„Ps{‚R A‚b‚‚t jsk‚„R >dMH 3$tsjjk q> $R Y‚ tZ8A‚„ BP

RZ88stIR $t Y‚ R‚„$‚R BP $t‚„sj ,‚„t‚jR stI $ I‚}‚tIR Bt Y‚ {sR‚ A‚$t stsjk9‚I wR‚‚ w;D wxD stI wDD

1n zs„$s$Btsj 3B„8BP Y‚ _„BAj‚8

qY‚ $t‚„sj ‚-}„‚RR$Bt PB„ Y‚ }B‚t$sj wnD $R sjRB Rs$Rh‚I Bt Y‚ ‚j‚{„BI‚ RZ„Ps{‚ > H bY‚„‚ Y‚ }B‚t$sj %sjZ‚

$R ,tBbt Ak Y‚ ABZtIs„k {BtI$$Bt ~KwD ) d ; ]BtR‚JZ‚tjk Y‚ j‚s,s‚ {Z„„‚t I‚tR$k 8ZR %‚„$Pk Y‚

PBjjBb$t 3„‚IYBj8 $t‚„sj ‚JZs$Bt BP Y‚ h„R ,$tI Bt d

;$K 88

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y $R $8}B„st B „‚8s„, Ys BAs$t$t Y‚ j‚s,s‚ {Z„„‚t I‚tR$k P„B8 wD $R Y‚ ,‚k B RBj%‚ Y‚ }„BAj‚8 R$t{‚

Y‚ }B‚t$sj I$R„$AZ$Bt }„BIZ{‚I bY‚t s PsZj {Z„„‚t $R I‚„$%‚I Y„BZY Y‚ „BZtI$t „$I {st A‚ ‚sR$jk BAs$t‚I

Ak 8‚stR BP ‚-}„‚RR$Bt wnD }„B%$I‚I Ys Y‚ %sjZ‚ BP$R ,tBbt 3Z„Y‚„8B„‚ 8BR BP Y‚ „‚8s$t$t RsP‚k stI I‚R$t

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>H

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88

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n e WZ8‚„${sj 3B„8Zjs$Bt

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wD )3[

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W‚- Y‚ $t‚„sj ‚-}„‚RR$Bt wnD PB„ Y‚ }B‚t$sj~w??????????????D {st sjRB A‚ I$R{„‚$9‚I sR

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(7)

!t Y‚ BY‚„ YstI PB„ s $%‚t R‚ BP[ ‚R PZt{$BtR\jiwDiI‚ht‚I Bt Y‚ %s„$s$Btsj PB„8 wd(D $R „‚IZ{‚I B Y‚ j$t‚s„ RkR‚8 BP ‚JZs$BtRU

[ 3

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s{Y$‚%‚I wqp)q>$P Y$R tZ8A‚„ $R ht$‚D

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R‚{$Bt BP Y‚ {kj$tI„${sj {BtIZ{B„R BP Y‚ „BZtI$t „$I stI I$R{„‚$9s$BtR wddD stI wd;D A‚{B8‚ 8Z{Y R$8}j‚„ R$t{‚ Y‚ {jsRR‚R BP ‚R stI „$sj PZt{$BtR s„‚ „‚R„${‚I B YBR‚ b$Y {$„{Z8P‚„‚t$sj Zt$PB„8$k bY$j‚ Btjk Y‚ s-$sj j$t‚R BP Y‚ „BZtI$t ‚j‚{„BI‚R Ys%‚ B A‚ I$R{„‚$9‚I >H ]BtR‚JZ‚tjk $t {B8}s„$RBt b$Y Y‚ ‚t‚„sj 1* ABZtIs„k ‚j‚8‚t PB„8Zjs$Bt Y‚ tZ8A‚„ BP ‚j‚8‚tsj {Bt„$AZ$BtRp#i7 stI"i# t‚‚I‚I B Rs‚ Y‚ RkR‚8 BP j$t‚s„ ‚JZs$BtR

wd;D stI Y‚ tZ8A‚„ BP Zt,tBbtR7 s„‚ tBb R$t$h{stjk R8sjj‚„ PB„ s $%‚t j‚%‚j BP 8‚RY „‚ht‚8‚t

yt R}$‚ BP Y‚ $8}B„st „‚IZ{$Bt $t Y‚ {B8}Zs$Btsj {BR ‚-‚tR$%‚ {B8}Z$t $R R$jj t‚{‚RRs„k 8s$tjk A‚{sZR‚ BP Y‚ {$„{Z8P‚„‚t$sj $t‚„s$Bt Bt Y‚ }‚„$8‚‚„ BP Y‚ ‚j‚{„BI‚R Ys s„‚ $t%Bj%‚I $t Y‚ $t‚„sj ,‚„t‚jR yt }„‚%$BZR bB„,R b‚ Ys%‚ }„B}BR‚I Y‚ s}}„B-$8s‚I ‚%sjZs$Bt BP Y‚R‚ {$„{Z8P‚„‚t$sj $t‚„sjR Ak ZR$t R}‚{$h{ JZsI„sZ„‚R>H qY‚ htsj „‚RZj $R st s}}„B-$8s‚I d* s}}„Bs{Y R$8$js„ B Y‚ }„‚R‚t‚I $t R‚{$Bt nd bY‚„‚ {B8}Z$t Y‚ {B‚^{$‚tR BP Y‚ ‚JZs$BtR RkR‚8 Btjk „‚JZ$„‚R $t‚„s$Bt Bt d* IB8s$tR $‚ Y‚ s-$sj j$t‚R BP Y‚ ‚j‚{„BI‚R>dMH

WBb R}‚{$h{ tZ8‚„${sj s}}„Bs{Y‚R {st A‚ I‚„$%‚I PB„ I$&‚„‚t R‚j‚{$BtR BP Y‚ R‚R BP „$sj stI ‚R PZt{$BtR w‚ _B$t ]BjjB{s$Bt B„ psj‚„,$t R{Y‚8‚RD 3Z„Y‚„ I$R{ZRR$Bt $t Y$R }s}‚„ $R „‚R„${‚I B Y‚ {sR‚ BP s psj‚„,$t k}‚ s}}„Bs{Y bY‚„‚ Y‚ 8s„$- BP {B‚^{$‚tR $R Rk88‚„${ stI }BR$$%‚ I‚ht$‚>H qY‚ sZYB„R Ys%‚ I‚„$%‚I s Y$Yjk ‚^{$‚t stsjk${sj ‚{Yt$JZ‚ B ‚%sjZs‚ Y‚ {B‚^{$‚tR BP Y‚ j$t‚s„ RkR‚8 BP ‚JZs$BtR>H PB„ _B$t ]BjjB{s$Bt stI

psj‚„,$t k}‚ b‚$Y$t $t Zt$PB„8 RB$j 8BI‚jR 7$t{‚ Y‚ d* s}}„B-$8s‚I ‚-}„‚RR$BtR PB„ Y‚ ‚„8R~q

,7 stIp#qi7 $t

wdnD stI wdxD s„‚ PB„8sjjk ‚JZ$%sj‚t B YBR‚ BAs$t‚I $t Y‚ {sR‚ BP Zt$PB„8 RB$j 8BI‚jR Y‚$„ {B8}Zs$Bt {st sjRB A‚ }‚„PB„8‚I stsjk${sjjk Ak 8‚stR BP Y‚ sAB%‚ 8‚t$Bt‚I ‚{Yt$JZ‚R >dMH

qY$R sR}‚{ BP Y‚ tZ8‚„${sj s}}„Bs{Y $R Y‚ ,‚k PB„ $R ‚t‚„sj$9s$Bt PB„ stk jsk‚„‚I RB$jR 7$t{‚ Y‚ $t‚„sj ,‚„t‚jR

s„‚ ‚-}„‚RR‚I $t Y‚ ‚t‚„sj PB„8 $%‚t Ak wMD Y‚ {B‚h{$‚tR BP Y‚ R$&t‚RR 8s„$- pi7 s„‚ {B8}Z‚I Ak Y‚ IBZAj‚

RZ8 $t Y‚&‚j‚8‚tR BP Y‚ R‚„$‚R BP qp ‚„8Rp#qi7 I‚ht‚I Ak wdxD VtI Y‚R‚ ‚„8R {st A‚ {B8}Z‚I Ak ZR$t Y‚

Y$Y ‚^{$‚t stsjk${sj ‚{Yt$JZ‚R I‚%‚jB}‚I PB„ Y‚ Zt$PB„8 RB$j {sR‚R >H

!P {BZ„R‚ st $8}B„st sR}‚{ BP Y‚ }„B}BR‚I tZ8‚„${sj PB„8Zjs$Bt 8ZR A‚ {BtR$I‚„U Y‚ {B„„‚R}BtI$t Bsj

{B8}Zs$Btsj {BR yt BZ„ {sR‚ PB„ s $%‚t R}‚{$h{ I$R{„‚$9s$Bt w&‚j‚8‚tR BP €tBI‚R ‚s{Y stI s Bsj tZ8A‚„

BP [ I‚„‚‚R BP P„‚‚IB8D s j$t‚s„ RkR‚8 wd;D BP B„I‚„ [ 8ZR A‚ ‚t‚„s‚I stI RBj%‚I s„$- ‚t‚„s$Bt }„B{‚RR

„‚JZ$„‚R 5w&1€1b1D B}‚„s$BtR R$t{‚ €1 R‚„$‚R BP {Bt„$AZ$BtR BP k}‚ wd(D Ys%‚ B A‚ {B8}Z‚I PB„ ‚%‚„k }s$„ BP

(8)

PB„8‚I Ak Btjk bB ‚„8R <Bb‚%‚„ $t bBTjsk‚„ 8BI‚jR Y‚ R‚„$‚R {st Ys%‚ st $tht$‚ tZ8A‚„ BP Y‚8 qY‚„‚PB„‚ s RZ^{$‚t tZ8A‚„ BP Y‚R‚ ‚„8R 8ZR A‚ tZ8‚„${sjjk sII‚I Z} Zt$j s Bj‚„st{‚ {BtI$$Bt $R PZjhjj‚I B„ st Z}}‚„ j$8$ BP RZ88stIR $R s{Y$‚%‚I ]BtR‚JZ‚tjk 8s„$- ‚t‚„s$Bt RYBZjI A‚ 8Z{Y 8B„‚ ‚-}‚tR$%‚ $t bBTjsk‚„ 8BI‚jR

!t Y‚ BY‚„ YstI R$t{‚ Y‚ 8s„$- $R Rk88‚„${ AZ tB R}s„R‚ Y‚ RkR‚8 RBj%$t }„B{‚RR „‚JZ$„‚R5w[nbnD B}‚„s$BtR

$P Y‚ „‚RBjZ$Bt $R {s„„$‚I BZ b$Y s I$„‚{ 8‚YBI

<‚t{‚ 8BR BP Y‚ {B8}Z$t ‚&B„ $R I‚%B‚I B 8s„$- ‚t‚„s$Bt $t R8sjj\8‚I$Z8 }„BAj‚8R bY$j‚ j$t‚s„ RkR‚8 „‚RBjZ$Bt RYBZjI }„‚%s$j $t 8‚I$Z8\js„‚ Bt‚R yt Y‚R‚ {sR‚R Y‚ ZR‚ BP I$„‚{ 8‚YBIR PB„ Y‚ j$t‚s„ RkR‚8 „‚RBjZ$Bt $R BZ BP „st‚ qY‚„‚PB„‚ $‚„s$%‚ B„ R‚8$$‚„s$%‚ ‚{Yt$JZ‚R b$jj A‚ }„‚P‚„sAj‚ >1dH qY‚ A‚R „‚RZjR Ys%‚ A‚‚t BAs$t‚I Ak s I$sBtsj _„‚{BtI$$Bt‚I ]Bt`Zs‚ p„sI$‚t sjB„$Y8 >11H b$Y sRR‚8Ajk BP Y‚ jBAsj 8s„$- >H qY$R ‚{Yt$JZ‚ YsR Z„t‚I BZ B A‚ ‚-„‚8‚jk ‚^{$‚t PB„ RBj%$t js„‚ R{sj‚ }„BAj‚8R b$Y s %‚„k jBb {B8}Zs$Btsj {BR $t {B8}s„$RBt b$Y Y‚ {B„„‚R}BtI$t B 8s„$- ‚t‚„s$Bt qY‚ „‚sRBt PB„ Y$R „‚8s„,sAj‚ ‚^{‚t{k 8ZR A‚ RBZY PB„ $t Y‚ Y‚B„‚${sj {Bt%‚„‚t{‚ A‚Ys%$BZ„ BP Y‚ {Bt`Zs‚ „sI$‚t 8‚YBI $t „‚js$Bt b$Y Y‚ {BtI$$Bt tZ8A‚„ BP Y‚ }„BAj‚8 >d( 11H

qsAj‚ d sjs$IBR yy p„BZtI$t 7kR‚8U p‚t‚„sj ]Ys„s{‚„$R${R sjs$IBR yy ]Ys„s{‚„$R${R

s- p„$I *$8‚tR$BtRU Edd 8d 8

p„$I *‚}YU (M( 8

WZ8A‚„ BP p„$I ej‚{„BI‚RU d(

WZ8A‚„ BP z‚„${sj iBIRU E

ej‚{„BI‚ *$s8‚‚„U dd1M 88

z‚„${sj iBI *$s8‚‚„U d;(( 88

z‚„${sj iBI N‚tYU dx 8

p„BZtI _B‚t$sj i$R‚ wp_iDU d( ,z

y

(61.1,79.1)

x

(0,0)

3$Z„‚ n sjs$IBR yy p„BZtI$t 7kR‚8U _jst BP Y‚ „BZtI$t „$I w%‚„${sj „BIR s„‚ 8s„,‚I b$Y Ajs{, }B$tRD

!t Y‚ BY‚„ YstI Bt{‚ Y‚ j‚s,s‚ {Z„„‚t YsR A‚‚t BAs$t‚I Y‚ {BR BP {B8}Z$t Y‚ ‚JZ$%sj‚t „‚R$Rst{‚ $R t‚j$$Aj‚ qY‚ sII$$Btsj {BR BP {B8}Z$t }B‚t$sj s stk $%‚t }B$t wtB„8sjjk Bt Y‚ ‚s„Y RZ„Ps{‚D Ak 8‚stR

BP wd1D Btjk „‚JZ$„‚R 5w&€D B}‚„s$BtR R$t{‚ € {Bt„$AZ$BtR BP k}‚ wdnD Ys%‚ B A‚ {B8}Z‚I PB„ ‚%‚„k ‚j‚8‚t

<Bb‚%‚„ {B8}Z$t $8‚ 8sk A‚ $8}B„st $P $ $R t‚{‚RRs„k B {B8}Z‚ }B‚t$sjR s s js„‚ tZ8A‚„ BP }B$tR PB„ ‚-s8}j‚ B I„sb {BtBZ„ j$t‚R $t s ‚-‚tR‚ s„‚s BP Y‚ „BZtI$t R$‚

(9)

-20.00 0.00 20.00 40.00 60.00 80.00 X (m.) -20.00

0.00 20.00 40.00 60.00 80.00 100.00 Y (m.)

3$Z„‚ ; sjs$IBR yy p„BZtI$t 7kR‚8U _B‚t$sj I$R„$AZ$Bt wd(,zD Bt Y‚ ‚s„Y RZ„Ps{‚ BAs$t‚I Ak ZR$t s Zt$PB„8

RB$j 8BI‚j w8BI‚j VD

; V}}j${s$Bt BP Y‚ tZ8‚„${sj s}}„Bs{Y B }„s{${sj {sR‚R

;d *‚R{„$}$Bt BP Y‚ ‚s„Y$t RkR‚8

qY‚ }„B}BR‚I tZ8‚„${sj s}}„Bs{Y AsR‚I Bt Y‚ BZtIs„k ej‚8‚t ‚YBI YsR A‚‚t $8}j‚8‚t‚I $t s ]B8}Z‚„ V$I‚I *‚R$t RkR‚8 PB„ ‚s„Y$t stsjkR$R >d;H yt Y$R R‚{$Bt b‚ b$jj }„‚R‚t „‚RZjR BAs$t‚I b$Y I$&‚„‚t k}‚ BP RB$j 8BI‚jR Ak ZR$t Y‚ „‚sj ‚B8‚„k BP s „BZtI$t „$IU Y‚ sjs$IBR yy RZARs$Bt {jBR‚ B Y‚ {$k BP z$B $t 7}s$t

qY‚ ‚s„Y$t RkR‚8 BP Y$R RZARs$Bt $R s „$I BP d( {kj$tI„${sj {BtIZ{B„R wI$s8‚‚„U dd1M 88D AZ„$‚I B s I‚}Y BP M( {8 RZ}}j‚8‚t‚I b$Y E %‚„${sj „BIR w‚s{Y Bt‚ YsR s j‚tY BP dx 8 stI s I$s8‚‚„ BP d;( 88D qY‚ Bsj

RZ„Ps{‚ }„B‚{‚I $R sABZ ;M(( 81 qY‚ Bsj s„‚s RZI$‚I $R s „‚{stj‚ BP dx( 8 Ak d;( 8 w$‚ s RZ„Ps{‚ sABZ PBZ„

$8‚R js„‚„ Yst Y‚ „BZtI$t „$ID qY‚ p„BZtI _B‚t$sj i$R‚ {BtR$I‚„‚I $t Y$R RZIk YsR A‚‚t d( ,z qY‚ }jst BP Y‚ „BZtI$t „$I $R }„‚R‚t‚I $t hZ„‚ n stI s RZ88s„k BP Y‚ {Ys„s{‚„$R${R BP Y‚ RkR‚8 $R $%‚t $t sAj‚ d

qsAj‚ 1 sjs$IBR yy p„BZtI$t 7kR‚8U ]Ys„s{‚„$R${R BP Y‚ WZ8‚„${sj BI‚j e WZ8‚„${sj BI‚j

qk}‚ BP V}}„Bs{YU psj‚„,$t

qk}‚ BP ]Z„„‚t *‚tR$k ej‚8‚tU N$t‚s„

WZ8A‚„ BP ej‚8‚tRU 1;d

*‚„‚‚R BP 3„‚‚IB8U 1(M

;1 i‚RZjR BAs$t‚I Ak ZR$t I$&‚„‚t RB$j 8BI‚jR

(10)

-20.00 0.00 20.00 40.00 60.00 80.00 X (m.) -20.00

0.00 20.00 40.00 60.00 80.00 100.00 Y (m.)

3$Z„‚ x sjs$IBR yy p„BZtI$t 7kR‚8U _B‚t$sj I$R„$AZ$Bt wd( ,zD Bt Y‚ ‚s„Y RZ„Ps{‚ BAs$t‚I Ak ZR$t st

YB„$9Btsj bBTjsk‚„ RB$j 8BI‚j w8BI‚j D

qsAj‚ n sjs$IBR yy p„BZtI$t 7kR‚8U WZ8‚„${sj „‚RZjR PB„ Y‚ I$&‚„‚t RB$j 8BI‚jR 7B$j BI‚jR

V ]

eJZ$% i‚R$Rst{‚ wD (nnE MM (;;;

qBsj ]Z„„‚t w,VD 1 ddd 11x

]_= q$8‚ wRD 1E d(nx ;1

qY‚ ‚-s8}j‚R }„‚R‚t‚I Ys%‚ A‚‚t „‚}‚s‚Ijk RBj%‚I $t{„‚sR$t Y‚ R‚8‚ts$Bt BP Y‚ ‚j‚{„BI‚R V Y‚ R{sj‚ BP Y‚ bYBj‚ „$I „‚RZjR stI }B‚t$sj I$R„$AZ$BtR Bt Y‚ ‚s„Y RZ„Ps{‚ b‚„‚ tB tB${‚sAjk $8}„B%‚I Ak $t{„‚sR$t R‚8‚ts$Bt VR s ‚t‚„sj „Zj‚ s „‚sRBtsAj‚ j‚%‚j BP R‚8‚ts$Bt $R RZ^{$‚t PB„ }„s{${sj }Z„}BR‚R stI $t{„‚sR$t Y‚ tZ8A‚„ BP ‚j‚8‚tR b$jj tB A‚ t‚{‚RRs„k Ztj‚RR Y$Y s{{Z„s‚ „‚RZjR 8ZR A‚ BAs$t‚I PB„ s j$8$‚I }s„ BP Y‚ bYBj‚ ‚s„Y$t RkR‚8 3Z„Y‚„8B„‚ Y‚ ZR‚ BP Y$Y‚„ B„I‚„ ‚j‚8‚tR b$jj A‚ $t ‚t‚„sj 8B„‚ sI%sts‚BZR Yst $t{„‚sR$t R‚8‚ts$Bt $t‚tR$%‚jk R$t{‚ s{{Z„s{k b$jj A‚ Y$Y‚„ PB„ s „‚8s„,sAjk R8sjj‚„ Bsj tZ8A‚„ BP I‚„‚‚R BP P„‚‚IB8 VtI {BtR‚JZ‚tjk $ RYBZjI „‚JZ$„‚ s {BtR$I‚„sAjk R8sjj‚„ {B8}Zs$Btsj ‚&B„ >H

yt Y‚ sjs$IBR yy „BZtI$t RkR‚8 b‚ Ys%‚ stsjk9‚I Y„‚‚ I$&‚„‚t ,$tI BP RB$j 8BI‚jR XBI‚j V" {B„„‚R}BtIR B s

Zt$PB„8 RB$j 8BI‚j b$Y ) x(d w8Dd X8BI‚j " {B„„‚R}BtIR B st YB„$9Btsj bBTjsk‚„ RB$j 8BI‚j wsR hZ„‚ dD

b$Yd ) x(d w8Dd1) x(((d w8Dd stII ) d3x 8 stI X8BI‚j ]" {B„„‚R}BtIR B s %‚„${sj bBTjsk‚„ RB$j

8BI‚j wsR hZ„‚ 1D b$Yd) x(d w8Dd1) x(((d w8DdstI Y‚ %‚„${sj $t‚„}YsR‚ $R jB{s‚I s s I$Rst{‚ BP

d 8 P„B8 Y‚ „BZtI$t „$I wk ) M(3d 8- $t Y‚ }jst BP hZ„‚ nD

3$Z„‚ ; RYBbR Y‚ }B‚t$sj I$R„$AZ$Bt Bt Y‚ ‚s„Y RZ„Ps{‚ BAs$t‚I Ak ZR$t Y‚ Zt$PB„8 RB$j 8BI‚j V 3$Z„‚R x stI E RYBb Y‚ }B‚t$sj I$R„$AZ$Bt Bt Y‚ ‚s„Y RZ„Ps{‚ BAs$t‚I Ak ZR$t Y‚ bBTjsk‚„ RB$j 8BI‚jR wYB„$9BtsjD stI ] w%‚„${sjD 3$Z„‚  $R s {B8}s„$RBt BP Y‚ }B‚t$sj I$R„$AZ$Bt Bt Y‚ ‚s„Y RZ„Ps{‚ BAs$t‚I b$Y 8BI‚jR V stI ] $t Y‚ 9Bt‚ bY‚„‚ Y‚ {BtIZ{$%$k BP Y‚ „BZtI %s„$‚R

qsAj‚ 1 RZ88s„$9‚R Y‚ {Ys„s{‚„$R${R BP Y‚ tZ8‚„${sj 8BI‚j stI qsAj‚ n RYBbR RB8‚ BP Y‚ „‚RZjR BAs$t‚I $t Y‚ Y„‚‚ I$&‚„‚t {sR‚RU Y‚ ‚JZ$%sj‚t „‚R$Rst{‚ BP Y‚ „BZtI$t RkR‚8 Y‚ Bsj {Z„„‚t I‚„$%‚I B Y‚ RB$j stI Y‚ ]_= $8‚

(11)

-20.00 0.00 20.00 40.00 60.00 80.00 X (m.) -20.00

0.00 20.00 40.00 60.00 80.00 100.00 Y (m.)

3$Z„‚ E sjs$IBR yy p„BZtI$t 7kR‚8U _B‚t$sj I$R„$AZ$Bt wd(,zD Bt Y‚ ‚s„Y RZ„Ps{‚ BAs$t‚I Ak ZR$t s %‚„${sj

bBT jsk‚„ RB$j 8BI‚j w8BI‚j ]D

{B8}Z‚„ s Y‚ eZ„B}‚st ]‚t‚„ PB„ _s„sjj‚j$R8 BP s„{‚jBts ]e_ V VjYBZY Y‚ !1((( $R s Y$YT}‚„PB„8st{‚ {B8}Z‚„ b$Y E; y_7 id(((( }„B{‚RRB„R s 1x( <9 Y‚ ]_= $8‚R $%‚t $t qsAj‚ 1 {B„„‚R}BtI B ‚-‚{Z$t Y‚ ‚-s8}j‚R $t R‚JZ‚t$sj 8BI‚ $t B„I‚„ B {B8}s„‚ Y‚ {B8}Zs$Btsj {BR y $R {j‚s„ Ys Y‚ {B8}Z$t $8‚ {B„„‚T R}BtI$t B 8BI‚j $R 8Z{Y jBb‚„ bY‚t Y‚ {BI‚ $R ‚-‚{Z‚I $t }s„sjj‚j 8BI‚ R$t{‚ Y‚ PB„8Zjs$Bt s{{‚}R 8sRR$%‚ }s„sjj‚j$9s$Bt>1nH

VR b‚ {st R‚‚ $t Y‚R‚ ‚-s8}j‚R Y‚ R‚j‚{$Bt BP s RZ$sAj‚ RB$j 8BI‚j $R ‚RR‚t$sj B Zs„st‚‚ Y‚ RsP‚k $t Y‚ „BZtI$t $tRsjjs$BtR R$t{‚ „‚RZjR BAs$t‚I Ak ZR$t s 8Zj$}j‚Tjsk‚„ RB$j 8BI‚j {st A‚ tB${‚sAjk I$&‚„‚t P„B8 YBR‚ BAs$t‚I Ak ZR$t s R$tj‚ jsk‚„ wB„ Zt$PB„8D RB$j 8BI‚j whZ„‚R ;xEM stI sAj‚ nD qY‚„‚PB„‚ $ {BZjI A‚ sI%$RsAj‚ B ZR‚ 8Zj$Tjsk‚„ RB$j PB„8Zjs$BtR B stsjk9‚ „BZtI$t RkR‚8R sR s ‚t‚„sj „Zj‚ $t R}$‚ BP Y‚ $t{„‚sR‚ BP Y‚ {B8}Zs$Btsj ‚&B„ yt Ps{ Y‚ ZR‚ BP Y$R ,$tI BP sI%st{‚I 8BI‚jR RYBZjI A‚ 8stIsB„k $t {sR‚R bY‚„‚ Y‚ {BtIZ{$%$k BP Y‚ RB$j {Yst‚R 8s„,‚Ijk b$Y I‚}Y B„ $t Y‚ %${$t$k BP Y‚ RZARs$Bt R$‚

!A%$BZRjk Y$R ABZtIs„k ‚j‚8‚t PB„8Zjs$Bt {st A‚ s}}j$‚I B stk BY‚„ {sR‚ b$Y s Y$Y‚„ tZ8A‚„ BP jsk‚„R <Bb‚%‚„ ]_= $8‚ 8sk $t{„‚sR‚ Z} B ZtsI8$R$Aj‚ j‚%‚jR 8s$tjk IZ‚ B Y‚ }BB„ „s‚ BP {Bt%‚„‚t{‚ BP Y‚ ZtI‚„jk$t R‚„$‚R ‚-}stR$BtR stI B Y‚ t‚‚I BP ‚%sjZs$t IBZAj‚ R‚„$‚R w$t Y„‚‚Tjsk‚„ 8BI‚jRD „$}j‚ R‚„$‚R w$t PBZ„Tjsk‚„ 8BI‚jRD stI RB Bt

WBbsIskR bY$j‚ R$tj‚Tjsk‚„ 8BI‚jR „Zt $t „‚sj $8‚ $t {Bt%‚t$Btsj {B8}Z‚„R PB„ Y‚ stsjkR$R BP 8‚I$Z8\A$ R$9‚ „BZtI$t „$IR> d;H stI bBTjsk‚„ 8BI‚jR „‚JZ$„‚ s tBt t‚j$$Aj‚ AZ R$jj s{{‚}sAj‚ {B8}Z$t ‚&B„ 8Zj$}j‚T jsk‚„ 8BI‚jR „‚JZ$„‚ $t ‚t‚„sj st BZ BP B„I‚„ {B8}Z$t $8‚ 3B„ Y$R „‚sRBt b‚ s„‚ RZIk$t Y‚ $8}„B%‚8‚t BP Y‚ {Bt%‚„‚t{‚ R}‚‚I BP Y‚ R‚„$‚R Ak ZR$t ‚-„s}Bjs$Bt ‚{Yt$JZ‚R>1;H stI Y‚ ZR‚ BP s{{‚j‚„s$Bt ‚{Yt$JZ‚R PB„ RjBbjk {Bt%‚„‚t R‚„$‚R >1x 1EH !t Y‚ BY‚„ YstI b‚ s„‚ sjRB bB„,$t Bt Y‚ }s„sjj‚j$9s$Bt BP Y‚ }„B}BR‚I s}}„Bs{Y R$t{‚ Y$R 8Zj$Tjsk‚„ e PB„8Zjs$Bt {BZjI A‚{B8‚ s „‚sjT$8‚ I‚R$t BBj $t s {jBR‚ PZZ„‚ sR Y$YT}‚„PB„8st{‚ }s„sjj‚j {B8}Z$t A‚{B8‚R s b$I‚R}„‚sI s%s$jsAj‚ „‚RBZ„{‚ $t ‚t$t‚‚„$t>1nH

x ]Bt{jZR$BtR

(12)

-10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.00 X (m.) 60.00

65.00 70.00 75.00 80.00 85.00 Y (m.)

-10.00 0.00 10.00 20.00 30.00 40.00 50.00 60.00 X (m.)

60.00 65.00 70.00 75.00 80.00 85.00 Y (m.)

Case A, detail

Case C, detail around vertical border in y=80.1m ( =1/50 ( ·m) in South,g1 W

-1 g W -1

2=1/5000 ( ·m) in North)

3$Z„‚  sjs$IBR yy p„BZtI$t 7kR‚8U ]B8}s„$RBt A‚b‚‚t Y‚ }B‚t$sj I$R„$AZ$Bt wd(,zD Bt Y‚ ‚s„Y RZ„Ps{‚

BAs$t‚I Ak ZR$t RB$j 8BI‚jR V stI ]wI‚s$j BP Y‚ „BZtI$t R$‚ {jBR‚ B Y‚ 9Bt‚ b$Y {Yst‚ $t Y‚ {BtIZ{$%$kD

yt Y$R }s}‚„ b‚ Ys%‚ }„‚R‚t‚I s ‚t‚„sj$9s$Bt BP Y$R ABZtIs„k ‚j‚8‚t s}}„Bs{Y PB„ „BZtI$t „$IR ‚8A‚II‚I $t R„s$h‚I RB$jR qY‚ }„B}BR‚I s}}„Bs{Y YsR A‚‚t s}}j$‚I B Y‚ stsjkR$R BP s „‚sj ‚s„Y$t RkR‚8 {BtR$I‚„$t I$&‚„‚t ,$tIR BP RB$j 8BI‚jRU Zt$PB„8 RB$j RB$j b$Y bB YB„$9Btsj jsk‚„R stI RB$j b$Y bB %‚„${sj jsk‚„R qY‚ jsk‚„‚I 8BI‚jR sjjBb B stsjk9‚ Y‚ $t4Z‚t{‚ BP Y‚ %s„$s$BtR $t Y‚ RB$j {BtIZ{$%$k b$Y I‚}Y stI $t Y‚ RZ„„BZtI$tR BP Y‚ „BZtI$t RkR‚8

qY‚ RZ$sAj‚ R‚j‚{$Bt BP s RB$j 8BI‚j $R s ,‚k }B$t $t „BZtI$t stsjkR$R G‚ Ys%‚ RYBbt Ys $ $R }BRR$Aj‚ B BAs$t Y$Yjk s{{Z„s‚ „‚RZjR b$Y Y‚ }„B}BR‚I ABZtIs„k ‚j‚8‚t tZ8‚„${sj s}}„Bs{Y stI Y‚R‚ „‚RZjR {st A‚ tB${‚sAjk I$&‚„‚t I‚}‚tI$t Bt Y‚ ,$tI BP RB$j 8BI‚j {BtR$I‚„‚I $t Y‚ RZIk ]BtR‚JZ‚tjk R$t{‚ Y‚ „BZtI$t RsP‚k }s„s8‚‚„R 8sk R$t$h{stjk {Yst‚ $ {BZjI A‚ sI%$RsAj‚ B ZR‚ Y‚ 8Zj$Tjsk‚„ RB$j PB„8Zjs$Bt sR s ‚t‚„sj „Zj‚ $t R}$‚ BP Y‚ $t{„‚sR‚ $t Y‚ {B8}Zs$Btsj {BR

V{,tBbj‚I‚8‚tR

qY$R bB„, YsR A‚‚t }s„$sjjk RZ}}B„‚I Ak Y‚ X$t$R‚„$B I‚ ]$‚t{$s k q‚{tBjB?s w}„B`‚{R 'd3*T(d(M stI '*_y1((dT(xxED" BP Y‚ 7}st$RY pB%‚„t8‚t {Bhtst{‚I b$Y 3e*ei PZtIR stI Ak „‚R‚s„{Y P‚jjBbRY$}R BP Y‚ XeZT „B}‚st ]‚t‚„ PB„ _s„sjj‚j$R8 BP s„{‚jBts ]e_ V" Y‚ XZts I‚ psj${$s" stI Y‚ X=t$%‚„R$IsI I‚ Ns ]B„ZKts"

i‚P‚„‚t{‚R

>dH VW7y\yeee 7IM( yeee pZ$I‚ PB„ RsP‚k $t V] RZARs$Bt „BZtI$t W‚b OB„, w1(((D

>1H 7%‚„s, Fp _„B„‚RR $t R‚} stI BZ{Y %Bjs‚ ‚JZs$BtR BP VW7y\yeee 7IM( yeee q„stR Bt _Bb‚„ *‚j$%‚„kdn E1uE wdD

>nH ps„„‚ *N _„Z$ Fp _„BAj‚8R ‚t{BZt‚„‚I b$Y Y‚ V_ BP stsjk9$t „BZtI$t RkR‚8R yeee q„stR Bt _Bb‚„ *‚j$%‚„kd(; ;((Eu;(1n wdMxD

>;H <ZY‚R qFi qY‚ 3$t$‚ ej‚8‚t ‚YBI _„‚t${‚ <sjj W‚b F‚„R‚k wdMD

>xH „‚AA$s ]V q‚jj‚R F]3 G„BA‚j N] BZtIs„k ‚j‚8‚t ‚{Yt$JZ‚R 7}„$t‚„ z‚„js =€ wdM;D >EH st‚„`‚‚ _€ qY‚ BZtIs„k ej‚8‚t ‚YBI $t ‚t$t‚‚„$t { p„sbT<$jj NBtIBt wdxD

(13)

A

C B

A C

x y Line x = 30.0m

Line y = 79.1m

-10. 0. 10. 20. 30. 40. 50. 60. 70. 80. 90.

y (x=30.0) (m)

8.0

8.5

9.0

9.5

10.0

10.5

Potential

(kV)

-10. 0. 10. 20. 30. 40. 50. 60. 70.

x (y=79.1) (m)

8.0

8.5

9.0

9.5

10.0

10.5

Potential

(kV)

B

G.P.R.=10 kV

G.P.R.=10 kV

3$Z„‚ M sjs$IBR yy p„BZtI$t 7kR‚8U _B‚t$sj }„Bhj‚R w,zD Bt Y‚ ‚s„Y RZ„Ps{‚ sjBt bB j$t‚R PB„ Y‚ Y„‚‚ ,$tIR BP RB$j 8BI‚jR WB${‚ Y‚ $8}B„st I$&‚„‚t{‚R $t Y‚ „‚RZjR

>MH Ws%s„„$ts 3 ]BjB8$tsR y ]sR‚j‚$„B Vtsjk${sj $t‚„s$Bt ‚{Yt$JZ‚R PB„ ‚s„Y$t „$I {B8}Zs$Bt Ak e yt XWZ8‚„${sj ‚YBIR $t et$t‚‚„$t stI V}}j$‚I 7{$‚t{‚R" ddud1(E ]yWe s„{‚jBts wd1D

>H ]BjB8$tsR y Ws%s„„$ts 3 ]sR‚j‚$„B V ABZtIs„k ‚j‚8‚t tZ8‚„${sj s}}„Bs{Y PB„ „BZtI$t „$I {B8}Zs$Bt ]B8} ‚Y V}} ‚{Y et„ d; nT( wdD

>d(H FBYtRBt ] WZ8‚„${sj RBjZ$Bt BP }s„$sj I$&‚„‚t$sj ‚JZs$BtR Ak Y‚ 3$t$‚ ej‚8‚t ‚YBI ]s8A„$I‚ =t$% _„‚RR ]s8A„$I‚ =7V wdMD

>ddH 7$„B„$ 7 s$‚„ p WB%s$ p ${{Bj$ 7 V psj‚„,$t Rk88‚„${ ABZtIs„k ‚j‚8‚t 8‚YBI $t ‚jsR${$kU PB„8ZT js$Bt stI $8}j‚8‚ts$Bt yt F WZ8 ‚Y et„ nx 1xxT1M1 wd1D

>d1H Btt‚ s$‚„ p _Bj$99BB ] !t Y‚ Rk88‚„${ psj‚„,$t ABZtIs„k ‚j‚8‚t 8‚YBI V}}j ‚{Y i‚% xd EET(; wdMD

>dnH Ws%s„„$ts 3 ]BjB8$tsR y ]sR‚j‚$„B GYk IB {B8}Z‚„ 8‚YBIR PB„ „BZtI$t stsjkR$R }„BIZ{‚ stB8sjBZR „‚RZjR2 yeee q„stR Bt _Bb‚„ *‚j$%‚„k w1((1D >V{{‚}‚I PB„ }ZAj${s$BtH

>d;H ]sR‚j‚$„B <‚„t?stI‚9 NV ]BjB8$tsR y stI Ws%s„„$ts 3 ‚8B„k stI =R‚„ pZ$I‚ BP RkR‚8 q!q e PB„ ]V* BP „BZtI$t „$IR $t ‚j‚{„${sj $tRsjjs$BtR ]$%$j et$t‚‚„$t 7{YBBj =t$%‚„R$IsI I‚ Ns ]B„ZKts wd;D >dxH ]BjB8$tsR y Ws%s„„$ts 3 ]sR‚j‚$„B V BZtIs„k ej‚8‚t 3B„8Zjs$Bt PB„ Y‚ 7ZARs$Bt p„BZtI$t *‚R$t

VI% et„ 7BP n( E(nu(( wdD

>dEH *Z„stI e ?ej‚{„BRs$JZ‚ sRRBt _s„$R wdEED

(14)

>dMH ]BjB8$tsR y Ws%s„„$ts 3 ]sR‚j‚$„B V tZ8‚„${sj PB„8Zjs$Bt PB„ „BZtI$t stsjkR$R $t R„s$h‚I RB$jR yeee q„stR Bt _Bb‚„ *‚j$%‚„k w1((dD >yt }„‚RRH

>dH qs p3 es„Y „‚R$Rst{‚R _$8st W‚b OB„, wdE;D

>1(H *sbsj$A$ 3_ ZIY‚,s„ * !}$8Z8 I‚R$t BP RZARs$Bt „BZtI$t $t s bBTjsk‚„ ‚s„Y R„Z{Z„‚ yeee q„stR Bt _Bb‚„ V}}s„sZR stI 7kR‚8R ; 1x1T11 wdxD

>1dH V-‚jRRBt ! y‚„s$%‚ RBjZ$Bt 8‚YBIR ]s8A„$I‚ =t$% _„‚RR ]s8A„$I‚ =7V wd;D >11H 7ssI O y‚„s$%‚ 8‚YBIR PB„ R}s„R‚ j$t‚s„ RkR‚8R =t$%‚„R$k BP $tt‚RBs =7V w1(((D

>1nH ]BjB8$tsR y Ws%s„„$ts 3 BRJZ‚$„s p e$„Bs F ]sR‚j‚$„B WZ8‚„${sj 8BI‚jj$t PB„ „BZtI$t „$IR $t Y$YT}‚„PB„8s{‚ }s„sjj‚j {B8}Z‚„R BZtIs„k ej‚8‚tR yy Gyq _„‚RR 7BZYs8}Bt =€ w1(((D

>1;H Vt‚$„BR F V tZ8‚„${sj PB„8Zjs$Bt PB„ „BZtI$t stsjkR$R BP ‚j‚{„${sj RZARs$BtR Ak ZR$t bBTjsk‚„ RB$j 8BI‚jR R7{ qY‚RkR ]$%$j et$t‚‚„$t 7{YBBj =t$%‚„R$IsI I‚ Ns ]B„ZKts wdED

>1xH €$tsk8st W V,RZt y ]B8}s„s$%‚ RZIk BP s{{‚j‚„s$Bt ‚{Yt$JZ‚R PB„ $t‚„sjR stI R‚„$‚R $t ‚j‚{„B8st‚${ }„BAj‚8R isI$B 7{$‚t{‚ n( ddnTd11 wdxD

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