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P e r g a m o nInt. J. Rock Mech. Min . Sci. Vol. 34, No. 8, pp. 1139-1152, 1997 1998 Publishedby Elsevier Science L~d.All rights reservedPII: S01 48-90 62(97 )0029 9-4 Printed in Great Britain0148-9062/97 $17.00 + 0.00

Three -d im ens iona l Ef f ec t s o f H ydrau l i cC o n d u c t i v i t y E n h a n c e m e n t a n dD e s a t u r a t i o n a r o u n d M i n e d P a n e l sJ. LIU#D. ELSWORTH~

Chang es in the three-dimensiona l hydraul ic conduct ivi ty f ield that accom panyunderm ining by a longwall pan el are evaluated to define the potent ial fo rchanges in f lo w pat tern s a nd desaturat ion. R elat ions l inking changes inconduct ivi ty wi th the mining-ind uced s train f ield that develops a round theadvancing fac e are def ined through the assumption of an equivalent poro usmedium wi th the s t ra in par t i tion be tween f rac tures and ma tr i x appor t ionedrelat ive to respect ive deformation constants . Model resul ts are val idatedagainst behavior recorded at a w el l ins trum ented f ie ld s i te , repl icat ing thecomplex s t eady f low pa t t ern tha t develops around an advancing longwal l face .Signi f icant hydraul ic con duct ivi ty increases a re restr icted to s trata at shal lowdepth, a head o f the advancing face, and to deep zones behind the fac e,part icularly in the caving zone and abutment shear zones . These very largeincreases in conductivity at depth, that include the out-of-section conductivityenhanc emen t that develops along the pan el r ib , exercise prim ary control oninduced water level changes and the poten t ial fo r satura t ion. Z one s o fdesa turation are readily defined, with these enabling locations o f we llvulnerability (to wate r loss) to be identified. The se zon es of vulnerability aredirect ly above the pane l , w i th their exte nt potent ial ly mo dulate d by thepresence and the location o f la t lying layers of low conduct ivi ty . The com plexresponse recorded in the near-face region mandates use of three-dimensionalmod els to adequately represent observed behavior . 1998 Publ i shed byElsevier Science Ltd

1. INTRODUCTIONUnderground mining by fu l l ex t rac t ion methods, such aslongwall mining, is becoming increasingly popular formining uninterrupted and near horizontal seams.Longwall mining involves extracting coal in large blockscalled panels using a mecha nized shearer. The fullthickness, of perhaps 1-2 m, is removed and panelextents are typically 200-350 m wide and up to 3000 min length. Multiple panels comprise a single miningoperation. With this method, the mine roof is supportedwith hydraulic supports that automatically advance asmining progresses. As the supports move, the mine roo fis allowed to collapse into the mine void. Strata abovethe mine level are altered as the mine roof caves behindthe shields (hydraulic supports), creating zones whereblocks of rock fill the mine void, or fracture or deformtDepartment of Mining, Minerals and Materials Engineering, TheUniversity of Queensland, Brisbane, QLD 4072, Australia.SDepartment of Mineral Engineering, PennsylvaniaState University,University Park, PA 16802, U.S.A.

as rock layers warp downward. These alterations inoverburden characteristics potentially induce largestrains in the overlying strata that in turn may result ina strongly heterogeneous and anisotropic hydraulicconductivity field. This strain-dependent conductivityfield is of special importance in evaluating the potentialimpact of longwall mining on ground water resources. Anumber of studies have indicated that subsidence-in-duced fracturing may increase hydraulic conductivitymagnitudes by up to several orders of magnitude [1-4].Consequently, the local ground water system may beappreciably altered [5-8]. Despite the acknowledgementthat changes in conductivity may be substantial, fewstudies document the interaction between deformationof the overlying strata and its influence on ground waterflow [9-13]. These studies have reported the researchresults for two-dimensional geometries but neglected thetrue three-dimensional complexity of the zone immedi-ately surrounding the advancing face. This studyrepresents the first known study documenting thecomplex three-dimensional response anticipated around1139

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1140 LI U and ELS W O R T H : TH R EE- D I MEN SI O N A L H Y D R A U LI C C O N D U C TI V I TY

t h e a d v a n c i n g mi n i n g f a c e t h r o u g h i mp l e me n t in g t h ep r e s c r ib e d d i s p l a c e me n t b o u n d a r y c o n d i t io n s , i n s t ea d o fthe p rescr ibed fo rce boundary cond i t ions [9 -13] , a rounda longwal l pane l . The fo l lowing document i s anapp roac h to def ine the fo rm of th i s in te rac t ion , i n ap red ic t ive capac i ty , enab l ing the in f luence on the g roun dwater sys t em to be def ined .

T h e u n d e r mi n e d s t r a t a t y p i c a l l y h a v e a c o mp l i c a t e din te rna l s t ruc tu re a nd s t res s s ta t e , bo th o f which a re , inlarge part , unknown a n d p e r h a p s unknowable. Thisw o u l d a p p e a r t o ma k e s o l u t i o n f o r t h e r e v i s e d ,min ing- induced , c ondu ct iv i ty f ie ld in t rac t ab le . Ho wev er ,s o me a l t e r n a t i v e s ma y b e p u r s u e d t o a v o i d u s i n gparameters tha t a re un l ike ly ava i l ab le in p rac t i ce . Thesubs idence f i e ld tha t deve lops a round a longwal l pane li s re l a t ive ly insens i t ive to the mater i a l p roper t i es o fd e f o r ma t i o n mo d u l u s a n d s t r e n g t h d u e t o t h e d i s p l a c e -ment ( subs idence) con t ro l l ed na tu re [14 ,15] . Therefo re ,the min ing- induced s t ra in f i e ld , def ined by the subs i -d e n c e p r of i le , ma y a l s o b e d e c o u p l e d f r o m t h e ma t e r i a lparameters descr ib ing the over ly ing s t ra t a . Once thes t ra in f i e ld i s def ined as un ique fo r any g iven min ingg e o me t r y , c h a n g e s i n t h e g r o u n d w a t e r b u d g e t ma y b ee v a l u a t e d p r o v i d i n g a l i n k ma y b e e s t a b l i s h e d b e t w e e ninduced s t ra ins and changes in hydrau l i c conduct iv i ty .This i s the und erlyin g scienti f ic rat iona le o f th is research.

2 . E V A L U A T I O N O F MINING-INDUCED STRAINFIELDThe complex 3 -D s t ra in f i e ld tha t deve lops a round the

a d v a n c i n g f a c e o f a l o n g w a ll p a n e l m a y b e e v a l u a t e don ly wi th recourse to numer ica l methods . Th i s loca lbeh avio r is s ignificant , s ince the dis t r ib ut ion of s t rains , .and hence conduct iv i t i es , a re s t rong ly cond i t ioned byh y s t e re t ic a n d p a t h d e p e n d e n t b e h a v i o r i n t h e 3 - D s t ra i nr e g i me t h a t d e v e l o p s a r o u n d t h e a d v a n c i n g f a c e , e v e nthough the u l t imate pane l sec t ion i s amenab le to p l anes t ra in rep resen ta t ion . However , even as a p l ane sec t ionwi th regard to d i sp laceme nt behav io r , t he f low beha v io rremains impl i c i t l y th ree-d imens iona l , w i th impor tan to u t - o f - se c t i o n f l o w c o m p o n e n t s .

In th i s work , a 3 -D f in i t e e l ement model i s deve lopedtha t i ncorpora tes s t ra in so f t en ing fo l lowing fa i lu re ,a s s u mi n g t h a t c h a n g e s i n t h e g r o u n d w a t e r r e g i me a r et r iv i a l i n compar i son wi th the mass ive changes in to t a ls t r e s s t h a t a c c o mp a n y mi n i n g . P r e v i o u s e v a l u a t i o n o f2 -D fu l ly coup led (poroe las t i c ) sys t ems invo lv ing s ing le[9] and dua l [10] por os i ty beh av io r hav e conf i rm ed theshor t - l ived n a tu re o f the t rans i en t poroe las t i c e f fec ts .S imi la r ly , 2 -D ana lyses wi th s t eady-s t a t e coup l ing fo reffect ive s t resses [11] have indica ted the t r iv ial co ntr i -bu t io n o f e f fec tive s t resses over the m ass ive rea l ignmento f t o t a l s t r e ss e s c o n d i t i o n e d b y m i n in g . Co r r e s p o n d -ingly, coupl ing in the fol lowing is res t r icted toc o n s i d e r a t i o n o f c h a n g e s i n h y d r a u l i c c o n d u c t i v i t y ,coup led to the evo lv ing s t ra in reg ime. Th i s s impl i f i ca t ioni s espec ia l ly impor tan t fo r 3 -D ana lyses , enab l ing as ign i f i can t reduc t ion in execu t ion t ime, wi th nos ign i f i can t los s o f re l evance in t rack ing p rocesses .

2.1. Finite element representationI t i s a s s u me d t h a t t h e r o c k ma s s i s i s o t r o p i c b u t

he te rogeneous . The resu l t ing f in i t e e l ement fo rmula t ionfo r the so l id phase i s symbol i ca l ly def ined as

K~d = f ( 1 )wh ere Ks is the s t i ffness m atrix of the so l id phase, d is thenodal d i sp lacement vec to r , and f i s t he nodal fo rcevecto r . The s t i ffness ma trix , Ks, in equ at io n (1) is defineda s

K s = ~ v ~ B T D B d x d y d z ( 2 )where B i s a geomet r i c mat r ix , D i s mater i a l p roper t i esma t r i x a n d a f u n c t i o n o f t h e e la s ti c mo d u l u s , E , a n d t h ePo i s son ra t io , v , and v i s t he vo lume. The min ing- in -d u c e d s t r a i n v e c t o r c a n b e o b t a i n e d a s

A E = B d . ( 3 )T h e d i s p l a c e me n t c o n t r o l l e d n a t u r e o f s u b s i d e n c e i si mp l e me n t e d i n t h e f in i te e l e me n t mo d e l ( FE M ) t h r o u g htwo d i f fe ren t non- l inear m ater i a l mod el s rep resen t ing theoverburden fa i lu re and the coa l ex t rac t ion , respec t ive ly .T h e s e t w o n o n - l i n e a r ma t e r i a l mo d e l s a r e p r e s e n t e d i nthe fo l lowing .2.2. Representation o f overburden failure

Not ice tha t t he B mat r ix in equa t ion (2 ) remains f ixedd u r i n g t h e s o l u t io n p r o c e d u r e , a n d o n l y th e D m a t r ix h a sto be adap ted a t each i t e ra t ion . Th i s i s ach ieved a t t hee n d o f e a c h i t e r a t i o n b y c a l c u l a t i n g t h e ma x i mu mpr inc ipa l s t res s, a l l , and mo di fy ing the "ef fec t ive" e las t icp a r a me t e r s a s

i

E 0 a . < OE = E 0 a H ~ > 0 (4 )R ~

IV1 till < 0v = ( 5 )v2 al l >~ 0where E i s e las t i c m odu lus o f the ove rburd en , E0 i s e l as ti cmo d u l u s o f e l e me n t s i n c o mp r e s s i o n , Eo/R~ is elasticmo dulu s o f e l ement s in ex tens ion , v j i s Po i s so n ra t io o fe l ement s in com press ion , v2 i s Po i s son ra t io o f e l ement sin ex tens ion , and a l l i s t he max imum pr inc ipa l s t res s .T h e m a g n i t u d e o f Ro is o b t a i n e d b y ma t c h i n g t h e" f i e l d - me a s u r e d " o r e s t i ma t e d ma x i mu m s u b s i d e n c e .2.3. Representation o f coal extraction

A s imi la r non- l inear modulus model i s used tor e p r e s e n t t h e p r o c e s s o f c o a l e x t ra c t io n . T h e ma i na d v a n t a g e o f th i s me t h o d i s t h a t e l e me n t s d o n o t h a v et o b e r e mo v e d f r o m t h e me s h i n o r d e r t o s i mu l a t e c o a le x t r a c t i o n , a n d e x c a v a t i o n b o u n d a r y t r a c t i o n s d o n o tn e e d t o b e c a l c u la t e d . M o r e i mp o r t a n t l y , t h e p r e s c r i b e dd i s p l a c e me n t b o u n d a r y c o n d i t i o n s a r o u n d t h e l o n g w a l lpane l can b e success fu l ly implem ented . T he D m at r ix , asshown in equa t ion (2 ) , fo r in -pane l e l ement s has to be

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LIU and ELSWORTH: THREE-DIMEN SIONAL HYDRA ULIC CONDUCTIVITY 1141

Fig. 1. Conceptual model for the effect of fractures on the principalhydraulic conductivities. The bracketed num bers represent three setsof orhtogonal fracture planes.

a d a p t e d a t e a c h i t er a t i o n . T h i s is a c h i e v e d a t t h e e n d o fe a c h i t e r a t i o n b y c a l c u l a t in g t h e v e r t i ca l s t r a i n E ,

J" Ep e z > - 1 ,0EP : ~1 0 Epo e ,~< - 1 .0 (6)w h e r e E p i s m o d u l u s o f t h e m a t e r i a l c o m p r i s i n g t h ep a n e l , E p0 i s i n i ti a l m o d u l u s o f t h e p a n e l m a t e r i a l ( b e f o r em i n i n g ) a n d ez i s v e r t i c a l s t r a i n w i t h i n t h e p a n e l m a t e r i a l .T h i s s i m p l e m o d e l p r e v e n t s t h e i n t e r p e n e t r a t i o n o f t h ep a n e l r o o f a n d f l o o r b y c h a n g i n g t h e p a n e l m o d u l u s a tc o n t a c t , w h e r e n m a y b e a s s ig n e d a n y r e a s o n a b l e l a r g en u m b e r s .

3 . E V A L U A T I O N O F P O S T - M I N I N G C O N D U C T I V I T YF I E L D

T h e d e p e n d e n c e o f p o s t - m i n i n g h y d r a u l i c c o n d u c -t i v it y o n m i n i n g - i n d u c e d s t r a in ( o r s t re s s ) is f re q u e n t l yn o t e d [ 1 , 2 ,1 6 ] , b u t n o t h r e e - d i m e n s i o n a l q u a n t i t a t i v er e l a t i o n s b e t w e e n t h e m a r e a v a i l a b l e . T h e s e r e l a t i o n s a r ed e v e l o p e d b a s e d o n t h e r e p o r te d t w o - d i m e n s i o n a l r e s u lt s[ 9 ,1 0 , 1 3 ] a n d a p p l i e d t o t h e d e t e r m i n a t i o n o f t h ep o s t - m i n i n g s t r a i n - d e p e n d e n t h y d r a u l i c c o n d u c t i v it yf i e l d i n t h e f o l l o w i n g .

3 . 1 . T h r e e - d i m e n s i o n a l r e l a t io n sT w o - d i m e n s i o n a l r e l a t io n s [ 13 ] l i n k in g c h a n g e s i n

h y d r a u l i c c o n d u c t i v i t y t o c h a n g e s i n a p p l i e d s t r a i n m a yb e e x t e n d e d f o r f l o w i n t h e t h i rd d i m e n s i o n . F o rt h r e e - d i m e n s i o n a l o r t h o g o n a l l y f r a c t u r e d m e d i a ,c h a n g e s i n o n e - d i r e c t i o n a l h y d r a u l i c c o n d u c t i v i t y a r e af u n c t i o n o f m i n i n g - i n d u c e d s t r a in s i n th e o t h e r t w oo r t h o g o n a l d i r e c t io n s , a s i l lu s t r a t e d i n F i g . 1 . A s s u m i n gt h a t t h e r o c k m a t r i x i s f u n c t i o n a l l y i m p e r m e a b l e , a n dt h a t t h e d o m i n a n t f l ui d f l o w w i t h i n t h e f ra c t u r e s m a y b ed e f i n e d b y a n e q u i v a l e n t p a r a l l e l p l a t e m o d e l , e n a b l e sc h a n g e s i n h y d r a u l i c c o n d u c t i v i t y t o b e d e t e r m i n e d i fi n d u c e d s t r a in s m a y b e a d e q u a t e l y p a r t i t io n e d b e t w e e nf r a c t u r e a n d s o l i d m a t r i x . F r a c t u r e a n d m a t r i xd e f o r m a t i o n a r e b o t h l in e ar , a n d d e f o r m a t i o n s i n n o r m a lc l o s u r e o r e x t e n s i o n a r e t h e p r e d o m i n a n t c o n d u c t i v i t ye n h a n c i n g m o d e . D e f o r m a t i o n s a r e fu l ly re c o v e r a b l e i nt h i s m o d e , w i t h s t r a i n s d e f i n e d p o s i t i v e i n e x t e n s i o n .C o n d u c t i v i t y c h a n g e s i n c o m p r e s s i o n a r e t y p i c a l l yt r u n c a t e d b y a l o w e r t h r e s h o l d d e f in i n g t h e li m i t s o fc o n d u c t i v i t y r e d u c t i o n . S t r a i n s a r e p a r t i t i o n e d b e t w e e nf r a c t u r e a n d m a t r i x a s d ef i n e d b y t h e m o d u l u s r e d u c t i o nf a c t o r . A d d i t i o n a l l y , f r a c t u r e s p a c i n g , s , d o e s n o t c h a n g ep o s t -m i n i n g . U n d e r t h e s e a s s u m p t i o n s t h e c h a n g e s inh y d r a u l i c c o n d u c t i v i t y i n t h e th r e e o r t h o g o n a l d i r e c ti o n s ,K x , K y a n d K z , a r e c o n d i t i o n e d b y f r a c t u r e a p e r t u r e s , b x,b y , b z , a n d f r a c t u r e s p a c i n g s , s x , s v , a n d s : , d e f i n e d w i t ht h e f r a c t u r e p l a n e n o r m a l a l i g n e d i n t h e c o o r d i n a t ed i r e c t i o n . A e x , A e y a n d A e z a r e m i n i n g - i n d u c e d s t r a in s i nt h e x - , y - a n d z - d i r e c t i o n s , r e s p e c t i v e l y , a n d R m i s am o d u l u s r e d u c t i o n r a ti o ( r a ti o o f r o c k m a s s m o d u l u s t or o c k m a t r i x m o d u l u s ) t h a t a p p o r t i o n s c h a n g e s i n s t ra i nb e t w e e n t h e f r a c t u r e a n d m a t r i x m a t e r i a l . F r o m t h i s ,c o n d u c t i v i t y m a g n i t u d e s m a y b e d e f i n e d r e l a t i v e t o t h ep r e - m i n i n g c o n d u c t i v i t y f i e ld , K , -0 , K y o , K ~ 0, a s

1K, = ~ K~o[(1 + f l y A E y ) 3 -}- (1 + f l z A E z )3 ] (7 )

10 ~ . . .. . .. . . f ~ .. .. ... ... ... . . . . . . . . . . . ~ ..................... ............................ ~

l o , . . . . . . . . . . . . . . . . 1

o 102 ) ! ~ i!ii ~!!i . i1

100 0.005 0 .0 1 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05Norm al Strain

Fig. 2. Relationship betw een mod ulus redution ra tion, Rm, and no rm al strain, AE, under conditions o f fracture spacings = 0.5 m and aperture b = 0005 m.

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1142 LIU and ELSWORTH: THREE-DIMEN SIONAL HYDRA ULIC CONDUCTIVITYr~ n ,q oln~l l~,-,,- , l+M~ (b) Pre-mining Equivalence

( d ) P o s t - m i n i n g E q u i v a l e n c e ( c ) P o s t - m i n i n g R o c k M a s sFig. 3. Transformation processes of hydraulic conductivity mode ls. The shad ed circle in (a) represents that the condu ctivityfield is isotropic. The shap e in (d) represents that the cond uctivity field is anisotropic.

w h e r e

1 K y 0 [ (1 + f ixAEx) 3 + ( 1 + f l : A E : ) 3 ] (8 )~=21 K ~0 [( 1 + / ~ A E x ) 3 + ( 1 + f lyAEy)3], (9 )~=~

E q u a t i o n s ( 7 ) -( 9 ) m a y b e r e w r i t te n a sR x g~0 - [ ( 1 -q- [ J y m E y ) 3 -'~ ( 1 + 3 z A E z ) 3 ]

RL 1R y = o a y'--~ = 2 [(1 + flxaEx) 3 + ( 1 + ] ~ a : ) 3 ]

(13 )

( 1 4 )1 m Rmfix = 1 + h-----S--. (1 0)

Sx1 i Rm

, B y = l + b---~-- ( 1 1 )Sy1 - - Rm/~z = 1 + b----~- (1 2)

Sza n d b x /& , b y / sy a n d b~/& m a y b e d e f i n e d a s a f u n c t i o no f e q u i v a l e n t f r a c t u r e p o r o s i t y o r f r a c t u r e d e n s i t y .

K ~ 1R z = K z-~ = 2 [(1 + /3xA E x) 3 + (1 + /3yA E y)3] . ( 15 )F o r f r a c t u r e d m e d i a th e p o s t -m i n i n g h y d r a u l i c c o n d u c -t iv i ti e s o f t h e o v e r b u r d e n a r e p r i m a r i l y c o n t r o l l e d b ym i n i n g - i n d u c e d s t ra i n s, o r i g i n a l h y d r a u l i c c o n d u c -t i v it ie s , o r t h e f r a c t u r e p a r a m e t e r s o f s p a c i n g a n da p e r t u r e , a s s h o w n i n e q u a t i o n s ( 7 ) - ( 1 5) . T h e m i n i n g -i n -d u c e d s t r a in s h a v e b e e n o b t a i n e d t h r o u g h e q u a t i o n ( 3) .T h e o t h e r p a r a m e t e r s a r e d i sc u s s e d i n th e f o l lo w i n g .3 . 2 . E f f e c t s o f R m o n c o n d u c t i v i t y r a t i o

T h e p o s t - m i n i n g h y d r a u l i c c o n d u c t i v i t y f ie ld c a n b eu n i q u e l y d e f i n e d b y b o t h t h e i n d u c e d f a c t o r ( t h e

, o o : _ , o o o _ 2 , :

m

Y ' ~ / I ~ ~ xFig. 4. FE models for both the determination of overburdened deformation and the post-mining hydrologic regime. Circlednumbers are nodal numbers. Model used quarte r symmetry of the panel, centered on the origin. Panel depth is 210 m belowsurface. Solid black represents un-mined coal.

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L I U a n d E L S W O R T H : T H R E E - D I M E N S I O N A L H Y D R A U L I C C O N D U C T I V I T Y 1 14 3

0.2o .O

~ 0 . 2 -

== _ 0 . 6~0.1t

( a )

AEvoe -

D

- 0 . 2- 0 . 4- 0 . 6- 0 . 8- 1 . 0

- 1 . 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .- 3 0 0 - 2 0 0 -1 O 0 0 1 O 0 2 0 0 3 0 0H o r i z o n t a l C o o r d i n a t e ( m )

( b )Fig . 5 . Subs ide nc e due to longw a l l m ining : (a ) subs ide nc e cone , (b) c om pa r i son o f m ode l da ta w i th f ie ld da ta in the c ros s s e c tiono f X = 0 .

min in g - in d u c e d s t r a in f i eld ) a n d t h e i n t r i n s i c f a c to r s ( t h em o d u l u s r e d u c t i o n r a t i o , R m , p r e - m i n i n g h y d r a u l i cc o n d u c t iv i t y , K 0 , o r e q u iv a l e n t f r a c tu r e sp a c in g s a n da p e r tu r e b ) . R m i s d e f in e d a s t h e r a t i o o f t h e e l a s ti cm o d u l u s o f t h e ro c k m a s s t o t h a t o f t h e i n ta c t r o ck .A c tu a l l y , i t i s a me a su r e o f s c a l e e ff e c t w h ic h i s d e f in e da s t h e v a r i a t i o n o f t e s t r e su l ts w i th sp e c ime n s iz es . T h i si s a p p a r e n t i n t h a t f o r a p p l i c a t i o n t o f i eld p r o b l e m s o fs u b s id e n c e , t h e l a b o r a t o r y v a l u es o f d e f o r m a t i o n a n dr i g id i t y m o d u l i s h o u l d b e r e d u c e d a t l e a s t a n o r d e r t om a g n i t u d e f o r b o t h i s o t ro p i c [ 1 7 ] a n d t r a n sv e r s e lyi so t r o p i c [ 18 ]. T h e e f fe c t s o f R m o n c h a n g e s i n h y d r a u l i cc o n d u c t i v i t y a re d e m o n s t r a t e d i n t h e f o l l o w i n g e xa m p l e .As sum ing Ae~ = 0 , b = 0 .0005 m, an d s = 0 .5 m, thee f fec ts of Rm, a s sh ow n in eq ua t ion (13) or (14) , a rei l l u s t r a t e d in F ig s 2 . T h e h y d r a u l i c c o n d u c t iv i t y ma yi n c re a s e b y u p t o 5 o r d e rs o f m a g n i t u d e w h e n R mc h a n g e s f r o m 0 . 0 t o 1 . 0 , a s sh o w n in F ig . 2 . W h e n th e

m o d u lu s r e d u c t io n r a t i o , R m = 1 , t h e r o c k ma ss a n din t a c t r o c k ma te r i a l mo d u l i a r e i d e n t i c a l a n d t h e s t r a ini s u n i f o r m l y d i s t r ib u t e d b e t w e e n f r a c tu r e s a n d m a t r i x .T h i s r e su l t s i n t h e sma l l e s t p o s s ib l e c h a n g e i nc o n d u c t iv i t y . W h e n R m = 0 , t h e s t r a in is a p p l i e d e n t i r e lyto t h e f r a c tu r e sy s t e m a n d p r e c ip i t a t e s t h e l a r g e s tp o s s ib l e c h a n g e i n c o n d u c t iv i t y . T h e se v a lu e s b o u n d th ep o s s ib l e r a n g e s in b e h a v io r o f t h e sy s t e m in a n a tu r a l ,a n d me c h a n i s t i c a l l y d e f e n s ib l e ma n n e r .

T h e m a g n i t u d e o f Rm m a y b e e s t i m a t e d b y s e v e ra lme th o d s . T h e s c a l e e f f e c t o f e l a s t i c mo d u lu s o n t h r e ety p e s o f r o c k h a s b e e n s t a t i s t i c a l ly s t u d i e d [ 1 9 ] a n d t h ef o l l o w in g r e l a t i o n s w e r e o b t a in e d b y e v a lu a t i n g 3 5 ,6 00tes t r e su l t s in s imple com pres s ion te s ts a s Rm = 1/(1 + e / ) , wh ere e = 0 .0859 for l imes ton e , ~ = 0 .1512 forgne iss and e = 0 .0417 for gran i te , wi th I r epresent ingf r a c tu r e f r e q u e n c y . T h e se r e l a t i o n s ma y b e u se d t oe s t i m a t e t h e m a g n i t u d e s o f R m , direc t ly .

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1 1 44 L I U a n d E L S W O R T H : T H R E E - D I M E N S I O N A L H Y D R A U L I C C O N D U C T I V I T Y

T h e b a s i c e q u a t i o n f o r t h e e l a st i c d e f o r m a t i o n o f at w o - c o m p o n e n t m e d i u m i n t h e d i r e c t i o n p e r p e n d i c u l a rt o t h e f r a c t u r e i s d e f i n e d a s [ 2 0 ]

b + s s d a b d a- E , + ~ E , ( 1 6 )

w h e r e d a i s th e n o r m a l s t r e ss a c t i n g p e r p e n d i c u l a r t o t h ef r a c t u r e , ~ i s t h e m i n e r a l c o n t a c t a r e a o n t h e f r a c t u r ew a l l , E ~ i s e l a s t i c m o d u l u s o f t h e r o c k m a s s , a n d E m i s

e l a s ti c m o d u l u s o f t h e r o c k m a t r i x . F o r a r o c k m a s sc o n t a i n i n g f r a c t u r e s f o r m i n g d i f f e r e n t a n g l e s w i t hr e s p e c t to t h e h o r i z o n t a l p l a n e , th e m o d u l u s r e d u c t i o nra t io , R r . , i s o b ta in ed [2 0 ] a s

Em 1- - ( 1 7 )Rm E, N

1 + Z r/ i (1 - - s i n 4 f l i )i = l

6 0 0

~ 4 0 0o

o~ 2 0 0

1000~ x( a )- 0 .0 0 - - ~ ,

". _0.20 ? .

1000 ~ y( b )60C ' " ' ' '

- - 0 .4

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i 2 0 0- : ~ , , ~ . ? , . ~ . . . .

200 400 600X - C o o r d i n o t e m )

8 0 0

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( h ), , , . , i . , .

(f)), 7 - ~ " j < _ _ . o ~ ") 2 " 0 0 . I

-7.00 1 1 1. . . . P A n e l ~ / 1 " ]

0 2 0 0 4 0 0 6 0 0 8 0 0X - C o o r d i n o t e (m )

4 0 0 6 0 0 B O OX - C o o r d i n o i e ( r n )

1 5 0 : -0v 0

2 0 0 4 0 0 6 0 0 B 0 0X - C o o r d i n o t e ( r n )

( i )2 0 0 1 " '\4 .. .. Z

0 2 0 0 4 0 0 6 0 0 B O OX - C o o r d i n o t e (m )

F i g . 6 . C o n t o u r s o f n o r m a l i z e d s t r a i n s a t d i f f er e n t c r o s s s e c t i o n s: ( a ) , ( b ) a n d ( c ) r e p r e s e n t s t r a i n s in a h o r i z o n t a l p l a n e i n t h en e a r s u r f a c e z o n e ; ( d ) , ( e ) a n d ( f ) r e p r e s e n t s t r a i n s i n a v e r t i c a l s e c t i o n a l o n g t h e p a n e l c e n t e r l i n e ; ( g ) , ( h ) a n d ( i ) r e p r e s e n ts t r a i n s i n a h o r i z o n t a l p l a n e i m m e d i a t e l y a b o v e t h e p a n e l r o o f . F i g u r e s i n t h e c o l u m n s r e p r e s e n t n o r m a l s t r a i n s in th e g l o b a l

x - , y - a n d z - d i r e c t i o n s , r e s p e c t iv e l y .

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L I U a nd E L S W O R T H : T H R E E - D I M E N S I O N A L H Y D R A U L I C C O N D U C T I V I T Y 11450

- 2 5- 5 0- 7 5

- 1 0 0~ . - 1 2 5, - ~ - 1 5 0

- 1 W 5- 2 0 0- 2 2 5- 2 5 0I e - 0 9 1 e - 0 8 I e - 0 7 I e - 0 6 I e - O 5Conduc t i v i t y ( m / s )

F i g . 7 . D i s t r i b u t i o n o f p r e - m i n i n g h y d r a u l i c c o n d u c t i v i ti e s .

a n dbt/i = ~ . (18)

wh ere i i s an index of f r ac tu re se ts , fl i i s the angle be tw eenth e f r a c tu r e a n d t h e a r e a p e r p e n d i c u l a r t o t h e d i r e c t i o no f t h e d e s i r e d m o d u lu s , ~ i i s g e o m e t r i c c h a r a c t e ri s t i c o ft h e i t h f r a c tu r e s e t , a n d N i s t h e n u m b e r o f t h e f r a c tu r es e t s in t h e r o c k m a s s . I t i s s u g g e s t e d [ 2 0 ] t h a t~ i = 3 x 10 -4 be ap pl ied a s a con s tan t . A ssu m ing th rees e t s o f o r t h o g o n a l f r a c tu r e s c o in c id e n t w i th t h e x - , y - ,a n d z - d i r e c t i o n s , r e s p e c t i v e ly , t h e n N i s e q u a l t o 3 .Fu r th e rm ore , a ssu mi ng t/1 = th = t/3 = b/s a n d

= 3 x 10 -4, then eq ua t ion (17) bec om es1Rm - 104b . (19)l + - - 3s

A s a n a l t e rn a t i v e t o t h e u s e o f m e a s u r e d o r e s t i m a t e dr o c k ma s s mo d u l i i , e q u a t i o n ( 1 9 ) ma y b e u s e d t od e t e r m i n e t h e m a g n i t u d e o f R ~ , d i re c tl y .3.3. Determination o f post-mining hydraulic conductivityfield

T h e p r o c e s s o f d e t e r m i n i n g t h e p o s t - m i n i n g h y d r a u l i cc o n d u c t i v i t y i s i l l u s t r a te d i n F ig . 3 . T h e in situ h y d r a u l i cc o n d u c t i v i t y is u s u a l l y a s s u m e d t o b e i s o t r o p i c , a s s h o w nin F ig . 3 (a ) , because of the huge enginee r ing sca le( t y p i c a l l y 2 0 0 - 3 5 0 m w id e a n d u p t o 3 0 0 0 m in l e n g th f o ra s i n g l e p a n e l ) . T h i s i s o t r o p i c c o n t i n u o u s mo d e l i ss u b s t i t u te d b y a d i s c o n t i n u o u s m o d e l , a s s h o w n i n F i g .3 (b ), w i th t h r e e i d e n t i c a l s e ts o f o r t h o g o n a l f r a c tu r es .T h e f r a c tu r e a p e r tu r e i s o b t a in e d a s

i s s u b j e c t e d t o c h a n g e s d u e t o me c h a n i c a l d e f o r ma t io ns u c h a s l o n g w a l l min in g , a s s h o w n in F ig . 3 ( c ) a n d t h em o d i f i e d d i s c o n t i n u o u s m o d e l i s t h e n s u b s t i t u t e d b y a ne q u i v a l e n t p o r o u s a n i s o t r o p i c m o d e l , a s s h o w n i n F i g .3 ( d) . C h a n g e s i n t h e f r a c tu r e a p e r tu r e , Abx , Ab> a n d A &. ,a r e d e t e r min e d b y min in g - in d u c e d s t r a in s a n d f r a c tu r ep a r a me te r s . T h e min in g - in d u c e d s t r a in s a r e o b t a in e dth r o u g h e q u a t i o n ( 3) , th e f r a c tu r e a p e r tu r e i s c a l c u l a t e db y e q u a t i o n (2 0), a n d t h e m o d u l u s r e d u c t i o n r a t i o , R m ,m a y b e o b t a in e d f r o m e q u a t i o n ( 1 9) , o r e q u iv a l e n t . W i thth e p o s t - min in g h y d r a u l i c c o n d u c t i v i t y f i e l d d e t e r min e d ,t h e p o s t - m i n i n g g r o u n d w a t e r f l o w r e g i m e c a n b ee v a lu a t e d .

4 . E V A L U A T I O N O F P O S T - M IN I N G G R O U N D W A T E RF L O WT h e r e s u l t i n g f i n i t e e l e me n t f o r mu la t i o n f o r t h e

p o s t - m in in g g r o u n d w a te r f l o w i s s y m b o l i c a l l y d e f i n e d a sK f h = q ( 2 1 )

wh ere Kf i s the s t i f fness m a t r ix of the f lu id phas e , h i s then o d a l h e a d v e c to r , a n d q i s t h e n o d a l f l u x v e c to r . T h es t i f fness ma t r ix for the f lu id phase , Kf , i s de f ined a s

Kr = S~L,~TTK(AE)Td x d y d z ( 22 )w h e r e t h e p r o p e r ty ma t r i x K ( A e ) i s a n a lo g o u s t o t h es t r e s s - s t r a in ma t r i x D in s o l i d e l e me n t s a n d d e f in e d a s( a s s u min g t h e a x e s o f t h e p e r me a b i l i t y t e n s o r c o in c id ew i th x , y a n d z )

K(Ae) = K, 0 (23)0 Kz

a n d t h e T ma t r i x r e p r e s e n t s t h e d e r i v a t i v e s o f s h a p ef u n c t i o n s d e f i n e d o v e r i n d iv id u a l e l e me n t s , i n t h e u s u a lma n n e r . P o s t - min in g h y d r a u l i c c o n d u c t i v i t i e s , K x , K ~ .a n d K , , a r e a f u n c t i o n o f m i n i n g - i n d u c e d s t r ai n s a n dd e t e r m in e d t h r o u g h e q u a t i o n s ( 7 ) - (9 ) . F o r a fr e e s u r f a c ep r o b l e m , t h e m a t r i x K r i s a f u n c t i o n o f t o t a l h e a d h . Af ree sur face i s de f ined by two con di t io ns [21] (1) f lu idp r e s s u r e p i s e q u a l t o z e r o w h e n a tm o s p h e r i c p r e s s u r e i st a k e n a s t h e r e f e r e n c e a s

P - h - z = 0 (2 4)7wwh ere s i s the pre -m ining f r ac ture spac ing , and /~k i s wh ere z is e leva t ion he ad a nd 7w is the un i t we ig htk in e m a t i c v i s c o s i t y o f t h e f l u id . T h e d i s c o n t i n u o u s mo d e l o f w a t e r ; a n d ( 2) e x c e p t i n c o n d i t i o n s o f r e c h a r g e

T a b l e 1 . I n p u t p a r a m e t e r s f o r th e d e t e r m i n a t i o n o f m i n i n g i m p a c t s o n g r o u n d w a t e r f o r c a se s t u d y 2

(mjso,>determ,,od asodon s m>M a t e r i a l H a s e n f u s e t a l . , 1 9 9 0 [ 16 ] e s t i m a t e d ( # m )I 4 . 72 x 10 - 7 0 . 5 66 0 . 69I I 4 . 72 x 10 - 9 0 . 3 12 0 . 88I I I 4 . 72 x 10 - 6 0 . 5 142 0 . 50

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1146 L I U a nd E L SW O R T H : T H R E E - D I M E N S I O N A L H Y D R A U L I C C O N D U C T I V I T YI o g ( K x )

~ 0 0 . . . . . . . . . ( a ) . . . . . . .

, o 0 - ' 0

~ 2 0 0

0 200 400 600 800 1000X-Coordinotem )

I o g ( K y )

~ o . . . . . . . . . ( b ) . . . . . . . . .

4 0

~ 2 0 0

200 400 600 I 800 1000X - C o o r d i n o t e (m )

I o g ( K z )~ o o . . . . . ~ i ' ( c ) . . . . . . . .

~ 40 0~ ' O Il S ~ Z ~c20 0

2 . . . . . . . . I _ t 0 ~,0 200 400 600 800 I 000X-Coord[notem )

4 0 0

~ 350300 ~

~ 25 0IN

I f /

1 5 0 [0 200 400 600 800 1000 \ 0 200 400 600 800 1000 0 200 400 600 800X-Coordinote m) ~ X-Coordinotern) X Coordinotem) 1000

2 0 0

1 5 0Eeo 10 0oo

( g ). , , , . . j , . , . . , . . . . . ~ . . . . . ( h ) . . . . . . . . . O )200 200 ' ' ' ' ' " ' ' ' ' '

1 a : 5 ' . . . . .

. . . . . . . ! . . . . . . . . . 0 [ . . . . . . . . . .200 400 600 800 1000 0 200 400 600 800 1000 200 400 600 800X-Coordinotem ) X-Coordinotem ) X-Coo rdinoterr )Fig. 8 . Contours of ra t ios o f post-mining hydraul ic conduct ivi ties to pre-mining hydraul ic conduct ivi ties a t d i f fe r e n t c r o s ss e c t i o n s : (a), (b) and (c) r e p r e s e n t h y d r a u l i c conductivities in a horizontal plane in t h e n e a r s u r f a c e zone; ( d ) , ( e ) and (f) r e p r e s e n th y d r a u l i c conductivities in a vertical section along t h e p a n e l centerline; (g), (h) and (i) r e p r e s e n t h y d r a u l i c conductivities ina horizontal p l a n e i m m e d i a t e ly a b o v e t h e p a n e l r o o f . F i g u r e s i n t h e c o l u m n s r e p r e s e n t h y d r a u l i c conductivities in the globalx- , y- and z-direct ions, r e s p e c t i v e l y .

1000

o r e v a p o r a t i o n , t h e f l u x a c r o s s t h e f r e e s u r f a c e i s z e r oa s

8h8n - q = 0 (2 5 )w h e r e q i s f l u x a c r o s s t h e f r e e s u r f a c e , d e f i n e d p o s i t i v ef o r e v a p o r a t i o n . I n t h e c a s e o f a f r ee s u r f a c e , t h e s u r f a c eh a s t o b e d e t e r m i n e d a s a p a r t o f t h e s o l u t i o n o f t h e f l o wp r o b l e m . T h e t r a n s i e n t c h a n g e s a f f e c t i n g t h i s fr e e s u r fa c e

a l te r t h e g e o m e t r y o f t h e f lo w s y s t e m s o t h a t t h er e l a t i o n s h i p b e t w e e n t h e c h a n g e s a t b o u n d a r i e s a n d t h ec h a n g e s i n p i e z o m e t r i c h e a d s a n d f l o w s m u s t b en o n - l i n e a r . A s t h e m i n i n g - i n d u c e d s t r a i n f i e l d t y p i c a l l yc h a n g e s t h e d i s t r i b u t i o n o f h y d r a u l i c c o n d u c t i v i t ym a g n i t u d e s i n a l l a d j a c e n t e l e m e n t s , t r a d i t i o n a l m e t h o d so f r e p r e s e n t i n g t h e f r e e s u r f ac e b y r e m e s h i n g a r ec u m b e r s o m e a n d n o t a p p r o p r i a te . A l t e r n a t i v e ly , an o n - l i n e a r c o n d u c t i v i t y m o d e l i s u s e d t o r e p r e s e n t

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LIU and ELSWORTH: THREE- DIMENSI ONAL HYDRA ULIC CONDUCTIVITY 1147changes in saturation in the overburden strata andenable representation of the ground water free surface[22,23]. The method requires a slightly more elaborate(non-linear) code than those remeshing methods used inpractice today, however, for the complex conductivitydistributions that develop in these studies, the methodperforms adequately. This kind of FE model has beendeveloped in this study enabling the characteristics of theunsaturated zone above the free surface to develop in aphysically natural manner.Notice that matrix T remains fixed during solutionprocedure and K(AQ has to be adapted at each iterationto represent the impact of desaturation. This is achievedat the end of each iteration by calculating the total head,h, for each element as

~" 1.0K(Ae) h > z (26)K(Ae) = [10-"K(Ae) h ~< z

where h is total head and z is elevation head, and n maybe assigned any reasonable large numbers. Thedevelopment of post-mining overburden desaturationzones is realized through modifying the conductivitymagnitude to represent changes in saturation of theoverburden strata.5 . RESULTANT FE FORMULATION AND

S O L U T I O N P RO CE D U REAs a summary, the resultant finite element represen-tation for the evaluation of the hydraulic conductivityenhancement and desaturation around mined panels isformulated as

K,(d)d=f (27)A ~ = B d ( 2 8 )

K ~ h = q . ( 2 9 )

400

350

~300

o 250N

200

1500 50 100Y-coordinate m)

150 200

L o n g i tu d i n a l S e c t i o n~__--o-Desatu ~m Z~ ne ~ z zoo~o~o~o~o~o~o~o~ \\~o~o~o~o~o~o~o~o~o~o

3 ~ O ~ O ~ O ~ O ~ 0 ~ O ~ O ~ O ~ O ~ \ \ \ \~o~o~o~o~o ~o~o~o~o \ ~\D~O~O~O~O~O~O~O~O~D3~0~0~0~0~0~0~0~o~ \ \\)~0~0~o~ ~0~0~o~o~) m o m o ~ o ~ o ~ o m o m o m ~ ~ \~o~o~o~o~o ~o~omo~ \ ~\ \

~oo \ -

Mining Oirectton Coal Seam ",100 200 300 400 500 600 700 800 900 1000

X-coordinate(m)

( a ) D i s tr ib u t i o n o f p o s t -m i n in g o v e r b u r d e n d e s a t u r a t i o n

g(..O

LU_.=t~t . -

34 032 030 028 026 024 022 020 018 0

G R 3 C C C ~

SM-83_W5(3-O SM-83-W3EH~ SM -83-W7

T r a n s v e r s e S e c t io n Face PassingTime50 100 150 200 250 300

Time (days)

3 4 0

c 3 3 5.o> I

3 3 0_.11-

3 2 5

3 2 0

, II

T r a n s v e r s e S e c t io n

- - S M -83-W 2. . . . $M-83-W4

Face PassingTime0 4 0 0 8 0 0 1 2 0 0 1 6 0 0

T i m e ( d a ys )( b ) O b s e r v e d w a t e r l e v e l f l u c t u a t io n in m o n i to r i n g w e l ls

Fig. 9. Di stributio n of post-mi ning overburden desaturati on zones and the observed water level fluctuation in monitoriing wells:(a) well locations are shown with co mpletion intervals defined, relative to the geometry of the transverse section. Predictionsof desatu ration zones are identified by small circles, (b) observed water well records during und ermin ing relative to time offace passage.

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1 1 4 8 L I U a n d E L S W O R T H : T H R E E - D I M E N S I O N A L H Y D R A U L I C C O N D U C T I V I T Y

T r a n s v e r s e S e c t i o n(a )

4 0 0 ~ : ~ c ~ = ~ o c o o o ~ o o o o o o

3 5 0E 3 0 08 2 s 0

2 O 0

1 50

o D e a a t u r a t i o n Z o n e ]- ~ c ~ c ~~ o

P a n e l

K 0 = 4 . 7 2 x l ~ ).s ~ = 0 . S mK 0 = 4 . ' / 2 x 1 0 " u

i ~ K 0 = 4 ' 72 X 1 0 " 7s = O . S m

Q = 1 0 . 4 4 m 2 / s

C o a l S e a m2 0 0 4 0 0Y - c o o r d i n a t e (m ) 6 0 0

L o n g i t u d i n a l S e c t i o n, o o . . . . . . . . . . . . . . . . . . . l L o3 5 0

3 0 0

2 0 0

1 5 0

~ ; ~ K ~ = 4 7 2 x 1 0 6 s , = O 5[ o D e s a t u r a t io n Z o n e I i - - ~ ~ ' ' ' :! ~ K 0 - - 4 . 7 2 x l f f 9 S= 0 . 3 :Q = 1 0 ,4 4 m ~ s | ] P A N E L C O A Lio o o o o o o o o c o o o o o c o o o ~ o o o o o o [

, o c o o o ~ o c o o c o o o ~ o c o o ~ o ~ o o o o o c oo o o K0-~L72Xt 0"7S=0.5~ o o c o o co o o c ~ o c o o ~ o ~ o c o o c o o ~ i, o ~ o o o o c o o ~ o c ~ o c o o ~ o c o o ~ o c o o,oor~o o o o c o o c c o a o o c o o c o o c o o c o o c o [, ~ oct c o o c o o c o o c o o ~, o o ~ o c o o c o o c o o o o o o o o o o o c o o c o c o o, o o c o o c o o c o o o ~ o ~ o ~ o ~ o c o o o

M i n i n g D i r e c ti o n C o a l S e a m1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0

X - c o o r d i n a t e ( m )

(b)4OO

~ o o o o o o o o o o o o o o o

) = t ~ a . " x l ~5 0 [ o O e s a t u r a t i o n Z o n e ] I ~ 1 ~ = 4 " 7 2 x 1 0 " 7~z-.o 5i _ T ..........................................................

Q = 1 . 8 4 's m 2 / s ]

o 3 0 0

2 5 0

2 0 0

1 5 0

P A N E L C O A L S E A M

2 0 0 4 0 0 6 0 0Y - c o o r d i n a t e (m ) \

o o o o o ct o c o o c o o ~ n o c o o oo ~ 8 8 ~ 8 ~ , o ~ o ~ o o o ,=, I, f = ; ~ = 4 . 7 2 ~ 1 0 ~ = 0 .s[ o D e s a t u r a t i o n Z o n e / = o ~ . . . . . 7 -, _ _ ~ 2 2 ~ _ - J . . . . ~-~ I ', ,~ . / z x l0 " S =U .3- . . . . . . . . . . . . . . -~ l - ~r ,~ , ~, ~OAL

Q = 1 . 8 , S m ~ s ~ E l K _ _ 4 7 ~ " 3 . 9 -- O - " z x % ~ s =u . bL o n g i t u d i n a l S e c t j o n ! ~ ! " t ,~ ~ " , , ,

0

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0X - c o o r d i n a te ( m )Z

( c )4 0 0 ~ o o o o o o o o o u o o o u u o u o

3 5 0E 3 0 0"o8 2s o,uN

2 0 0

1 5 0

= ~ 0 = i, = , ~ -[ D e s a t u r a t io n Z o n e l E K ~ . 6 7 2 x 1 0 " 7Q = O . 2 0 0 0 m 2 / s ~ K__~.3"72x 10 10

P A N E L C O A L S E A M

2 0 0 4 0 0 6 0 0Y - c o o r d i n a t e (m )

4 0 O . . . . . . . . . . . . . . . . . . . . . l ~ . . . . .

3 5 0E 3 0 08 2s 0o

2O O

1 5 0

~ K Q = 4 . 7 2 X 10 6 S = 0 . 5I o D e s a t u r a t i o n Z o n e 1 ~ K 0 _ = 4 . 7 2 x 1 0 . T s = O . 3 {

i i P A N E L C O A LQ = O,2000m 2/s ' ~

o o ~ o ~ o c ~ o m o c e o c o o o I "o o o o o o o c o o c o o o o o c o o m o oo o o o o c o o o o o c o o 0 o o c o o o o o o

o o c o o c o o c o o ~ o ~ o c n o c o o oo o G o o c o o ~ o c o o : p o e t o ~ o o I

M i n i n g D i r e c ti o n C o a l S e a m ]. . . . . . . , . . . . , . . . . . . . . . . . . . t1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0X - c o o r d i n a te ( m )

F i g . 1 0 . D i s t r i b u t i o n o f o v e r b u r d e n e d d e s a t u r a t i o n z o n e s u n d e r d i f fe r e n t p r e -m i n i n g h y d r a u l i c c o n d u c t i v i t y f i e ld s . U n i t s f o rK 0 a n d s a r e m / s e e a n d m , r e s p e c t i v e ly .

Equat ions (27) - (29) are coupled through the re la t ionsbe tween the mining- induced s tra ins and the post -mininghydraul i c conduct iv i t i e s , as de f ined in the fo l l owing

1K x = ~ K ~ 0 [ ( 1 + f l yA E y )3 (1 f l=A E=)~] (30)

1Ky = ~ K y0[(1 + f lxA 6x) 3 + (1 + f l=A E~)3 ] ( 3 1 )1K z = 2 K = 0 [ ( 1 + f l x A c x ) 3 + ( 1 + f l y A G ) 3 ] ( 3 2 )

T h e h y d r a u l i c c o n d u c t i v i t y e n h a n c e m e n t a n d d e s a t u r a -t ion around mined pane l s are eva luated through the

fol lowing straightforward steps: 1 . The strain f ie ld thatdeve lops aroun d a l ongwa l l pane l as a re sult o f miningi s obta ined through so lv ing equat ions (27) and (28) ,u s i n g a n o n - l i n e a r F E m o d e l t h a t a c c o m m o d a t e s t h einf luence o f mater ia l fa ilure and se l f -we ight ; 2 . Fr om thi spredic ted s tra in f i e ld , and from knowledge o f thepre -mining hydraul i c proper t i e s o f the over ly ing s trata ,post -mining hydraul i c conduct iv i ty f i e ld i s obta inedt h r o u g h s o l v i n g e q u a t i o n s ( 3 0 ) - ( 3 2 ) ; 3 . W i t h t h epost -mining hydraul i c conduct iv i ty f i e ld de termined, thepost -mining hydro log ic system i s subsequent ly de f inedt h r o u g h s o l v i n g e q u a t i o n ( 2 9 ) , u s i n g a g r o u n d w a t e rm o d e l . A g a i n , d e t e r m i n a t io n o f th e p o s t - m i n i n gh y d r o l o g i c s y s t e m u t i l i z e s a n o n - l i n e a r F E m o d e l t h a t

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LIU and ELSWORTH: THREE-DIMENSIONALHYDRAULIC CONDUCTIVITY 1149incorporates the development of the ground water freesurface. The validation of the resultant FE model is welldocumented in studies [8,14,24-26]. The FE model isalso applied to a well instrumented longwall mine site asa two-dimensional example [26]. The following docu-ments the application of this FE model to another wellinstrumented longwall mine site as a three-dimensionalexample. Through this application, the complexthree-dimensional hydraulic response of overburden tolongwall mining around the advancing mining face arethoroughly examined. These results are reported in thefollowing sections.

6. APPLICATION OF THE FEM MODELAn extensive hydrological and geomechanical moni-toring program was conducted at a longwall coal minein West Virginia [16]. Ground water levels, pre-mining

hydraulic conductivity, overburden movement, andsurface subsidence relative to the passage of the longwallpanel were obtained through this monitoring program.Based on this information, the mining-induced overbur-den strain field, the post-mining overburden hydraulicconductivity field and the post-mining ground water flowregime are evaluated. Results of the evaluation areverified against the in situ monitoring results.6. I . S i te speci fication and f ield mon i toring

The mine is located within the Pittsburgh seam, withan average extraction thickness at the study site rangingfrom 1.7 to 1.8 m (5.5 to 6 feet). The instrumented panelis 183 m (600 feet) wide by 2195 m (7200 feet) long. Theoverburden monitoring test site is located at approxi-mately center-panel length. The test site lies on top of abroad crest at the end of a long steep-side ridge. Reliefto the stream valley below is 91-122 m (300-400 feet).The coal seam is approximately 213-219m (700-720feet) deep at the test site. The mined seam lies directlybeneath about 85m (280 feet) of highly competentlimestone and sandstone strata as contrasted with thelow strength shales and claystones close to the surface.The shallow water-bearing strata at the test locationare considered to be perched or semiperched aquifers,which consist of a vertical succession of water tablesseparated by unsaturated zones. Low permeability shalesand claystones impede the downward migration ofground water, and water levels decrease as well depthincreases. Aquifer recharge is almost entirely fromprecipitation in the form of snow and rain, and dischargeoccurs via springs, seeps along hillsides and viaevapotranspiration.. Pre-mining water levels in wellsdrilled within the upper 60 m (200 feet) fluctuated widelywith seasonal changes in precipitation patterns andevapotranspiration. Steep topography is known to haveplayed an important role in shallow aquifer water levelfluctuation, since the high runoff and small recharge areagreatly limit recharge. Pre-mining water levels below122 m (400 feet) remained fairly constant.Ground water monitoring was conducted in a total o feight monitoring wells and one private well. Six of the

monitor ing wells and the private well were located nearthe panel-center. Three of those wells (W1, W3 and W5)were completed to a depth of 183 m (600 feet). Of thetwo wells drilled over the panel headgate, well W7 wascompleted to a depth of 123 m (405 feet). The other fourwells W2, W4, W6 and the private well were completedto a depth of less than 62 m (200 feet).6.2. Field grou nd water moni toring resul ts

Hydraulic responses were observed through eightmonitoring wells. In general, water levels in shallowwells [W2, W4 and W6, less than 62 m (200 feet) deep]and near center-panel were lowered (or went dry) within1 month of being undermined, then recovered to nearpre-mining levels, 4-5 months after mining. Sustainedpost-mining water levels in these shallow wells exhibitedless fluctuation and were slightly lower than averagepre-mining levels. The 183-m (600-foot) deep wells (Wl ,W3, and W5) went dry after the face had passed 15 m(50 feet) and did not recover. The 123-m (405-foot) well(W7) over the headgate was relatively unaffected in thelong term by passage of the face.6 .3 . Three-d imens iona l numer ica l mod el

The three-dimensional FE model developed for boththe determination of overburden deformation andpost-mining hydrologic effects is illustrated in Fig. 4.Boundary mesh deformations in the x-direction at thecross sections of X = 0 and X= 1000m, in they-direction at the cross sections of Y = 0 andY = 600 m, and in the z-direction at the bottom (Z = 0)are constrained for the determination of overburdendeformation. No flow boundary conditions are appliedat the cross sections of X = 0 and Y = 0, and constanthead boundary conditions are applied (h = 400 m) at thecross sections ofX = 1000 m and Y = 600 m and aroundthe panel (h = 188.2 m for the floor, h = 190 m for theroof). This enables the post-mining ground water regimeto be determined, with the inclusion of deformationaleffects.The values of the modulus of elasticity for theoverburden are assumed as E = 4 109 Pa and 0.30,respectively. The post-failure values of the Poisson ratioand elastic modulus in extensional elements, areobtained as 0.45 and E / 4 , respectively, by matching themaximum model subsidence with the field measuredmagnitude.6.4. D is tr ibut ion of mining-ind uced s trains

The model subsidence cone is illustrated in Fig. 5(a)and the final subsidence profile at the cross section ofX = 0 is compared with field data in Fig. 5(b). It isapparent t hat the model subsidence profile is flatter thanthe field measured one. This may be due to the possiblediscontinuous deformation of overburden which is notincorporated in the continuous deformation model.Nevertheless, the mismatch between the measured andmodeled subsidence profiles may be considered adequatefor the subsequent analyses.

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1150 LIU and ELSWORTH: THREE-DI MENSIONAL HYDRA ULIC CONDUCTIVI TY

The s t ra in f i e ld , modu la ted by the su r face subs idenceprof i l e , i s i l l u s t ra t ed in F ig . 6 . Apparen t f rom thesef igures i s tha t s ign i f i can t min ing- induced overburdenex tens iona l defo rmat ion i s res t r i c t ed to sha l low dep ths( les s than t00 m deep) ahead o f the advancing face , bu tmore s ign i f i can t min ing- induced ex tens iona l defo r -mat ion deve lops beh ind the advancing face , par t i cu la r lyin the cav ing zone and in shear zones above thea b u t me n t s .6.5 . Evaluation o f pos t -min ing conduc tiv ity f ie ld

Pos t -m in ing hydrau l i c conduct iv i t i es fo r the s tudy [16]are def ined as a func t ion o f min ing- induced s t ra in f ie ldand the p re-min ing hydrau l i c conduct iv i ty f i e ld (o rf rac tu re parameters ) . The min ing- induced s t ra in magn i -tudes , def ined by eva lua t ion o f the subs idence p ro f i l e ,a re incorpora ted d i rec t ly in to the ana lys i s . Th i s s t ra inf i e ld , toge ther wi th the p re-min ing hydrau l i c conduc-t iv i ty , i s used to de te rmine the pos t -min ing hydrau l i cconduct iv i ty f i e ld . Pre-min ing hydrau l i c conduct iv i tyma g n i t u d e s f o r t h e o v e r b u r d e n a r e d e t e r mi n e d a c c o r d -ing to the p re-min ing conduct iv i ty measurement s , ass h o w n i n F i g . 7 [ 1 6 ] . T h e o v e r b u r d e n ma y b e d i v i d e din to th ree mater i a l un i t s to approx imate ly rep resen t therea l d i s t r ibu t ion o f conduct iv i ty , compr i s ing a cen t ra la ci uit ar d, b o u n d e d a b o v e a n d b e l o w b y mo r e c o n d u c t i v eun i t s . The th icknesses fo r each mater i a l un i t a re 60 , 70 ,and 6 0m , respec t ive ly . The p re-min ing hyd rau l i cconduct iv i ty f i e ld i s as sumed to be i so t rop ic and i ss u b s t i t u t e d b y a d i s c o n t i n u o u s f l o w mo d e l w i t h t h r e eiden t i ca l se t s o f o r thogon al f rac tu res . The f rac tu rep a r a me t e r s o f sp a c in g , a p e r t u r e a n d m o d u l u s r e d u c t i o nra t io a re de te rmined f rom the p re-min ing hydrau l i cc o n d u c t i v i t y w i t h e s t i ma t e d ma g n i t u d e s o f f r a c t u r es p a c i n g . I n p u t p a r a me t e r s f o r t h e d e t e r mi n a t i o n o fmi n i n g i mp a c t s o n t h e g r o u n d w a t e r r e s o u r c e a r e l is te din Tab le 1 .

The ra t ios o f pos t -min ing hydrau l i c conduct iv i t ies top re-min ing hydrau l i c conduct iv i t i es a t d i f fe ren t c rosssect ions are i l lus t rated in Fig. 8 . The f igure i l lus t ratestha t s ign i f i can t conduct iv i ty increases a re res t r i c t ed tosha l low dep ths ( l ess than 100 m deep) ah ead o f theadvancing face , bu t more s ign i f i can t conduct iv i tyincreases deve lop beh ind the advanc ing face , par t icu la r lyin the cav ing zone , and in shear zones above thea b u t me n t s .6.6. Three-dimensional effects

A s t h e w o r k i n g f a c e a d v a n c e s , t h e a b u t me n t a t t h eface exper i ences a t ru ly th ree-d imens iona l s t res s reg imetha t inc ludes the s t res s -con cen t ra t ion e f fec ts a t t he pane lc o r n e r . I f d a m a g e a n d s t r a in s a r e n o n - l i n ea r a n di r recoverab le , t h i s may l eave remnan t changes inhydrau l i c conduct iv i t i es tha t a re l a rger than thema g n i t u d e s p r e d i c t e d b y t h e p la n e - s tr a i n F E m o d e l . T h eimp or tanc e o f th is e f fec t i s observed , as shown in F ig .8 (b ) , (c ) and ( f ) . As shown in F ig . 8 (b ) , t he reg ion o ft ransverse hydrau l i c conduct iv i ty enhancement s ign i f i -can t ly sh r inks beh ind the work ing face . Th i s sugges t stha t the increase o f hydrau l i c co nduc t iv i ty in the

t ransverse d i rec t ion wi l l be underes t imated by thep lane-s t ra in FE model . As shown in F ig . 8 (c) and ( f ) ,s ign i f i can t increase o f hydrau l i c conduct iv i ty in thev e r ti c a l d ir e c t io n m a y o c c u r a h e a d o f t h e w o r k i n g f a c e .T h e r e m n a n t i n c re a s e ma y c o u n t e r a c t t h e d e c r e a se i n th ever t i ca l hydrau l i c conduct iv i ty p red ic ted by the p lane-s t ra in FE model [26] .6. 7. Determination o f overburden desaturation

T h e i mp a c t s o f lo n g w a l l m i n i n g o n g r o u n d w a t e rr e s o u r c e s a r e e v a l u a t e d i n t e r ms o f t h e d i s t r i b u t i o n o fo v e r b u r d e n d e s a t u r a t i o n z o n e s a s d e f i n e d i n t h elong- te rm, where s t eady-s t a t e f low cond i t ions p reva i l .Th i s rep resen t s behav io r fo l lowing passage o f thelongwal l face , and def ines the mos t impor tan t behav io rf r o m a p r a c t i c a l s t a n d p o i n t . T h e e v a l u a t i o n o fdesa tu ra t ion zone ex ten t s i s impor tan t in def in ingexpec ted su rv ivab i l i ty o f water supp ly wel l s toundermin ing .

T h e d i s t r i b u ti o n o f p o s t - mi n i n g o v e r b u r d e n d e s a t u r a -t ion zones , eva lua ted based on the pos t -min ing hydrau l i cconduct iv i ty f i e ld and the app l i ed boundary cond i t ions ,wi th the observed water l eve l f luc tua t ion in moni to r ingwel ls , are i l lus t rated in Fig. 9 . Under the appl iedb o u n d a r y c o n d i t i o n s f o r t h e f lo w mo d e l , t w o s e p a r a t ed e s a t u r a t i o n z o n e s a r e d e v e l o p e d f o l l o w i n g mi n i n g o fthe pane l . O ne i s a t t he su r face (ab ou t 10 m in dep th ) ,a n d t h e o t h e r i s d i r e ct l y a b o v e t h e p a n e l ( a b o u t t 7 5 min depth), as i l lus t rated in Figure 9(a) . The wel lsc o mp l e t e d w i t h i n t h e r a n g e o f 1 0 - 1 20 m i n d e p t h ( W 2 ,W4, W6, W7, and the p r iva te wel l ) wi l l l i ke ly su rv ivemi n i n g b e c a u s e t h e y a r e l o c a t e d w i t h in t h e p o s t - mi n in gsa tu ra te d zon e (aqu i fe r ) and wel l s com ple ted wi th in ther a n g e o f 1 2 0 - 2 1 0 m i n d e p t h ( W 1 , W 3 , a n d W 5 ) ma ydra in because they a re loca ted d i rec t ly wi th in thepos t -min ing desa tu ra t ion zone . These model resu l t s a recons i s t en t wi th bo th observ ed resu l t s , as repor t ed in F ig .9 (b ) . The observed resu l t s ind ica te tha t the impact s o flongwal l min ing on sha l low wel l s a re ex t reme ly loca li zedwi th respec t to the min ing f ron t . However , t he impact so f longwal l min ing on deep wel l s may be ex tens ive ,p e r ma n e n t a n d u n l i k e l y t o r e c o v e r .

6.8 . E f fec ts o f le ss permea ble layersAssuming tha t the p re-min ing hydrau l i c conduct iv i tyof les s perm eab le l ayers p resen t abo ve the pane l i si s o tr o p i c , b e h a v i o r ma y b e r e p r e s e n t e d b y a n e q u i v a l e n tp o r o u s me d i u m. T h i s ma y b e d e f i n e d , a c c o r d i n g t oequat ion (17) , where the modulus reduct ion ra t io , R, , ,can be def ined as

1R m = //6/~X-1/3. ] ( 3 3 )

I f there a re no f rac tu res ( s ~ oc), equa t ion (33) beco me sRm = 1 .0 . Acc ord ing to equ a t ions (13) - (15) condu ct iv i tyra t ios ( R x , R y , and Rz) can be def ined asR:, = 1 [1 + Ae:~) + (1 + AE~) 1 (34 )

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L I U a nd E L S W O R T H : T H R E E - D I M E N S I O N A L H Y D R A U L I C C O N D U C T I V I T Y 11511Ry = i [1 + AEx)3 + (1 + Aez)3] (35)

Rz = 1 [1 + AEx)3 + (1 + AEy) ] .(36)Phys ica l ly , equa t ions (34) - (36) def ine tha t the s t ra in i su n i f o r ml y d i s t r ib u t e d b e t w e e n f r a c t u re s a n d ma t r ix . T h i sresu l t s in the smal l es t poss ib le change in hydrau l i cconduct iv i ty due to longwal l min ing .T h r e e d i f f e r e n t c o mb i n a t i o n s f o r t h e d i s t r i b u t i o n o fthe p re-min ing hydrau l i c conduct iv i ty a re chosen fo r thenumer ica l model as i l l u s t ra t ed in F ig . 4 . Th i srepresen ta t ion i s used to inves t iga te the e f fec t s o f l es sp e r me a b l e l a y er s o n t h e h y d r a u l i c i mp a c t s o f l o n g w a llmin ing . The hydrau l i c param eters used in the mo del , andthe num er ica l resu l t s a re show n in F ig . 10. The e f fec ts o fl es s permeab le l ayers a re eva lua ted in t e rms o f thed i s t ri b u t io n o f p o s t- mi n i n g o v e r b u r d e n d e s a t u r a t i o nzones and d ra inage in to the mine . I t i s apparen t tha t thed i s t ri b u t io n o f p o s t - mi n i n g o v e r b u r d e n d e s a t u r a t i o nz o n e s a n d d r a i n a g e i n t o t h e mi n e a r e d e t e rmi n e d b y b o t hthe loca t ion o f the l es s permeab le l ayer and thema gni tude o f i t s p re-min ing h ydrau l i c condu ct iv i ty . Thep o t e n t i a l f o r d e w a t e r i n g t h e s h a l l o w a q u i f e r ma y b ereduced by the p resence o f a l es s perm eab le l ayer . I f twoaqu i fe rs a re separa ted by th i s l ayer , however , t he deepaqu i fe r m ay be severe ly dew atered as show n in F ig . 10 (a)and (d ) . The m agn i tude o f the p re-min ing h ydrau l i cc o n d u c t i v i t y o f a l e s s p e r me a b l e l a y e r ma y a f f e c t b o t ht h e d i s tr i b u t io n o f p o s t - mi n i n g o v e r b u r d e n d e s a t u r a t i o nzones and the d ra inage in to the mine i f t he aqu i fe r i ssepara ted f rom the mine by th i s l es s permeab le l ayer , asshown in Fig. 10(b), (c) , (e) and (f) .

7 . CO N CL U SI O N SThree-d imens iona l e f fec t s o f hydrau l i c conduc t iv i ty

e n h a n c e m e n t a n d o v e r b u r d e n d e s a t u r a t i o n a r o u n d al o n g w a l l m i n i n g a d v a n c i n g f a c e a r e e v a l u a t e d t h r o u g huse o f a th ree-d imens iona l coup led f in it e e l ementh y d r o me c h a n i c a l mo d e l .

T h e c o mp l e x h y d r o me c h a n i c a l c o u p l i n g p r o c e s sb e t w e e n mi n i n g - i n d u c e d o v e r b u r d e n d e f o r ma t i o n a n dd e s a t u r a t i o n i s r e p r e s e n t e d t h r o u g h t h r e e - d i me n s i o n a lre l a t ions be tween induced s t ra in and chan ge in hydrau l i cc o n d u c t i v i ty d e v e l o p e d i n t h is s t u d y . D a t a r e q u i r e me n t sf o r t h e mo d e l a r e mi n i ma l b e c a u s e t h e d i s p l a c e me n tbo un dar y cond i t ion i s success fu l ly app l i ed to rep resen tthe p rocess o f coa l ex t rac t ion .

T h e c o mp l e x d i s t r i b u ti o n o f p o s t - mi n in g h y d r a u l i cc o n d u c t iv i t ie s a r o u n d t h e a d v a n c i n g f a c e is d e t e r mi n e db y t h e mi n i n g l a y o u t , p a r t i c u l a r l y t h e mi n i n g g e o me t r ysuch as min ing dep th , pane l wid th and he igh t , wi the x t e n t l a r g e l y mo d u l a t e d b y t h e p r e s e n c e a n d t h el o c a t i o n o f f l at ly i n g l a ye r s o f l o w c o n d u c t i v it y . A p p a r e n tf rom th i s s tudy i s tha t s ign i f i can t hydrau l i c conduct iv i tyincreases a re res t r i c t ed to the sha l low dep ths ahead o fthe advancing face , bu t more s ign i f i can t increasesdevelop beh ind the advancing face , par t i cu la r ly in thec a v i n g z on e , a n d i n t h e s h e a r z o n e s a b o v e t h e a b u t me n t s .

Because s ign i f i can t hydrau l i c conduct iv i ty increasesb e h i n d t h e a d v a n c i n g f a c e a r e mu c h l a r g e r t h a n t h o s eahead o f it , bo th in the su r face zone and in theimmedia te zones a long the pane l edges , long i tud ina ld r a i n ag e ma y p l a y a v e r y imp o r t a n t r o l e in e v a l u a t in gt h e i mp a c t o f l o ng w a l l m i n i n g o n g r o u n d w a t e r l ev elsa r o u n d t h e mi n in g f r o n t . D r a m a t i c c h a n g e s i n h y d r a u li cc o n d u c t i v i t y a r o u n d t h e a d v a n c i n g f a c e ma y a l s o c a u s edramat i c changes in g round water l eve l s . However , t hesec h a n g e s ma y b e m o d u l a t e d b y t h e p r e s e n c e o f f la t ly i n gless permeab le l ayers . I f t he p resence o f a f l a t ly ing l es sp e r me a b l e l a y e r c a n n o t p r e v e n t t h e d i r e c t c o n n e c t i o nb e t w e e n t h e s u r f a c e z o n e a n d t h e i mme d i a t e z o n e o fhydrau l i c conduct iv i ty enhancement , water l eve l f luc tu -a t ions wi th in bo th zones resu l t fo l lowing undermin ing .I f the p resence o f a f l a t ly ing l es s permeab le l ayer canp r e v e n t t h e d i r e c t c o n n e c t i o n b e t w e e n t h e s u r f a c e z o n ea n d t h e i mme d i a t e z o n e o f h y d r a u l ic c o n d u c t i v i t yenhancement , water l eve l s wi th in the su r face zone wi l lf luc tua te much l es s s ign i f i can t than those wi th in theimmedia te zone . These conclus ions a re cons i s t en t wi thobserved resu l t s .

Al though th i s model i s app l i ed to a par t i cu la rlongwal l mine s i t e , conc lus ions d rawn f rom th i s s tudyma y b e u s e d t o e x p l a i n o b s e r v e d r e s u l t s f r o m o t h e rmi n i n g s i t u a t i o n s . H o w e v e r , c a u t i o n s a b o u t t h e FEmo d e l l i m i t a t i o n s s h o u l d b e ma d e w h e n a p p l y i n g t h e s econclus ions . These l imi ta t ions inc lude tha t the FE modelf o r t h e s o l i d p h a s e d o e s n o t i n c o r p o r a t e t h e p o t e n t i a ld i s c o n t i n u o u s d e f o r ma t i o n o f t h e o v e r b u r d e n a n d t h a tthe re l a tions be tw een min ing- induced s t ra ins andpos t -min ing hydrau l i c conduct iv i t i es do no t inc lude theef fec t o f shear s t ra ins . These l im i ta t ions need to bea d d r e s s e d i n t h e f u t u r e w o r k .Acknowledgemen ts - -Th is work has been pa r t ia l ly suppor ted by theN a t i o n a l S c i e n c e F o u n d a t i o n , U . S . A . , u n d e r G r a n t N o . C M S -9 2 09 0 59 , a n d b y t h e N a t i o n a l M i n e d L a n d R e c l a m a t i o n C e n t e r u n d e rGra n t N o . CO388962. T h is suppor t i s g ra te fu l ly acknowledged . Theau thors a l so thank two anonymous rev iewers and the Ed i to r fo rp rov id ing c r i t ica l comm ents and cons t ruc t ive sugges t ions in rev is ingthe manuscr ip t .

Accep ted for publication 12 June 1997.

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