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    Table 9.2.2 So bsidence Fador and R atio of M2Ximom HoriUlntal Dis pJacement toMaximUm Possible So bsidenl'e . .

    !oa" Field and Met#od of Pac$in%S&bsidence

    Factor Raticf

    004 5 . ( ).9 .()

    . *+ .,+.. - . *+ ..+ .,+ / -*+..90 ' . .,+ .*+

    .2+.'-' .,+ : .... .*

    .*+ .++ .*.1 .9 ' .*

    .(2 .

    .3

    .1 .,.1 .9 .,*.* .1 .,

    .3+ .1+ .,

    .1+ .9 .,+

    .)+ .9 ., .+

    .( 4)

    .+ .)0.10-0040.,, .)+ .

    5ritisb coa6 fields'716 .Solid stowing

    8!a in% (' strip pac$in%RUM coal :eld4 ;ermant#er solid sto=in%?-. .!a i n%

    @ort# and Pasode !al ais coAJ fBeld4France

    H

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    288

    : .

    ~I/

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    I"IJ

    290 S tJRFA CE StJ BSJ1)EN CE

    o1 0

    20

    30

    'l O

    F I.... a l f ac e poalllonI t\. '1', k::' R;~l d ~ 8 f 1 .1 1-s u s ldence -

    1 I I I I1 0 . Su s ld e!ce lp! o f lle\01- #$en f ace stopp e%

    & & \

    F IJa l ' ul s& (e n~ ) b *~ I ...& h .~~ p!ot lle 2 .1 d e+ s: . ~ . \ \ af . te! fa ce s* o ppe &

    -, . \ 1 I I I I&-~ I .J. ..d- .-l--

    . &

    -& s : 50E " 60

    ! , 7bE. : 80o . /~ 1//

    2 .0 2 .01.0 - 1.0 0 .5 O 0 . 5 1 . 0 .1 . 5

    Fa c e a d "8 c eept $

    FIg. 9.2.7 Resid !l s bside"#e $%o&ile 12(. )o "es * + . . !lio"!l )o ! / o!%d.

    s %&!#e - $o " !"d %ed #es o 2 o 3 i& b e &!#e h!s $ ! ssed be #% i i#!4id h. 2$ e . %!e' o& & !#e !d !" #e dete!3 n es t$e i e "eeded o $!ssh%o gh he #%ii#! 4i d h. 7s lo"g !s he &!#e is s i ll 4i h i" he #%i i#!4id h , & % he% s bside"#e is e $e# ed . .

    o4 e ei, /%! "e% 13 (, #i i"g R ssi!" d! l! , s ! ed h! i" !#l di io " ohe %!e o& !d !"#e !"d s 4e o& #%ii#! !% e! , he d %! io" o & s %&!#es b side" #e de$e"ds o" s%!! #o"di io"s , de$ h o& e %!# o" , ki"d s o& $!#k "g s, !"d $%e io s e %!# io" !"d b ! i %!"ges &%o se e%!l d!*s tose e %! *e!%s. 2$ e d %! io" islo"ge% &o% t$"c5- edded o% s %o" ge% o5e%

    b!%de", f o r

    g%e! e% de$ bs, !"d &o% #o $le e #! "g . Fo% ! s !Il e %!eio" !% e! o .&! %el! i el* ob le.o e%b %de" i"ed i" ! e%* sbo% i e, h e%! e o ' s bside!#e is. $%o$o% io"!l o be d&& e% e" #e be 4e e" t$ e &i"!ls bside"#e ;, !"< he - "s =" !"eo s s bside" #e S r : . .

    :. : . . . . : " " fJs~' .' ::.:. :' dJ' . * 6 ; * ~ ( S . - S ,) . 9 .

    9.3 )Ol'o?b + IE E ) I ); G ORl ; 291

    ' , 0

    10 0'-

    1 0.6

    o ?', < 8 9 s H :. & i" :-- ) 6 o BI h .? F";. 9.2.8 . Gi e ! ? E ) l l); 2@E=R~ ES

    )o" i '" e #h!"i #s he

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    292StJ RPA ~ sBs IDENC B

    ", '"

    : : : ~ C. . . . . .' ' .: . : ",

    ',.:: . :.....

    3 , 'C om pl'et e 'C 'to s ur aFl e . 9.3. 1 Berry ', models oC surfac esu bs.idencc (15) .

    seam. h is the de th of e! ca ation belo# surf ace, X is the hori$ontaldistance from th e center of the e! ca ati on, and % , and K . are t# ocharacteristic constants :

    : : .

    . K ,' ~ &l ' vl ) J1'l ( E :zJE" " . V:) -IIS . (9.3. )" . : .: -:, :' K s:" r E ;rl2M . - 11,,(1.) . v..,) (E ..,j E II . P :',) ' . (9.3.3)

    .! ~ " #~ E ,,> v lI '; ; n d ' ,; ; ~ ~ are*.th.+ +un- ++:noduli ~$ . oisson *ia ti s' in '...+.:,:/" e+ici0 ( 'e 'r +ndicular (o beddiri-s ) .and.2 ori+o,ntal,( + ali l t o beddin-s) ': . : / d4recti ons, res ect 4ely , and M sthe sh ear modulus . 6be .r estriction on

    .:.',.' .t" +e.,++:+o.ns ,iant s!s ' th7i, both %,:'l8nd X , ' .%K , must be , osit4 e . &is .. . seen 4rom + :9 .3'.1 thatsurface subsidence is li4-hly de endent on K , and'

    K . 6+ erefor e, the determin 7tion of K, and % t is + r y criti ca1. Berry (s)su.--ested the c+n et io+' or;9' 9.3.1. +o a dimensi onless u antity , ":

    " # S () ''< A (K, %K # ) J l 2

    (9.3.0)

    9.3 ! C* N)IN++, -'. ECBANICS '/0E*RlES

    sueh that = ... 1at! > o or m7!imum subsiden ce occur s aboye the ce nter of the e! ca ati on. 6h en

    . h ' $ a s " ) 1 1 (K, ::t (.r '' ?!, 8:r 1 .)I

    (9.3.5)

    ./,. ..#. s, > > h : 5 5 ' % a s ]

    @, 8:r ,....r ,# her e x - /8:@ are the o ints # here = ... t (i.e., .ha5f the ma!i mumsubsid ence). n d etermin in- K . and K " fir st findin th esubsid ence area the

    oints A@ 2' # here= - , measure the s lo ea=

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    .~: .t'

    ,"VIU'A "-V.os:;Wr:NL'K

    elastic limit. ~s a m~er of fact, surface ore!oles rille i# t!e $% of alo#$&all roce.ID t e (tts ur$! coal seam i#"icate" t!at roc) mas s u* lo

    + ft a o e t e ~o~ seam &as su ecte to a /ertical stra(# ra#$i#$ from0 to 1. ,%%%2 *.I3 .4m. Dahl a# 5!oi t erefor e su$$este" a mo el t!at e!.a/es 1, ;~# elas~c-elaslo*last~c ma##er. 6 e mo el is li#earl elasticU~t11 ~e ~7%.tr %I55oul om yield or t!e anisotr o p e Voa 8ises ielcf9lter ~~1 sarisfie . ecause of t!e com*le=(t i# ou# ar co# itio#s,~e fi~te-eleme#t met o &as use &it! a# i#cr eme#tal co#stituu/e .rela-tio#s! ( *: :

    (d U hx, = ?@.=s4a~>.=l 4.+.B@. &!ere < 4 t ! ) a# (d ~ ) c u :e s~ss a# strai# te#sors, res*ect(/el , a# [ E ] is. 2t!e mat#= of *ro*ortto#a!t co#sta#ts of stress a# stra(#. 6! e li#ear

    Coo~~ r elat(c#s!(* 4?@ is use" elo& t!e iel" *oi#t, &!ereas for a**!~ stre~s aDo/e t!e iel *oi#t ?@ is stress. e *e# e#t as s *ecifie t!e ( el cr#e#a.2 .:.Usi~2.t!is mD el, .3a! :. a# 5!oi 4B@ re*o#e a case stu of t! e

    lo#$&al *~el . ID l ac)s/i lle No. I 8i# E, lac)s/ille, West Vir$i#ia,&!ere t!e ltts ur$! coal seam F ft t!ic) &as mi#e. 6!e surface su siGe#ce22sur/e .is 7!%W3in Hi$. .+.+. 3otte li#es are surface to*o$r a *!(e

    co#tours, soli ~ots are surv eying statio#s, soli cur/e Ii#es are su s(Ge #ce co#tour Ii#es, a# !ea/ r o)e# li#es are face locatio#s 6!ee~elo*me#t of su s~ e# ceas ~e lo#$&al retreat mi#i#$ *r ocee e fo r a

    *~#~ ~f ~ ~ #t! 1 s!o I3 A to ?. 7u si e #ce is s mmetri.c &it!#uru#$ae%/ltles a# $eometr a# is #%Isi$#ifica#tl affecte suJaceto *o$ra *!~. ~6t!er more, it is time-i# e*e# e#t e cause su si e #cesmeasure lJl HI.$s.~.+.+3 a# ? .are esse#tial t!e same alt!ou$! t!e&ere measure.4 5 . a sa* rt ; U7I3$t!e t!r ee- ime#sio#al ti#ite-e eme#t :m.et!o , su sl e# ce *rofiles ID Hi$. .+.+? &as r e *r o uce as s! o i#H$. .+ .+H. Co&e/er, t!e material *ro *erties us%%a# s!o e o&&ere etermi#e trials a# errors u#til t e re*ro uce t e fie ata .

    5a/e oe) I#tact oc) Mou#s's mo u us:4*si@oisso# ratio

    6~#sile'str e#$t! 4*si@

    N x l OP.0

    24

    0, x lOP.0

    0P

    Hro~ t!e t&o

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    u.0 .- ..

    : .

    . . . . .. .

    ' ~ ', ' .' .

    " "

    ; . v"

    "

    ,' .. :'.

    296

    ': .

    . ., .

    .. '

    . , : :-.' '-;.._ E . '

    o

    o 1 00 200 ft

    9

    . ; . . ~ .: . _ . - : ,' \ ~ .~ : . " . 0 .. ' . ... .9.3'.,3:(A -B i. D.cVeloii!eril~~~face su s i~c c'e~"#r a lo $:%&ill 'a ~ f ()'a *e .

    . % +, *~or a& o !s/ *ae0s.(or .&0re1- 2i e s o al . o2cl. A3 u 4er s:iri &0eIn ~ : A . fter Da0l :a 2 1 0ol (Tj..... ' . .' ' .: . " .: :...'. " .,

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    :),

    " .i ;

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    , T ' , , : ,

    r

    r ., , . ' LECEND :

    , S :SUBSIOENCE

    S .SUBSIOENCE ATBOTTO M

    V: OISP~C E MENT

    'F i i . 9.4.1 l-{oriZOntaland vertical components ~r gr ound oiovemenl (8 . !o urtcs" # .$ .:: ' % & (n a) ! o&l *oard.

    " .:.

    +, ,-T,% /O% .- : CONTRACTION"f : LlMtT ANC LE

    ' A gra.p0ic&1met0od oi predicting t0e complete su sidence protile 2asdeve/oped " t0e #.$. %ational !oa/*oard (13 ased on a large num er o ield o servation. For e5amp)e, the su sidence proti)e or a long2all!acew meters 2ide-6n a-seamm meters t0ic7 al a dept0 o h meters elo2t0e s r ace can e determined rom Fig. 9.4.3 as ol)o2s:

    For w .. 1 , ); - 4 , and m ... 1.4.S / m - .

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    :~-;C .', '. /

    I j.

    I I .:~

    ..

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    r

    300

    :; o

    ~ ~~d

    l > : ~ ~ ~. . . .~ ~ s ::. . d 2-

    . . .!:!;; . . .. . . . d . . .

    ~ S l ::l S. . . d

    ~2 . . . N~ d . . .d

    ~ . . .: : : : ;:; ". . . .~ ~ : : ! t ~< > C> < >

    ~ '" ~ ~~d < >

    ~ ! ;J, ~< > . .C> . . .

    ~ !!d ;Sd

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    ;s : ee

    ~ S< > < > . . . . .

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    S i " .~~"~~~aa~~~;~~~~~;S .~~~~ .~~~~~~~"!!~ .!!~!. t SM~"~"ft~M~ ~~-22.-~""""~ Mft"""""NN""NNN""ftM. """. I~l':#dd:;d:i~a~$lda ~ d; ~~%~~ dd;d;d;~;;;;;d;5 1 ~ l!: .~!&"."'~:!'~,..~ '~ . l h . . !" ts: :1!. - o ~ . .. e . . . ., . . .. . . . . . . . .nrn InV l\ftW 'l"''' ' ' ' ' ' '