A study on conceptual evaluation of structural stability of room-and-pillar underground space

(1)

*Corresponding author: Hyu-Soung Shin E-mail: [email protected]

Received November 1, 2013; Revised November 7, 2013;

Accepted November 8, 2013

ᵝႊ᜾ḡ⦹Ŗe᮹Ǎ᳑ᱢᦩᱶᖒ⠪a}ֱᱶพᨱš⦽ᩑǍ

ଲశ෹ ȵୋ৤෹ ȵ਑ิন

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵ֬ۻےٍĵڙ

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵٍ֬ĵڦڙ

A study on conceptual evaluation of structural stability of room-and-pillar underground space

Chulho Lee

¹

, Soo-Ho Chang

²

, Hyu-Soung Shin

²

*

1

Research Specialist, Geotechnical Engineering Research Division, SOC Research Institute, Korea Institute of Construction Technology

2

Research Fellow, Geotechnical Engineering Research Division, SOC Research Institute, Korea Institute of Construction Technology

ABSTRACT: In this study, in order to evaluate stability of the room-and-pillar underground structure, a series of preliminary numerical analyses were performed. Design concept and procedure of an underground structure for obtaining a space are proposed, which should be different from structural design for the room-and-pillar in mine. With assumed material properties, a series of numerical analyses were performed by varying size ratios of room and pillar and then the failure modes and location at yielding initiation were investigated. From the results, relationship between the ratio of pillar width to the roof span (w/s) and overburden pressure at failure initiation shows a relatively linear relation, and the effect of w/s on structural stability is much more critical than the ratio of pillar width and height (w/H) which is a crucial parameter in design of the room-and-pillar mining. It means that roof tensile failure and shear failure at shoulder and pillar are necessary to be considered together for confirming overall structural stability of the room-and-pillar structure, rather than considering the pillar stability only in mining. Failure modes and location at failure initiation were varied with respect to the ratio of room and pillar widths. Therefore, it is necessary to simultaneously consider stability of both roof span and pillar for design of underground structure by the room-and-pillar method.

Keywords: Room and pillar method, Rock pillar, Roof span, Tension failure, Numerical analysis

ߣ΀ ٍ҆ĵقԴəܳѓ֩ݓॠĵܓНۆ؋܁Ձêࢹѓ؋ںυʹॠşڦ३ؒܳٮߎۤҙۆäʴںս࠘३ԵѓѪڷͿêࢹॠٕɰ

̚ॢ şܕۙڙÒьқآقԴČͲॠəܳѓ֩ėѪۆԺćÒȝęəɵ͆܋آॠə ėÂঝ҃޲ڙقԴۆ०νۺۍܳѓ֩ėѪۆ

Ժćۼ޲фÒȝں܃֨ॠٕɰܳرݕݓъܓæقԴؒܳۆ঍ԜҼٮߎۤҙۆţۋق˰δս࠘३Եںսॱॠٕڷ϶ߣş

ۋٰۋ֨ۚʼə֨۾قԴۆࣷĨڮ঍ęڦ࠘Ѻজεêࢹॠٕɰ३ԵĀę ߎۤҙफęؒܳफęۆҼ XTٮࣷĨ֨۾ۆԜۦॠܼ

ÂۆěćəԸ঍ěćεٕ҃ڷ϶ ߎۤҙफęؒܳफۆҼÀܳѓ֩޽ġԺćقԴəϔڍܼڅॢԺćۍۙͿɰΘرݓəؒܳۆ

फęȭۋҼ X)҃ɰĵܓНۆ؋܁Ձঝ҃޲ڙقԴəʌڎлÇॢԺćۍۙۍìڷͿǣࢍǮɰۋə ؒܳۆ؋܁Ձχںঝ҃ॠə

޲ڙقԴսॱʼəܳѓ֩޽ġԺćѪęəɵν ؒܳҙٮ॥ƍĵܓНߎۤҙфرŷҙۆ؋܁Ձūݓʪ॥ƍČͲॠيݓॠ

ĵܓНۆ؋܁Ձںঝ҃ॣսەəĵܓНԺćÀʼرآ॥ںۆйॢɰ̚ॢ ݓॠĵܓНۆ঍Ԝق˰͆ߣşۋٰʂÀьԦॠə

ڦ࠘ٮۻɳ̚əۍۤࣷĨˣࣷĨڮ঍ʪɰβóǣࢍǣ ܳѓ֩ݓॠĵܓНقʂॢԺćəԜۦॠܼق˰δߎۤҙٮؒܳۆ

؋܁Ձںٍćॠيսॱॠəìۋज़څॠɰ

ܳڅرܳѓ֩ėѪ ؒܳ ߎۤҙ ۍۤࣷĨ ս࠘३Ե

$PQZSJHIU ,PSFBO5VOOFMMJOHBOE6OEFSHSPVOE4QBDF"TTPDJBUJPO

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ᕽು

ܳѓ֩ėѪ(Room and pillar method)ڹġԓқآ قԴ֨ۚʽėѪڷͿԴսथ̚əäۆսथڷͿ

ϔۤʼرەəġНں޽ĹॣЀۺڷͿۺڌʼəė ѪڷͿ(Hartman and Mutmansky, 2002) Ĺ޳ϸęս ݔڷͿĹ޳ںݕॱॠČġНۆϔۤ঍ࢗق˰͆

ێ܁ÂüڷͿѓ(room)ں঍ՁॠيѓęѓԐۋق

ؒܳ(rock pillar)εǫûȮə঍ࢗͿي͠Ėۆۚغ

ۤںڏٖॠəѓ֩ںێ࠹əɰ. ܳѓ֩ėѪۋۺڌ ʽġԓۆथϸڹυ࠘ߕࣺ֟ۋǣц˄ࣺ֩ʪͿۆ

Ͽتں̺óʼ϶ي͠Ĺ޳ϸقԴʴ֨قۚغۋ

ۋΘرݓəѓ֩ڷͿݕॱʼş˺ЛقԦԓՁęমڱ ՁۋȭڹėѪڷͿ؎Ͳ܋ەɰ. ̚ॢ޽ġۚغۆ

ԦԓՁęমڱںȭۋşڦ३ज़څق˰͆Դǫû

Ȯؕʏؒܳε޽Ĺॠşʪॢɰ. ۋ͠ॢėѪڹȉڹ

ݓًقèߝսथॠóқपॠəġНں޽Ĺॠəʚ قۋԜۺۍėѪڷͿԴйĶˣںܼ֮ڷͿԐڌʼ رٵɰ.

йĶࠬۙ֟(Kansas)قԴə1960țʂҙࢢşܕۆ

Եধؒġԓںܳѓ֩ėѪںটڌॠيঝۤॠČН ΪՅࢢ, ڍठНݚܼĶ, ԐИ֬ˣۆʂőϿԜغݓॠ ėÂ(Subtropolis)ڷͿটڌॠČەڷ϶, Subtropolis قԴԐڌʽܳѓ֩ĵܓəफۋأ12 mۍݔگϸߕ

ėÂڷͿĵՁʼرەČ, ؒܳۆफ(w)ęȭۋ(H)ۆ

Ҽə1҃ɰࡾɰ(Carmody and Sterling, 1993; Lee et al., 2013). ۋ͠ॢܳѓ֩ݓॠĵܓНقԴۆؒܳ

əۙڙÒьқآقԴٮəՁüۋɰβɰ. şܕۙڙ ÒьقԴۆܳѓ֩޽ġڹ޽ġşÂʴ؋ɳşۺۍ

ؒܳۆ؋܁Ձںڮݓॣսەں܁ʪۆؒܳԺćε

ࣀ३߯ʂॢψڹ޽ġ͟ںঝ҃ॠəìۋܳ؋۾ۋ ɰ. ˰͆Դ, ߣş޽ġɳćقԴə޽ġۤҼۆڏڌՁ

ˣںČͲॠي޽ĹۤںڍԸĀ܁ॠČ, ޽ġۚغʴ

؋޽Ĺۤۆ؋܁Ձںঝ҃ॠşڦॠي߿қॢ؋ۻ ڱۆؒܳफںঝ҃ॢɰ. يşԴ, ҝٍ՚ϸܕۦˣۆ

ۋڮͿĵܓۺڷͿࠄأॢؒܳ͆ʪؒܳҙۆĵܓۺ

؋܁Ձںঝ҃εڦ३҃ÌėѪں࣊ۓॠݓ؍ڷ϶,

ؒܳफۆݒÀͿڅĵʼəĵܓۺ؋ۻڱںঝ҃ॢ

ɰ. ۋə, ߸঳1ɳć޽ġۚغۋٰΒʼϸ߸Àؒܳ

ҙٮцɱҙۆ߸À޽Ĺںࣀ३߸À޽ġ͟ںঝ҃

ॣսەڷдͿ, ؒܳҙǣцɱҙͿҙࢢ޽ݚʼəġ Нۆ١ّں߯ՙজॠČ߸À޽ĹۚغۆڌۋՁں

Ç؋ॢìۋɰ. ॠݓχ, ėÂঝ҃ࠑϸقԴۆܳѓ֩

Ĺ޳ėѪڹܼۤşۺۍėÂĵܓНۆ؋܁Ձঝ҃

قʌڎܳ؋۾ں˃رߎۤҙٮؒܳҙÀٍćʽ

ॠǣۆࣀ०ĵܓНͿ׆ԺćÀۋΘر܋آॢɰ.

يşԴ, ޽ġÒȝęəɵνԺćʽؒܳۆőüڹ߸

঳قѺąʼݓ؍ڷ϶, ߎۤҙԺćٮؒܳҙԺćÀ

ɳćۺڷͿқνʼݓսॱʼݓ؍ڷдͿ, ॠǣۆٍ

ćĵܓߕͿ׆ĵܓۺ؋ۻՁںঝ҃ॠəԺćÀۋ Θر܋آॢɰ. ˰͆Դ, ėÂঝ҃޲ڙۆܳѓ֩Ĺ޳

قԴəۻߕܳѓ֩ĵܓНۋԜۦॠܼںܼۤşۺڷ ͿݓݓॣսەرآॠČؒܳԐۋق঍ՁʽėÂۆ

ߎۤҙ(roof)ٮÁÁۆؒܳÀ؋܁Ձںڮݓॠيė ÂটڌقЛ܃Àػرآॢɰ.

şܕܳѓ֩޽ġėѪقԴؒܳۆԺćəؒܳۆ

ÌʪٮؒܳۆڿͳԜࢗεČͲॠي؋ۻڱںԓ܁ॠ əѓѪڷͿݕॱʼرٵɰ. ࣢০, ؒܳۆ؋܁Ձڹ

ܳѓ֩ĵܓۆ؋܁ۺۍڮݓقज़սۺۍڅՙͿي ûݕɰ(Esterhuizen et al., 2008). ܳѓ֩޽ġėѪق Դĵܓۆ؋܁قěॢٍĵəܳͿؒܳۆÌʪق

ʂॢٍĵÀʂҙқۋ϶ۋ˞ܼʂɰսəؒܳۆ

Ìʪε ąॹ֩(Hedley & Grant, 1972; Hardy &

Agapito, 1982; Kimmelmann et al, 1984; Potvin et al, 1989; Krauland & Soder, 1987; Lunder & Pakalnis, 1997; Sheorey et al, 2000) ঍ࢗͿ܃֨ॠČەɰ.

ॠݓχ, ۋ͠ॢѓѪ˞ڹইۤۆߣşڿͳԜࢗٮ

ؒܳٮşъؒԐۋۆąćܓæˣںČͲॠşرͲ ڏɳ۾ۋەɰ. ̚ॢ, ߎۤҙ(roof) ؋܁Ձêࢹقə

ؒъۆąॹۺۍˣśқΪεࣀॢज़څݓ҃ۦ͟

ԓ܁ۋڮমॠČս࠘३ԵѓѪںۋڌॠيҝٍ՚ϸ

ۆٖॳںČͲॠəѓѪں࢘ॠČەɰ(Esterhuizen

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et al., 2011)

҆ȦЛقԴəşܕ޽ġÒȝۆܳѓ֩ĵܓНۆ

ԺćѓѪęę܁ں܁νॠي܃֨ॠٕČ, ėÂঝ҃

ࠑϸۆܳѓ֩ĵܓНۆԺćÒȝęę܁ںԺ܁ॠي

ʪ֩জॠČ, şܕ޽ġÒȝęҼİêࢹॠٕɰ. ۋر,

޽ġÒȝۆԺćѪقԴəČͲʼݓ؍ڷ϶, ؒъǴ

ܕۦॠəҝٍ՚ϸۆٖॳۋػəێߕজĵܓͿ׆ۆ

ࣷĨäʴ࣢ՁںқԵॠşڦॠي, Ĺ޳ėÂۆߎۤ

ҙٮؒܳҙőüۋٍćʽս࠘३ԵϿʝںԺ܁ॠ يϔÒѺսٍĵεսॱॠٕɰ. ۋεࣀ३Ԝۦॠܼ

ۆݒÀق˰͆ܳѓ֩ݓॠėÂĵܓНۆۋٰʂ

ьԦ֨۾ۆڦ࠘Ѻজٮۋٰʂьɵ߸ۋεқԵॠ

ٕɰ. ̚ॢ, Ժ܁ʽėÂфؒܳőüҼڱѻͿĵܓ Н؋܁Ձঝ҃ࠑϸقԴۆ߯ʂԜۦॠܼսܵѺজ

߸ۋεқԵॠٕڷ϶, şܕ޽ġԺćѪęҼİêࢹ εࣀ३ėÂÒȝۆĵܓН؋܁Ձঝ҃εڦॢԺć Òȝęۆ޲ۋε܃֨ॠٕɰ.

ʑ᳕ᦩᱶᖒ⧕ᕾႊჶ

ᦵᵝ᮹vࠥၰᦩᱥᮉ

şܕؒܳۆ؋܁Ձ३ԵۆѓѪڹݓΪ΁(tributary theory) قŖäॠيԓ܁ʽԜۦॠܼęؒܳۆÌʪԐ ۋۆěćεʪ߻ॠəѓ֩ۋɰ(Lee et al., 2013).

ݓΪ΁قŖäॢؒܳۆڿͳԓ܁ѓ֩ڹϿ˜Ԝۦ ॠܼںؒܳÀݓݓॢɰəÀ܁ںǴपॠ϶৉ڿͳۋ ǣ؉ࠡমęəČͲʼݓ؍əɰ(Hoek and Brown, 1980; Shin & Kim, 2010). ˰͆Դ, ؒܳقۚڌॠə

ڿͳ(ň Ǝ ) ڹ܁ԐÁ঍Ĺ޳ėÂ(room)ęؒܳܓæق ԴԜҙۆࢹक़Č(rock cover, h)εČͲॠيɰڼę

Ïۋԓ܁ʾսەɰ.

ň _Ǝ á Ĺ Z ƆZ ć Ǝ

ƒ

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يşԴ, həĹ޳ėÂۆࢹक़Č(rock cover)ۋ϶, A t ə

ԜҙۆϸۺۋČA p əؒܳۆϸۺۋɰ. ؒܳۆÌʪ əؒܳε঍ՁॠəؒԵۆێ߹ؓ߹Ìʪٮҝٍ՚ϸ

ܓæˣںÇ؋ॠيԓ܁ॢɰ. ۋ˺, ؒܳۆÌʪ(S p ) əąॹۺۍѓѪقۆ३߸܁ʼəìۋێъۺۋɰ (Gonzalez-Nicieza et al., 2006). ؒܳۆÌʪəş҆ۺ ڷͿؒԵۆێ߹ؓ߹ÌʪقŖäॠČەڷ϶ؒܳۆ

঍ԜҼق˰͆ɰβóԓ܁ʽɰ. ۋٮěʹʽʂशۺ ۍąॹ֩˞ںTable 1ęFig. 1ق܁νॠٕɰ. şܕۆ

ąॹ֩˞قԴəؒъۆÌʪ(rock mass strength, ¬ ƍ ) εИĀؒ(intact rock)ۆێ߹ؓ߹ÌʪقԴأ40

60% ܁ʪÇՙॠيČͲॠČەɰ(Table 1 ޷ܓ).

ۋəؒъقܕۦॠəۼνˣۆҝٍ՚ϸę঍ԜҼ ق˰δÌʪ۹ॠεÂۿۺڷͿČͲॠşڦॢìڷ Ϳ׆ٍĵυɰ۹Çćսεɰβó܃֨ॠČەɰ.

йĶNIOSH (National Institute for Occupational safety and Heath) Àۋ˚͆ۍ(Esterhuizen et al., 2008a; Esterhuizen et al., 2011) قԴəইۤćࠑۙΒ εࢹʂͿؒܳقܕۦॠəۼνٮ঍ԜҼεČͲॢ

ؒܳۆÌʪ߸܁֩ںɰڼۆ֩(2)ٮÏۋ܃֨ॠČ

ەɰ.

¬ _Ǝ á ×íÓÒ Z ň _Ɓ Z ¥ Z ć ¡ ^×íÒÖ

ƕ ^×íÐ× (2)

يşԴ, LDF (Large discontinuity factor)əҝٍ՚ϸ

ܓæق˰δÌʪ۹ÇćսͿԴҝٍ՚ϸۆԜࢗق

˰͆ ߯ՙ 0.06قԴ ߯ʂ 1ūݓۆ Éں Íəɰ.

NIOSH Àۋ˚͆ۍقԴʪИĀؒۆێ߹ؓ߹Ìʪ εşܵڷͿ65% ۹Ç֨ࡈČͲॠČەڷ϶, ߸Àۺ ڷͿҝٍ՚ϸćսεʪۓॠČەɰə۾ۋ޲ۋ۾

ۋ͆Čॣսەɰ. ۋ͠ॢąॹۺۍѓѪٽقʪ

ս࠘३ԵѓѪںԐڌॠي঍ԜҼق˰δؒܳۆÌ ʪε߸܁ॣսەəѓѪں܃֨ॢٍĵʪՙÒʽ

цەɰ(Esterhuizen, 2006; Mortazavi et al., 2009).

ۋ͠ॢę܁ڷͿؒܳقۚڌॠəڿͳęؒܳۆÌ ʪÀԓ܁ʼϸؒܳۆ؋ۻڱ(FOS)ڹɰڼęÏۋ

ćԓʽɰ.

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(a) (b)

Fig. 1. Comparison of the pillar strengths estimated by four-different kinds of empirical equations (a) and Relationship between w/H ratio and pillar strength (b) (Lee et al., 2013)

Table 1. Empirical equations for the pillar strength dependent upon the ratio of its width to height (Lee et al., 2013)

Reference Pillar strength ( ¬

_Ǝ

) Rock mass

strength ( ¬

_ƍ

) Note Hedley and Grant (1972) ¬

_Ǝ

á ¬

_ƍ

ć ¡

^×íÔÒ

ƕ

^×íÒ

0.578 ň

_Ɓ

ň Ɓ = 230 MPa

Kimmelmann et al. (1984) ¬

_Ǝ

á ¬

_ƍ

ć ¡

^×íÓÓ

ƕ

^×íÑÓ

0.691 ň

_Ɓ

ň Ɓ = 94 MPa

Lunder and Pakalnis (1997) ¬

_Ǝ

á ¬

_ƍ

Þ ×íÓÕ×â×íÒÏ×ć ¡ ƕ ß ^0.440 ^ň

^Ɓ

^-

Sheorey et al. (2000) ¬

_Ǝ

á ¬

_ƍ

Þ ^ć ^¡ ^Î ß

^×íÐÓ

^â Þ ^ć ^ÏÒ× ^{¡ âÎ} ßÞ ^ć ^¡ ^{ƕ àÎ} ß ^0.270 ^ň

^Ɓ

^-

¨¬ á ć ¬ Ǝ

ň Ǝ

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⃽ᰆᇡ᮹ᦩᱶᖒ

йĶNIOSH Àۋ˚͆ۍقԴəߎۤҙȃҼ(roof span) قʂ३ي͠ġԓۆۙΒ˞ںսݚॢԐͻٍĵ εࣀ३ۺۼॢԺćȃҼε܃֨ॠČەɰ. NIOSH

ٍĵقԴəߎۤҙţۋÀ1015 m ێ˺, ʂҙқ

؋܁ʽ֨ėۋÀɠ॰ڷ϶ۋۋԜں֨ėॠČۙॣ

ąڍقəݓ҃ۦεČͲ३آॢɰČ܃֨ॠČەɰ (Esterhuizen et al., 2011). Fig. 2 əNIOSHقԴ܃֨

ॠə؋܁Ձ޲࣡ͿйĶۆԐͻٍĵεࣀ३܃֨ʽ

Āęۋɰ.

ɰɳ޽ġںսॱॠəܳѓ֩ġԓۆąڍقԴġ ԓۆңĨԐͻεࣀ३ߎۤҙۆ˃ƍε܃֨ॠٕə ʚ, ߎۤҙۆ˃ƍÀ1.2 m ۋॠێąڍʂߕۺڷͿ

҃Ìۋज़څ॰Čأ2 m ˃ƍۋԜقԴ؋܁ॠó

ڮݓʼؽɰČ҃Čॠٕɰ(Esterhuizen et al., 2011).

يşԴ, ߎۤҙۆ˃ƍəߎۤҙԜҙۆҝٍ՚ϸˣ ںČͲॠيߎۤҙÀٍأʂٮĵқʼرێߕäʴں

҃ۋə˃ƍεϊॢɰ. ̚ॢ, ߎۤҙقۚڌॠəսथ ڿͳۋߎۤҙۆܟĹںڮьॠيࣷĨʾսەş

˺ЛقܳۆÀڅĵʽɰČ҃Čॠٕɰ(Dolinar, 2003, Iannacchione et al., 2003)

ۋ͠ॢąॹۺۍѓѪٽقʪߎۤҙ؋܁Ձ३Ե

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Fig. 2. Stability chart showing stone mine case histories (Esterhuizen et al., 2011)

ڹߎۤҙεɳտ҃ͿÂܳॠي३ԵॠəѓѪںԐ ڌॠşʪॢɰ(Obert and Duvall, 1967; Smith, 1990;

Ömer et al., 2000; Swift and Reddish, 2002). ۋ˺

ߎۤҙəؒܳقۆ३تɳۋČ܁ʽ҃ͿÂܳॠ϶

ߎۤҙۆ˃ƍق˰͆ߎۤҙۆ߯ʂڿͳںԓ܁ॠ əѓ֩ۋɰ. ۋ͠ॢۿŖѓ֩ڹߎۤҙۆҝٍ՚ϸ ۋսथڷͿܕۦॠäǣ΀҇࣡εČͲॣ˺قʪ؋

܁Ձ३ԵۋÀɠॢۤ۾ۋەݓχߎۤҙۆ˃ƍε

رɗ܁ʪͿČͲ३آॠəݓقʂॢşցۺۍêࢹ Àڅĵʼəɳ۾ۋەɰ.

ᵝႊ᜾₥Ųŝḡ⦹Ŗeᖅĥ}ֱ᮹እƱ

á☁

ؘԴسśॠٕˢۋşܕܳѓ֩޽ġقԴۆܳ؋۾

ڹ޽Ĺںࣀ३ঝ҃ʼəġНقەČ, ėÂঝ҃Òȝ ۆĹ޳ڹĹ޳ʼرǫڹėÂĵܓНۆܼۤşۺۍ

؋܁Ձঝ҃قەɰ. ŔνČ޽ġÒȝقԴۆؒܳۆ

ًॣڹ޽ĹşÂʴ؋޽ġܼقەə޽Ĺۤۆێ֨

ۺۍĵܓۺ؋܁Ձںঝ҃ॠəًॣۋ϶, ߸঳ق߸

À޽ġ͟ঝ҃εڦ३ؒܳҙۆ߸À޽ĹۋÀɠॠ

ɰ. ۋقъ३ėÂঝ҃ࠑϸقԴۆؒܳۆًॣڹ

څĵʼəėڌėÂۆܼۤşۺۍ؋܁Ձںঝ҃ॠə

ìۋ϶, ҝٍ՚ʂۆǴपٮܼۤşۺۍǴĵՁ۹ॠ

ˣںČͲॠيؒܳۆĵܓۺ҃ÌۋսॱʾսەČ

ؒܳ঍Ձۋ঳قə߸ÀĹ޳ۋەںսػɰ.

ş҆ۺڷͿԜş˃ÒȝۆԺćę܁ںԕट҃ϸ, şܕܳѓ֩޽ġԺćѪقԴəFig. 3(a)قԴٮÏۋ

ڍԸ޽ġݓًۋԸ܁ʼϸ, ޽ġۤҼ˞ۆڏڌڌۋ ՁيҙεČͲ३޽Ĺۤۆफں1015 m սܵڷͿ

ԸĀ܁ॠ϶(Esterhuizen et al., 2011), ۤҼˣęٍć ʽ޽ĹܓæںČͲ३1ɳć޽Ĺۤȭۋ(ؒܳۆ

ȭۋ)ÀĀ܁ʽɰ. ɰڼ, ؒܳٮԜěػۋܳرݕࢹक़ ČͿҙࢢۆԜۦॠܼսܵęԜҙؒъۆࠗԜĵܓ

ˣۆĵܓݓݗॡۺࠑϸˣںČͲ३ߎۤҙ҃Ì

يҙεĀ܁ॠČ޽Ĺۤۆ؋܁ՁںڍԸঝ҃ॢɰ.

ɰڼ, ۚغ޽Ĺۤۆ؋܁Ձঝ҃εڦॢؒܳۆĵܓۺ

؋ۻڱۋ2.0 ۋԜڷͿ߿қ০ܳرݓϸ(Esterhuizen et al., 2011) şܕۆܳѓ֩޽ġԺćѪق˰͆ࠄأॢ

ҝٍ՚ϸܕۦٮؒܳۆԜॠǚɳۆĵ՚ܓæںÇ

؋ॢێʹۆؒԵۆێ߹ؓ߹Ìʪۆ҃܁ę܁ںä

ߝ߯ܛؒܳۆफںĀ܁ॣսەɰ. ۋ˺, Ͽ˜ܳѓ

(6)

(a) mine (b) underground structure Fig. 3. Comparison of both design procedures for roon-and-pillar mining (a) and underground structure (b)

֩޽ġѪڹٍۙԜࢗۆؒܳۆࣷĨٮĵܓۺ؋܁

Ձঝ҃εڦॢؒܳԺćقݚܼʼرەڷ϶, ݓъˣ śфؒܳǴܕۦॠəҝٍ՚ϸۆܕۦÀÒѻۺڷ Ϳؒܳۆ؋܁ՁقϔڍлÇॠóۚڌॠдͿɰت

ॢąॹۺۍԺć܁ս˞ۆ҃܁ѓѪ˞ۋ܃؋ʼر

ԺćقъٖʼČەɰ.

ۋقъ३, şܕࢢȇфݓॠėÂĵܓНۆԺć

Òȝقşߣॠيܳѓ֩ݓॠėÂԺćę܁ںԺ܁३

҃ϸFig. 3(b)ٮÏɰ. ڍԸ, څĵʼəėÂսڅٮ

ॱ܁ۺۍڌݓ҃ԜˣںÇ؋३ÀڌėÂѩڦÀܳ

رݓϸ, ܳرݕࢹक़Čٮݓъܓæقʂॠيݓॠĵ ܓНۆࣷĨݓ۾фѩڦٮИěॠóۻߕėÂĵܓ ćۆ؋܁Ձںঝ҃ॠəѓॳڷͿԺćʼرآॢɰ.

ۋ͠ॢę܁ԜقԴėÂ޲ڙقԴۆߎۤҙٮࠑѹ

ؒܳҙۆ؋܁Ձۋʴٍ֨ćČͲʼرآॠČ, رɗ

ҙڦۋ˜ҝ؋܁ՁۆڮьڹėÂĵܓۆҝ؋܁ڷͿ

ࣺɳʽɰ. ۋقԺćʽėÂфؒܳɳϸقʂॠي

ۻߕۺۍĵܓ؋܁ՁںêࢹॠóʼČ, ؒܳҙںप

॥३êࢹʽҝ؋ۻًٖęսܵںÇ؋ॠيĵܓۺ

؋܁Ձঝ҃޲ڙقҙ०ʼə҃Ì؋ںԺćॠóʽ ɰ. ˰͆Դ, ėÂ޲ڙۆɳϸԺćəܳرݕܓæقԴ

ėÂҙٮؒܳҙۆɳϸںٍćêࢹॠيĀ܁ॠə

ìۋ०νۺۋɰ.

҆ȦЛقԴəۋ͠ॢÒȝԜۆ޲ۋ۾ںʪ֩ۺڷ Ϳ҃ۋşڦ३, ɰتॢėÂҙфؒܳҙफҼڱ

ܓ०قʂॢս࠘३ԵϿʝںԺ܁ॠČ, ܳرݕࢹक़ Čٮݓъܓæقʂ३ߣşࣷĨݓ۾ьԦڦ࠘ٮ

ۋٰʂьۻتԜ߸ۋѺজεқԵॠٕɰ.

ᙹ⊹⧕ᕾᱢá☁

ġԓқآقԐڌॠʏܳѓ֩ėѪۆ؋܁Ձ३Եę

ԺćəؒܳۆÌʪ̚əߎۤҙεқνॠيČͲॠ Čەɰ. ̚ॢؒъۆҝٍ՚ϸęۼνˣںČͲॠş

رͷş˺ЛقʂҙқۆٍĵقԴąॹۺۍѓѪں

܃֨ॠČەɰ. ݓॠĵܓНͿԴۆܳѓ֩ĵܓقԴə

ġԓқآۆ޽ġমڱՁںȭۋəࠑϸ҃ɰəĵܓۺ

ۍ؋܁Ձںঝ҃ॠيėÂটڌقЛ܃Àػʪ΀३

(7)

(a) Roof failure (b) Failure at the pillar-roof contact Fig. 4. Failure at the roof span and pillar-roof contact (Esterhuizen et al., 2008b)

آॠş˺Лقĵܓۺۍ؋܁Ձ३ԵۋڍԸʼرآ

ॢɰČ҇սەɰ. ̚ॢ, ġԓқآقԴؒܳəے֨

ĵܓߕۆՁüںÍČەرԴݓॠĵܓНقԴۆٖĵ

ĵܓߕۆՁüę޲ѻজʽɰČ҇սەɰ. ٍ҆ĵق Դə2޲ڙս࠘३ԵѓѪںԐڌॠيܳѓ֩ĵܓق ԴԜۦॠܼق˰δؒܳٮߎۤҙۆäʴں॥ƍ

қԵॠيĵܓۺۍ؋܁ՁںêࢹॠČۙॢɰ. ३Ե قԐڌʽս࠘३Ե॒ͿŔ͖ڹݓъۆҼԸ঍äʴ ںϿԐॣսەəڮॢڅՙ॒ͿŔ͖ۍMIDAS GTS εۋڌॠٕɰ.

Esterhuizen et al. (2008b) əşܕܳѓ֩ėѪۋ

ۺڌʽġԓۆࣷĨԐͻقʂ३҃Čॠٕڷ϶ܳڅ

ࣷĨڦ࠘ÀߎۤҙٮߎɳҙقԴܳͿьԦॢɰČ

҃Čॠٕɰ(Fig 4). ۋ͢Ԑͻ˞ڹܳѓ֩ĵܓۆߎ܁

ܼؖҙٮؒܳߎɳҙ, ܼؒܳؖϸۋ؋܁Ձۆܳڅ

ČͲʂԜےںǣࢍǶɰ. ҆ս࠘३ԵêࢹقԴəԐ ۻêࢹɳćͿԴܳѓ֩ݓॠĵܓߕۆࣷĨäʴ

࣢Ձںࣷ؊ॠşڦॠيؒъ҃ÌڹԦ͜ॠٕڷ϶, ڍԸۺڷͿĹ޳ۤҼۆĹ޳ȭۋ(H)εČͲॠيė ÂۆȭۋεČ܁ॠČĹ޳ėÂफфؒܳफܓ०

ϿʝںԺ܁ॠيݓ՚ۺڷͿݒÀॠəԜۦॠܼ(ࢹ क़ČٮҼͻ)قʂॢėʴܳѺۆߣşۋٰʂьԦ

ݓ۾фۋٰʂьۻ߸ۋѺজεČ޶ॠٕɰ. ۋر, ÁɳϸԺćܓ०قԴۆࣷĨ֨۾ۆԜۦॠܼ, ߎۤ

ҙȃҼٮęؒܳȃҼۆҼڱقʂ३ٚԜʼəࣷĨ Ͽ˚ٮÁࣷĨϿ˚ѻॴڌؒܳڿͳ(ԜۦॠܼÒȝ) ںथÀॠٕɰ.

⧕ᕾ᳑Õ

Fig. 5(a) əٍĵقԴČͲॢս࠘३ԵϿʝۆϿ֩

ʪۋČFig. 5(b)əԐڌʽڅՙϐۆٚۋɰ. ३Եق

ԐڌʽϿʝڹ঍ԜҼϿʝق˰͆ڿͳݚܼۋٚԜ ʼəݓ۾ۆڅՙࡾşٮ঍ࢗεČͲॠي1,041

25,521 Òۆۼ۾ę10,80025,200ÒۆԐÁ঍εԐ ڌॠيڮॢڅՙϐ३ԵϿʝںĵইॠٕɰ. ѓۆȃ Ҽ(s)ٮؒܳۆ঍ԜҼ(w/H)ق˰δĵܓНۆäʴں

êࢹॠşڦ३, ؒܳۆȭۋəۤҼݕۓۋڌۋॢ

߯ՙȭۋͿ5 mεԺ܁ॠٕڷ϶ѓۆȃҼə5, 7.5, 10 m εۺڌॠٕɰ. ؒܳۆ঍ԜҼ0.5, 1.0, 1.5ق

˰͆ؒܳۆȃҼ(w)ə2.5, 5, 7.5 mεۺڌॠيÁ

঍Ԝܓæقʂ३ߪ9 Àݓۆąڍεêࢹॠٕɰ.

ݓъۆ३ԵѩڦəؒܳϸڷͿҙࢢԜॠҙ20 mͿ

Ժ܁ॠٕڷ϶(ؒܳϸԜɳۆߣşսݔڿͳ= 490

(8)

(a) Schematic diagram (b) Example of a MIDAS grid

Fig. 5. Schematic diagram and example of a MIDAS grid used for modelling a room-and-pillar underground structure Table 2. Material property of rock mass

Unit weight (kN/m

³

)

Deformation Modulus (MPa)

Poisson’s ratio

Cohesion (kPa)

Friction Angle (°)

Tensile strength (kPa)

24.5 9,000 0.22 1,700 36 1,100

kPa), ࠑϸڹٍ՚ʽܳѓ֩ĵܓεϿԐॠşڦ३

ʂࠡϸۋʼʪ΀ϿʝτॠČԜҙقԴ߸ÀԜۦॠܼ

ۋÀ३ݓəìڷͿϿԐॠٕɰ. ؒъۆܓæڹLee et al. (2013) قԴ܃֨ॢؒъқΪÀڏʚ2ɳćؒъ

ϿʝęMohr-Coulomb ࣷĨşܵںۺڌॠٕɰ. ३Ե قԐڌʽؒъۆНՁ࠘əTable 2ق܁νॠٕɰ.

̚ॢؒܳԜҙٮॠҙۆؒъڹؒܳٮʴێॢНՁ ںÀݓəìڷͿÀ܁ॠٕɰ.

ٍ҆ĵقԴəভѓॳڷͿИॢʂͿܕۦॠəܳѓ

֩ĵܓقʂॢ३ԵڷͿ֬܃3޲ڙĵܓقʂॢ

܁нॢ३Ե҃ɰə2޲ڙ३Եںࣀ३ߣşۋٰʂÀ

ьԦॠəڦ࠘εқԵॠşڦॢѓѪڷͿ҆३Եں

սॱॠٕɰ. ˰͆Դ, ३ԵقԴϿԐʽؒܳٮѓۆ

ţۋəИॢʂͿԴԜۦॠܼقۆॢĵܓۺۍäʴں

қԵॠəǴڌ҃ɰəş҆ĵܓقʂॢқԵقߣ۾

ںϑߺìڷͿ३ԵǴڌۋ܃ॢʽɰ. ̚ॢ, ३Եۆ

ठۆεڦ३ߣşܼۙقۆॢѺ঍ڹߣşজॠٕڷ

϶ܼۙۺڌۋ঳ѓںĹ޳ॠəɳćεèߝԜۦ

ॠܼںɳćѻͿۺڌॠəѓѪںԐڌॠٕɰ. ३Ե

ę܁قԴܳѓ֩ĵܓقԴߣşۋٰʂÀьԦॠə

ݓ۾фۋٰʂьۻ߸ۋѺজεêࢹॠيܳѓ֩

ĵܓۆ঍Ԝق˰δٖॳںқԵॠٕɰ.

⧕ᕾđŝ

Fig. 6 ڹʂशۺڷͿؒܳȃҼٮߎۤҙۆҼ(w/s) À1.0, ؒܳ঍ԜҼ(w/H)ə1.0ۍϿʝقԴߎۤҙ

ۍۤࣷĨ֨۾ęۍۤࣷĨÀԜۦॠܼۆɳćق˰

͆ݕॱʼəϿ֥ںǣࢍǶɰ. ŔρقԴə३Եڅՙ ۆՙՁԜࢗ, ॠܼԜࢗŔνČۍۤࣷĨيҙε

ǣࢍǻɰ. Fig. 6(a)əߎۤҙقԴߣşۋٰʂÀьԦ ॠə֨۾ۆԜࢗۋČFig. 6(b)ٮ(c)əۋٰʂÀۻۋ ʽԜࢗقԴߎɳҙقԴьԦॢՙՁًٖۋؒܳ

ܼؖҙͿۻۋʼəϿ֥(Fig. 6(d))ۋɰ. ३ԵĀęق

(9)

(a) 1,800 kPa (b) 2,000 kPa

(c) 2,500 kPa (d) 3,000 kPa

Fig. 6. Tensile failure and plastic state of element at each stage

Դǣࢍǣˢۋ, ٍ҆ĵقԴۺڌॢݓъНՁܓæق Դݓॠĵܓۆ঍Ԝق˰͆ߣşۋٰʂۆьԦڦ࠘

Àߎ܁ܼؖҙٮؒܳۆߎɳҙقԴ֨ۚॠيۋٰ

ʂÀۻۋʼəϿ֥ں҇սەɰ. ؒܳقԴьԦॠə

ՙՁًٖڹşܕٍĵٮԐͻقԴʪǣࢍǣˢۋؒ

ܼܳؖϸۆՙՁًٖۋÀۤ˃ƉóьԦॠϸԴߎ ɳҙͿÄս΀ܙ؉ݓəۻ঍ۺۍֻčϸ(hyperbolic)

঍ࢗۆࣷĨ঍Ԝں҃ۍɰ.

Fig. 7 ڹࢹक़Čق˰δԜۦؓۆҼٮؒܳۆ঍Ԝ Ҽق˰δؒܳۆȃҼٮߎۤҙȃҼۆҼ(w/s)Ϳ

ǣࢍǶìۋɰ. ३ԵĀęؒܳۆȃҼٮߎۤҙȃҼ ۆҼÀۚڹąڍ(ߎۤҙۆȃҼÀؒܳۆȃҼ҃ɰ

ۚں˺) ԜʂۺڷͿǰڹԜۦॠܼԜࢗقԴʪؒܳ

ۆՙՁًٖۋϤ۹ьԦॠٕڷ϶, ؒܳۆȃҼٮ

ߎۤҙȃҼۆҼÀࢀąڍ(ߎۤҙۆȃҼÀؒܳۆ

ȃҼ҃ɰࢁ˺) ԜʂۺڷͿȭڹԜۦॠܼԜࢗقԴ

(10)

Fig. 7. Pressure ratio at the failure or plastic state

ߎۤҙۆۍۤࣷĨÀ֨ۚʼؽɰ. ҆३ԵقԴəؒ

ܳۆȃҼٮߎۤҙȃҼۆҼڱۋ1.0 ۋԜقԴߎۤ

ҙۍۤࣷĨÀϤ۹֨ۚʼؽČŔۋॠقԴəؒܳ

ՙՁѺ঍ۋϤ۹֨ۚʼؽɰ. ݌, ܳرݕݓъܓæق ԴߎۤҙۆۍۤࣷĨÀьԦॠş֨ۚॠəڿͳս

ܵقʪɵॠşۻقؒܳҙқقԴϤ۹ՙՁًٖۋ

ьԦ॰ɰČ҇սەɰ. ҆३ԵĀęəʴێॢݓъ

НՁقʂॢ३ԵĀęͿ, ݓъНՁۋǣࠑؓęÏڹ

ݓъܓæق˰͆ߣşۋٰʂۆьԦڦ࠘Àǣࢍǣ ə֨۾ڹɰεսەڷ϶ۋəԺćɳćقԴইۤ

ݓъܓԐεࣀ३йνêࢹॠي҃Ìѓ֩ęսܵں

ܳѓ֩ĵܓԺćقъٖॠəìۋц͊ݔॣìۋɰ.

şܕܳѓ֩ėѪۆ؋܁Ձ३ԵقԴə, ߎۤҙ

ࣷĨ҃ɰəܳͿؒܳۆÌʪࠑϸقܼ۾ں˃Č

ٍĵÀݕॱʼرٵɰ. ս࠘३ԵۺۍٍĵقԴʪؒ

ܳεս࠘ۺڷͿϿʝτॠيԜۦॠܼق˰δؒܳۆ

ॠܼ-ѺڦěćεࢹʂͿؒܳۆÌʪε߸܁ॠə

ٍĵÀ ܳε ۋΚɰ(Murali Mohan et al., 2001;

Esterhuizen, 2006; Mortazavi et al., 2009; Wang et al., 2011). ߎۤҙəąॹۺڷͿ΀҇࣡҃ÌęÏڹ

ݓ҃ۦεԐڌॠيٵڷ϶ݓ҃ۦۆţۋǣÂüڹ

ߎۤҙεɳտ҃ͿÀ܁ॠيćԓॢĀęقŖäॠٕ

ɰ. ٍ҆ĵقԴǣࢍǦ३ԵĀęٮÏۋ, ߎۤҙۆ

ۍۤࣷĨəؒܳۆՙՁѺۋ҃ɰǰڹԜۦॠܼ

սܵقԴʪьԦॣսەڷдͿߎۤҙ؋܁Ձêࢹ ٮؒܳ؋܁Ձêࢹεʴ֨قսॱॠəìۋ०νۺ ۍѓ؋ۋʾìۋɰ. Ŕ͠ǣܳѓ֩ėѪقԴؒܳۆ

ąڍ, ٍۙԜࢗۆؒъںĵܓߕͿԐڌॠş˺Лق

ݓ҃ۦԐڌں߯ՙজॠيؒܳۆԜࢗεী՜ॠݓ

؍əìۋؒܳۆÌʪٮą܃ۺۍࠑϸقԴ०νۺ ۋдͿ, ߎۤҙۆ҃Ìں߿қ০êࢹॢ঳Ԝۦॠܼ

ق˰δؒܳۆ؋ۻڱںԓ܁ॠəìۋ҃ɰۺ०ॢ

ѓѪڷͿ҇սەɰ. ݌, Ԝۦॠܼق˰δߎۤҙ

؋܁Ձڹؒܳۆ؋܁ՁںêࢹॠşۋۻقԐͻٍ

ĵٮս࠘३Եںܼ֮ڷͿۺۼॢȃҼ(span)εঝ҃

ॠي΀҇࣡ٮÏڹ҃ÌѓѪڷͿߎۤҙ؋܁Ձں

ঝ҃ॠČؒܳҙқۆ؋܁ՁڹԜۦॠܼق˰δؒܳ

ۆÌʪεҼİॠəѓ֩ڷͿؒܳٮߎۤҙ؋܁Ձ ںʴ֨قêࢹॠəìۋɰ.

३ԵĀęقԴəؒܳٮߎۤҙۆҼٮߣşۋٰ

ʂÀьԦॠə֨۾ۆěćəҼİۺԸ঍ěćͿǣ

ࢍǮɰ. ॠݓχ, ؒܳۆ঍ԜҼ(w/H)ق˰δ޲ۋə

ࡾóǣࢍǣݓ؍؉şܕܳѓ֩ėѪԺćÀܳͿ

ؒܳۆ঍ԜҼقşъॠČەəǴڌęəࢀ޲ۋε

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҃ۍɰ. ˰͆Դ, ĵܓНۆ؋܁Ձ޲ڙقԴؒܳۆ

঍ԜҼ҃ɰəߎۤҙٮؒܳۆȃҼۆěćÀԺćق

й࠘əٖॳۋࡾɰČ҇սەڷ϶ۋəߎۤҙٮ

ؒܳȃҼۆҼڱق˰δॠܼқपÀɵ͆ݓş˺Л ڷͿࣺɳʽɰ. ۋ͠ॢ३ԵĀęəؒъܓæۋǣ

ࠑؓܓæۋɰεąڍ, ३ԵĀęÀԜۋॠóǣࢍǨ

սەڷǣ, ߎۤҙۆۍۤࣷĨÀؒԵۆێ߹ؓ߹Ì ʪقŖäॢؒܳۆÌʪ(Fig. 1, Table 1 ޷ܓ)ق

Ҽ३ԜʂۺڷͿǰڹսܵۆԜۦॠܼقԴʪьԦॣ

սەş˺ЛقؒܳۆÌʪࣺɳۋۻقߎۤҙۆ

३ԵۋڍԸʼرآ॥ںǣࢍǴəĀęͿ҇սەɰ.

ॳ঳ɰتॢݓъܓæęؒܳ঍Ԝقʂॢ३Եۺۍ

êࢹÀۋΘرݓČ, ҃ÌėѪںप॥ॢǴڌۋČͲ ʽɰϸݓъܓæęؒܳ঍Ԝق˰δܳѓ֩ĵܓۆ

؋܁ՁںथÀॣսەə०νۺۍѓ؋ۋʪ߻ʾ

ìڷͿࣺɳʽɰ.

đು

ٍ҆ĵقԴəս࠘३Եںࣀॠيܳѓ֩ėѪقԴ

ĵܓۺ؋܁ՁںथÀॠşڦॢşߣۺۍٍĵεս ॱॠٕڷ϶, ۋεࣀ३صرݕܳڅĀ΁˞ںڅأॠ ϸɰڼęÏɰ.

1. ݓॠėÂںটڌॠəѓ؋قԴܳѓ֩ėѪڹş ܕġԓқآۆėѪقԴٮəɰβóėÂ޲ڙق Դۆߎۤҙٮࠑѹؒܳҙۆ؋܁Ձۋʴٍ֨ć

ČͲʼرآॠČ, رɗҙڦۋ˜ҝ؋܁Ձۆڮь ڹėÂĵܓۆҝ؋܁ڷͿࣺɳʼرآॢɰ. ۋق

ԺćʽėÂфؒܳɳϸقʂॠيۻߕۺۍĵܓ

؋܁Ձںêࢹॠيؒܳҙεप॥३ĵܓۺ؋܁

Ձঝ҃޲ڙقҙ०ʼə҃Ì؋ںԺć३آॢɰ.

˰͆Դ, ėÂ޲ڙۆɳϸԺćəܳرݕܓæقԴ

ėÂҙٮؒܳҙۆɳϸںٍćêࢹॠيĀ܁ॠ əìۋ०νۺۋɰ.

2. ٍ҆ĵقԴۺڌॢݓъНՁܓæęMohr-Coulomb

ࣷĨşܵقԴəؒܳۆȃҼٮߎۤҙۆȃҼۆ

Ҽڱق˰͆ߣşۋٰʂьԦڦ࠘Àɰβóǣࢍ

Ǯɰ. ݌, ؒܳۆफقҼ३ėÂߎۤҙÀܙڷϸ

ؒܳߎɳҙǣؒܳߕقԴۻɳࣷĨ঍ࢗͿࣷĨ ÀÒ֨ʼəąॳۋ϶, ߎۤҙۆफۋȉرݗս΀

ߎۤҙܼؖقԴۍۤࣷĨ঍ࢗͿࣷĨÀÒ֨ʼ əąॳۋɰ. ̚ॢ, ܳѓ֩޽ġԺćѪقԴəܳڅ

ԺćۍۙͿيûݓəؒܳۆ঍ԜҼ(w/H)قʂ३ ԴəĵܓН؋܁ՁࠑϸقԴəࡾóлÇॠݓ

؍əìڷͿқԵʼؽڷ϶, ъϸق, ؒܳٮߎۤҙ

ȃҼҼڱ(w/s)ۋėÂĵܓНۆ؋܁ՁقлÇॠ óۚڌॠəìڷͿࣷ؊ʼؽڷ϶, ؒܳٮߎۤҙ ۆȃҼҼڱق࠶ݗս΀ॴڌԜۦॠܼڹҼİۺ

Ը঍ڷͿݒÀॠəąॳںٕ҃ɰ.

3. ؒܳۆȃҼٮߎۤҙȃҼۆҼ(w/s)Àۚڹąڍ ( ߎۤҙۆȃҼÀؒܳۆȃҼ҃ɰࢁ˺) Ԝʂۺڷ ͿǰڹԜۦॠܼԜࢗقԴʪؒܳۆՙՁًٖۋ

Ϥ۹ьԦॠٕڷ϶, ؒܳۆȃҼٮߎۤҙȃҼۆ

ҼÀࢀąڍ(ߎۤҙۆȃҼÀؒܳۆȃҼ҃ɰ

ۚں˺) ԜʂۺڷͿȭڹԜۦॠܼԜࢗقԴߎۤ

ҙۆۍۤࣷĨÀ֨ۚʼؽɰ.

qᔍ᮹ɡ

ٍ҆ĵəॢĶæԺşցٍĵڙۆܳڅԐغۍ“ڏ ڌܼėÂঝۤۋÀɠॢݓॠĹ޳ф؋܁জşց

Òь”ۆٍĵҼݓڙقۆ३սॱʼؽ֥ɦɰ.

3FGFSFODFT

1. Carmody, J., Sterling, R. (1993), “Underground space design - A guide to subsurface utilization and design for people in underground spaces”, International Thomson Publishing company, p. 110.

2. Dolinar, D.R. (2003), “Variation of horizontal

stresses and strains in mines in bedded deposits

in the eastern and midwestern united states”,

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Proceedings of 22nd International Conference on Ground Control in Mining, Morgantown, WV, Aug. 5-7, pp. 178-185.

3. Esterhuizen, G.S. (2006), “Evaluation of the strength of slender pillars”, Trans Soc Min Explor Geol 320, pp. 69-76.

4. Esterhuizen, G.S., Dolinar, D.R., Ellenberger, J.L.

(2008a), “Pillar strength and design methodology for stone mines”, In: Proceedings of the 27th international conference on ground control in mining.

Morgantown WV: West Virginia University, pp.

241-253.

5. Esterhuizen, G.S., Dolinar, D.R., Iannacchione, A.T. (2008b), “Field observations and numerical studies of horizontal stress effects on roof stability in US limestone mines”, Journal of the South African Institute of Mining and Metallurgy, Vol.

108, No. 6, pp 345-352.

6. Esterhuizen, G.S., Dolinar, D.R., Ellenberger, J.L, Prosser, L.J. (2011), “Pillar and roof span design guidelines for underground stone mines”, Department of Health And Human Services, NIOSH, IC 9526.

7. Gonzalez-Nicieza, C., Alvarez-Fernadez, M.I., Menendez-Diaz, A., Alvarez-Vigil, A.E. (2006),

“A comparative analysis of pillar design methods and its application to marble mines”, Rock Mech.

Rock Engng., Vol. 39, No. 5, pp. 421-444.

8. Hardy, P., Agapito, J.F.T. (1982), “Induced horizontal stress method of pillar design in oil shale”, XV Oil Shale Symp. Colorado School of Mines, Golden, Colorado.

9. Hartman, H.L., Mutmansky, J.M. (2002), Introductory Mining Engineering, 2 ^nd edtion, Wiley, New Jersey.

10. Hedley, D.G.F., Grant, F. (1972), “Stope-and-pillar design for the elliot lake uranium mines”, Bull.

Can. Inst. Min. Metallurg. Vol. 63, pp. 37-44.

11. Hoek, E., Brown, E.T. (1980), Underground excavation in rock, Institution of Mining and Metallurgy.

12. Iannacchione, A.T., Marshall, T.E., Burke, L., Melville, R., Litsenberger, J. (2003) “Safer mine layouts for underground stone mines subjected to

excessive levels of horizontal stress”, Mining Engineering, Vol. 55, No. 4, pp. 25-31.

13. Kimmelmann, M.R., Hyde, B., Madgwick, R.J.

(1984), “The use of computer applications at BCL limited in planning pillar extraction and design of mining layouts”, In: Proc., ISMR Symp. Design and Performance of Underground Excavations. Brit. Geotech. Soc., London, pp.

53-63.

14. Krauland, N., Soder, P.E. (1987), “Determinating pillar strength from pillar failure observations”, Eng. Min. J. Vol. 8, pp. 34-40.

15. Lee, C., Chang, S-H, Shin, H-S, (2013), “A numerical study on evaluation of unsupported pillar strength in the room and pillar method”, J.

of Korean Tunn Undergr Sp Assoc, Vol. 15, No.

4, pp 443-453 (in Korean).

16. Lunder, P.J., Pakalnis, R. (1997), “Determination of the strength of hard-rock mine pillars”, Bull.

Can. Inst. Min. Metall. Vol. 90, pp. 51-59.

17. Mortazavi, A., Hassani, F.P., Shabani, M. (2009),

“A numerical investigation of rock pillar failure mechanism in underground openings”, Computers and Geotechnics, Vol. 36, Issue 5, pp. 691-697.

18. Murali Mohan, G., Sheorey, P.R., Kushwaha, A.

(2001), “Numerical estimation of pillar strength in coal mines”, International Journal of Rock Mechanics and Mining Sciences, Vol. 38, Issue 8, pp. 1185-1192.

19. Obert, L., Duvall, W.I. (1967), Rock mechanics and the design of structures in rock, Wiley, Londen.

20. Ömer, A., Akio, S., Noritoshi, Y., Kenrou, S., Toshikazu, K. (2000) “The characteristics of soft rocks and their effects on the long term stability of abandoned room and pillar lignite mines”, Post Mining 2005, Nov. 16-17, Nancy, France.

21. Potvin, Y., Hudyma, M.R., Miller, H.D.S. (1989),

“Design guidelines for open stope support”, Bull.

Can. Min. Metall. Vol. 82, pp. 53-62.

22. Sheorey, P.R., Loui, J.P., Singh, K.B., Singh,

S.K. (2000), “Ground subsidence observations

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and a modified influence function method for complete subsidence prediction”, Int. J. Rock Mech. Min. Sci. Vol. 37, pp. 801-818.

23. Shin, Y.-W., Kim, Y.-G. (2010) “Review of mechanical behaviors of pillar in large parallel tunnel”, Journal of Korean Society for Rock Mechanics, Vol. 20, No. 3, pp. 131-144 (in Korean).

24. Smith, S. (1990), Structural stability, support and excavation aspects of mine openings in stratified

iron ore deposits, PhD Thesis, University of Nottingham.

25. Swift, G.M., Reddish, D.J. (2002), “Stability problems associated with an abandoned ironstone mine”, Bull. Eng. Geol. Environ 61, pp. 227-239.

26. Wang, S.Y., Sloan, S.W., Huang, M.L., Tang,

C.A. (2011) “Numerical study of failure mechanism

of serial parallel rock pillars”, J Rock Mechanics

and Rock Engineering, Vol. 44, No. 2, pp 179-198.

A study on conceptual evaluation of structural stability of room-and-pillar underground space

*Corresponding author: Hyu-Soung Shin E-mail: [email protected]

Received November 1, 2013; Revised November 7, 2013;

Accepted November 8, 2013

ᵝႊ᜾ḡ⦹Ŗe᮹Ǎ᳑ᱢᦩᱶᖒ⠪a}ֱᱶพᨱš⦽ᩑǍ

ଲశ෹  ȵୋ৤෹  ȵ਑ิন 

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵ֬ۻےٍĵڙ

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵٍ֬ĵڦڙ

A study on conceptual evaluation of structural stability of room-and-pillar underground space

Chulho Lee

, Soo-Ho Chang

, Hyu-Soung Shin

*

Research Specialist, Geotechnical Engineering Research Division, SOC Research Institute, Korea Institute of Construction Technology

Research Fellow, Geotechnical Engineering Research Division, SOC Research Institute, Korea Institute of Construction Technology

Keywords: Room and pillar method, Rock pillar, Roof span, Tension failure, Numerical analysis

ߣ΀ ٍ҆ĵقԴəܳѓ֩ݓॠĵܓНۆ؋܁Ձêࢹѓ؋ںυʹॠşڦ३ؒܳٮߎۤҙۆäʴںս࠘३ԵѓѪڷͿêࢹॠٕɰ

̚ॢ şܕۙڙÒьқآقԴČͲॠəܳѓ֩ėѪۆԺćÒȝęəɵ͆܋آॠə ėÂঝ҃޲ڙقԴۆ०νۺۍܳѓ֩ėѪۆ

Ժćۼ޲фÒȝں܃֨ॠٕɰܳرݕݓъܓæقԴؒܳۆ঍ԜҼٮߎۤҙۆţۋق˰δս࠘३Եںսॱॠٕڷ϶ߣş

ۋٰۋ֨ۚʼə֨۾قԴۆࣷĨڮ঍ęڦ࠘Ѻজεêࢹॠٕɰ३ԵĀę ߎۤҙफęؒܳफęۆҼ XTٮࣷĨ֨۾ۆԜۦॠܼ

ÂۆěćəԸ঍ěćεٕ҃ڷ϶ ߎۤҙफęؒܳफۆҼÀܳѓ֩޽ġԺćقԴəϔڍܼڅॢԺćۍۙͿɰΘرݓəؒܳۆ

फęȭۋҼ X)҃ɰĵܓНۆ؋܁Ձঝ҃޲ڙقԴəʌڎлÇॢԺćۍۙۍìڷͿǣࢍǮɰۋə ؒܳۆ؋܁Ձχںঝ҃ॠə

޲ڙقԴսॱʼəܳѓ֩޽ġԺćѪęəɵν ؒܳҙٮ॥ƍĵܓНߎۤҙфرŷҙۆ؋܁Ձūݓʪ॥ƍČͲॠيݓॠ

ĵܓНۆ؋܁Ձںঝ҃ॣսەəĵܓНԺćÀʼرآ॥ںۆйॢɰ̚ॢ ݓॠĵܓНۆ঍Ԝق˰͆ߣşۋٰʂÀьԦॠə

ڦ࠘ٮۻɳ̚əۍۤࣷĨˣࣷĨڮ঍ʪɰβóǣࢍǣ ܳѓ֩ݓॠĵܓНقʂॢԺćəԜۦॠܼق˰δߎۤҙٮؒܳۆ

؋܁Ձںٍćॠيսॱॠəìۋज़څॠɰ

ܳڅرܳѓ֩ėѪ ؒܳ ߎۤҙ ۍۤࣷĨ ս࠘३Ե

$PQZSJHIU ,PSFBO5VOOFMMJOHBOE6OEFSHSPVOE4QBDF"TTPDJBUJPO

ᕽು

ܳѓ֩ėѪ(Room and pillar method)ڹġԓқآ قԴ֨ۚʽėѪڷͿԴսथ̚əäۆսथڷͿ

ϔۤʼرەəġНں޽ĹॣЀۺڷͿۺڌʼəė ѪڷͿ(Hartman and Mutmansky, 2002) Ĺ޳ϸęս ݔڷͿĹ޳ںݕॱॠČġНۆϔۤ঍ࢗق˰͆

ێ܁ÂüڷͿѓ(room)ں঍ՁॠيѓęѓԐۋق

ؒܳ(rock pillar)εǫûȮə঍ࢗͿي͠Ėۆۚغ

ۤںڏٖॠəѓ֩ںێ࠹əɰ. ܳѓ֩ėѪۋۺڌ ʽġԓۆथϸڹυ࠘ߕࣺ֟ۋǣц˄ࣺ֩ʪͿۆ

Ͽتں̺óʼ϶ي͠Ĺ޳ϸقԴʴ֨قۚغۋ

ۋΘرݓəѓ֩ڷͿݕॱʼş˺ЛقԦԓՁęমڱ ՁۋȭڹėѪڷͿ؎Ͳ܋ەɰ. ̚ॢ޽ġۚغۆ

ԦԓՁęমڱںȭۋşڦ३ज़څق˰͆Դǫû

Ȯؕʏؒܳε޽Ĺॠşʪॢɰ. ۋ͠ॢėѪڹȉڹ

ݓًقèߝսथॠóқपॠəġНں޽Ĺॠəʚ قۋԜۺۍėѪڷͿԴйĶˣںܼ֮ڷͿԐڌʼ رٵɰ.

йĶࠬۙ֟(Kansas)قԴə1960țʂҙࢢşܕۆ

Եধؒġԓںܳѓ֩ėѪںটڌॠيঝۤॠČН ΪՅࢢ, ڍठНݚܼĶ, ԐИ֬ˣۆʂőϿԜغݓॠ ėÂ(Subtropolis)ڷͿটڌॠČەڷ϶, Subtropolis قԴԐڌʽܳѓ֩ĵܓəफۋأ12 mۍݔگϸߕ

ėÂڷͿĵՁʼرەČ, ؒܳۆफ(w)ęȭۋ(H)ۆ

Ҽə1҃ɰࡾɰ(Carmody and Sterling, 1993; Lee et al., 2013). ۋ͠ॢܳѓ֩ݓॠĵܓНقԴۆؒܳ

əۙڙÒьқآقԴٮəՁüۋɰβɰ. şܕۙڙ ÒьقԴۆܳѓ֩޽ġڹ޽ġşÂʴ؋ɳşۺۍ

ؒܳۆ؋܁Ձںڮݓॣսەں܁ʪۆؒܳԺćε

ࣀ३߯ʂॢψڹ޽ġ͟ںঝ҃ॠəìۋܳ؋۾ۋ ɰ. ˰͆Դ, ߣş޽ġɳćقԴə޽ġۤҼۆڏڌՁ

ˣںČͲॠي޽ĹۤںڍԸĀ܁ॠČ, ޽ġۚغʴ

؋޽Ĺۤۆ؋܁Ձںঝ҃ॠşڦॠي߿қॢ؋ۻ ڱۆؒܳफںঝ҃ॢɰ. يşԴ, ҝٍ՚ϸܕۦˣۆ

ۋڮͿĵܓۺڷͿࠄأॢؒܳ͆ʪؒܳҙۆĵܓۺ

؋܁Ձںঝ҃εڦ३҃ÌėѪں࣊ۓॠݓ؍ڷ϶,

ؒܳफۆݒÀͿڅĵʼəĵܓۺ؋ۻڱںঝ҃ॢ

ɰ. ۋə, ߸঳1ɳć޽ġۚغۋٰΒʼϸ߸Àؒܳ

ҙٮцɱҙۆ߸À޽Ĺںࣀ३߸À޽ġ͟ںঝ҃

ॣսەڷдͿ, ؒܳҙǣцɱҙͿҙࢢ޽ݚʼəġ Нۆ١ّں߯ՙজॠČ߸À޽ĹۚغۆڌۋՁں

Ç؋ॢìۋɰ. ॠݓχ, ėÂঝ҃ࠑϸقԴۆܳѓ֩

Ĺ޳ėѪڹܼۤşۺۍėÂĵܓНۆ؋܁Ձঝ҃

قʌڎܳ؋۾ں˃رߎۤҙٮؒܳҙÀٍćʽ

ॠǣۆࣀ०ĵܓНͿ׆ԺćÀۋΘر܋آॢɰ.

يşԴ, ޽ġÒȝęəɵνԺćʽؒܳۆőüڹ߸

঳قѺąʼݓ؍ڷ϶, ߎۤҙԺćٮؒܳҙԺćÀ

ɳćۺڷͿқνʼݓսॱʼݓ؍ڷдͿ, ॠǣۆٍ

ćĵܓߕͿ׆ĵܓۺ؋ۻՁںঝ҃ॠəԺćÀۋ Θر܋آॢɰ. ˰͆Դ, ėÂঝ҃޲ڙۆܳѓ֩Ĺ޳

قԴəۻߕܳѓ֩ĵܓНۋԜۦॠܼںܼۤşۺڷ ͿݓݓॣսەرآॠČؒܳԐۋق঍ՁʽėÂۆ

ߎۤҙ(roof)ٮÁÁۆؒܳÀ؋܁Ձںڮݓॠيė ÂটڌقЛ܃Àػرآॢɰ.

şܕܳѓ֩޽ġėѪقԴؒܳۆԺćəؒܳۆ

ÌʪٮؒܳۆڿͳԜࢗεČͲॠي؋ۻڱںԓ܁ॠ əѓѪڷͿݕॱʼرٵɰ. ࣢০, ؒܳۆ؋܁Ձڹ

ܳѓ֩ĵܓۆ؋܁ۺۍڮݓقज़սۺۍڅՙͿي ûݕɰ(Esterhuizen et al., 2008). ܳѓ֩޽ġėѪق Դĵܓۆ؋܁قěॢٍĵəܳͿؒܳۆÌʪق

ʂॢٍĵÀʂҙқۋ϶ۋ˞ܼʂɰսəؒܳۆ

Ìʪε ąॹ֩(Hedley & Grant, 1972; Hardy &

Agapito, 1982; Kimmelmann et al, 1984; Potvin et al, 1989; Krauland & Soder, 1987; Lunder & Pakalnis, 1997; Sheorey et al, 2000) ঍ࢗͿ܃֨ॠČەɰ.

ॠݓχ, ۋ͠ॢѓѪ˞ڹইۤۆߣşڿͳԜࢗٮ

ؒܳٮşъؒԐۋۆąćܓæˣںČͲॠşرͲ ڏɳ۾ۋەɰ. ̚ॢ, ߎۤҙ(roof) ؋܁Ձêࢹقə

ؒъۆąॹۺۍˣśқΪεࣀॢज़څݓ҃ۦ͟

ԓ܁ۋڮমॠČս࠘३ԵѓѪںۋڌॠيҝٍ՚ϸ

ۆٖॳںČͲॠəѓѪں࢘ॠČەɰ(Esterhuizen

et al., 2011)

҆ȦЛقԴəşܕ޽ġÒȝۆܳѓ֩ĵܓНۆ

ԺćѓѪęę܁ں܁νॠي܃֨ॠٕČ, ėÂঝ҃

ࠑϸۆܳѓ֩ĵܓНۆԺćÒȝęę܁ںԺ܁ॠي

ʪ֩জॠČ, şܕ޽ġÒȝęҼİêࢹॠٕɰ. ۋر,

ଲశ෹ ȵୋ৤෹ ȵ਑ิন

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵ֬ۻےٍĵڙ

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵٍ֬ĵڦڙ

ߣ΀ ٍ҆ĵقԴəܳѓ֩ݓॠĵܓНۆ؋܁Ձêࢹѓ؋ںυʹॠşڦ३ؒܳٮߎۤҙۆäʴںս࠘३ԵѓѪڷͿêࢹॠٕɰ

Ժćۼ޲фÒȝں܃֨ॠٕɰܳرݕݓъܓæقԴؒܳۆ঍ԜҼٮߎۤҙۆţۋق˰δս࠘३Եںսॱॠٕڷ϶ߣş

ۋٰۋ֨ۚʼə֨۾قԴۆࣷĨڮ঍ęڦ࠘Ѻজεêࢹॠٕɰ३ԵĀę ߎۤҙफęؒܳफęۆҼ XTٮࣷĨ֨۾ۆԜۦॠܼ

फęȭۋҼ X)҃ɰĵܓНۆ؋܁Ձঝ҃޲ڙقԴəʌڎлÇॢԺćۍۙۍìڷͿǣࢍǮɰۋə ؒܳۆ؋܁Ձχںঝ҃ॠə

ĵܓНۆ؋܁Ձںঝ҃ॣսەəĵܓНԺćÀʼرآ॥ںۆйॢɰ̚ॢ ݓॠĵܓНۆ঍Ԝق˰͆ߣşۋٰʂÀьԦॠə

؋܁Ձںٍćॠيսॱॠəìۋज़څॠɰ

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