A numerical study on evaluation of unsupported pillar strength in the room and pillar method

(1)

*Corresponding author: Soo-Ho Chang E-mail: [email protected]

Received July 15, 2013; Revised July 25, 2013;

Accepted July 28, 2013

ᵝႊ᜾Ŗჶᨱᕽྕḡᅕᦵᵝ᮹vࠥᔑᱶᨱš⦽ᙹ⊹⧕ᕾᱢ

ᩑǍ

ଲశ෹ ȵୋ৤෹ ȵ਑ิন

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵ֬ۻےٍĵڙ

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵٍ֬ĵڦڙ

A numerical study on evaluation of unsupported pillar strength in the room and pillar method

Chulho Lee

¹

, Soo-Ho Chang

²

*, Hyu-Soung Shin

²

1

Geotechnical Engineering Research Division, Korea Institute of Construction Technology, Researcher

2

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

ABSTRACT: This study aims to evaluate the mechanical behaviors of unsupported rock pillars in a room-and-pillar underground structure by a series of numerical analyses. In addition, rock pillar strengths estimated by a few empirical equations proposed for underground mines are compared with those from numerical analyses. Based on the results from the numerical analysis, the ratio of pillar strength to rock mass strength increases as the ratio of the width of a pillar to its height becomes bigger. It means that higher ratio of pillar width to its height is much more favorable for stabilizing a room-and-pillar underground structure. Especially, unsupported pillar strengths estimated from numerical analyses are higher than rock mass strength when the ratio of pillar width to height is approximately over 1.5. It is also found that the choice of an empirical equation appropriate for a given geometric condition of a pillar is important for its feasible application to the stability analysis of a pillar in the room-and-pillar method.

Keywords: Room and pillar method, Rock pillar, Uniaxial compression strength, Rock classification, Numerical analysis

ߣ΀ ٍ҆ĵقԴəܳѓ֩ݓॠĵܓНۆ؋܁ՁںܟڍॠəИݓ҃ؒܳۆäʴںս࠘३Եقۆ३êࢹॠٕɰؒܳۆÌʪε

ؒܳÌʪٮؒъÌʪۆҼڱۋݒÀॠي؋܁Ձঝ҃قڮνॢìڷͿǣࢍǮɰ࣢০ ٍ҆ĵۆ३ԵܓæقԴəؒܳۆफę

ȭۋۆҼڱۋأۋԜۋϸИݓ҃ؒܳۆÌʪÀؒъۆؓ߹Ìʪ҃ɰࡾóصرܐɰ̚ॢؒܳۆ঍Ԝܓæق˰͆ս࠘३Ե

ĀęٮڮԐॢĀęεԓ߻ॠəąॹ֩ۋɰՙԜۋॠي ইۤۙΒşъۆąॹ֩ںটڌॠşڦ३Դəؒܳۆ঍Ԝܓæق˰͆

ۺ०ॢąॹ֩ںۺڌॠəìۋज़څॠɰ

ܳڅرܳѓ֩ėѪ ؒܳ ێ߹ؓ߹Ìʪ ؒъқΪ ս࠘३Ե

$PQZSJHIU ,PSFBO5VOOFMMJOHBOE6OEFSHSPVOE4QBDF"TTPDJBUJPO

ᕽು

ܳѓ֩ėѪ(Room and pillar method)ڹġԓқآ قԴ֨ۚʽėѪڷͿԴսथ̚əäۆսथڷͿ

ϔۤʼرەəġНں޽ĹॣЀۺڷͿۺڌʼəė Ѫۋɰ(Hartman and Mutmansky, 2002). ܳѓ֩ėѪ قԴəġНۆϔۤ঍ࢗق˰͆սथॠóĹ޳ں

ݕॱॠϸԴێ܁ॢÂüڷͿѓ(room)ں޽ġॠČ

ؒܳ(rock pillar)εǫûȮə঍ࢗͿي͠Ėۆۚغ

ۤںڏٖॢɰ. ۋεࣀ३޽ġۚغۆԦԓՁęমڱ

ںȭۋ϶ज़څق˰͆ԴǫûȮؕʏؒܳε޽Ĺॠ

şʪॢɰ. ۋ͠ॢėѪڹȉڹݓًقèߝսथॠó

(2)

қपॠəġНں޽ĹॠəʚقۋԜۺۍėѪڷͿԴ

йĶˣںܼ֮ڷͿԐڌʼرٵɰ.

йĶࠬۙ֟(Kansas)قԴə1960țʂҙࢢܳѓ֩

ėѪقۆ३şܕۆԵধؒġԓںঝۤॠيНΪՅ ࢢ, ڍठНݚܼĶ, ԐИ֬ˣۆʂőϿԜغݓॠėÂ (Subtropolis) ڷͿটڌॠČەɰ. يşԴۆܳѓ֩

ĵܓəफۋأ12mۍݔگϸߕėÂڷͿĵՁʼر

ەڷ϶, ؒܳۆफ(w)ęȭۋ(H)ۆҼə1҃ɰࡾɰ (Carmody & Sterling, 1993). ۋ͠ॢܳѓ֩ࢹЀĵܓ НقԴۆؒܳəۙڙÒьқآقԴٮəՁüۋɰβ ɰ. şܕۙڙÒьقԴۆܳѓ֩޽ġڹ޽ġşÂʴ

؋ɳşۺۍؒܳۆ؋܁Ձںڮݓॣսەں܁ʪۆ

ؒܳԺćεࣀ३߯ʂॢψڹ޽ġ͟ںঝ҃ॠə

ìۋܳ؋۾ۋ͆ϸ, ėÂঝ҃ࠑϸقԴۆܳѓ֩Ĺ

޳ėѪڹܼۤşۺۍėÂĵܓНۆ؋܁Ձঝ҃ق

ʌڎܳ؋۾ں˃رؒܳԺćÀۋΘر܋آॢɰ.

˰͆Դ, ėÂঝ҃޲ڙۆܳѓ֩Ĺ޳قԴəۻߕܳ

ѓ֩ĵܓНۋԜۦॠܼںܼۤşۺڷͿݓݓॣս

ەرآॠČؒܳԐۋق঍ՁʽėÂۆߎ܁ҙ(roof) ٮÁÁۆؒܳÀ؋܁ՁںڮݓॠيėÂটڌق

Л܃Àػرآॢɰ. şܕܳѓ֩޽ġėѪقԴؒܳ

ۆԺćəؒܳۆÌʪٮؒܳۆڿͳԜࢗεČͲॠ ي؋ۻڱںԓ܁ॠəѓѪڷͿݕॱʼرٵɰ. ࣢০,

ؒܳۆ؋܁Ձڹܳѓ֩ĵܓۆ؋܁ۺۍڮݓقज़ սۺۍڅՙͿيûݕɰ(Esterhuizen et al., 2008).

߯ŖйĶۆNIOSH (National Institute for Occupational safety and Heath) قԴə؋ۻॢؒܳԺćεࣀ३

ġԓۆԐČεѓݓॠşڦॢÀۋ˚͆ۍںьशॢ

цەɰ(Esterhuizen et al., 2011). şܕق܃֨ʼؽʏ

ؒܳÌʪԓ܁قěॢąॹ֩˞(Hedley & Grant, 1972; Hardy & Agapito, 1982; Kimmelmann et al, 1984; Potvin et al, 1989; Krauland & Soder, 1987;

Lunder & Pakalnis, 1997; Sheorey et al, 2000) ęυ޴

ÀݓͿNIOSHۆÀۋ˚͆ۍقԴʪرɗ܁ʪąॹ ۺۍҙқęě޶ںࣀ३ؒܳԺćقěॢ०νۺۍ

ѓॳں܃֨ॠČەɰ. şܕܳѓ֩ėѪۆؒܳԺć

قԴÀܼۤڅॠóČͲʼČەə۾ڹؒܳۆÌʪ εۺۼ০ԓ܁ॠČؒܳقۚڌॠəսݔڿͳقʂ

ॢؒܳۆ؋ۻڱںČͲॠيԺćقъٖॠəìۋ ɰ. ۋəŖۿॢѿԺࢢȇԐۋق঍Ձʽज़͆ҙ३Ե (Shin & Kim, 2010; Kim et al., 2012) ęɰՙڮԐॢ

۾ۋەڷǣŖ҆ۺڷͿИݓ҃ԜࢗۆؒܳεܳͿ

ČͲॢɰə۾قԴÀۤࢀ޲ۋε҃ۍɰ.

ٍ҆ĵقԴəؒъۆқΪˣśق˰͆ؒъۆێ

߹ؓ߹Ìʪε߸܁ॢ঳2޲ڙս࠘३Եںսॱॠي

ؒܳۆ঍Ԝق˰δИݓ҃ԜࢗۆؒܳÌʪε߸܁

ॠٕɰ. ̚ॢ३ԵĀęεц࢖ڷͿؒъˣśęؒܳ

ۆ঍ԜҼق˰δÌʪεԓ܁ॠيҼİॠٕɰ.

ᦵᵝ᮹ᦩᱶᖒ⠪aႊჶᨱݡ⦽Łₑ

ėÂঝ҃ࠑϸقԴܳѓ֩ėѪقČͲʼəؒܳ

əԜҙۆॠܼںݓݓ३ܳəĵܓߕͿԴ߿қॢ؋

܁Ձںڮݓ३آॢɰ. şܕٍĵ˞قԴ܃֨ॢؒܳ

ۆԺćѪقԴəێъۺڷͿؒܳۆ঍Ԝق˰δؒ

ܳۆÌʪ(strength)ٮڿͳ(stress)ںԓ܁ॠيۺ०

ॢ؋ۻڱ(FOS, Factor of Safety)ںԓ܁ॠəѓ֩ڷ Ϳ܃֨ॠČەɰ. يşԴؒܳۆȭۋʂҼफۆ

Ҽق˰͆ؒԵۆێ߹ؓ߹ÌʪٮؒܳۆࣷĨÌʪۆ

޲ۋÀьԦॠəܳڙۍڹڙؒęٍĀʼرەəؒܳ

ԜॠǚɳۆսथѺ঍ڱۆĵ՚মę(end-effect)Ϳ

ۍ३ؒܳȭۋقҼ३ؒܳफۋȉرݓϸۚڌʼə

սݔॠܼقʂॢսथĵ՚মęÀ࠶ݓϸԴؒܳۆ

ࣷĨÌʪÀȭ؉ݓş˺ЛڷͿࣺɳʽɰ. ˰͆Դؒ

ܳقۚڌॠəսݔۦॠॠܼقʂॢ؋ۻڱćԓڹ

ؒܳۆࣷĨÌʪεşܵڷͿԓ܁ʽɰ. ؒܳقۚڌ ॠəսݔॠܼقʂॢؒܳۆ؋ۻڱڹؒܳۆथŒ

Ìʪ( ¬ _Ǝ ) ٮؒܳۆथŒڿͳ( ň _Ǝ ) ڷͿशইʼ϶ɰڼ

֩(1)ęÏɰ.

¨¬ á ć ň Ǝ

¬ _Ǝ

(1)

(3)

Table 1. Empirical equations for the pillar strength dependent upon the ratio of its width to height

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

0.691ň

_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

^-

ؒܳۆथŒڿͳ( ň _Ǝ ) ڹؒܳۆȃҼÀۚČؒܳ

ԐۋۆѓۆȃҼÀ࠶ݗս΀ؒܳقݚܼʼəڿͳ ۋݒÀॠóʽɰ. ݌, Ԝۦॠܼقʂ३ؒъقԴؒܳ

À޲ݓॠəɳϸۺۆҼÀǰ؉ݗս΀ؒܳقۚڌ ॠəڿͳۋ࠶ݕɰəìڷͿ׆, ۋəێъۺڷͿݓ Ϊ΁(tributary theory)ڷͿԺϼʽɰ. ݓΪ΁قԴə

ܳѓ֩ĵܓقԴѓۆɳϸۺęؒܳۆϸۺҼق˰

͆܁३ݓəؒܳۆڿͳęؒܳۆ঍Ԝق˰͆ɵ͆

ݓəڿͳݚܼʪقěॢԐ२ڷͿĵқॣսەɰ (Hoek and Brown, 1980; Shin & Kim, 2010). ݓΪ΁ق

ŖäॢؒܳۆथŒڿͳڹɰڼۆ֩(2)ٮÏۋ

शইʽɰ.

ň Ǝ á ć ƕ ^Ï Þƕ âƑß ^Ï ³Ĺ _Ƒ

(2)

يşԴ, wəؒܳۆȃҼ(m), səѓۆफ(m), Zə

ݓशقԴҙࢢۆ ֮ʪ(m), Ɛ Ƒ ə ؒъۆ ɳڦܼ͟

(kN/m ³ ) ۋɰ.

ݓΪ΁قŖäॢؒܳۆڿͳԓ܁ѓ֩ڹϿ˜

ԜۦॠܼںؒܳÀݓݓॢɰəÀ܁ںǴपॠ϶৉ڿ ͳۋǣ؉ࠡমęəČͲʼݓ؍əɰ. ۋ˺ؒܳۆÌ ʪ(S p ) əąॹۺۍѓѪقۆ३߸܁ʼəìۋێъۺ ۋɰ(Gonzalez-Nicieza et al., 2006). ؒܳۆÌʪə

ş҆ۺڷͿؒԵۆێ߹ؓ߹ÌʪقŖäॠČەڷ϶

ؒܳۆ঍ԜҼق˰͆ɰβóԓ܁ʽɰ. ۋٮěʹʽ

ʂशۺۍąॹ֩˞ںTable 1ق܁νॠٕɰ. şܕۆ

ąॹ֩˞قԴəʂҙқؒъۆÌʪ(rock mass strength,

¬ _ƍ ) εИĀؒ(intact rock)ۆێ߹ؓ߹ÌʪقԴأ40

60% ܁ʪÇՙॠيČͲॠČەɰ(Table 1 ޷ܓ).

ۋəؒъقܕۦॠəۼνˣۆҝٍ՚ϸę঍ԜҼ ق˰δÌʪ۹ॠεČͲॠşڦॢìڷͿ׆ٍĵυ ɰ۹Çćսεɰβó܃֨ॠČەɰ. ࣢০, Hedley

& Grant (1972) ٮKimmelmann et al. (1984)ڹؒԵۆ

ێ߹ؓ߹ÌʪεşܵڷͿؒܳۆÌʪεशܵজॠي

܃֨ॠٕڷ϶ۋ˞ۆٍĵقԴԐڌʽێ߹ؓ߹Ìʪ əÁÁ230 MPa ф94 MPaۋɰ. Table 1قԴʪ

؎սەˢۋؒܳۆ঍ԜڹؒܳۆȃҼ(w)ٮȭۋ ( H)ۆҼۆ঍ࢗͿČͲʼČەɰ.

Fig. 1 ڹؒԵۆێ߹ؓ߹ÌʪÀ120 MPaۋČؒ

ܳۆȃҼ(w)À10 mۍąڍεÀ܁ॠٕں˺, şܕ

ٍĵ˞قԴ܃֨ॢTable 1ۆ֩˞Ϳԓ܁ʽؒܳۆ

Ìʪεؒܳۆȭۋق˰͆ʪ֨ॢìۋɰ. Fig. 1ę

ÏۋLunder & Pakalnis (1997)ۆ܃؋֩ۋɰδ܃؋

֩قҼ३ÀۤࡾóؒܳۆÌʪεԓ܁ॠ϶Sheorey et al. (2000) ۆ܃؋֩ۋÀۤ҃սۺۋČHedley

& Grant (1972) ۆ܃؋֩ۋथŒ܁ʪۆÌʪεԓ܁

ॠəìں؎սەɰ.

йĶNIOSH Àۋ˚͆ۍ(Esterhuizen et al., 2011) قԴəইۤۙΒεࢹʂॠيؒܳقܕۦॠəۼν εČͲॢؒܳۆÌʪ֩ںɰڼۆ֩(3)ęÏۋ

܃֨ॠČەɰ.

(4)

Fig. 1. Comparison of the pillar strengths estimated by four-different kinds of empirical equations (w=10 m)

¬ Ǝ á ×íÓÒ Z ň _Ɓ Z ¥ Z ć ¡ ^×íÒÖ ƕ ^×íÐ×

(3)

يşԴ, LDF (Large discontinuity factor)əۼνܓæ ق˰δÌʪ۹ÇćսͿԴۼνۆԜࢗق˰͆߯ՙ

0.06 قԴ߯ʂ1ūݓۆÉںÍəɰ. NIOSH Àۋ˚

͆ۍ(Esterhuizen et al., 2011)قԴəLDFÀ ҝٍ՚ϸ ۆÁʪćս(DDP, discontinuity dip factor)ٮۼνۆ

Ҿʪćս(FF, frequency factor)ۆĕڷͿशইʼ϶

( 1-DDP×FF) ÁąڍقʂॢÉۋशͿ܃֨ʼر

ەɰ. ٍ҆ĵقԴəۼνقʂॢٖॳںѕ܃ॢ

Иݓ҃ؒܳۆथÀεڦॠي, Ìʪ۹Çćս(LDF) ε ۼνÀܕۦॠݓ؍əܓæۍ1Ϳۺڌॠٕɰ (Esterhuizen et al., 2011).

ڍνǣ͆ۆࢢȇԺć֨قəRMR (Rock Mass Rating) ق˰͆ؒъں5ˣśڷͿǣɀرԺćقۺڌ ॠČەəìۋێъۺۋɰ(Kim et al., 2012). ъϸ, Bieniawski (1973; 1988; 1989; 1993) ə5Àݓۆˣś ѻͿؒۆۻɳÌʪćս(c, ŋ ) ε܃֨ॢцەɰ.

Mohr-Coulomb ࣷĨۋ΁قŖäॠيˣśق˰δۻ ɳÌʪćսͿҙࢢ֩(4)ٮÏۋؒԵۆێ߹ؓ߹Ì ʪεԓ܁ॣսەɰ.

ň Ɓ á ÏƁŋîÞÎ à ŋß (4)

ॠݓχBieniawskiÀ܃֨ॢˣśѻۻɳÌʪćս ε֩(4)قۺڌॠيԓ܁ॢێ߹ؓ߹Ìʪə֬ॹ֬

قԴࠑ܁ॢ֬܃ÌʪقҼ३ϔڍǰڹÉںǣࢍǶ ɰ. ٚε˞ر, RMRۋ80ۋČ60ێ˺ԓ܁ʽێ߹ؓ

߹ÌʪəÁÁ1.97 MPa ф1 MPa ۋॠͿԴ৚ۆ

Ìʪٮ ڮԐ३ ݕɰ(Ramamurthy, 2004). ˰͆Դ

Kalamaras & Bieniawski (1995) əCarter et al. (1991) ۆٍĵεц࢖ڷͿؒъۆێ߹ؓ߹ÌʪٮؒԵۆ

ێ߹ؓ߹ÌʪÂۆԜěěćεɰڼۆ֩(5)ٮÏۋ

܃֨ॢцەɰ.

ć ®¬ _Ƈ

®¬ «¦

á ãÞyty àÎ××ßîÏÑä (5)

يşԴ, ®¬ «¦ ڹؒъۆێ߹ؓ߹Ìʪ, ®¬ Ƈ əؒ

Եۆێ߹ؓ߹Ìʪۋɰ. ؒъۆێ߹ؓ߹ÌʪٮؒԵ ۆێ߹ؓ߹ÌʪԐۋۆԜěěćəيٍ͠ĵۙ˞ق

ۆ३ɰتॢąॹ֩ۋ܃֨ʼرەڷǣ(Yudhbir et al., 1983; Ramaurthy, 1986; Palmström, 1995;

Sheorey, 1997; Aydan and Dalgic, 1998; Hoek et

al., 2002), ٍ҆ĵقԴəۼνćսεʪۓॢąڍق

ԴʪڮԐॢԜěěćε҃ۋ϶(Ramamurthy, 2004)

şܕق܃֨ʽąॹ֩˞ÀڏʚथŒ܁ʪۆÉ(Dinc

et al., 2011) ں҃ۋə֩(5)εʪۓॠٕɰ. ˰͆Դ

(5)

Fig. 2. Schematic diagram of the numerical model in this study

ڍνǣ͆ۆێъۺۍࢢȇԺć֨قԐڌʼə5Ò

ˣśۆؒъÌʪεÁÁۆRMRÉق˰͆֩(5)ε

Ԑڌॠيؒъۆێ߹ؓ߹Ìʪε߸܁ॣսەɰ. ۋ ԜęÏۋٍ҆ĵقԴəRMRˣśق˰δИݓ҃

ԜࢗۆؒܳÌʪεşܕąॹ֩ڷͿҙࢢԓ܁ॠي

঍Ԝق˰δؒܳۆ؋܁ՁںथÀॠəʚقটڌॠ

ٕɰ.

ᙹ⊹⧕ᕾᨱ᮹⦽ᦵᵝvࠥ᮹⇵ᱶ

⧕ᕾ᳑Õ

Fig. 2 əٍ҆ĵقԴČͲॢս࠘३ԵϿʝۆϿ֩

ʪۋ϶, ٍ҆ĵقԴԐڌʽս࠘३Ե॒ͿŔ͖ڹݓ ъۆҼԸ঍äʴںϿԐॣսەəڮॢڅՙ॒ͿŔ

͖ۍMidas GTSۋɰ. ս࠘३ԵقԴؒܳۆȃҼ(w) ٮѓۆȃҼεϿ˃6 mͿԺ܁ॠٕČ, ؒܳۆ঍ԜҼ ( w/H)ε0.4, 0.8, 1.0, 1.5, 2.0ͿČͲॠşڦॠي

ؒܳٮѓۆȭۋε15 m, 7.5 m, 6 m, 4 m ф3 m Ϳۺڌॠٕɰ. ؒъۆϿʝτѩڦəؒܳϸڷͿҙ

ϿʝτॠČԜҙقԴॠܼۋÀ३ݓəìڷͿϿԐॠ

ٕɰ. ̚ॢؒܳԜҙٮॠҙۆؒъڹؒܳٮʴێॢ

НՁںÀݓəìڷͿÀ܁ॠٕɰ. ؒܳə2Òۆѓ

ܼÂقڦ࠘ॠ϶ԜۦॠܼۆݒÀق˰δؒܳۆڿ

ͳ-Ѻڦäʴںêࢹॠٕɰ. ؒܳۆथŒսݔڿͳں

थÀॠşڦॠيս࠘३ԵĀęͿҙࢢܼؒܳؖҙۆ

थŒڿͳںԓ܁ॠٕڷ϶, ̚ॢѺڦəؒܳۆԜҙ ٮॠҙۆࠑ۾ڷͿҙࢢѺڦεࠑ܁ॠيԓ܁ॠٕɰ

(Fig. 2 ޷ܓ). ̚ॢ३ԵقԴࠑؓćս(K 0 ) ə1ͿԴ

܁սؓԜࢗεÀ܁ॠٕɰ.

ᦵၹ᮹ᩎ⦺ᱢ✚ᖒᔑᱶ

ٍ҆ĵقԴəڍνǣ͆ۆێъۺۍࢢȇԺć֨ق

ۺڌॠČەəRMRقŖäॢ5ɳćۆؒъқΪÀڏ ʚҼİۺت঒ॢؒъܓæۍ13ɳćۆؒъں

Ͽʝقۺڌॠٕɰ. ۋٮÏۋ३ԵقԐڌʽؒъۆ

НՁںTable 2ق܁νॠٕɰ. ؒъڹMohr-Coulomb

ࣷĨşܵںۺڌॢ࢏ՙՁϿʝͿϿԐॠي, ३Եں

ࣀ३ԓ܁ॢؒܳۆڿͳ-Ѻ঍έčԸقԴؒܳÀ

ՙՁäʴں҃ۋə֨۾ۆڿͳں঍Ԝق˰δؒܳ

ۆÌʪͿۺڌॠٕɰ.

Fig. 3 ڹTable 1 ф֩(3)ڷͿćԓʽؒܳۆ ƕ / ¡ Ҽڱق˰δؒܳۆÌʪٮؒԵۆێ߹ؓ߹ÌʪԐ ۋۆěćۋɰ. Fig. 3ęÏۋHedley & Grant (1972) ۆ܃؋֩ęNIOSHۆ܃؋֩(Esterhuizen et al., 2011) ۋथŒ܁ʪۆąॳں҃ۋ϶ۻߕۺڷͿ ƕ / ¡ Ҽڱ ۋݒÀॣս΀ؒܳۆÌʪٮێ߹ؓ߹ÌʪۆҼÀ

ݒÀॠə঍ࢗε҃ۍɰ.

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Table 2. Input parameters for rock masses

Rock mass properties Case 1 Case 2 Case 3

RMR (Rock mass classification) 90 (Type I) 70 (Type II) 50 (Type III)

UCS

i

(MPa) 250 175 75

UCS

RM

(MPa)

(Kalamaras and Bieniawski, 1995) 164.8 50.1 9.3

Unit weight (kN/m

³

) 26 24.5 24

Deformation Modulus (MPa) 15,000 9,000 4,200

Poisson’s ratio 0.20 0.22 0.23

Cohesion (kPa) 2,700 1,700 600

Friction angle (°) 40 36 32

Fig. 3. Relationship between ƕî¡ ratio and pillar strength

ᙹ⊹⧕ᕾđŝᇥᕾ

Fig. 4 əٍ҆ĵۆս࠘३ԵقԴصرݕؒܳۆ

ڿͳ-Ѻ঍έčԸۆٚۋ϶, Fig. 5ə঍ԜҼ( ƕ / ¡ ) À

0.8 ێ˺Case 3ۆ३ԵĀęε҃يܵɰ. ؘԴԺϼॢ

цٮÏۋ, ҆३ԵقԴəؒܳۆܼؖҙقԴࠑ܁ॢ

սݔڿͳۋսͶॠəݓ۾ۆڿͳ(२҄ڿͳ)ںؒܳ

ۆÌʪͿÂܳॠٕɰ. Fig. 5(a)ٮÏۋॠܼۋݒÀ॥

ق˰͆ؒܳۆࠑϸҙÀϤ۹२҄ॠيՙՁäʴں

҃ۍ঳۾޲ܼؖҙͿՙՁًٖۋঝʂʼəąॳں

ǣࢍǴؽɰ. ̚ॢKim et al. (2012)ۆٍĵĀęٮ

υ޴ÀݓͿܼؒܳؖҙۆսݔڿͳڹܳѺۆĵ՚

ͳڷͿۍ३ڿͳۋԜʂۺڷͿ࠾ڷ϶ࠑϸҙͿÄ ս΀Çՙॠə঍ࢗͿǣࢍǮɰ.

Fig. 6 ڹşܕąॹܼ֩߯ʂÉ(Lunder & Pakalnis, 1997) ęथŒÉ(Hedley & Grant, 1972), ŔνČÀۤ

҃սۺۍÉ(Sheorey et al., 2000)ں҃ۋə܃؋֩ں

Ը܁ॠي३ԵĀęٮ॥ƍʪ֨ॢìۋɰ. ঍ԜҼÀ

ԜʂۺڷͿۚں˺( ƕî¡ < 1.0), ս࠘३ԵڷͿ߸܁

ʽؒܳۆÌʪəşܕąॹ֩˞҃ɰǰóԓ߻ʼə

ъϸ, ঍ԜҼÀ࠶ݗս΀ս࠘३ԵقԴصرݕؒܳ

ÌʪÀݒÀॠəąॳںٕ҃ɰ. ࣢০, Case 1ۆąڍ,

঍ԜҼÀ2ێ˺ؒܳۆÌʪəێ߹ؓ߹Ìʪٮäۆ

ڮԐॢÌʪεٕ҃ɰ. ঍ԜҼÀ1.5ۍąڍقəRMR ۋ90, 70 ф50ێ˺ۆؒܳÌʪٮێ߹ؓ߹Ìʪۆ

ҼڱۋÁÁ0.56, 0.42 ф0.19ۋؽɰ. ъϸ, ঍ԜҼÀ

1 ێ˺ս࠘३ԵڷͿҙࢢصرݕؒܳÌʪəؒԵ

ێ߹ؓ߹Ìʪۆأ10% սܵڷͿǣࢍǮɰ. ۋԜę

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(a) (b) Fig. 4. Examples of the stress-strain curve of the pillar; (a) ƕî¡=0.8, (b)ƕî¡=1.0

Fig. 5. Results of the numerical analysis ( ƕî¡ = 0.8); (a)Equivalent plastic strain, (b)Vertical stress

Ïۋܳѓ֩ĵܓۆ؋܁ՁࠑϸقԴؒъۆ࣢ՁӼ χ؉ɦ͆ؒܳۆ঍ԜҼÀИؼ҃ɰܼڅॢԺć२ Ѐےں؎սەɰ.

ս࠘३ԵĀę, ۻъۺڷͿ঍ԜҼÀ1҃ɰǰڹ

ąڍقəSheory et al. (2002)ۆąॹ֩ęڮԐॠٕڷ

϶, ঍ԜҼÀ1҃ɰࢀąڍقəҼİۺHedley &

Grant (1972) ۆąॹ֩قÀūڝɰ. ̚ॢս࠘३Ե

ĀęͿҙࢢ߸܁३҃ϸ, ٍ҆ĵقԴۺڌॢܓæॠ

قԴRMRۋ50йχڷͿԴԜʂۺڷͿҝ͟ॢؒъ

ܓæێąڍقəÀۤ҃սۺۍؒܳÌʪεԓ߻ॠ əSheorey et al. (2000)ۆąॹ֩҃ɰʪؒܳÌʪÀ

ǰóथÀʾÀɠՁۋەəìڷͿǣࢍǮɰ. ॠݓχ

ܳѓ֩ėѪڹؒܳۆۙςۋرɗ܁ʪÀɠॢت঒

ॢܓæقԴۺڌʼəìۋێъۺۋɰ. ˰͆Դ҆

ٍĵقԴҼİॢąॹ֩˞ÀڏʚقԴəս࠘३Ե

ĀęٮԜʂۺڷͿÀūڏؒܳÌʪε߸܁ॠ϶҃

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Fig. 6. Comparisons between empirical equations and numerical analyses at different rock mass conditions

Table 3. Comparisons between pillar strength and rock mass strength at different ƕî¡ ratios

ƕî¡ ratio ¬

_Ǝ

î®¬

_«¦

Case 1 Case 2 Case 3

0.4 0.08 0.14 0.16

0.8 0.15 0.36 0.48

1.0 0.25 0.52 0.81

1.5 0.86 1.47 1.60

2.0 1.58 2.20 2.42

սۺۍԺćÀÀɠॢSheorey et al. (2000)ۋۺڌՁ ۋȭںìڷͿԐΒʽɰ.

Esterhuizen (2006) ۆٍĵقԴʪս࠘३Եںࣀ३

ؒܳۆÌʪε߸܁ॠٕڷ϶, RMRۋ70ۋČؒܳۆ

঍ԜҼÀ1.0, 1.5 ф2.0ێ˺ؒԵۆێ߹ؓ߹Ìʪٮ

ؒܳۆÌʪҼڱڹÁÁ0.4, 0.55 ф0.6ڷͿǣࢍǮ ڷ϶RMRۋ80ێąڍقəÁÁ0.5, 0.92 ф1.05Ϳ

ݒÀॠٕɰ. ̚ॢRMRۋ70ۋԜۆؒъقԴێ߹ؓ

߹ÌʪٮؒܳۆÌʪҼڱڹ঍ԜҼÀ1.0ێąڍҙ ࢢśü০ݒÀॠČRMR 70ۋॠقԴəԜʂۺڷͿ

ÌʪҼڱۋǰóǣࢍǣəìڷͿ҃Čॠٕڷ϶, ۋ

͠ॢĀęəؘԸٍ҆ĵۆս࠘३ԵĀę˞ęʴێ ॠɰ.

Ŕ͠ǣۋԜۆ३ԵĀę(Fig. 6)əؒܳۆÌʪٮ

ؒԵۆێ߹ؓ߹ÌʪεҼİॢìڷͿԴ, ؒъǴۆ

ҝٍ՚ϸ˞ۆٖॳęࡾşমę(size effect)εČͲॠ

şڦॠيؒъۆؓ߹Ìʪε߸܁ॠČۋεؒܳ

ÌʪٮҼİॠيؒܳۆ؋܁ՁںथÀॠəìۋज़ څॠɰ. ֬܃ͿؒԵۆێ߹ؓ߹ÌʪٮؒܳÌʪε

ҼİॢĀę(Fig. 6)ق˰βϸ, ؒܳÌʪٮؒԵێ߹

ؓ߹ÌʪۆҼڱڹ঍ԜҼÀ2ۋČRMRۋ90ۍą ڍε܃ٽॠČəϿ˃1ۋॠۋɰ. ˰͆ԴKalamaras

& Bieniawski (1995) À܃؋ॢؘԸ֩(5)ںটڌॠي

ؒԵۆێ߹ؓ߹ÌʪٮRMRͿҙࢢؒъۆؓ߹Ì ʪε߸܁ॠČۋεս࠘३ԵقԴصرݕؒܳÌʪ ٮҼİॠٕɰ(Table 3 фFig. 7).

қԵĀę, Case 1ڹRMRۋ90ڷͿϔڍت঒ॢ

ؒъܓæۍěćͿ֩(5)Ϳ߸܁ʽؒъۆؓ߹Ìʪ əؒԵێ߹ؓ߹Ìʪۆأ66% սܵڷͿԴ঍ԜҼÀ

1.5 ҃ɰ࠶آχؒܳÌʪٮؒъÌʪۆҼڱۋ

1 ۋԜںχܔॠəìڷͿǣࢍǮɰ. ࣢০, ইݓڿͳ

սܵۋȭČÌʪÀȭڹؒъقԴəؒъَࣷ(rock

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Fig. 7. Ratios of pillar strengths to rock mass and intact rock strengths at different ƕî¡ ^ratios

spalling) ۋě޶ʼəąڍʪەڷдͿ, ॳ঳قəϔڍ

ت঒ॢؒъܓæقԴəؒܳۆࠄՁࣷĨقʂॢêࢹ ʪज़څॣìڷͿԐΒʽɰ. ъϸ, Case 2ٮCase 3 قԴə঍ԜҼÀ11.5 ԐۋۋϸؒܳÌʪٮؒъ ۆؓ߹ÌʪۆҼڱۋ1ۋԜۋʼəìڷͿǣࢍǮɰ.

࣢০, Case 3ۋԜʂۺڷͿࢀÌʪҼڱں҃ۋə

ìڷͿǣࢍǮəʚۋəؘԴسśॢцٮÏۋRMR ۋۚںս΀ؒъۆؓ߹ÌʪÀԜʂۺڷͿۚóथ Àʼş˺Лۋɰ. ۋԜڷͿҙࢢܳѓ֩ĵܓۆ؋܁

ՁथÀقەرԴؒܳÌʪۆԓ߻Ӽχ؉ɦ͆०ν ۺۍؒъÌʪۆथÀÀϔڍܼڅॠɰəìں؎

սەɰ.

đು

ٍ҆ĵقԴəս࠘३Եںࣀॠيܳѓ֩ėѪقԴ

Иݓ҃ؒܳۆÌʪεथÀॠşڦॢşߣۺۍٍĵ εսॱॠٕڷ϶, ۋεࣀ३صرݕܳڅĀ΁˞ں

څأॠϸɰڼęÏɰ.

1. RMR قŖäॢ3Àݓܓæۆؒъقʂ३Иݓ҃

ؒܳۆࡾşٮफںɵνॠ϶ڮॢڅՙ३Եں֬

֨ॢĀę, ؒܳۆफۋȭۋ҃ɰ࠶ݗս΀ؒܳ

ÌʪٮؒъÌʪۆҼڱۋݒÀॠəìڷͿǣࢍ

Ǯɰ. ࣢০ؒܳۆफęȭۋۆҼڱ( ƕî¡ ) ۋ1ۋԜ ێąڍقۋ͠ॢÌʪҼڱۆݒÀफۋԜʂۺڷ ͿࡾóǣࢍǮɰ. ˰͆Դܳѓ֩ĵܓۆ؋܁Ձ

ࠑϸقԴؒъۆ࣢ՁӼχ؉ɦ͆ؒܳۆ঍Ԝۋ

ܼڅॢԺćêࢹ२Ѐےں؎սەؽɰ.

2. ؒܳÌʪε߸܁ॠşڦ३܃֨ʽşܕۆąॹ֩

˞ęս࠘३ԵĀęεҼİॢĀę, ƕî¡ ۋ1҃ɰ

ǰڹąڍقəSheory et al. (2002)ۆąॹ֩ę

ڮԐॠٕڷ϶, ъϸ ƕî¡ ۋ1҃ɰࢀąڍقə

Hedley & Grant (1972) ۆąॹ֩ęڮԐॠٕɰ.

ۋٮÏۋܳѓ֩ĵܓۆ؋܁ՁںÒ͜ۺڷͿथ ÀॠşڦॢইۤۙΒşъۆąॹ֩ںটڌॠş

ڦ३Դəؒܳۆ঍Ԝܓæق˰͆ۺ०ॢąॹ֩

ںۺڌॠəìۋज़څॣìڷͿࣺɳʽɰ.

3. ؒܳۆ؋܁ՁںथÀॠəʚەرؒܳÌʪٮ

ИĀؒۆێ߹ؓ߹ÌʪεҼİॠəìڹؒܳۆ

؋܁ՁںęՙथÀॣսەəÀɠՁۋەڷдͿ, ҝٍ՚ϸ˞ۆٖॳęࡾşমęεČͲॣսەə

ؒъۆؓ߹ÌʪٮҼİॠəìۋज़څॠɰ. ҆

ٍĵۆ३ԵܓæقԴə ƕî¡ Àأ1.5 ۋԜۋϸ

ؒܳۆÌʪÀؒъۆ߸܁ؓ߹ÌʪεԜধॠə

ìڷͿǣࢍǮɰ. ۋԜۆ३ԵۺۍêࢹĀę, ؒܳ

ۆ؋܁Ձں֪΋ۺڷͿथÀॠşڦ३Դəؒъ

Ìʪε०νۺڷͿԓ߻ॠəìۋИؼ҃ɰܼڅ

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ॠɰəìں؎սەؽɰ.

4. ٍ҆ĵəս࠘३Եфąॹ֩˞ںটڌॠيИݓ

ॳ঳قə҃ɰɰتॢؒъܓæфؒܳ঍Ԝق

ʂ३ݓ҃মęٮؒܳۆࣷĨϭ࠶ɦݏں॥ƍ

ČͲॣսەəؒܳۆ؋܁ՁथÀقʂॢ঳՚

ٍĵÀज़څॠɰ. ̚ॢؒъқΪѪęИĀؒۆ

ێ߹ؓ߹ÌʪˣںটڌॠيؒъÌʪε०νۺ ڷͿ߸܁ॠşڦॢѓѪقʂ३Դʪݓ՚ۺۍٍ

ĵÀڅĵʽɰ.

qᔍ᮹ɡ

ٍ҆ĵəॢĶæԺşցٍĵڙۆܳڅԐغۍ“ڏ ڌܼėÂঝۤۋÀɠॢݓॠĹ޳ф؋܁জşց

Òь”ۆٍĵҼݓڙقۆ३սॱʼؽ֥ɦɰ.

ₙŁྙ⨭

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5. Bieniawski, Z.T. (1993), “Classification of rock masses for engineeringthe RMR system and future trends”, J.A. Hudson (Ed.), Comprehensive rock engineering, Vol. 3, Pergamon Press, UK, pp.

553-573.

6. 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. 7. Carter, B.J., Duncan, E., Scott, J., Lajtai, E.Z.

(1991), “Fitting strength criteria to intact rock”, Int. J. Geotechnol. Geol. Eng., Vol. 9, pp. 73-81.

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

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(2008), “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.

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preprint 06-003. Society for Mining, Metallurgy, and Exploration, Inc., Littleton.

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

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

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stress method of pillar design in oil shale”, XV Oil Shale Symp. Colorado School of Mines, Golden, Colorado.

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

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27. Ramamurthy, T. (1986), “Stability of rock mass”, Indian Geotech J, pp. 1-74.

28. Sheorey, P.R. (1997), Empirical rock failure criteria, Balkema, Rotterdam.

29. Sheorey, P.R., Loui, J.P., Singh, K.B., Singh, S.K. (2000), “Ground subsidence observations and a modified influence function method for complete subsidence prediction”, Int. J. Rock Mech.

Min. Sci. Vol. 37, pp. 801-818.

30. 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).

31. Yudhbir, Y., Lemanza, W., Prinzl, F. (1983), “An empirical failure criterion for rock masses”, In:

Proceedings of the fifth international congress

society of rock mechanics, Melbourne, Vol. 1,

pp. B1-8.

A numerical study on evaluation of unsupported pillar strength in the room and pillar method

*Corresponding author: Soo-Ho Chang E-mail: [email protected]

Received July 15, 2013; Revised July 25, 2013;

Accepted July 28, 2013

ଲశ෹  ȵୋ৤෹  ȵ਑ิন 

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵ֬ۻےٍĵڙ

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵٍ֬ĵڦڙ

A numerical study on evaluation of unsupported pillar strength in the room and pillar method

Chulho Lee

, Soo-Ho Chang

*, Hyu-Soung Shin

Geotechnical Engineering Research Division, Korea Institute of Construction Technology, Researcher

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

Keywords: Room and pillar method, Rock pillar, Uniaxial compression strength, Rock classification, Numerical analysis

ߣ΀ ٍ҆ĵقԴəܳѓ֩ݓॠĵܓНۆ؋܁ՁںܟڍॠəИݓ҃ؒܳۆäʴںս࠘३Եقۆ३êࢹॠٕɰؒܳۆÌʪε

ؒܳÌʪٮؒъÌʪۆҼڱۋݒÀॠي؋܁Ձঝ҃قڮνॢìڷͿǣࢍǮɰ࣢০ ٍ҆ĵۆ३ԵܓæقԴəؒܳۆफę

ȭۋۆҼڱۋأۋԜۋϸИݓ҃ؒܳۆÌʪÀؒъۆؓ߹Ìʪ҃ɰࡾóصرܐɰ̚ॢؒܳۆ঍Ԝܓæق˰͆ս࠘३Ե

ĀęٮڮԐॢĀęεԓ߻ॠəąॹ֩ۋɰՙԜۋॠي ইۤۙΒşъۆąॹ֩ںটڌॠşڦ३Դəؒܳۆ঍Ԝܓæق˰͆

ۺ०ॢąॹ֩ںۺڌॠəìۋज़څॠɰ

ܳڅرܳѓ֩ėѪ ؒܳ ێ߹ؓ߹Ìʪ ؒъқΪ ս࠘३Ե

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ܳѓ֩ėѪ(Room and pillar method)ڹġԓқآ قԴ֨ۚʽėѪڷͿԴսथ̚əäۆսथڷͿ

ϔۤʼرەəġНں޽ĹॣЀۺڷͿۺڌʼəė Ѫۋɰ(Hartman and Mutmansky, 2002). ܳѓ֩ėѪ قԴəġНۆϔۤ঍ࢗق˰͆սथॠóĹ޳ں

ݕॱॠϸԴێ܁ॢÂüڷͿѓ(room)ں޽ġॠČ

ؒܳ(rock pillar)εǫûȮə঍ࢗͿي͠Ėۆۚغ

ۤںڏٖॢɰ. ۋεࣀ३޽ġۚغۆԦԓՁęমڱ

ںȭۋ϶ज़څق˰͆ԴǫûȮؕʏؒܳε޽Ĺॠ

şʪॢɰ. ۋ͠ॢėѪڹȉڹݓًقèߝսथॠó

қपॠəġНں޽ĹॠəʚقۋԜۺۍėѪڷͿԴ

йĶˣںܼ֮ڷͿԐڌʼرٵɰ.

йĶࠬۙ֟(Kansas)قԴə1960țʂҙࢢܳѓ֩

ėѪقۆ३şܕۆԵধؒġԓںঝۤॠيНΪՅ ࢢ, ڍठНݚܼĶ, ԐИ֬ˣۆʂőϿԜغݓॠėÂ (Subtropolis) ڷͿটڌॠČەɰ. يşԴۆܳѓ֩

ĵܓəफۋأ12mۍݔگϸߕėÂڷͿĵՁʼر

ەڷ϶, ؒܳۆफ(w)ęȭۋ(H)ۆҼə1҃ɰࡾɰ (Carmody & Sterling, 1993). ۋ͠ॢܳѓ֩ࢹЀĵܓ НقԴۆؒܳəۙڙÒьқآقԴٮəՁüۋɰβ ɰ. şܕۙڙÒьقԴۆܳѓ֩޽ġڹ޽ġşÂʴ

؋ɳşۺۍؒܳۆ؋܁Ձںڮݓॣսەں܁ʪۆ

ؒܳԺćεࣀ३߯ʂॢψڹ޽ġ͟ںঝ҃ॠə

ìۋܳ؋۾ۋ͆ϸ, ėÂঝ҃ࠑϸقԴۆܳѓ֩Ĺ

޳ėѪڹܼۤşۺۍėÂĵܓНۆ؋܁Ձঝ҃ق

ʌڎܳ؋۾ں˃رؒܳԺćÀۋΘر܋آॢɰ.

˰͆Դ, ėÂঝ҃޲ڙۆܳѓ֩Ĺ޳قԴəۻߕܳ

ѓ֩ĵܓНۋԜۦॠܼںܼۤşۺڷͿݓݓॣս

ەرآॠČؒܳԐۋق঍ՁʽėÂۆߎ܁ҙ(roof) ٮÁÁۆؒܳÀ؋܁ՁںڮݓॠيėÂটڌق

Л܃Àػرآॢɰ. şܕܳѓ֩޽ġėѪقԴؒܳ

ۆԺćəؒܳۆÌʪٮؒܳۆڿͳԜࢗεČͲॠ ي؋ۻڱںԓ܁ॠəѓѪڷͿݕॱʼرٵɰ. ࣢০,

ؒܳۆ؋܁Ձڹܳѓ֩ĵܓۆ؋܁ۺۍڮݓقज़ սۺۍڅՙͿيûݕɰ(Esterhuizen et al., 2008).

߯ŖйĶۆNIOSH (National Institute for Occupational safety and Heath) قԴə؋ۻॢؒܳԺćεࣀ३

ġԓۆԐČεѓݓॠşڦॢÀۋ˚͆ۍںьशॢ

цەɰ(Esterhuizen et al., 2011). şܕق܃֨ʼؽʏ

ؒܳÌʪԓ܁قěॢąॹ֩˞(Hedley & Grant, 1972; Hardy & Agapito, 1982; Kimmelmann et al, 1984; Potvin et al, 1989; Krauland & Soder, 1987;

Lunder & Pakalnis, 1997; Sheorey et al, 2000) ęυ޴

ÀݓͿNIOSHۆÀۋ˚͆ۍقԴʪرɗ܁ʪąॹ ۺۍҙқęě޶ںࣀ३ؒܳԺćقěॢ०νۺۍ

ѓॳں܃֨ॠČەɰ. şܕܳѓ֩ėѪۆؒܳԺć

قԴÀܼۤڅॠóČͲʼČەə۾ڹؒܳۆÌʪ εۺۼ০ԓ܁ॠČؒܳقۚڌॠəսݔڿͳقʂ

ॢؒܳۆ؋ۻڱںČͲॠيԺćقъٖॠəìۋ ɰ. ۋəŖۿॢѿԺࢢȇԐۋق঍Ձʽज़͆ҙ३Ե (Shin & Kim, 2010; Kim et al., 2012) ęɰՙڮԐॢ

۾ۋەڷǣŖ҆ۺڷͿИݓ҃ԜࢗۆؒܳεܳͿ

ČͲॢɰə۾قԴÀۤࢀ޲ۋε҃ۍɰ.

ٍ҆ĵقԴəؒъۆқΪˣśق˰͆ؒъۆێ

߹ؓ߹Ìʪε߸܁ॢ঳2޲ڙս࠘३Եںսॱॠي

ؒܳۆ঍Ԝق˰δИݓ҃ԜࢗۆؒܳÌʪε߸܁

ॠٕɰ. ̚ॢ३ԵĀęεц࢖ڷͿؒъˣśęؒܳ

ۆ঍ԜҼق˰δÌʪεԓ܁ॠيҼİॠٕɰ.

ᦵᵝ᮹ᦩᱶᖒ⠪aႊჶᨱݡ⦽Łₑ

ėÂঝ҃ࠑϸقԴܳѓ֩ėѪقČͲʼəؒܳ

əԜҙۆॠܼںݓݓ३ܳəĵܓߕͿԴ߿қॢ؋

܁Ձںڮݓ३آॢɰ. şܕٍĵ˞قԴ܃֨ॢؒܳ

ۆԺćѪقԴəێъۺڷͿؒܳۆ঍Ԝق˰δؒ

ܳۆÌʪ(strength)ٮڿͳ(stress)ںԓ܁ॠيۺ०

ॢ؋ۻڱ(FOS, Factor of Safety)ںԓ܁ॠəѓ֩ڷ Ϳ܃֨ॠČەɰ. يşԴؒܳۆȭۋʂҼफۆ

Ҽق˰͆ؒԵۆێ߹ؓ߹ÌʪٮؒܳۆࣷĨÌʪۆ

޲ۋÀьԦॠəܳڙۍڹڙؒęٍĀʼرەəؒܳ

ԜॠǚɳۆսथѺ঍ڱۆĵ՚মę(end-effect)Ϳ

ۍ३ؒܳȭۋقҼ३ؒܳफۋȉرݓϸۚڌʼə

սݔॠܼقʂॢսथĵ՚মęÀ࠶ݓϸԴؒܳۆ

ࣷĨÌʪÀȭ؉ݓş˺ЛڷͿࣺɳʽɰ. ˰͆Դؒ

ܳقۚڌॠəսݔۦॠॠܼقʂॢ؋ۻڱćԓڹ

ؒܳۆࣷĨÌʪεşܵڷͿԓ܁ʽɰ. ؒܳقۚڌ ॠəսݔॠܼقʂॢؒܳۆ؋ۻڱڹؒܳۆथŒ

Ìʪ( ¬ Ǝ ) ٮؒܳۆथŒڿͳ( ň Ǝ ) ڷͿशইʼ϶ɰڼ

֩(1)ęÏɰ.

¨¬ á ć ň Ǝ

ଲశ෹ ȵୋ৤෹ ȵ਑ิন

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵ֬ۻےٍĵڙ

܁ধڙ ॢĶæԺşցٍĵڙ40$Ձɠٍĵՙ(FPۍٍ॒͆ĵٍ֬ĵڦڙ

ߣ΀ ٍ҆ĵقԴəܳѓ֩ݓॠĵܓНۆ؋܁ՁںܟڍॠəИݓ҃ؒܳۆäʴںս࠘३Եقۆ३êࢹॠٕɰؒܳۆÌʪε

ؒܳÌʪٮؒъÌʪۆҼڱۋݒÀॠي؋܁Ձঝ҃قڮνॢìڷͿǣࢍǮɰ࣢০ ٍ҆ĵۆ३ԵܓæقԴəؒܳۆफę

ȭۋۆҼڱۋأۋԜۋϸИݓ҃ؒܳۆÌʪÀؒъۆؓ߹Ìʪ҃ɰࡾóصرܐɰ̚ॢؒܳۆ঍Ԝܓæق˰͆ս࠘३Ե

ۺ०ॢąॹ֩ںۺڌॠəìۋज़څॠɰ

ܳڅرܳѓ֩ėѪ ؒܳ ێ߹ؓ߹Ìʪ ؒъқΪ ս࠘३Ե

$PQZSJHIU ,PSFBO5VOOFMMJOHBOE6OEFSHSPVOE4QBDF"TTPDJBUJPO

ᕽು

ᦵᵝ᮹ᦩᱶᖒ⠪aႊჶᨱݡ⦽Łₑ

Ìʪ( ¬ _Ǝ ) ٮؒܳۆथŒڿͳ( ň _Ǝ ) ڷͿशইʼ϶ɰڼ

¨¬ á ć ň Ǝ

¬ _Ǝ

Þ ×íÓÕ×â×íÒÏ×ć ¡ ƕ ß ^0.440 ^ň

^-

Þ ^ć ^¡ ^Î ß

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

^-

ؒܳۆथŒڿͳ( ň _Ǝ ) ڹؒܳۆȃҼÀۚČؒܳ

ň Ǝ á ć ƕ ^Ï Þƕ âƑß ^Ï ³Ĺ _Ƒ

(kN/m ³ ) ۋɰ.

¬ _ƍ ) εИĀؒ(intact rock)ۆێ߹ؓ߹ÌʪقԴأ40