Behavior and pillar stability of enlarged existing parallel tunnels

(1)

*Corresponding author: Bumjoo Kim E-mail: [email protected]

Received September 15, 2013; Revised September 23, 2013;

Accepted September 29, 2013

ʑ᳕ᄲᖅ░ձ᮹⪶⡎ᨱ঑ෙ░ձÑ࠺ၰ⦥௝ᦩᱶᖒᇥᕾ

ଲࡣ෉ ȵ׌࣐ச ȵୋ઴৤ ȵଗ஺ْ ȵࢮ෮յ

Ҽধڙ ɳڍşցɳݓъėॡҙ şԐ

܁ধڙ ʴĶʂॡİæԺঞąėॡę ҙİս

܁ধڙ ʴĶʂॡİæԺঞąėॡę İս

Ҽধڙ प֟ࡑæԺࢹЀঞąԐغ҆ҙԺćŔΝ ޲ۤ

Ҽধڙ ॢĶʪͿėԐʪͿİࣀٍĵڙ ٍĵÒь֬ ٍĵڙ

Behavior and pillar stability of enlarged existing parallel tunnels

Myeong-Han Lee

¹

, Bumjoo Kim

²

*, Yeon-Soo Jang

³

, Ji-Nam Yun

⁴

, Hyun-Gon Park

⁵

1

Danwoo E&C, Geotechnical Department, Engineer

2

Dongguk University, Department of Civil and Environmental Engineering, Associate Professor

3

Dongguk University, Department of Civil and Environmental Engineering, Professor

4

Posco E&C, Civil and Environmental Division, Design Group, Deputy General Manager

5

Korea Expressway Corporation, Expressway & Transportation Research Institute, Researcher

ABSTRACT: Traffic congestion in existing tunnels has increased due to increased traffic volume and enlarged vehicles.

Enlarging existing tunnels has advantages over constructing new tunnels by reducing land purchasing costs as well as minimizing natural environment destruction. In fact, many overseas projects for enlarging existing tunnels have been reported. Thus, it appears that the demand on enlarging existing tunnels continues to rise in Korea in near future. Nonetheless, the studies related to the enlarged tunnels have been relatively rare since there have been few tunnel enlargement projects in Korea. In the present study, the tunnel behavior and the stability of rock pillar when enlarging existing parallel tunnels were investigated by performing FE analysis and using existing theory and empirical relationships. Four different enlarging cases, depending on the enlargement types and directions, were examined in the study. According to the results, for the tunnels with the same pillar width after enlarged, the uni-laterally enlarged tunnel indicated 5 to 20% higher crown settlement compared to the bi-laterally enlarged tunnel, and for the tunnel with the narrowest pillar, the highest shotcrete stress was observed. Also, the strength/stress ratio for rock pillar was more than 1.0 for all four enlargement cases, and the Matsuda’s method was found to give higher strength/stress ratio by about 50% compared to the Peck’s method.

Keywords: Tunnel enlargement, Parallel tunnels, Pillar stability, Crown settlement, Strength/stress ratio

ߣ΀ ߯Ŗİࣀ͟ۆݒÀٮ޲͟ۆʂ঍জͿۍ३şܕࢢȇقԴԜ֥ۺۍ܁ߕÀьԦʼəąڍÀݒÀॠČەɰۋ͠ॢЛ܃

३ĀۆێঞڷͿşܕࢢȇںঝफॠəąڍə֪ԺࢢȇںæԺॠəąڍٮҼİॠيڌݓϔۓҼڌۆۼÇęٍۙঞąۆী՜ں

߯ՙজ֨࢈սەɰəۤ۾ۋەɰ֬܃Ϳێ҆ęڮͥˣ३ٽقԴəşܕࢢȇںঝफ֨ėॠəԐͻÀψۋ҃ČʼČەɰ

ۋ͠ॢ৔ζقԴĶǴقԴʪॳ঳şܕࢢȇۆঝफ֨ėقʂॢսڅəƴܵ০ݒÀॣìڷͿٚԜʼǣ ইۦūݓəşܕࢢȇۆ

ঝफقěॢ֬ۺęąॹۋψݓ؍؉ۋقěॢşъٍĵÀज़څॢԜডۋ͆Č҇սەɰٍ҆ĵقԴəڮॢڅՙ३Եęşܕۆ

ۋ΁ ąॹ֩ˣںۋڌॠيşܕѿԺࢢȇںঝफॠəąڍঝफѓ֩ęŔق˰δज़͆फѺজÀࢢȇۆäʴęज़͆؋܁Ձق

й࠘əٖॳںथÀॠٕɰܓԐĀę ज़͆फڹʴێॠǣठࠑęتࠑڷͿঝʂॠəąڍۆ޲ۋق˰͆ठࠑঝʂࢢȇۆߎɳࠞॠə

تࠑঝʂࢢȇقҼ३أ_ۆࢀÉں҃ۋəॢठ ߯ՙज़͆फںÍóʼəठࠑঝʂࢢȇقԴջࡾν࣡ڿͳۋ߯ʂε

҃ۋəìڷͿǣࢍǮɰ̚ॢ ÌʪڿͳҼۆąڍܓԐʽȐܛΪۆঝफःࢤقʂॠيϿ˃ۋԜںǣࢍǴؽČ.BUTVEBۆ

ѓѪۋ1FDLۆѓѪقҼ३أ܁ʪÌʪڿͳҼεࡾóԓ܁ॠóʿںঝۍॠٕɰ

ܳڅرࢢȇঝफ ѿԺࢢȇ ज़͆؋܁Ձ ߎɳࠞॠ ÌʪڿͳҼ

$PQZSJHIU ,PSFBO5VOOFMMJOHBOE6OEFSHSPVOE4QBDF"TTPDJBUJPO

(2)

Fig. 1. Yielding load acting on the central pillar (Kang, 2008)

ᕽು

ĶǴقԴࢢȇæԺۋ҆üۺڷͿ֨ۚʽݓ40ي țۋݓǦইۦ, ɾ֨֨ėʽࢢȇɳϸڷͿəşॠś սۺڷͿɚرǦİࣀ͟ęʂ঍জʽ޲͟˞ںڙট০

ՙࣀ֨ࢅəʚرͲړںýČەɰ. ̚ॢ, şܕࢢȇۆ

Ȥ঳ͿۍॢŒَ, ɀս, чνইԜˣڷͿࢢȇǴ

؋ۻԐČقʂॢڦॹՁʪ࠶ݓČەɰ. ۋقʂॢ

ʂ޾ڷͿ֪ԺࢢȇںæԺॠäǣşܕʪͿεঝ߿

ॠəˣۆψڹ࣊ۙÀۋΘرݓČەݓχ, ʪ֮ݓ

ǴقԴəҙݓϔۓ, ঞąী՜, ࢢȇ҃սėԐق˰δ

ڍধȤԸԸ܁ԜۆرͲړںýČەر֪Ժࢢȇ

æԺقψڹ܃أۋܕۦॢɰ. ۋ͠ॢЛ܃˞Ϳۍ३

३ٽ࣢০, ێ҆قԴəۋй40ي޲ͻۋԜşܕ

ࢢȇقঝफėԐεݕॱॣսшقػəইۤۋǣࢍ

Ǯڷ϶, ۋεՁėۺڷͿսॱॢԐͻ˞ۋ҃ČʼČ

ەɰ(Seo et al., 2008)(Baek et al., 2007). şܕࢢȇۆ

ঝफقʂॢսڅə۾޲Ȥ঳ࢢȇۆҼܼۋȭ؉ݓ óʾڍνǣ͆قԴʪśü০ݒÀॠóʾìڷͿ

ٚԜʼ϶, Ŕ͠ॢѓѪڷͿԴࢢȇںঝफॠəѓѪ قʂॠيĶǴقԴʪě֮ۋݒʂʼČەɰ.

ĶǴۆ֨ėşցۋ֪ԺࢢȇۆæԺقʂ३Դۋй

Ճćۺۍսܵقۋβͧɰॣݓ͆ʪşܕࢢȇۆঝ फ֨ėқآقەرԴəąॹۆҙۦͿۍ३ψڹ

şցۆьۻۋڅĵʼəԜডۋ϶, ঝफۋज़څॢࢢ ȇۆսڅÀś՚০ݒÀॠóʾìےںČͲ३҇

˺, ĶǴ֬܁قϑəěʹٍĵÀϔڍ֨śॢ֬܁ۋ

͆ॣսەɰ. ۋقByun et al. (2010)ڹս࠘३Եۆ

څՙࡾşۆлÇʪқԵںࣀ३ؒъˣśѻфज़͆

फقʂॢज़͆ۆäʴںêࢹॠٕČ, Choi et al.

(2011) ڹ֨ėܼۍ2޲ͿʪͿࢢȇۆ3޲Ϳঝۤ

ԺćǴڌںۋڌॠيࢢȇঝۤ֨Ը঍ćন, ࢢȇ

ঝۤѓ؋ˣں܃֨ॠٕɰ.

ٍ҆ĵə۾޲ݒÀʾìڷͿٚԜʼəȤ঳জʽ

şܕࢢȇۆঝफقʂॠي, şܕѿԺࢢȇۆɳϸں

Ͽ˃ঝʂ֨ėॠəąڍقʂॠيࢢȇۆäʴę

؋܁ՁۆܼڅॢݓशÀʼəؒъज़͆ۆ؋܁Ձں

ࢢȇঝʂѓѪق˰͆қԵॠٕɰ.

⦥௝ᦩᱶᖒ⠪a

Tunnel design criteria (2007) قۆॠϸ‘ࢢȇں2Ò

ۋԜѿ͵ͿԺ࠘ॣąڍقəۍۿࢢȇقǣԄٖॳ ںй࠘ݓ؍ʪ΀߿қ০ۋü֨ࡈآॢɰ’ ͆Čϼ֨

ʼرەڷ϶, Tunnel design manual (Korea expressway corporation) قə ‘ࢢȇۋüäν Ժ܁֨ PW=1.5D (PW : ज़͆फ, D : ࢢȇफ)εşܵڷͿࢢȇÚĵҙۆ

ݓъНՁ࠘قۆॢս࠘३Եˣۆêࢹε֨ॱॠي, Úĵҙݓ঍ܓæęࢢȇۆĵܓۺ؋܁Ձфą܃Ձ ( ڌݓҼ, ۋüäν߹ՙق˰δÚĵҙ҃ÌėԐҼˣ) êࢹĀęق˰͆ۺ܁ۋüäνÀʼʪ΀ݒ, Çॠي

ۺڌॢɰ’ ͆Čϼ֨ॠيज़͆ۆԜࢗق˰͆ѿԺࢢ ȇÂۺ܁ۋüäνεԓ܁ॠʪ΀ॠٕɰ(Jung et al., 2007). ʴێॢ֮ʪۆѿԺࢢȇقԴࢢȇÂۋüäν Àࢢȇݔąۆ1ѕۋԜێąڍ, Ŕٖॳڹ10% йχ ڷͿ؎Ͳ܋ەڷǣ(Jung et al., 2007) ѿԺࢢȇۆ

ۺ܁ۋüäνεԓ܁ॠşڦ३ԴəইۤيæںČͲ

ॢՃҙۺۍêࢹÀज़څॠɰČ҇սەɰ. Table 1 ڹѿԺࢢȇۋüäνقěॢԺćşܵںڅأॠي

ǣࢍǶìۋɰ.

ज़͆ۆ؋܁ՁथÀεڦॢąॹۺѓѪڷͿə

Peck (1969) ۆѓѪ, Matsuda (1998)ۋەڷ϶, ս࠘

३Եںࣀॢ܁нêࢹѓѪڹज़͆ҙقۚڌॠə

(3)

Table 1. Parallel Tunnels separation distance design criteria(Road Design Guideline. 2009)

Division Contents Note

Road design guideline (‘92 Korea expressway

corporation )

ࡐ Original ground can be considered to behave perfectly elastic : 2D ࡐ Original ground is a soft ground(e.g. clay) : 5D

ࡐ General : 2૫3D

Center to Center Standard manual for tunneling

(‘94 Ministry of land, transport and maritime affairs, KTA)

ࡐ Original ground can be considered to behave perfectly elastic : 2D ࡐ Original ground is a soft ground(e.g. clay) : 5D

Tunnel design manual (‘95 Korea expressway

corporation)

ࡐ Center to center distance - Two lane tunnel : 30m - Three lane tunnel : 40m Tunnel design manual

(‘00 Korea expressway corporation)

ࡐ Separation distance shall be either increased or decreased from PW=1.5D according to the results of the investigation of ground condition, tunnel structural stability and economical aspect by performing numerical analysis using geotechnical properties for tunnel portal area and other investigations

Pillar Width

Tunnel design criteria (‘07 Construction and transportation ministry, KTA)

ࡐ Parallel tunnels should be separated enough such that blasting, vibration and ground behavior by the tunnel construction do not adversely affect adjacent tunnel by considering tunnel size, ground characteristics, blasting/vibration effect, land compensation, hindrance and civil complaint

Table 2. Safety factor calculation formula based on experience

Applied stress (¬

_Ǝ

) Strength of pillar (ň

_Ǝ

) Safety factor Peck's method

(1969) Ĺ_¡ _ÞÎâî©ß Ï__ŋîÞÎà ŋß

_Ƒ

á ň

_Ǝ

î¬

_Ǝ

Matsuda's method

(1998)

(if H>D) Ĺ__î©

Ə

_Ɠ

(if H<D) Ĺ_¡ _î©

Ĺ : Density, H : Depth, D : Tunnel Width, B : Yielding Load Width

P : Pillar Width, C : Cohesion, Ə

_Ɠ

: Uniaxial Strength of Rock,

_Ƒ

: Safety Factor, ŋ : Friction Angle

ܳڿͳںۋڌॠيؒъࣷĨőܵقŖäॢÌʪ-ڿ ͳҼεۋڌॢѓѪۋەɰ. Fig. 1ڹܼؖज़͆ق

ۚڌॠəۋٰॠܼÒȝʪεशইॢìۋ϶, ۋεц

࢖ڷͿTable 2قÁąॹ֩ۆ؋ۻڱ֩قʂ३܁ν ॠٕɰ.

1FDL ႊჶ

Peck ѓѪڹѿԺࢢȇĹ޳֨ज़͆ҙقьԦॠə

थŒڿͳęێ߹ؓ߹ÌʪۆҼİεࣀ३؋܁Ձں

थÀॠəŖԐۺۍşѪڷͿज़͆ۆथŒڿͳ( ¬ Ǝ ) ę

ज़͆ۆێ߹ؓ߹Ìʪ( ň Ǝ ) ε߸܁ॠي؋ۻڱںԓ܁

ॠəşѪں܃؋ॠٕɰ.

˃ࢢȇقەرԴज़͆ۆथŒڿͳ( ¬ _Ǝ ) ڹɰڼ֩

(1) ęÏۋŖԐۺڷͿशইॣսەɰ.

¬ _Ǝ á Ĺ_ ¡_ ÞÎ âî©ß (1)

يşԴ, Ĺ : ɳڦܼ͟(kN/m ³ )

H : ݓशϸڷͿҙࢢۆࢢȇŪۋ(m) D : ࢢȇफ(m)

P : ज़͆फ(m)

̚ॢ, ज़͆ۆؓ߹Ìʪ( ň _Ǝ ) əɰڼ֩(2)ٮÏۋ

ԓ܁ॣսەɰ.

ň Ǝ á Ï _ _ ŋÞÎ à ŋß (2)

(4)

Fig. 2. The relation curve according to safety(

_Ƒ

) P/D and ň

_Ǝ

îĹ_¡

يşԴ, C : ۾޳ͳ(kN/m ² ) ŋ : Ǵҙυ޶Á

˰͆Դज़͆ۆߣş२҄قʂॢ؋ۻڱ( _Ƒ ) ڹ֩

(3) ęÏۋǣࢍǷսەɰ.

_Ƒ á ć ¬ _Ǝ ň _Ǝ

(3)

ɰڼ Fig. 2ə P/D(ज़͆फ/ࢢȇफ)ٮ Ԝۦڿͳ ( Ĺ_ ¡ ) قۆॠيज़͆Ìʪ( ň Ǝ ) ε܁őজ֨ࢇÉę ۆěćε؋ۻڱͿǣࢍǶìۋɰ.

.BUTVEB ႊჶ

Matsuda əԜۦॠܼۋ1D (D=ࢢȇۆफ)҃ɰۚ

ڹąڍ, Fig. 1قڼٖڷͿश֨ʽًٖۆۻॠܼۋ

ܼؖज़͆ҙًٖۆݓъقۚڌॠəìڷͿ܃؋ॠ

ٕɰ. ۋ͠ॢąڍćনʽܼؖज़͆ҙĵܓߕۆÌʪ ÀٚԜʼرݓəڿͳ҃ɰࡾϸ߿қॢ؋܁Ձںঝ҃

ॣ ս ەɰ. ɰՙ ҃սۺۋݓχ, ইۦ ֬ИقԴʪ

Matsuda ѓѪںۋڌॢज़͆؋܁ՁêࢹÀսॱʼČ

ەɰ.

ܼؖѹߕقۚڌॠəۚڌڿͳ( ¬ Ǝ á © _Ɛ î© ) ęؒъ

ज़͆ۆ؋ۻڱڹ؉͒֩(4)(6)قۆ३ĵ३ݕɰ.

ࢹक़(H)Àࢢȇफ(D)҃ɰࢀąڍ:

© _Ɛ á Ĺ_ _ (4)

ࢹक़(H)Àࢢȇफ(D)҃ɰۚڹąڍ:

© _Ɛ á Ĺ_ ¡_ (5)

Matsudaۆ ؋ۻڱ : _Ƒ á ć ¬ _Ǝ Ə _Ɠ

(6)

يşԴ, Ĺ : ɳڦܼ͟(kN/m ³ ) H : ࢹक़Č(m) D : ࢢȇफ(m) P : ज़͆फ(m) Ə Ɠ : ؒъÌʪ(kN/m ² )

vࠥ᮲ಆእ 4USFOHUI4USFTT3BUJP

ɰتॢĵ՚ؓͳ( ň _Ð ) قʂॠيՙՁࣷĨۆ֨ۚڹ

Mohr-Coulomb ࣷĨşܵقۆ३őϼʽɰČÀ܁ॠ ϸ؉͒֩(7)ęÏۋशইʽɰ.

ň ÎƄ á ň _ƁƋ âƉň _Ð (7)

يşԴ, ؒъۆێ߹ؓ߹Ìʪ ň ƁƋ ڹ֩(8)ęÏۋ

܁ۆʽɰ.

ň ƁƋ á ć Î à ŋ ÏƁŋ (8)

̚ॢ, ň _Ð قʂॢ ň _Î ۆşڐşƉə֩(9)ٮÏɰ.

Ɖ á ć Î à ŋ Î âŋ

(9)

يşԴ, ň Î : ࣷĨ֨߹ѓॳڿͳ(Ìʪ) ň Ð : ĵ՚ڿͳ

Ɓ : ؒъۆ۾޳Ìʪ

ŋ : ؒъۆǴҙυ޶Á

(5)

Fig. 3. Strength-Stress Ratio and distribution chart of stress (Kang, 2008)

֩(7)ںࣀ३Դ߯ܛۺڷͿÌʪڿͳҼə֩(10) ęÏۋ܁ۆʽɰ.

୬ጛ⚨᝼ᶛ á ć ň _Ð à ň _Î ň Ð à ň _ÎƄ

(10)

؉͒Fig. 3ڹؒъज़͆ۆÌʪقʂॢڿͳԜࢗε

शইॢìۋ϶, ज़͆ۆÌʪ-ڿͳҼÀPillar ۻߕۆ

؋ۻڱںʂѺॠݓə؍ݓχ, ݕॱՁࣷĨ(progressive failure) ǣڿͳۻۋę܁(stress transfer progress)ں

ČͲॠيPillar ܼؖɳϸقԴۆथŒÌʪ-ڿͳҼ (average strength-stress ratio) À1.0ۋॠÀʼϸज़͆

ۻߕÀҝ؋३ݓəìڷͿ؎Ͳ܋ەɰ(Hoek and Brown, 1980).

⪶⡎ᨱ ঑ෙ ᦵၹ ⦥௝ᇡ ᦩᱶᖒ

ᇥᕾ

҆ۼقԴəşܕѿԺࢢȇۆ˃ɳϸںϿ˃ঝफ ॠóʼəąڍѿԺࢢȇۆ؋܁ՁۆܼڅॢݓशÀ

ʼəؒъज़͆ۆ؋܁ՁںࢢȇঝʂѓѪق˰͆

êࢹॠٕڷ϶, êࢹѓѪڷͿəşܕۆąॹ֩˞ںࣀ ३؋ۻڱںԓ܁ॠəѓѪęս࠘३Եںࣀ३صر ݕؒъज़͆ۆܳڿͳÉںۋڌॠيÌʪ-ڿͳҼε

ԓ܁ॠəѓѪںۺڌॠٕɰ.

░ձ༉ߙย

şܕѿԺࢢȇۆঝफ֨ঝफ঍֩ęज़͆फق˰δ

şॠॡۺڅՙεϔÒѺսͿॠيѩڌݓъڮॢڅ ՙ३Ե॒ͿŔ͖ۍMidas-GTSεԐڌॠيMohr- Coulomb ࣷĨşܵق˰δ࢏ՙՁ३Եںսॱॠٕ

ɰ. ३ԵʂԜࢢȇͿəইۦڏٖܼقەəठʪ

2 ޲Ϳۆۻܳ-ġتČ՚ʪͿࢢȇ(फ12.91 m, ȭۋ8.2 m)ęठʪ4޲ͿۆԴڐٽĚտঞʪͿ

ࢢȇ(फ19.14 m, ȭۋ10.39 m)ۆɳϸںۺڌॠٕɰ (Table 3 ޷ܓ). ३ԵًٖۆԺ܁ڹԜҙəʪͿܼ֮

قԴ20 mۋԜ(ࢹक़Č30.5 m), ࠑϸڹࢢȇĹ޳फۆ

3 ѕۋԜ, ॠҙąćəࢢȇܳѺڷͿҙࢢࢢȇȭۋۆ

3 ѕۋԜںČͲॠيݓъąćÀ३ԵĀęقٖॳں

й࠘ݓ؍ʪ΀ČͲॠٕɰ.

ࢢȇঝफڹ2޲ͿࢢȇقԴ4޲ͿࢢȇͿۆঝफ ںÀ܁ॠٕڷ϶, ܳѺؒъˣśڹ3ˣśۆНՁں

ۺڌॠٕɰ(Table 4 ޷ܓ). şܕࢢȇфঝफ֨ࢢȇ ۆĹ޳ڹۻɳϸĹ޳ں֬֨ॠٕڷ϶, ΀҇࣡Ϳۍ

ॢज़͆ҙۆ҃ÌমęεČͲॠݓ؍şڦ३ݓ҃ۦ əջࡾν࣡χ֨ėॠəìڷͿϿʝτॠٕČ(Table 5 ޷ܓ), ۺڌʽॠܼқɺڱڹTable 6ęÏɰ.

şܕ2޲Ըɳϸۆࢢȇں4޲ԸࢢȇͿۆঝफں

ॠəʚەرԴ, Case 1ڹࢢȇܼ֮ԸںşܵڷͿ

تࠑঝफںॢąڍۋ϶, Case 2əঝफѓॳںؒъ

ज़͆ҙޅڷͿॳॢąڍۋɰ. ̚ॢCase 3ڹCase

(6)

Table 3. The cross section and size of tunnel Cross section and size

2-lane tunnel

4-lane tunnel

Table 4. Soil Properties

Rock mass rating III

Unit weight, ഓt (kN/m

³

) 25 Elastic Modulus (MPa) 4,400

Cohesion, C (kPa) 700

Friction angle, ౝ(°) 40

Poisson ratio ( ഝ) 0.25

K

0

1.0 Table 5. Tunnel support properties Elastic

Modulus (MPa)

Thick-ness (cm)

Unit weight (kN/m

³

)

Design strength (MPa) Soft

Shotcrete 5,000 12 24 10

Hard

Shotcrete 15,000 12 24 21

Table 6. Load distribution factor

Excavation 0.5

Soft Shotcrete 0.25

Hard Shotcrete 0.25

Table 7. Analysis cases for tunnel enlargement Case 1

(both sides enlargement)

Case 2 (one side enlargement)

9.58 m (0.5D) 3.68 m (0.19D) Case 3

(one side enlargement)

Case 4 (one side enlargement)

15.47 m (0.81D) 9.56 m (0.5D) Pillar width after enlargement

2 ٮъʂͿঝफѓॳںࢢȇٽĚޅڷͿॳॠٕڷ϶, Case 4 əԸ঳ॱࢢȇϿ˃ÁÁÏڹޅڷͿঝफں

ॢąڍۋɰ(Table 7 ޷ܓ).

ᦩᱶᖒᇥᕾđŝ

⪶⡎⬥░ձÑ࠺ᇥᕾ

Table 8 قঝफ঍֩ق˰δࢢȇäʴںߎɳѺڦ ٮǴėѺڦÉ, ջࡾν࣡ڿͳڷͿǣࢍǴؽɰ. Á

ࡀۋ֟ѻߎɳѺڦÉںঝۍॢĀęࢢȇঝफ঳

ज़͆फۋܙ؉ݗս΀ߎɳѺڦÉۋʌڎࡾóьԦॠ əąॳںǣࢍǴؽɰ. ঝफ঳ज़͆फۋÀۤܙڹ

Case 2 ۆąڍşܕʂҼज़͆फۆٖॳۋԜʂۺڷͿ

ۺڹCase 3ۆߎɳѺڦقҼ३1832% ܁ʪʌ

ࡾóьԦॠٕڷ϶, ज़͆फڹÏڷǣঝफ঍֩قԴ

޲ۋÀەəCase 1ęCase 4ۆąڍقəठࠑঝफ (Case 4) ںॢąڍÀܘʌࡾóьԦ॥(520%)ں

ঝۍॣսەؽɰ.

ǴėѺڦəߎɳѺڦٮəɵνज़͆फۋÀۤܙڹ

Case 2 ۆąڍÀɰδCase˞قҼॠيÀۤۺó

ьԦॠٕڷ϶, تࠑঝफۆCase 1قԴÀۤࢀǴė ѺڦÀьԦ॥ںঝۍॣսەؽɰ. Ըॱࢢȇ(ܟࠑࢢ ȇ)ۆąڍǴėѺڦÀ֨ė5ɳćۋ঳ҙࢢəъʂͿ

ÇՙॠəتԜںǣࢍǴر঳ॱࢢȇ(ڍࠑࢢȇ) Ĺ޳

ڷͿۍॢݓъۋٰۆٖॳںঝۍॣսەؽɰ.

ज़͆फۋÏڹCase 1ę4قʂ३Դəتࠑঝफں

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Table 8. Tunnel behavior for different types of tunnel enlargement

ῂ⿚ Crown settlement Tunnel convergence Shotcrete stress

Going up tunnel

Going down tunnel

Table 9. Results of rock pillar stability using empirical formula

Division Empirical formula Applied stress

¬

_Ǝ

(kN/m

²

)

Strength of pillar

ň

_Ǝ

(kN/m

²

) Safety factor Case1

(both sides expansion)

Peck 2248.4

3002.3

1.34 Matsuda 1434.5 2.09

Case2 (one side expansion)

Peck 4650.8 0.65

Matsuda 2967.2 1.01

Case3 (one side expansion)

Peck 1677.9 1.79

Matsuda 1070.5 2.80

Case4 (one side expansion)

Peck 2251.6 1.33

Matsuda 1456.0 2.06

֬֨ॢCase1 ۆǴėѺڦÀCase 4قҼ३28%

ʌࡾóьԦॠيߎɳѺڦٮъʂąॳںǣࢍǴؽ ɰ. ज़͆फۋܙںս΀ջࡾν࣡ڿͳۋʌڎࡾó

ьԦॠəąॳںٕ҃ڷ϶, ज़͆फۋÀۤܙڹCase 2 ۆąڍջࡾν࣡ڿͳڹ֨ėɳćÀݕॱʿق˰͆

ć՚ݒÀॠٕڷǣ, ǣϢݓCase˞ۆąڍəԸॱࢢ ȇۆݓ҃ۦԺ࠘ÀٰΒʽɳć(4ɳć) ۋ঳ҙࢢ۾

޲սͶॠəتԜںǣࢍǴؽɰ. ߯ʂڿͳۋьԦॢ

ąڍۍCase 2ۆąڍ֨ėɳćܼ߯ʂÉڹ6.06 MPa

Ϳ28ێşܵÌʪقʂ३Դəॴڌ࠘( Ƅ _Ɓſ á ×íÑƄ _ƁƉ á ÕíÑ MPa) ۋǴٕڷǣ, ڿͳÉۋսͶॠəتԜںǣࢍǴ ݓ؍؉֨ėۋ঳قə؋܁Ձۋঝ҃ʼݓ؍ںìڷ Ϳࣺɳʽɰ.

Ğ⨹᜾ᨱ᮹⦽ᦵၹ⦥௝᮹ᦩᱶᖒá☁

ąॹ֩ق˰δؒъज़͆ۆ؋܁Ձںêࢹॠşڦ

३PeckۆѓѪęMatsudaۆѓѪںۋڌॠيؒъ

(8)

Table 10. Results of Strength-Stress Ratio

૟ Principal Stress (Min) ౚ

3

(kPa)

Principal Stress (Max) ౚ

1

(kPa)

Compression strength ౚ

cm

(kPa)

Strength-Stress Ratio

Case 1 769.55 2020.92 3002.3 2.32

Case 2 437.58 3324.82 3002.3 1.02

Case 3 849.41 1547.63 3002.3 4.14

Case 4 763.77 2027.36 3002.3 2.30

(a) Case 1 (b) Case 2

(c) Case 3 (d) Case 4

Fig. 4. Principal stress distributions for different analysis cases

ज़͆ۆ؋ۻڱںԓ܁ॠٕɰ. ԓ܁֩ڹؘԸ2.1, 2.2 ۼقşցॠٕڷ϶, ԓ܁֩ںц࢖ڷͿঝफ঍֩ق

˰͆қΪॢ4Àݓąڍقʂॠيąॹ֩؋ۻڱں

शTable 9قǣࢍǴؽɰ.

؋ۻڱԓ܁ĀęMatsudaۆѓѪۋPeckۆѓѪ҃

ɰ؋ۻڱۋʌȭóćԓʼəìڷͿǣࢍǮڷ϶, ज़͆फۆÂüۋȉڹս΀؋ۻڱۋݒÀॠٕɰ. ज़

͆फۋÀۤܙڹCase 2(ज़͆फ0.19D)ۆąڍPeck ѓѪقۆॢ؋ۻڱۋ0.65εǣࢍǴرҝ؋܁ॢìڷ ͿǣࢍǮڷ϶, ǣϢݓCase˞ڹϿ˃1 ۋԜۆ؋ۻ ڱںǣࢍǴؽɰ(Table 10). Ŕ͠ǣ҆ѓѪ˞قۆॢ

Āęəɳտ০ؒъۆÌʪقşߣॢìۋ϶, ؋ۻڱ

ۋęʂथÀʾսەڼںÇ؋ॣ˺Case 2ۆąڍə

ۻߕۺڷͿҝ؋܁ॠɰ҇սەɰ.

vࠥ᮲ಆእᨱ᮹⦽ᦵၹ⦥௝᮹ᦩᱶᖒ

á☁

ؘԴşցॢ2.3ۼۆÌʪ-ڿͳҼԓ܁֩ęս࠘३ ԵĀęεц࢖ڷͿصرݕԸ঳ॱࢢȇÂؒъ

ज़͆ҙܼ֮ҙۆܳڿͳÉںۋڌॠيÌʪ-ڿͳҼ εԓ܁ॠٕɰ(Table 10).

ս࠘३ԵĀęज़͆फۆÂüۋܙ؉ݗս΀߯ՙܳ

ڿͳڹÇՙॠČ߯ʂܳڿͳڹݒÀॠəąॳںٕ҃

(9)

Fig. 5. Mohr-Coulomb failure criterion for rock mass in terms of principal stresses

Fig. 6. Principal stress for four cases

ڷ϶, Ȑࡀۋ֟قʂॠيϿ˃Ìʪ-ڿͳҼ1.0 ۋԜ ۆÉںǣࢍǴؽɰ. ज़͆फۋÀۤܙڹCase 2(ज़͆

फ0.19D)ۆąڍÌʪ-ڿͳҼə1.02ͿÀۤҝ؋ॢ

ԜࢗۍìڷͿǣࢍǮڷ϶, ঝफ঳ۆज़͆फڹÏݓ χঝफ঍֩ۋɰδCase 1ęCase 4ۆąڍÌʪ-ڿͳ Ҽۆ޲ۋəййॢսܵڷͿ׆ज़͆ҙۆ؋܁Ձق

ەرԴঝफ঍֩҃ɰəज़͆फۆٖॳۋʌࡾɰə

ìں؎սەɰ. Fig. 4əÁCaseѻ߯ʂܳڿͳÉں

ˣČԸ(Contour)ڷͿǣࢍǴؽČ, Fig. 5əܳڿͳÉ قʂॢMohr-CoulombۆࣷĨşܵԸںǣࢍǴ϶.

ۋεࣀ३ Fig. 6ق Á Caseѻ ܳڿͳÉ Ԝࢗε

Mohr-Coulomb ۆࣷĨşܵԸę॥ƍʪ֨জॠٕɰ.

Case 2 ۆąڍज़͆ҙܼ֮ۆܳڿͳԜࢗÀࣷĨşܵ

ԸقŖۿॠيҝ؋܁ॢԜࢗےں؎սەɰ.

đು

ٍ҆ĵقԴəࢢȇǴχՁ܁ߕইԜ३ՙٮȤ঳

ࢢȇۆ؋܁ՁЛ܃ε३Āॠşڦ३ॳ঳ĶǴقԴ

սڅÀݒÀॣìڷͿۻϐʼəşܕѿԺࢢȇۆঝ फ֨ࢢȇäʴęज़͆؋܁ՁںܓԐॠٕڷ϶, ۋε

ڦ३şܕۆ2޲ͿѿԺࢢȇں4޲ͿࢢȇͿঝफॠ əąڍقʂॠيঝफѓ֩(تࠑфठࠑ)ęঝफѓॳ ( ठࠑ, ܟڍ)ق˰δȐÀݓcase˞قʂॠيڮॢڅ ՙ३ԵںࣀॢäʴқԵęşܕۆąॹ֩ˣںۋڌ

ॢ؋ۻڱęÌʪ/ڿͳҼԓ܁ĀęεҼİ, қԵॠٕ

ɰ. ۋεࣀ३صڹĀ΁ںڅأॠϸɰڼęÏɰ.

1. ज़͆फڹʴێॠǣठࠑęتࠑڷͿঝʂॠəą ڍۆ޲ۋق˰͆ठࠑঝʂࢢȇۆߎɳࠞॠə

تࠑঝʂࢢȇقҼ३أ520%ۆࢀÉں҃ۋ əॢठ, Ըॱę঳ॱࢢȇںϿ˃تࠑڷͿঝफॠ əąڍÀۤࢀǴėѺڦÀьԦॠČۻъۺڷͿ

঳ॱࢢȇ(ڍࠑࢢȇ) ঝफں֨ۚ॥ق˰͆Ըॱࢢ ȇ(ܟࠑࢢȇ)ۆǴėѺڦÀъʂͿÇՙॠيݓъ ۋۋٰʼəٖॳںঝۍॣսەؽɰ.

2. ज़͆फۋÀۤۺóʼəज़͆ѓॳڷͿठࠑঝफ

֨ջࡾν࣡ڿͳڹ֨ėɳćÀݕॱʿق˰͆ć

՚ۺڷͿݒÀॠəъϸ, Ŕٽۆąڍ˞(تࠑঝफ ęज़͆ъʂࠑڷͿठࠑঝफ)ڹϿ˃Ըॱࢢȇۆ

ݓ҃ۦԺ࠘ÀٰΒʽۋ঳ҙࢢ۾޲սͶॠəت ԜںǣࢍǴؽɰ.

3. ज़͆؋܁Ձقʂॢşܕۆąॹ֩ںۋڌॢ؋ۻ ڱęÌʪ/ڿͳҼԓ܁Āę, ۻߕۺڷͿMatsuda ѓѪقۆॢ؋ۻڱۋPeckۆѓѪ҃ɰ50%܁ʪ

ʌࢀìڷͿǣࢍǮڷ϶, ˃ѓѪϿ˃ɳտ০

ؒъۆÌʪقşߣॠيԓ܁ʼəìےںÇ؋ॣ

˺, ঝफ঳ज़͆फۋÀۤۺóʼəज़͆ѓॳۆ

ठࠑঝफۋ؋܁ՁࠑϸقԴÀۤҝνॢѓ֩ۍ

ìڷͿǣࢍǮɰ.

4. ঝफ঳ज़͆फڹÏݓχتࠑęठࠑڷͿঝफ঍

(10)

֩ۋɰδ˃ąڍÌʪ/ڿͳҼۆ޲ۋəййॢ

սܵں҃يঝफ঍֩҃ɰəज़͆फۋज़͆ۆ

؋܁Ձقʌࢀٖॳںй࠘əìڷͿǣࢍǮɰ.

ₙ Ł ྙ ⨭

1. Baek, K.H., Roh, J.R. (2007), “Case study on the widening construction of tunnel under use”, Korean Society of Civil Engineers Conference, pp. 2935-2938.

2. Byun, Y.S., Kim, H.G., Lee, S.S, Chun, B.S.

(2010), “A study on pillar behavior of twin parallel tunnels by numerical approach”, Korean Geo-Environmental Society, Vol. 11, No. 8, pp.

49-55.

3. Choi, H.J., Kim, D.K. (2011), “A study on the enlargement of 2-Lane road tunnel under construction”, Korean Tunnelling and Underground Space Association, Vol. 13, No. 1, pp. 33-50.

4. Hoek, E., Brown, E.T. (1980), “Empirical strength criterion for rock masses”, J. Geotech Engineering Div. ASCE 106, pp. 1013-1035.

5. Jung, Y.J., Song, H.C., Lee, S.H., Shin, S.H.

(2007), “A study on the reinforcing method and

the evaluation of stability for pillar in closely-spaced tunnel.”, Korean Society for Rock Mechanics Symposium, pp. 486-500.

6. Kang, C.M. (2008), “Big close reinforce parallel tunnel section applies pilla and reliability evaluation”, Master these, Kyungpook National University., pp. 14-18.

7. Matsuda, T. (1998), “Ground behavior and settlement control of twin tunnels in soil ground” Tunnels and Metropolises, Vol. 16, No. 2, pp. 1193-1198.

8. Peck, R.B. (1969), “Deep excavations and tunneling in soft grounding”. 7th Internation Conferences, Soil Mechanics and Foundation Engineering., pp.

225-290.

9. Seo, K.W., Baek, K.H., Roh, J.R. (2008), “An analyzing overseas cases about enlargement of a tunnel in operation(I)”, Korean Tunnelling and Underground Space Association, Vol. 10, No. 1, pp. 40-50.

10. Tunnel Design Criteria (2007), Construction and Transportation Ministry, KTA, pp. 17.

11. Tunnel Design Manual. Korea Expressway Corporation, pp. 6-2-2.

12. Road design guideline (2009) Korea Expressway

Corporation), Vol. 4 pp. 26-27.

Behavior and pillar stability of enlarged existing parallel tunnels

*Corresponding author: Bumjoo Kim E-mail: [email protected]

Received September 15, 2013; Revised September 23, 2013;

Accepted September 29, 2013

ଲࡣ෉  ȵ׌࣐ச  ȵୋ઴৤  ȵଗ஺ْ  ȵࢮ෮յ 

Ҽধڙ ɳڍşցɳݓъėॡҙ şԐ

܁ধڙ ʴĶʂॡİæԺঞąėॡę ҙİս

܁ধڙ ʴĶʂॡİæԺঞąėॡę İս

Ҽধڙ प֟ࡑæԺࢹЀঞąԐغ҆ҙԺćŔΝ ޲ۤ

Ҽধڙ ॢĶʪͿėԐʪͿİࣀٍĵڙ ٍĵÒь֬ ٍĵڙ

Behavior and pillar stability of enlarged existing parallel tunnels

Myeong-Han Lee

, Bumjoo Kim

*, Yeon-Soo Jang

, Ji-Nam Yun

, Hyun-Gon Park

Danwoo E&C, Geotechnical Department, Engineer

Dongguk University, Department of Civil and Environmental Engineering, Associate Professor

Dongguk University, Department of Civil and Environmental Engineering, Professor

Posco E&C, Civil and Environmental Division, Design Group, Deputy General Manager

Korea Expressway Corporation, Expressway & Transportation Research Institute, Researcher

ABSTRACT: Traffic congestion in existing tunnels has increased due to increased traffic volume and enlarged vehicles.

Keywords: Tunnel enlargement, Parallel tunnels, Pillar stability, Crown settlement, Strength/stress ratio

ߣ΀ ߯Ŗİࣀ͟ۆݒÀٮ޲͟ۆʂ঍জͿۍ३şܕࢢȇقԴԜ֥ۺۍ܁ߕÀьԦʼəąڍÀݒÀॠČەɰۋ͠ॢЛ܃

३ĀۆێঞڷͿşܕࢢȇںঝफॠəąڍə֪ԺࢢȇںæԺॠəąڍٮҼİॠيڌݓϔۓҼڌۆۼÇęٍۙঞąۆী՜ں

߯ՙজ֨࢈սەɰəۤ۾ۋەɰ֬܃Ϳێ҆ęڮͥˣ३ٽقԴəşܕࢢȇںঝफ֨ėॠəԐͻÀψۋ҃ČʼČەɰ

ۋ͠ॢ৔ζقԴĶǴقԴʪॳ঳şܕࢢȇۆঝफ֨ėقʂॢսڅəƴܵ০ݒÀॣìڷͿٚԜʼǣ ইۦūݓəşܕࢢȇۆ

ঝफقěॢ֬ۺęąॹۋψݓ؍؉ۋقěॢşъٍĵÀज़څॢԜডۋ͆Č҇սەɰٍ҆ĵقԴəڮॢڅՙ३Եęşܕۆ

ۋ΁ ąॹ֩ˣںۋڌॠيşܕѿԺࢢȇںঝफॠəąڍঝफѓ֩ęŔق˰δज़͆फѺজÀࢢȇۆäʴęज़͆؋܁Ձق

й࠘əٖॳںथÀॠٕɰܓԐĀę ज़͆फڹʴێॠǣठࠑęتࠑڷͿঝʂॠəąڍۆ޲ۋق˰͆ठࠑঝʂࢢȇۆߎɳࠞॠə

تࠑঝʂࢢȇقҼ३أ_ۆࢀÉں҃ۋəॢठ ߯ՙज़͆फںÍóʼəठࠑঝʂࢢȇقԴջࡾν࣡ڿͳۋ߯ʂε

҃ۋəìڷͿǣࢍǮɰ̚ॢ ÌʪڿͳҼۆąڍܓԐʽȐܛΪۆঝफःࢤقʂॠيϿ˃ۋԜںǣࢍǴؽČ.BUTVEBۆ

ѓѪۋ1FDLۆѓѪقҼ३أ܁ʪÌʪڿͳҼεࡾóԓ܁ॠóʿںঝۍॠٕɰ

ܳڅرࢢȇঝफ ѿԺࢢȇ ज़͆؋܁Ձ ߎɳࠞॠ ÌʪڿͳҼ

$PQZSJHIU ,PSFBO5VOOFMMJOHBOE6OEFSHSPVOE4QBDF"TTPDJBUJPO

Fig. 1. Yielding load acting on the central pillar (Kang, 2008)

ᕽು

ĶǴقԴࢢȇæԺۋ҆üۺڷͿ֨ۚʽݓ40ي țۋݓǦইۦ, ɾ֨֨ėʽࢢȇɳϸڷͿəşॠś սۺڷͿɚرǦİࣀ͟ęʂ঍জʽ޲͟˞ںڙট০

ՙࣀ֨ࢅəʚرͲړںýČەɰ. ̚ॢ, şܕࢢȇۆ

Ȥ঳ͿۍॢŒَ, ɀս, чνইԜˣڷͿࢢȇǴ

؋ۻԐČقʂॢڦॹՁʪ࠶ݓČەɰ. ۋقʂॢ

ʂ޾ڷͿ֪ԺࢢȇںæԺॠäǣşܕʪͿεঝ߿

ॠəˣۆψڹ࣊ۙÀۋΘرݓČەݓχ, ʪ֮ݓ

ǴقԴəҙݓϔۓ, ঞąী՜, ࢢȇ҃սėԐق˰δ

ڍধȤԸԸ܁ԜۆرͲړںýČەر֪Ժࢢȇ

æԺقψڹ܃أۋܕۦॢɰ. ۋ͠ॢЛ܃˞Ϳۍ३

३ٽ࣢০, ێ҆قԴəۋй40ي޲ͻۋԜşܕ

ࢢȇقঝफėԐεݕॱॣսшقػəইۤۋǣࢍ

Ǯڷ϶, ۋεՁėۺڷͿսॱॢԐͻ˞ۋ҃ČʼČ

ەɰ(Seo et al., 2008)(Baek et al., 2007). şܕࢢȇۆ

ঝफقʂॢսڅə۾޲Ȥ঳ࢢȇۆҼܼۋȭ؉ݓ óʾڍνǣ͆قԴʪśü০ݒÀॠóʾìڷͿ

ٚԜʼ϶, Ŕ͠ॢѓѪڷͿԴࢢȇںঝफॠəѓѪ قʂॠيĶǴقԴʪě֮ۋݒʂʼČەɰ.

ĶǴۆ֨ėşցۋ֪ԺࢢȇۆæԺقʂ३Դۋй

Ճćۺۍսܵقۋβͧɰॣݓ͆ʪşܕࢢȇۆঝ फ֨ėқآقەرԴəąॹۆҙۦͿۍ३ψڹ

şցۆьۻۋڅĵʼəԜডۋ϶, ঝफۋज़څॢࢢ ȇۆսڅÀś՚০ݒÀॠóʾìےںČͲ३҇

˺, ĶǴ֬܁قϑəěʹٍĵÀϔڍ֨śॢ֬܁ۋ

͆ॣսەɰ. ۋقByun et al. (2010)ڹս࠘३Եۆ

څՙࡾşۆлÇʪқԵںࣀ३ؒъˣśѻфज़͆

फقʂॢज़͆ۆäʴںêࢹॠٕČ, Choi et al.

(2011) ڹ֨ėܼۍ2޲ͿʪͿࢢȇۆ3޲Ϳঝۤ

ԺćǴڌںۋڌॠيࢢȇঝۤ֨Ը঍ćন, ࢢȇ

ঝۤѓ؋ˣں܃֨ॠٕɰ.

ٍ҆ĵə۾޲ݒÀʾìڷͿٚԜʼəȤ঳জʽ

şܕࢢȇۆঝफقʂॠي, şܕѿԺࢢȇۆɳϸں

Ͽ˃ঝʂ֨ėॠəąڍقʂॠيࢢȇۆäʴę

؋܁ՁۆܼڅॢݓशÀʼəؒъज़͆ۆ؋܁Ձں

ࢢȇঝʂѓѪق˰͆қԵॠٕɰ.

⦥௝ᦩᱶᖒ⠪a

Tunnel design criteria (2007) قۆॠϸ‘ࢢȇں2Ò

ۋԜѿ͵ͿԺ࠘ॣąڍقəۍۿࢢȇقǣԄٖॳ ںй࠘ݓ؍ʪ΀߿қ০ۋü֨ࡈآॢɰ’ ͆Čϼ֨

ʼرەڷ϶, Tunnel design manual (Korea expressway corporation) قə ‘ࢢȇۋüäν Ժ܁֨ PW=1.5D (PW : ज़͆फ, D : ࢢȇफ)εşܵڷͿࢢȇÚĵҙۆ

ݓъНՁ࠘قۆॢս࠘३Եˣۆêࢹε֨ॱॠي, Úĵҙݓ঍ܓæęࢢȇۆĵܓۺ؋܁Ձфą܃Ձ ( ڌݓҼ, ۋüäν߹ՙق˰δÚĵҙ҃ÌėԐҼˣ) êࢹĀęق˰͆ۺ܁ۋüäνÀʼʪ΀ݒ, Çॠي

ۺڌॢɰ’ ͆Čϼ֨ॠيज़͆ۆԜࢗق˰͆ѿԺࢢ ȇÂۺ܁ۋüäνεԓ܁ॠʪ΀ॠٕɰ(Jung et al., 2007). ʴێॢ֮ʪۆѿԺࢢȇقԴࢢȇÂۋüäν Àࢢȇݔąۆ1ѕۋԜێąڍ, Ŕٖॳڹ10% йχ ڷͿ؎Ͳ܋ەڷǣ(Jung et al., 2007) ѿԺࢢȇۆ

ۺ܁ۋüäνεԓ܁ॠşڦ३ԴəইۤيæںČͲ

ॢՃҙۺۍêࢹÀज़څॠɰČ҇սەɰ. Table 1 ڹѿԺࢢȇۋüäνقěॢԺćşܵںڅأॠي

ǣࢍǶìۋɰ.

ज़͆ۆ؋܁ՁथÀεڦॢąॹۺѓѪڷͿə

Peck (1969) ۆѓѪ, Matsuda (1998)ۋەڷ϶, ս࠘

३Եںࣀॢ܁нêࢹѓѪڹज़͆ҙقۚڌॠə

Table 1. Parallel Tunnels separation distance design criteria(Road Design Guideline. 2009)

ଲࡣ෉ ȵ׌࣐ச ȵୋ઴৤ ȵଗ஺ْ ȵࢮ෮յ

ߣ΀ ߯Ŗİࣀ͟ۆݒÀٮ޲͟ۆʂ঍জͿۍ३şܕࢢȇقԴԜ֥ۺۍ܁ߕÀьԦʼəąڍÀݒÀॠČەɰۋ͠ॢЛ܃

߯ՙজ֨࢈սەɰəۤ۾ۋەɰ֬܃Ϳێ҆ęڮͥˣ३ٽقԴəşܕࢢȇںঝफ֨ėॠəԐͻÀψۋ҃ČʼČەɰ

ঝफقěॢ֬ۺęąॹۋψݓ؍؉ۋقěॢşъٍĵÀज़څॢԜডۋ͆Č҇սەɰٍ҆ĵقԴəڮॢڅՙ३Եęşܕۆ

й࠘əٖॳںथÀॠٕɰܓԐĀę ज़͆फڹʴێॠǣठࠑęتࠑڷͿঝʂॠəąڍۆ޲ۋق˰͆ठࠑঝʂࢢȇۆߎɳࠞॠə

تࠑঝʂࢢȇقҼ३أ_ۆࢀÉں҃ۋəॢठ ߯ՙज़͆फںÍóʼəठࠑঝʂࢢȇقԴջࡾν࣡ڿͳۋ߯ʂε

҃ۋəìڷͿǣࢍǮɰ̚ॢ ÌʪڿͳҼۆąڍܓԐʽȐܛΪۆঝफःࢤقʂॠيϿ˃ۋԜںǣࢍǴؽČ.BUTVEBۆ

ѓѪۋ1FDLۆѓѪقҼ३أ܁ʪÌʪڿͳҼεࡾóԓ܁ॠóʿںঝۍॠٕɰ

ܳڅرࢢȇঝफ ѿԺࢢȇ ज़͆؋܁Ձ ߎɳࠞॠ ÌʪڿͳҼ

$PQZSJHIU ,PSFBO5VOOFMMJOHBOE6OEFSHSPVOE4QBDF"TTPDJBUJPO

ᕽು

⦥௝ᦩᱶᖒ⠪a

(1969) Ĺ_¡ _ÞÎâî©ß Ï__ŋîÞÎà ŋß

(if H>D) Ĺ__î©

(if H<D) Ĺ_¡ _î©

: Uniaxial Strength of Rock,

1FDL ႊჶ

˃ࢢȇقەرԴज़͆ۆथŒڿͳ( ¬ _Ǝ ) ڹɰڼ֩

¬ _Ǝ á Ĺ_ ¡_ ÞÎ âî©ß (1)

يşԴ, Ĺ : ɳڦܼ͟(kN/m ³ )

̚ॢ, ज़͆ۆؓ߹Ìʪ( ň _Ǝ ) əɰڼ֩(2)ٮÏۋ

ň Ǝ á Ï _ _ ŋÞÎ à ŋß (2)

Fig. 2. The relation curve according to safety(

يşԴ, C : ۾޳ͳ(kN/m ² ) ŋ : Ǵҙυ޶Á

˰͆Դज़͆ۆߣş२҄قʂॢ؋ۻڱ( _Ƒ ) ڹ֩

_Ƒ á ć ¬ _Ǝ ň _Ǝ

.BUTVEB ႊჶ

ܼؖѹߕقۚڌॠəۚڌڿͳ( ¬ Ǝ á © _Ɛ î© ) ęؒъ