Received March 4, 2013/ revised May 6, 2013/ accepted June 29, 2013
Copyright ⵑ 2013 by the Korean Society of Civil Engineers
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)
ǣǣȀȀǤǤȀͳͲǤͳʹͷʹȀ ǤʹͲͳ͵Ǥ͵͵ǤͷǤͳͻͷ
Ǥ ǤǤ
⮫㬲⛛ⴂ#ⴲⱧ㬚#㔖㘪Ὢ㡶ᴺⴲᢛ#⽾⇖#ⴲⰂ㬖⻏#♮ⷓ⇧≓#⮮ጪ
ࢮ׆ฅ ȵઽ ȵ୨ச ȵକָ
Park, Ki Hwan*, Shin, Young Wan**, Kim, Jung Joo***, Yoo, Han Kyu****
A Study on the Estimation Method of Rock Load Applied to Concrete Lining Using Back Analysis
ABSTRACT
Design criteria for rock load on tunnel concrete lining has not been established yet. Generally rock load on tunnel concrete lining is empirically estimated, which leads to a conservative design. Ordinary estimation method of rock load includes various problems.
Estimating by numerical analysis is very complicated and has not been verified with field measurements. Therefore, it is necessary to conduct a study on practical method of estimating rock load which is more accurate to the real rock load on tunnel concrete lining. This study, presents estimation method of rock load on tunnel concrete lining. Crown settlement of the tunnel construction site has been measured and it was been back analyzed to estimate the rock load. The rock load was estimated to be smaller compare to the ordinary estimation method.
Key words : Rock load, Back analysis, Field measurements, Crown settlement, Concrete lining
Ⅹಾ
░ձ⎹Ⓧญ✙ᯕܾᖅĥᱢᬊࡹ۵ḡၹᯕ᪥⦹ᵲᮡᱶพࡽᖅĥʑᵡᯕᨧ۵ᔢ┽ᯕ݅. ੱ⦽, Ğ⨹ᱢᯙḡၹᯕ᪥⦹ᵲᮥᔑᱶ⦹ᩍᖅĥᨱ
ᱢᬊ⧉ᮝಽ៉݅ᗭᅕᙹᱢᯙᖅĥaᯕᨕḡŁᯩ۵äᮝಽᯝၹᱢᮝಽᯙࡹŁᯩ݅. ʑ᳕᮹ḡၹᯕ᪥⦹ᵲᔑᱶႊჶᮡbb݅᧲⦽ྙᱽᱱ
ᮥԕᰍ⦹ŁᯩŁ, ᙹ⊹⧕ᕾᨱ᮹⦽ḡၹᯕ᪥⦹ᵲᔑᱶႊჶᮡᅖᰂ⦹໑ᝅᱽḡၹᯕ᪥⦹ᵲŝ᮹እƱá᷾ᯕᯕᨕḡḡᦫᮡྙᱽᱱᯕᯩ݅.
ᕽ, ᝅᱽ░ձ⩥ᰆ᮹Ñ࠺ᮥၹᩢ⧁ᙹᯩ۵⧊ญᱢᯙḡၹᯕ᪥⦹ᵲᔑᱶႊჶᨱݡ⦽ᩑǍa⦥⦹݅. ᅙᩑǍᨱᕽ۵░ձŖ⩥ᰆᨱᕽ
⊂ᱶࡽĥ⊂ᯱഭ᮹݉⋉⦹ෝŁಅ⦽ᩎ⧕ᕾᮥ☖⦹ᩍḡၹᯕ᪥⦹ᵲᮥᔑᱶ⦹۵ႊჶᮥᱽᦩ⦹ᩡ݅. ʑ᳕ḡၹᯕ᪥⦹ᵲᔑᱶႊჶᅕ݅݅ᗭ
᯲ᮡḡၹᯕ᪥⦹ᵲᯕᔑᱶࡹᨩ݅.
áᔪᨕ ḡၹᯕ᪥⦹ᵲ, ᩎ⧕ᕾ, ĥ⊂ᯱഭ, ݉⋉⦹, ⎹Ⓧญ✙ᯕܾ
1. ᕽು
NATM ŖჶᨱᕽᙰⓍญ✙᪡ಾᅝ✙॒1₉ḡᅕᰍa░ձ᮹ԕǍᩑ⦽࠺ᦩ∊ᇥ⦽ḡᅕᩎ⧁ᮥ⦽݅໕⎹Ⓧญ✙ᯕܾᨱ۵ḡၹ
ᯕ᪥⦹ᵲᯕ᯲ᬊ⦹ḡᦫᮥᙹᯩ݅. ə్ӹḡၹ᳑Õᯕᇩప⦹ᩍᰆʑᱢᯙᗭᖒᄡ⩶ᯕၽᔾ⦹ÑӹᙰⓍญ✙᮹ᩕ⪵॒1₉ḡᅕᰍa
ḡᅕ܆ಆᮥ ᔢᝅ⧁ Ğᬑ, ੱ۵ ᄡ᭥a ᙹಕࡹḡ ᦫᮡ ᔢ┽ᨱᕽ ⎹Ⓧญ✙ᯕܾᮥ ┡ᖅ⧁ Ğᬑᨱ۵ ḡၹ ᯕ᪥⦹ᵲᮥ Łಅ⧕ ⦽݅.
ࢢȇėॡ
Table 1. Ground Characteristic of Type A at Tunnel
Classification Cohesion(kPa) Internal friction angle( °) Specific weight(kN/m3) Deformation modulus(MPa) Remarks Ground
characteristic 70 29 20 28
width of tunnel: 13.20 m height of tunnel: 9.80 m overburden: 60.00 m Fig. 1. Assumption of Bierb쭢umer’s Rock Load Theory
ḡၹᯕ᪥⦹ᵲ᮹ݡ⢽ᱢᯙᔑᱶႊჶᮝಽBierb쭢umer, Terzaghi᮹
ᯕುŝ Terzaghi᮹ ᦵၹ⦹ᵲᇥඹ⢽, RMR ၰ Qsᮥ ᯕᬊ⦽
Ğ⨹ᯕᯩᮝ໑ᯕෝŁₑ⦽đŝᯕᨱ⪶⦽ᔑᱶႊჶᨱݡ⦽
ȽᯕᯕᨕḡŁᯩḡᦫᦹ݅. ᯕ్⦽ྙᱽ᮹⧕đᮥ᭥⧕ǎԕ᮹
Ğᬑ Chun et al.(2000)ᮡ NATM ░ձ ⎹Ⓧญ✙ᯕܾ ᖅĥ
ᱢᬊࡹ۵ᦵၹᯕ᪥⦹ᵲᔑᱶႊჶᨱݡ⧕Łₑ⦹ᩡᮝ໑, ᩍ్
⩶┽᮹ᦵၹ⦹ᵲŝඹᙹᦶᮥ ᳑⧊⦹ᩍǍ᳑⧕ᕾᮥᝅ⦽⬥
⎹Ⓧญ✙ᯕܾᨱၽᔾ⦹۵᮲ಆ᮹ⓍʑෝእƱ⦹Ł, ᱢᱩ⦽⦹ᵲ
᳑⧊ᮥᱽ⦹ᩡ݅. Seo et al.(2002)ᮡḩప-ᜅ⥥ย༉ߙᮥ☖⦹ᩍ
ḡၹ, 1₉ḡᅕᰍ, ⎹Ⓧญ✙ᯕܾᔢ⪙᯲ᬊ✚ᖒᮥၹᩢ⦽ᙹ⊹⧕
ᕾᮥᙹ⧪⦹ᩍ⎹Ⓧญ✙ᯕܾᨱ ᯲ᬊ⦹۵ḡၹᯕ᪥⦹ᵲᔑᱶ
ၰ ✚ᖒᨱ š⦽ ᩑǍෝ ᙹ⧪⦹ᩡ݅. ੱ⦽ Kim et al.(2012)ᮡ
ḡၹ-ᯕܾᔢ⪙᯲ᬊ༉ߙᮥᯕᬊ⦽ᙹ⊹⧕ᕾ đŝෝḡၹᄡᙹෝ
ᯕᬊ⦽ ݅ᵲ⫭ȡᇥᕾᮥ ☖⦹ᩍ ḡၹ-ᯕܾ ᔢ⪙᯲ᬊ šĥᮥ
ᱽᦩ⦹ᩡ݅.
ə్ӹ░ձǕ₊ᅕvŖჶᮝಽᯙ⦽ḡၹྜྷᖒs᮹ᄡ⪵᪡
༉ुḡၹ᮹ᇩ⪶ᝅᖒᮥŁಅ⦹ḡ༜⦹Ł, ʑ᳕ᔑᱶŝᩑǍॅᮡ
ᝅᱽᱢᯙḡၹᯕ᪥⦹ᵲᯕᦥܭ⇵ᱶ⦽sᯕ۵⦽ĥᱱᯕᯩʑ
ভྙᨱᅙᩑǍᨱᕽ۵ᝅᱽ░ձŖᵲ⊂ᱶ⦽ĥ⊂ᯱഭᵲaᰆ
Ⓧíၽᔾ⦹ᩡŁ░ձÑ࠺ᮥaᰆӹ┡ԕ۵݉⋉⦹ෝᯕᬊ⦹
ᩍ ḡၹ ᯕ᪥⦹ᵲᮥ ᔑᱶ⦹۵ ႊჶᮥ ᱽᦩ⦹ᩡ݅. ๅ}ᄡᙹಽ
Terzaghi ᦵၹ⦹ᵲᇥඹ⢽᮹ ᦵၹᔢ┽ᄥ ⠪Ɂsᮥ ᱢᬊ⦽ ḡၹ
ᯕ᪥⦹ᵲᮥᖁᱶ⦽⬥༊⢽⧉ᙹෝĥ⊂ᄡ᭥ಽᖁᱶ⦹ᩡ݅. ኵ-ᜅ⥥
ย༉ߙᮥᯕᬊ⦽Ǎ᳑⧕ᕾᮥ☖⦹ᩍḡၹᯕ᪥⦹ᵲŁ᪡݉⋉⦹
᮹ᖁ⩶⫭ȡᮥࠥ⇽⦹Ł݉⋉⦹ෝ☖⦹ᩍḡၹᯕ᪥⦹ᵲŁෝ
ᔑᱶ⦹ᩡ݅.
2. ḡၹᯕ᪥⦹ᵲᔑᱶႊჶŁₑ
⎹Ⓧญ✙ᯕܾ᮹ᖅĥᱢᬊ⧁ᙹᯩ۵ݡ⢽ᱢᯙḡၹᯕ᪥⦹ᵲ ᔑᱶႊჶᮡBierb쭢umer ᯕು, Terzaghi ᯕು, Terzaghi᮹ᦵ ၹ⦹ᵲᇥඹ⢽, RMR ၰQsᮥᯕᬊ⦽Ğ⨹ŝḡၹ-ᯕܾᔢ⪙
᯲ᬊ(GLI) ༉ߙšĥ॒ๅᬑ݅᧲⦹݅. ᅙᱩᨱᕽ۵Table 1ŝ
zᮡḡၹ✚ᖒ⊹ෝᱢᬊ⦹ᩍbb᮹ႊჶᨱݡ⦹ᩍ☁⦝ŁෝŁಅ
⦹۵ŝ☁⦝ŁෝŁಅ⦹ḡᦫ۵ᮝಽӹ٥ᨕႊჶᄥ✚Ḷᮥ
ᇥᕾ⦹ᩡ݅.
2.1 ഠճࠜճߙۀਐ 2.1.1 Bierb쭢umer ଲߨਐ
Bierb 쭢umer۵Fig. 1ŝzᯕḡၹᯕ᪥⦹ᵲ᮹ᩢᩎᯕ⡍ྜྷᖁ
⩶┽ಽ ၽᔾ⦹۵ äᮝಽ Eq. (1)ᮥ ᱽᦩ⦹ᩡ݅.
©
ƐƍƍƄá ķ Z ¡Z Ĺ (1)
☁⦝Ła ᯲ᮥ Ğᬑ : ķ = 1 (2)
¡ = Ò é ķ á Î à ć ƀâÏƋ Z ÞÑÒ à ćÏ ŋ ß
ŋ Z
ÏÞÑÒ à ćÏ ŋ ßZ¡
(3)
¡ð Ò é ķ á
ÑÞÑÒ à ćÏ ŋ ß (4)
ᩍʑᕽ, á ÏãćÏ ƀ âƋ_ÞÑÒà ć Ï ŋ ßä (5)
©
ƐƍƍƄ: ḡၹ ᯕ᪥⦹ᵲ : ᯕ᪥ᩢᩎ ⡎ ķ : qᗭĥᙹ ŋ : ԕᇡษₑb
¡ : ☁⦝Ł Ƌ : ░ձ᮹ ׳ᯕ
Ĺ : ᦵၹ᮹ ݉᭥ᵲప ƀ : ░ձ᮹ ⡎
Fig. 2. Relationship Between Rock Load and Overburden by Bierbäumer’s Rock Load Theory
Fig. 3. Assumption of Terzaghi’s Rock Load Theory(1946)
(a) Relationship Between Rock Load and Overburden (
ŋ
=29°, K=1)(b) Relationship Between Rock Load and In-Situ Stress Ratio (H=60 m,
ŋ
=29°, C=70 kPa)Fig. 4. Rock Load of Terzaghi’s Theory
☁⦝ŁᨱෙBierb쭢umer ᯕು᮹ḡၹᯕ᪥⦹ᵲᔑᱶđŝ۵
Fig. 2 ᪡ zᮡ đŝෝ ᅕᩡ݅. Bierb쭢umer ᯕು᮹ ☁⦝Ła
᷾a⧉ᨱḡၹᯕ᪥⦹ᵲᮡ᷾a⦹݅aᯕ᪥ᩢᩎ᮹⡎(B)ᨱ
᧞2.7႑aࡹ۵☁⦝Ł68mᨱᕽ↽ݡs641 kN/m²ᮥᅕᯙ⬥
݅qᗭ⦹۵Ğ⨆ᮥᅕᩡᮝ໑, Bierb쭢umer ᯕು᮹ḡၹᯕ᪥⦹
ᵲ ᔑᱶᨱ ᯩᨕ ᵝᯙᯱ۵ ☁⦝Łᯥᮥ ᙹ ᯩᨩ݅.
2.1.2 Terzaghi ଲߨਐ
Terzaghi(1946)۵እᱱ₊ᖒ᮹Õ᳑⦽᳑พ☁ᨱݡ⧕ᕽFig. 3 ŝzᮡ⩶┽᮹❭ƕ໕ᨱݡ⦹ᩍEq. (6)ᮥᱽᦩ⦹ᩡŁ, ↽ɝḡၹ᮹
ᦥ⋎⬉ŝෝŁಅ⦹ᩍᱱ₊ಆ✚ᖒᮥၹᩢ⦽Eq. (7)ᮥᯕᬊ⦹ᩍ
ḡၹ ᯕ᪥⦹ᵲ ᔑᱶ ၰ ᖅĥᨱ ၹᩢ⦹ᩡ݅(Kim et al, 2010).
ᱱ₊ಆ ၙŁಅ : ©
ƐƍƍƄá ć Ϥŋ Ĺ ÞÎàƃ
à¤ŋćÏ¡ß (6)
ᱱ₊ಆ Łಅ : ©
ƐƍƍƄá ć Ĺ à Ï ÞÎàƃ Ϥŋ
à¤ŋćÏ¡ß (7)
ᩍʑᕽ, á ÏãćÏ ƀ âƋ_ÞÑÒà ć Ï ŋ ßä (8)
©
ƐƍƍƄ: ḡၹ ᯕ᪥⦹ᵲ : ᯕ᪥ᩢᩎ ⡎
¡ : ☁⦝Ł Ĺ : ☁ḩ᮹݉᭥ᵲప ŋ : ԕᇡษₑb ¤ : ⊂ᦶĥᙹ Ƌ : ░ձ᮹ ׳ᯕ ƀ : ░ձ᮹ ⡎
: ᱱ₊ಆ
Terzaghi ᯕುᮥᯕᬊ⦹ᩍḡၹᯕ᪥⦹ᵲᔑᱶᱱ₊ಆᮥ
Łಅ⦹۵Ğᬑ᪡Łಅ⦹ḡᦫ۵Ğᬑ᮹✚ᖒᮥእƱá☁⦹ᩡ݅.
Fig. 4(a)ᨱᕽ᪡zᯕԕᇡษₑbᯕᯝᱶ⦽Ğᬑ☁⦝Ła᷾a⧉ᨱ
ḡၹᯕ᪥⦹ᵲᯕ᷾a⦹ḡอ᷾aᮉᯕᱱ₉qᗭ⦹໕ᕽᯝᱶ
(a) Relationship between Rock Load and Overburden
(b) Relationship between Rock Load and Deformation Modulus Fig. 5. Rock Load of GLI Model
⦽sᨱᙹಕ⦹۵Ğ⨆ᮥӹ┡ԕ໑, ᱱ₊ಆᮥŁಅ⦽Ğᬑ᪡Łಅ⦹
ḡᦫ۵Ğᬑ᮹ḡၹᯕ᪥⦹ᵲ᮹₉ᯕ۵↽ݡ᧞76.8 kN/m²᮹
₉ᯕෝᅕᯕŁᯩ݅. ੱ⦽Fig. 4(b)ᨱᕽ᪡zᯕ⊂ᦶĥᙹᨱෙ
ḡၹᯕ᪥⦹ᵲ᮹s᮹ᄡ⪵۵222~1052 kN/m²ಽⓑ₉ᯕෝӹ┡
ԕŁᯩ݅. ᯕౝTerzaghi ᯕು᮹ᵝᯙᯱ۵☁⦝Ł᪡⊂ᦶĥ ᙹ əญŁ ᱱ₊ಆᯥᮥ ᙹ ᯩ݅.
2.1.3 ࢱ-ޭଲەঃୁ(GLI) ࡦ܄ւծਐ
ḡၹ-ᯕܾᔢ⪙᯲ᬊ༉ߙᮥᯕᬊ⦽ᙹ⊹⧕ᕾႊჶᮡʑ᳕᮹
░ձᙹ⊹⧕ᕾᯕǕ₊ŝḡᅕᖅ⊹ŝᱶᮝಽ⦽ᱶࡽäᮥ⎹Ⓧญ✙
ᯕܾ Ŗŝᱶʭḡ ⪶ᰆ⦽ }ֱᮝಽᕽ 1₉ ḡᅕᰍ᮹ ᩕ⪵ᨱ
᮹⧕ḡၹŝḡᅕᰍ᮹⠪⩶ᔢ┽aˉᨕḱᮝಽᇩ⠪⩶ಆᯕၽᔾ⦹
ᩍ2₉⠪⩶ᔢ┽ᨱࠥݍ⧁ভʭḡ⎹Ⓧญ✙ᯕܾᨱ⦹ᵲᯕ᯲ᬊ⦹
íࡽ݅۵}ֱᯕ݅. ݅᧲⦽ḡၹ᳑Õ, ḡ⊖ၰḡᅕᰍ᮹✚ᖒᮥ
ၹᩢ⦹ᩡʑভྙᨱʑ᳕᮹ʼn᳑༉ߙ⧕ᕾᅕ݅ḡၹŖ⦺ᱢ✚ᖒᮥ
Łಅ⦹ᩍ ḡၹ ᯕ᪥⦹ᵲᮥ ᱶపᱢᮝಽ ᔑᱶ⧁ ᙹ ᯩ۵ ᰆᱱᯕ
ᯩᮝӹ, Ǎ᳑ĥᔑჶ᮹ᅖᰂᖒ॒ᮝಽᯙ⦹ᩍ⩥ᝅᱢᮝಽḢᱲᱢᬊ
⦹ʑᨱ۵݅ᗭྙᱽᱱᯕʑࢁa܆ᖒࠥ႑ᱽ⧁ᙹᨧ݅. ᕽ, ᯝၹ℁ࠥ᪡Łᗮ℁ࠥ݉໕ᨱݡ⦹ᩍʑ᳕ᖅĥᔍಡᇥᕾᮥ☖⦽
ᦵၹ॒ɪᄥݡ⢽ྜྷᖒ⊹, ☁⦝Ł(20m, 30m, 60m, 80m)ෝๅ}ᄡ ᙹಽᙹ⊹⧕ᕾᱢᯙႊჶᮥᔍᬊ⦹ᩍḡၹᯕ᪥⦹ᵲⓍʑෝᔑᱶ⦹
ᩡᮝ໑, đŝsᨱݡ⦽݅ᵲ⫭ȡᇥᕾᮥ☖⦹ᩍEq. (9)ෝᱽᦩ⦹ᩡ
݅(Kim at el, 2012).
© á ãć Ĺ_ Þ â¡ß à ä_ƃ Ôŋ
à ćÎ×××ÞĹ_ß(9) ᩍʑᕽ, á Ï ƙ
Ɯ ƚ ć
Ï ƀ âƆ_ÞÑÒà ć Ï ŋ ßƛ Ɲ ƞ (10)
©
ƐƍƍƄ: ḡၹ ᯕ᪥⦹ᵲ Ɔ : ░ձ׳ᯕ ƀ : ░ձ᮹ ⡎ Ĺ : ḡၹ᮹݉᭥ᵲప
: ᄡ⩶ĥᙹ ŋ : ԕᇡษₑb
: ᱱ₊ಆ ¡ : ☁⦝Ł (݉, ¡ ð Õ×Ƌ ᯙ Ğᬑ, ¡ á Õ×Ƌ ෝ ᱢᬊ)
ḡၹ-ᯕܾᔢ⪙᯲ᬊ(GLI) ༉ߙšĥᮡFig. 5(a)ᨱᕽ᪡zᯕ
ԕᇡษₑbᯕᯝᱶ⦽Ğᬑ☁⦝Ł᮹᷾aᨱḡၹᯕ᪥⦹ᵲᮡ
ᖁ⩶ᱢᮝಽ᷾a⦹۵äᮥᙹᯩᮝ໑(80mᯕᔢ᮹☁⦝Łᨱᕽ۵
ḡၹᯕ᪥⦹ᵲᮥᱽ⦽) Fig. 5(b)ᨱᕽ᪡zᯕḡၹᯕ᪥⦹ᵲŝᄡ⩶
ĥᙹ᪡᮹šĥෝᇥᕾ⦽đŝᄡ⩶ĥᙹsᯕ3,700MPa ᯕᔢ᮹
Ğᬑ0ᮝಽᙹಕ⦽݅۵ äᮥᙹᯩᨩ݅. ᯕಽ៉ḡၹ-ᯕܾ
ᔢ⪙᯲ᬊ(GLI) ༉ߙšĥᮡ☁⦝Ł80mᯕᔢᨱᕽ᮹ḡၹᯕ᪥⦹
ᵲᮥᯥ᮹ಽᱽ⦽⦹ᩍŖ⦺ᱢᯙɝÑa݅ᗭᇡ᳒⦽ྙᱽᱱᯕᯩ݅.
2.2 ഠճࠜճߙੴۀਐ 2.2.1 Terzaghiଭࢱணंࠑඝ
ᙹᱶࡽTerzaghi ᦵၹ⦹ᵲᇥඹ⢽۵Table 2᪡zᯕᦵၹᔢ┽ᨱ
9݉ĥಽǍᇥ⦹ᩡᮝ໑, ᱢᬊࡽ░ձ݉໕⩶ᔢࠥษᱽ⩶ᮝಽ
aᱶ⦹ᩡ݅.
ᦵၹᔢ┽ᨱෙḡၹᯕ᪥⦹ᵲ׳ᯕෝᔑᱶ⧉ᨱᯩᨕ⦹ᵲĥᙹ
ᱢᬊʑᚁᯱ᮹Ğ⨹ᱢ❱݉ᯕǍࡹအಽʑᚁᯱษ݅⠙₉a
ᯩᮥäᮝಽ❱݉ࡹ໑, }ťᱢᯕᨕᕽᦵḩ᮹~šᱢᯙ⠪aaŅ
⧁äᮝಽ❱݉ࡽ݅. Fig. 6ᮡType A᮹░ձ⡎ŝ׳ᯕෝ☖⦹ᩍ
ᦵၹ ᔢ┽ᄥ ḡၹ ᯕ᪥⦹ᵲᮥ ᔑᱶ⦽ sᮥ ӹ┡ԕᨩᮝ໑, ḡၹ
ᯕ᪥⦹ᵲᮡ ↽ᗭ 26 kN/m²ᨱᕽ ↽ݡ 1104 kN/m²ʭḡ ₉ᯕෝ
ᅕᯕŁ ᯩ݅.
2.2.2 RMR ࢱंࠑଭࢺ࣑
Unal(1983) ŝ ᯙࠥ᮹ Venkateswarlu(1986)۵ Bieniawski
Table 2. Modified Rock Load Classification Table of Terzaghi(Deere et al. 1970 : Rose, 1982)
Rock condition RQD Rock load height Hp(m) Remarks
1. Hard and intact 95100 0 Light lining required only if spalling or popping
occurs
2. Hard stratified or schistose 9099 00.5B
Light support, mainly for protection against spalls
Load may change erratically from point to point
3. Massive, moderately jointed 8595 00.25B -
4. Moderately blocky and seamy 7585 0.25B0.20(B+Ht) Types 4, 5, and 6 reduced by about 50% from Terzaghi value because water table has little effect on rock load(Terzaghi, 1946: Brekke 1968)
5. Very blocky and seamy 3075 (0.200.60)(B+Ht) 6. completely crushed but chemically intact 330 (0.601.10)(B+Ht)
6a. Sand and gravel 03 (1.101.40)(B+Ht)
7. Squeezing rock, moderate depth NA (1.102.10)(B+Ht) Heavy side pressure invert struts required Circular ribs are recommended
8. Squeezing rock, great depth NA (2.104.50)(B+Ht) -
9. Swelling rock NA Up to 250ft irrespective of value of (B+Ht)
Circular ribs required
In extreme cases, use yielding support
Fig. 6. Comparison of Rock Load by Terzaghi’s Rock Load Classification Table
Fig. 7. Rock Load Change by RMR(Unal and Venkateswarlu)
(1973)ᨱ ᮹⧕ᱽᦩࡽRMRᮥᯕᬊ⦹ᩍḡၹᯕ᪥⦹ᵲ( ©
ƐƍƍƄ)ᮥ
ᔑᱶ⦹۵ Ğ⨹ (11)ŝ (12)ෝ ᱽᦩ⦹ᩡ݅.
Unal ᮹ ႊჶ
©
ƐƍƍƄá ć Î×× à « Ĺƀ Î×× (11)
Venkateswarlu᮹ ႊჶ
©
ƐƍƍƄá ƀZ ĹZ ÞÎíÔ à×í×ÐÔ« â×í×××Ï«
ÏßÞZ Î×
Ϧ©ſß (12)
ᩍʑᕽ, ©
ƐƍƍƄ: ḡၹ ᯕ᪥⦹ᵲ
Ĺ : ḡၹ᮹ ݉᭥ᵲప ƀ : ░ձ᮹ ⡎
Fig. 7 ŝ zᯕ Unal(1983)ᯕ ᱽᦩ⦽ Ğ⨹ᮥ ᯕᬊ⦽ ḡၹ
ᯕ᪥⦹ᵲᔑᱶđŝRMRᯕ᷾a⧁ᙹಾḡၹᯕ᪥⦹ᵲᯕᖁ⩶ᱢᮝ ಽqᗭ⦹íࡹ໑RMRᯕ100ᯕࢁĞᬑᨱ۵ḡၹᯕ᪥⦹ᵲ᮹
Ⓧʑ۵ 0ᯕ ࡽ݅.
Venkateswarlu(1986) ᯕᱽᦩ⦽Ğ⨹᮹ĞᬑRMRŝḡၹ
ᯕ᪥⦹ᵲᔍᯕ᮹šĥ۵2₉⧉ᙹ᮹šĥෝᅕᯕ໑RMRᯕ⍅ḩᙹ
ಾḡၹᯕ᪥⦹ᵲᮡqᗭ⦹íࡹ໑RMRᯕ85ᯕᔢᯕ໕ᮭ᮹sᮥ
wí ࢉᮥ ᙹ ᯩ݅.
Table 3. Conversion of Q Value
Q range Q'
10 < A 5Q
0.1 GQ G10 2.5Q
Q < 0.1 Q
Fig. 8. Conceptual Displacement Diagram for Tunnel Excavation
2.2.3 Q-systemଭࢺ࣑
Grimstad ᪡Barton(1993)ᮡᱩญǑᙹ3ᮥĞĥಽQsᨱ᮹⦽
ḡၹᯕ᪥⦹ᵲᮥᔑᱶ⦹۵Ğ⨹(13)ŝ(14)ෝᱽᦩ⦹ᩡ݅. ੱ⦽
ᙹ⠪ᦵၹ⦹ᵲ( ©
ƕſƊƊ) ᮡTable 3ŝzᯕQෝᅕ݅᧲⪙⦽sᯙ
Q'ᮝಽ⪹ᔑ⦽⬥ᱩญǑᙹᨱෙᩑḢᦵၹ⦹ᵲ( ©
ƐƍƍƄ) ŝ࠺ᯝ⦽
ᮝಽ ĥᔑ⦹ᩡ݅.
ᱩญǑᙹ ⴍ 3 :
©
ƐƍƍƄá ãć Ïí× äª £
Ɛ à ćÐÎÞZ Î×
ÏƉ©ſß (13)
ᱩญǑᙹ < 3 :
©
ƐƍƍƄá ć Ðí×£
ƐÏí×£
ƌćÏΪ
à ćÐÎ
ÞZ Î×
ÏƉ©ſß (14)
3. ᩎ⧕ᕾᮥᯕᬊ⦽ḡၹᯕ᪥⦹ᵲᔑᱶႊჶᱽᦩ
3.1 લැজԹ૬ࢫࢺ࣑
ᯝၹᱢᮝಽᩎ⧕ᕾྙᱽ۵ᩎᔑჶ(inverse method)ŝḢᱲჶ (direct method) ᮹2aḡႊჶᯕᔍᬊࡹŁᯩᮝӹ, ᅙᩑǍᨱᕽ۵
ḡၹ᮹ ┥ᗭᖒ Ñ࠺ᮥ ᅕ݅ ᱶ⪶⯩ ၹᩢ⦹ʑ ᭥⧕ᕽ Ḣᱲჶᮥ
ᔍᬊ⦹ᩡ݅. Ḣᱲჶᮡĥ⊂đŝ᪡⧕ᕾđŝෝእƱ⦹ᩍə₉ᯕa
↽ᗭa ࢁভʭḡ ᙹ⊹⧕ᕾ ŝᱶ᮹ၹᅖ ᩑᔑᮥ ☖⦹ᩍᩎ⧕ᕾ
ݡᔢᯙၙḡᄡᙹෝᙹᱶ⦹۵ႊჶᯕ݅. Ḣᱲჶᮡၙḡᄡᙹ᮹ᙹᱶ ŝ əᨱ ෙ ၹᅖĥᔑŝᱶᯕ ᨧ۵ ᩎᔑჶᨱ እ⧕ ĥᔑeᯕ
᪅௹Ùญӹ, እᖁ⩶ྙᱽ॒݅᧲⦽ྙᱽᨱᱢᬊ⧁ᙹᯩ݅۵ᰆᱱᮥ
ḡܩŁᯩ݅. Ḣᱲჶᮥᯕᬊ⦹ᩍᙹ⧪a܆⦽ᩎ⧕ᕾႊჶᮝಽ۵
ⓍíḡၹŖ⦺ᱢႊჶŝǍ᳑⧕ᕾᱢႊჶᮝಽݡᄥࡹŁᯝၹᱢᮝ ಽḡၹŖ⦺ᱢႊჶᮡḡၹÑ࠺ᵲᝍ᮹ᇥᕾᮥ⦹íࡹŁ, Ǎ᳑
⧕ᕾᱢႊჶᮡǍ᳑ྜྷÑ࠺ᵲᝍ᮹ᇥᕾᮥᙹ⧪⦹íࡽ݅. ᕽ
ᅙ ᩑǍᨱᕽ۵ Ǎ᳑ྜྷ Ñ࠺ ᵲᝍ᮹ ᇥᕾᨱ ᮁญ⦽ Ǎ᳑⧕ᕾᱢ
ႊჶᮥᯕᬊ⦹ᩡᮝ໑ĥ⊂ᄡ᭥ෝ༊⢽⧉ᙹಽᖅᱶ⦽⬥⧪₊᪅ ჶᮥ ᱢᬊ⦽ Ḣᱲჶᮥ ᯕᬊ⦹ᩡ݅.
3.2 ծ౸ୀ߹ंজଡധࡧඝէ୨ࢺ࣑
3.2.1 ࠻Թ࣡է୨
░ձĥ⊂ᯱഭᵲ༊ᱢ⧉ᙹಽđᱶࡽ⧎༊ᨱݡ⦹ᩍᩎ⧕ᕾᮥ
ᙹ⧪⧁ভ, ᩎ⧕ᕾđŝa༊ᱢ⧉ᙹᨱࠥݍ⦹ࠥಾ⦹۵⧕ᕾ᯦ಆs
ᮥๅ}ᄡᙹŁ⦽݅. ᯝၹᱢᮝಽ, ᩎ⧕ᕾđŝᨱᩢ⨆ᮥၙ⊹۵
ᩢ⨆ᯙᯱಽ۵ʑ⦹⦺ᱢᗭ, ŖᗭၰḡၹᗭಽǍᇥࡹ໑, ᯕᵲ༊ᱢ⧉ᙹᨱࠥݍࡹʑ᭥⦽ᵝᩢ⨆ᯙᯱෝᖁᄥ⦹ᩍᩎ⧕ᕾ
ᮥᙹ⧪⦹íࡽ݅. ᅙᩑǍᨱᕽ۵Terzaghi ᦵၹ⦹ᵲᇥඹ⢽ᨱ᮹⦽
ḡၹ ᯕ᪥⦹ᵲᮥ ๅ}ᄡᙹಽ đᱶ⦹ᩡ݅.
3.2.2 ࡧୡॺ୨
༊ᱢ⧉ᙹᩎ⧕ᕾᮥ☖⧕░ձᵝᄡḡၹ᮹✚ᖒsᮥᰍᔑᱶ⦹
ʑ᭥⦹ᩍእƱ, á☁ࡹ۵ʑᵡᮝಽ░ձŖᵲĥ⊂ᨱ᮹⦹ᩍ
íࡽ݅. ᯝၹᱢᮝಽ, ░ձŖᵲĥ⊂ᮡ݉⋉⦹, ԕŖᄡ᭥
ၰḡᅕᰍ᮹᮲ಆ॒ᮥḡᗮᱢᮝಽ⊂ᱶ⦹۵ߑ, ░ձᵝᄡḡၹ᮹
እɁḩᖒ, እ॒ႊᖒ, ᇩᩑᗮᖒၰǕ₊ᮝಽᯙ⦽░ձᵝᄡḡၹ
ᯕ᪥॒ᨱ᮹⦹ᩍ, ░ձᄡ᭥᪡ḡᅕᰍ᮲ಆ᮹ᔢšᖒᯕŁಅࡽ
༊ᱢ⧉ᙹđᱶᮡๅᬑᨕಅᬡᯕᯩ݅. ᕽ, ᅙᩑǍᨱᕽ۵⦹ᵲ⩶
┽ෝ░ձ⩶ᔢᨱKG= 1.0(॒ᇥ⡍)ಽ᯲ᬊ⦽݅Łaᱶ⦹ᩡᮝ໑
Ǎ᳑⧕ᕾđŝ݉ᇡᨱᕽaᰆⓑᄡ᭥aၽᔾ⦹Ł░ձÑ࠺ᮥ
aᰆ ӹ┡ԕᨕ ༊ᱢ⧉ᙹಽ ᱶ⦹ᩡ݅.
ᩎ⧕ᕾ᮹↽᳦༊⢽ĥ⊂sᮡEq. (15)᪡zᯕĥ⊂ʑᖅ⊹
⬥ᝅᱽಽĥ⊂ࡽĥ⊂ᄡ᭥᪡ᖁ⧪ᄡ᭥ၰၙĥ⊂ᄡ᭥᮹⧊ᮝಽ
đᱶࡽ݅. ᖁ⧪ᄡ᭥۵Ǖ₊สᰆ໕ᱥႊᨱᕽᯕၙၽᔾ⦽ᄡ᭥ಽᕽ Ŗeᱢ₉ᯕᨱ᮹⦹ᩍၽᔾ⦹۵ĥ⊂ᯕᇩa܆⦽ᄡ᭥ᯕအಽᯝၹ ᱢᮝಽᩩ⊂sᮥᱢᬊ⦽݅. ၙĥ⊂ᄡ᭥ੱ⦽Ǖ₊⬥ĥ⊂ʑᖅ⊹
ᱥʭḡၽᔾ⦽ᄡ᭥ಽᕽeᱢ₉ᯕᨱ᮹⦹ᩍၽᔾ⦹۵ĥ⊂ᯕ
ᇩa܆⦽ ᄡ᭥ᯕအಽ ᯝၹᱢᮝಽ ᩩ⊂sᮥ ᱢᬊ⦽݅. Fig. 8ᮡ
░ձǕḥᨱ ෙ ᄡ᭥ }ֱࠥᯕ݅.
®
á ®
Ƌâ
ƍâ®
ſ(15)
ᩍʑᕽ, ®
: ↽᳦ ᄡ᭥ప
®
Ƌ: ĥ⊂ᄡ᭥
Fig. 9. Flow Chart of Back Analysis Computing Rock Load
ƍ: ၙĥ⊂ᄡ᭥
®
ſ: ᖁ⧪ᄡ᭥
ᖁ⧪ᄡ᭥( ®
ſ)۵ᯝၹᱢᮝಽᔢၹǕ₊⬥ᯕᔢᄡ᭥aၽᔾ⦹ʑ
ᯕᱥᨱ ၽᔾ⦽ ↽ݡᄡ᭥᮹ ᧞ 30%ಽ ᱢᬊ⦹ᩡᮝ໑(Carranza- Torres C., Fairhurst C., 2000), ၙĥ⊂ᄡ᭥(
ƍ)۵ĥ⊂⩥ᰆᯕ
ၽ❭Ǖ₊ᮥ⧪⦹ḡᦫŁʑĥǕ₊ᮥ⧪⦹ᩡᮝအಽĥ⊂ʑa
᳑ʑᨱᖅ⊹ࡹᨩ݅Łaᱶ⦹Łๅᬑၙᗭ⦽äᮝಽ❱݉⦹ᩍᔾఖ
⦹ᩡ݅.
3.3 લැজଡଲࢱଲணॺ୨ෘܑࠝ
ᅙᩑǍᨱᕽ۵Terzaghi᮹ᦵၹ⦹ᵲᇥඹ⢽ᨱ᮹⦽ḡၹᯕ᪥⦹
ᵲᮥๅ}ᄡᙹಽđᱶ⦹Łĥ⊂ᄡ᭥ෝ༊ᱢ⧉ᙹಽđᱶ⦽⬥Ǎ᳑
⧕ᕾᮥ☖⧕ၽᔾ⦽݉⋉⦹ෝᯕᬊ⦹ᩍ░ձǕ₊ၽᔾ⦹۵
ḡၹ ᯕ᪥⦹ᵲᮥ Fig. 9᪡ zᮡ ⮱ࠥಽ ᔑᱶ⦹ᩡ݅. ᷪ, 1₉
ḡᅕᰍ᮹ʑ⦹⦺ᱢ᳑Õŝᩎ⧕ᕾݡᔢᮥᱽ⦽ӹນḡᄡᙹෝ
ᯕၙ Ł ᯩ۵ sᮝಽ ᯦ಆ⦹໑ ḡၹ ᯕ᪥⦹ᵲᮡ Terzaghi᮹
ᦵၹ⦹ᵲᇥඹ⢽᮹ᦵၹᔢ┽ᄥ⦹ᵲĥᙹ᮹⠪Ɂsᮥ☖⦹ᩍᮡ
⦹ᵲᮥ Ⅹʑ sᮝಽ ᯦ಆ⦽݅. ᱶ⧕ᕾᨱ ⦥⦽ ༉ु ᄡᙹॅ᮹
᯦ಆᯕ᪥ഭࡹ໕Ǎ᳑⧕ᕾᮥᙹ⧪⦹ᩍ݉⋉⦹ෝǍ⦽݅. ᱶ⧕ᕾ
ᙹ⧪⬥ḡၹᯕ᪥⦹ᵲ᮹ၹᅖᱢᯙᄡ⪵ෝ☖⦹ᩍḡၹᯕ᪥⦹ᵲŁ
᪡݉⋉⦹e᮹⫭ȡᇥᕾᮥ ᝅ⦹ᩍᖁ⩶⫭ȡᮥࠥ⇽⦽⬥
ᝅᱽ ĥ⊂ᄡ᭥ෝ ݡ᯦⦹ᩍ ḡၹ ᯕ᪥⦹ᵲŁෝ ᔑᱶ⦽݅.
4. ⷃⷃ⩥ᰆĥ⊂ᯱഭᇥᕾ
░ձ Ŗ ᨱ۵ Ǖ₊ᨱ ᮹⧕ ᵝᄡḡၹᨱ ၽᔾ⦹۵ ᮲ಆŝ
ḡၹvࠥ᪡᮹ݡᗭšĥᨱ⧎ᔢᮁ᮹⦹Łḡၹᯱℕaw۵ԕ⦹܆
ಆ, ᷪḡᅕ܆ಆᮥᱢɚᱢᮝಽ⪽ᬊ⦹ᩍ⦽݅. ə్ӹ░ձᯕ
ᖁ⩶Ǎ᳑ྜྷᯕ۵✚ᙹᖒভྙᨱᔍᱥ ḡၹ᳑ᔍಽᇡ░❭ᦦࡽ
ᱶᅕ۵ᱽ⦽ᱢᮝಽᯕᬊࡹ໑, ၽᔾ᮲ಆᯕӹḡၹvࠥ۵Ǖ₊Ŗჶ ŝḡᅕ᮹Ŗႊჶᨱ᮹⧕ᕽࠥᄡ⦹အಽᔍᱥᨱ░ձၰḡၹÑ࠺
✚ᖒᮥ⪶⦹í❭ᦦ, ᩩ⊂⦽݅۵äᮡÑ᮹ᇩa܆⦹݅. ᕽ
Ŗb᳦ĥ⊂ᮥᝅ⦹Łĥ⊂đŝෝ᳦⧊ᱢᮝಽᇥᕾ, ⠪a⦹
ᩍᖅĥ, Ŗᨱၹᩢ⧕ӹa۵ᯝᮡŖᔍ᮹ᦩᱥᖒŝǍℕᱢᯙ
ĥ⊂ᯱഭ᮹⪶ᅕ₉ᬱᨱᕽๅᬑᵲ⦹݅. ݅ั⧕░ձᖅĥ݉ĥ ۵᳑ᔍ݉ĥᨱᕽĥ⫮ࡽᔍᱥᖅĥ}ֱᯕအಽ░ձǕḥḡၹÑ
࠺ᮥ ⊂ᱶ⦹Ł ə đŝෝ ᖅĥ᮹ ᩩ⊂ŝ እƱ⧉ᮝಽ៉ ݚⅩ
ᖅĥ᮹┡ݚᖒၰŖჶ᮹ᱢᇡෝá☁⦹ᩍ⦽݅. ᯕ్⦽ŝᱶᮡ
Ğᱽᱢᯕ໑, ᦩᱥ⦹íÕᖅ⧁ᙹᯩí⦹۵ᙹ݉ᯝᐱอᦥܩ
⨆⬥᮹ᖅĥၰŖᮥ᭥⦽ᵲ⦽ᯱഭෝᱽŖ⦹ʑভྙᨱ░ձŖ ᔍᨱ ᯩᨕᕽ ĥ⊂᮹ ᵲᖒᮥ ∊ᇥ⯩ ᯙ⦹ᩍ ⦽݅.
4.1 ùù෮ୋ෴ࢫாন
⧕ݚḡᩎᮡĞᔢᇥḡԉ࠺ᇡᨱ᭥⊹⦹໑, ⮲ᔪᗑᯝಽǍᖒࡽ
⦹᧲⊖ǑᯕᵝෝᯕŁᯕෝᇩǎᔍ⪵vᦵඹaš᯦⦽⬥ᝁᔾݡ
ᱽ3ʑᩎᦵ⊖ᯕᇡᱶ⧊ᮝಽᯱญ⦹Łᯩᨕ݉⊖ᯕၽݍࡹᨕᯩ݅.
ᅙ⩥ᰆ᮹ⷂⷂ░ձᮡⅾᩑᰆᯕ4.35kmᨱᯕ۵ᰆݡ░ձಽᕽ
Ǖ₊Ǎe᮹ᔢݚᇡᇥᯕ⣮⪵☁⊖, ᩎᦵ⊖, ᗑᯝ⊖ᮝಽᯕᨕᲙ
ᯩᨕ░ձ᮹ᄡ⩶, ӺၹᔍŁၰŝ݅⦽ᩍǕᯕၽᔾ⧁ᬑಅaᯩ݅.
əญŁ݉⊖❭ᘥݡaᝍ⦽ᇩǎᔍ݉⊖ݡෝ☖ŝ⦹ᩍ░ձԕಽ
ฯᮡ ᧲᮹ ḡ⦹ᙹa ᮁ᯦ࡹŁ ᯩ݅.
4.2 ഉٮۚࢫඝஜ࣪൪ഋ
Type A ᪡E-Type B Ǎe᮹⢽ᵡḡᅕ➉▕ŝǕḥᰆ1.0m, H-200᮹ ݉ᯝḡᅕ ➉▕ᮥ Table 4᪡zᯕ ᱢᬊ⦹ᩡ݅.
4.3 ծ౸ୀ߹ंজ
⢽ᵡḡᅕ➉▕ᄥಽ ↽ݡᄡ᭥a ၽᔾ⦽ ᭥⊹᮹ ĥ⊂ Ğᄡ⪵
ᇥᕾ đŝ Type A᪡ E-Type B۵ Fig. 10(a)᪡ Fig. 10(b)᪡
zᮝ໑ ↽᳦ᱢᯙ ݉⋉⦹ෝ ↽᳦ᄡ᭥ಽ ᖁᱶ⦹ᩡ݅.
Type A᮹ĥ⊂ᯱഭෝᇥᕾ⦽đŝĥ⊂ᄡ᭥۵20.3mm, ᔢၹǕ
₊݉⋉⦹۵6.1mmಽĥ⊂ࡹᨩ݅. ᦿᕽᨙɪ⦽ၵ᪡zᯕ
ᖁ⧪ᄡ᭥۵ᔢၹǕ₊ᄡ᭥᮹30%ෝᱢᬊ⦹ᩍ1.8mmಽᩩ⊂⦹
ᩡŁ↽᳦ᄡ᭥۵ĥ⊂ᄡ᭥᪡ᖁ⧪ᄡ᭥᮹⧊ᯙ22.1mmಽᖁᱶ⦹ᩡ
݅. E-Type B᮹ĥ⊂ᯱഭෝᇥᕾ⦽đŝĥ⊂ᄡ᭥۵18mm, ᔢၹ
Table 4. Standard Support Pattern of Type A and E-Type B
Classification Type A E-Type B
Supporting pattern
᧶ḞԨ⸮ฎ ՋՔ
ԹԺԸ֎ ࣾ⑶ᦂ⾶
ռջՅԹԽիյԱ ՐԵԺԸԸओ⚾᧲
ռջՅԺԸԸյյԱ⑶ԨᦂԨ⾶
ओ⚾᧲ՂՐԵԺԸԸ ՔՅԽԶԸյᕛԨ᧺Ԩ⾶
ࣾ≓ΊԨ㏞ヲᚿ
⬟ᦻ⚾⚾《⑺㉂⎒ῚԱ
֟ԾԸԶԽԴԨՔՅԽԶԸյ
ᭂᶿ◺⤦Ԩ⸮ฎ ՋՔ
ԹԺԸ֎ ࣾ⑶ᦂ⾶
ռջՅԹԽիյԱ ՔՅԽԶԸյᕛԨ᧺Ԩ⾶
ռջՅԺԸԸյյԱ⑶ԨᦂԨ⾶
ओ⚾᧲ՂՐԵԺԸԸ
ࣾ≓ΊԨ㏞ヲᚿ ओ⚾᧲
ՐԵԺԸԸ
⬟ᦻ⚾⚾《⑺㉂⎒ῚԱ
֟ԾԸԶԽԴԨՔՅԽԶԸյ
Tunnel characteristic width : 13.20 m
height : 9.8 0m
width : 14.28 m height : 10.41 m
Advance 1.0 m 1.0 m
Primary support Steel rib H-200 H-200
S/C 250 mm 250 mm
Rock bolt L=5.0 m, CTC(T)=1.2 m L=5.0 m, CTC(T)=1.2 m
Invert Steel rib H-200 H-200
S/C 200 mm 200 mm
Temporary invert 150 mm 150 mm
(a) Type A (b) E-Type B
Fig. 10. Measuring Condition of Tunnel
Ǖ₊ ݉⋉⦹۵6.2mmಽĥ⊂ࡹᨩ݅. ᖁ⧪ᄡ᭥۵ᔢၹǕ₊
ᄡ᭥᮹30%ෝᱢᬊ⦹ᩍ1.9mmಽᩩ⊂⦹ᩡᮝ໑↽᳦ᄡ᭥۵ĥ⊂
ᄡ᭥᪡ᖁ⧪ᄡ᭥᮹⧊ᯙ19.9mmෝᖁᱶ⦹ᩡ݅. ⢽ᵡḡᅕ➉▕ᄥಽ
↽ݡᄡ᭥aၽᔾ⦽ݡ⢽݉໕ᨱ ݡ⦹ᩍĥ⊂ᇥᕾᮥᙹ⧪⦽đŝ
↽᳦ᄡ᭥۵Type A᮹ᗱᔢݡ᮹Ğᬑ22.1mm, E-Type B ᗱᔢݡ᮹
Ğᬑ 19.9mma ၽᔾ⦹۵ äᮝಽ ӹ┡ԍ݅.
5. ᩎ⧕ᕾᮥᯕᬊ⦽⎹Ⓧญ✙ᯕܾḡၹᯕ᪥⦹ᵲᔑᱶ
5.1 ౿ැজՍ
ᔢ⦹ၹǕ₊ᯕ᪥ഭࡽⷂⷂ░ձ⩥ᰆ༉ᔍෝ᭥⦹ᩍᯕܾ᮹
Ğĥ᳑Õᮥx⇶ŝy⇶ႊ⨆᮹ᄡ᭥ෝǍᗮ⦹ḡᦫᦹᮝ໑░ձᱥℕ ᨱᦶ⇶ಆᨱอ᯲ᬊ⦹۵┥ᖒᜅ⥥ยยⓍෝჶᖁႊ⨆ᮝಽᖅ⊹⦹
ᩍ ⧊ᖒᇡᰍ᪡ ḡၹŝ᮹ ᔢ⪙᯲ᬊᮥ Łಅ⧁ ᙹ ᯩ۵ ኵ-ᜅ⥥ย
༉ߙᮥᱢᬊ⦹ᩡ݅. ⧕ᕾᨱᔍᬊࡽ݉໕ᮡ Table 4ᨱᕽ᪡zᯕ
Table 5. Main Ground Material Property Applied Numerical Analysis
Classification Specific weight(kN/m3) Deformation modulus(MPa) Cohesion(kPa) Internal friction angle(°) Poisson’s ratio(쩔)
Damage zone 20 280 70 29 0.31
Table 6. Material Property of Composite Member Applied in Numerical Analysis
Classification Cross section area(m2) Elastic modulus(MPa) Geometrical moment of inertial(m4)
Lining 0.249998 19593.95 0.000461
Invert 0.195738 21194.00 0.00054479
Table 7. Rock Load Computation by Using Terzaghi’s Rock Load Classification Table
Classification Rock condition Rock load height(m) Rock load(kN/m2)
Type A
5. Very blocky and seamy 0.4(B+Ht) 9.2
E-Type B 0.4(B+Ht) 9.88
(a) Type A
(b) E-Type B Fig. 11. Modeling Analysis
㧊㢚䞮㭧
Fig. 12. KG= 1.0 Condition Load Shape
Type A ᮹ Ğᬑ ⡎ᯕ 13.20mᯕŁ ׳ᯕa 9.80mᯕ໑ E-Type
B᮹ Ğᬑ ⡎ᯕ 14.28mᯕŁ ׳ᯕa 10.41mᯕ݅. ੱ⦽, ᝅݡ⩶
ᝅ⨹đŝ᪡ᩍ్ᙹ⊹⧕ᕾʑჶᮥᱢᬊ⦹ᩍࠥ⇽⧕ԙ⮉༉ູ✙۵
vḡᅕa༉ࢱᇥݕ⦹Ł⇶ಆᮡvḡᅕ᪡ᙰⓍญ✙aᦶ⇶vᖒእ ᨱ እಡ⦹ᩍ ᇥݕ⦹۵ äᮝಽ ⧊ᖒᇡᰍෝ ༉ߙย⦹ᩡ݅(Moon et al, 2012). ᝅᱽĥ⊂݉⋉⦹᪡ᙹ⊹⧕ᕾᮥ☖⦽݉⋉⦹᮹
እƱෝ᭥⦹ᩍᙹ⊹⧕ᕾ᮹݉⋉⦹۵Fig. 11(a)ŝFig. 11(b)᪡
zᯕ░ձ⩶ᔢ᮹ ݉ᨱᕽ᮹ᄡ᭥อᮥ݉⋉⦹ಽaᱶ⦹ᩡ݅. ੱ
⦽⧕ᕾݡᔢ᮹ḡၹྜྷᖒŝḡᅕᰍ᮹ྜྷᖒᮡTable 5᪡Table 6ᨱ
ӹ┡ԕᨩ݅.
5.2 Terzaghiଭࢱணंࠑඝଭࢱଲணॺ୨ ḡၹᯕ᪥⦹ᵲᔑᱶᯝၹᱢᮝಽᔑᱶࡹ۵Terzaghi᮹ᦵၹ⦹
ᵲᇥඹ⢽ ႊჶᮥ ⪽ᬊ⦹ᩡŁ, ⷂⷂ░ձ᮹ ḡၹ᳑Õᮥ Łಅ⦹ᩍ
ᦵၹᔢ┽5᮹⦹ᵲĥᙹ᮹⠪Ɂ⊹ᯙ0.4ෝᔍᬊ⦹ᩡ݅. Table 7ᮡ
Terzaghi ᮹ ᦵၹ⦹ᵲᇥඹ⢽ෝ ⪽ᬊ⦽ ḡၹ ᯕ᪥⦹ᵲŁ᪡ ḡၹ
ᯕ᪥⦹ᵲᮥ ᔑᱶ⦽ sᯕ໑ ᯕෝ ᙹ⊹⧕ᕾᨱ ၹᩢ⦹ᩡ݅.
ੱ⦽, ᙹ⊹⧕ᕾᨱᱢᬊࡽḡၹᯕ᪥⦹ᵲ᮹ᱢᬊ⩶ᔢᮡFig. 12
᪡ z݅.
5.3 ࢱࢱߚծॺ୨
░ձ᮹ 1₉ ḡᅕᰍ Ǎ᳑ĥᔑ ḡၹၹಆĥᙹ۵ Ǎ᳑⧕ᕾ᮹
đŝᨱၙ⊹۵ᩢ⨆ᯕᔢݚ⯩Ⓧအಽ⧊ญᱢᯙᔑᱶႊჶᯕ⦥⦹
݅. ⧕ᕾᨱᔍᬊࡽḡၹၹಆĥᙹ۵┥ᖒᯕುᨱɝÑ⦽ḡၹŖ࠺ᯕ
ುᮝಽᔍᬊ⦹ᩡ݅. ᯕ۵ၙŖᄲ݉, AFTESᨱᕽᔍᬊ⦹۵ᯕು
ᱢɝÑa∊ᇥ⦽Ŗᮝಽ(16)ᮥ☖⦹ᩍᙹ⊹⧕ᕾᨱᱢᬊࡽ
b ḡၹ᮹ ḡၹၹಆĥᙹෝ Table 8ŝ zᯕ ᔑᱶ⦹ᩡ݅.
Table 8. Result of Ground Reaction Coefficient Computation
Classification Cross section area(m2) Deformation modulus(MPa) Poisson’s ratio Equivalent transformed section(m)
Ground reation coefficient(kN/m3)
Type A 108.8
280 0.31 5.00 42,748
E-Type B 125.0
Table 9. Forecasting Crown Settlement by Using Terzaghi Rock Load Classification Table
Classification Type A E-Type B
Rock load(m) 9.2 9.88
Crown settlement(mm) 38.71 44.16
Table 10. Crown Settlement for Field Measurement
Classification Type A E-Type B
Crown settlement(mm) 22.1 57.09(%)
19.9 45.06(%)
ratio by Terzaghi’s rock load classification table (a) Type A
(b) E-Type B
Fig. 13. Relationship Between Rock Load and Crown Settlement by Back Analysis
¤
Ƒá ć ÞÎ âŊß«
Ƒ¥ (16)
ᩍʑᕽ, ¤
Ƒ: ݉᭥ᱲᖁ ʙᯕ ݚ ᜅ⥥ยĥᙹ
: ᄡ⩶ĥᙹ Ń : ⡍ᦥᘂእ
¥ : ᇡᰍʙᯕ
« é ᯕܾ᮹ ॒aၹĞ ( « á ö ć Þîņß ⴌ 5)
5.4 ծ౸ंজଡധType AE-Type Bଭవۚಅ
⎹Ⓧญ✙ᯕܾǍ᳑á☁ᱢᬊࡹ۵ḡၹᯕ᪥⦹ᵲ᮹Ⓧʑ۵
Ǖ₊ḡᅕᰍᨱ᯲ᬊ⦹۵ḡၹᯕ᪥⦹ᵲⓍʑ᪡Ḣᱲᱢᮝಽšĥ⦹
အಽǍ᳑⧕ᕾᮥ☖⦹ᩍᩩ⊂ࡽ݉⋉⦹᪡ᝅᱽŖᵲĥ⊂ᄡ᭥᪡
᮹እƱá☁ෝ☖⦽ᇥᕾᮡๅᬑᵲ⦹݅Ł❱݉ࡽ݅. Table 9۵
Ǎ᳑⧕ᕾᮥ ☖⦽ ݉⋉⦹᮹ ᩩ⊂sᯕ݅.
ᱽ4ᰆᨱᕽ᮹ĥ⊂ᇥᕾđŝᖁ⧪ᄡ᭥ෝ⡍⧉⦹ᩍŖᵲĥ⊂
ࡽ݉⋉⦹᮹Ⓧʑ۵Table 10ŝzᮝ໑Ǎ᳑⧕ᕾᮝಽᩩ⊂ࡽ
݉⋉⦹᮹Ⓧʑ۵45.06ⴇ57.09% ᙹᵡᮝಽ៉እƱᱢ᯲íၽᔾ
⦽äᮝಽᇥᕾࡹᨩ݅. ᕽǍ᳑⧕ᕾᮥ☖⦽ᩩ⊂ࡽ݉⋉⦹a
ᝅᱽ⩥ᰆ᮹݉⋉⦹ᅕ݅ ᯲íᇥᕾࡹᨩᮝအಽᝅᱽ⩥ᰆᨱᕽ
ၽᔾ⦹۵ḡၹᯕ᪥⦹ᵲ᮹Ⓧʑ۵Terzaghi᮹ᦵၹ⦹ᵲᇥඹ⢽ᨱ
᮹⦽ ⦹ᵲᅕ݅ ᯲ᮥ äᮝಽ ❱݉ࡽ݅.
5.5 ծ౸էրࠜଲࢱଲணճॺ୨
ᦿᕽ3ᰆᨱᕽ᮹ᩎ⧕ᕾᙹ⧪ࠥ(Fig. 9)᮹ŝᱶᮥ☖⦹ᩍ⧪₊
᪅ჶᮥᱢᬊ⦹ᩍType A᪡E-Type B᮹ḡၹᯕ᪥⦹ᵲŝ݉⋉⦹
ෝᔑᱶ⦽ ⬥ ḡၹᯕ᪥⦹ᵲᮥ ḡၹ᮹ ݉᭥ᵲప( Ĺ ) ᮝಽ ӹ٥ᨕ
ḡၹᯕ᪥⦹ᵲŁෝᩎᔑ⦹ᩡ݅. ḡၹᯕ᪥⦹ᵲŁ᪡݉⋉⦹Ⓧʑ ۵ᖁ⩶ᱢᯙšĥෝᅕᩡᮝ໑, ⫭ȡᇥᕾđŝType A۵Fig. 13(a), E-Type B۵ Fig. 13(b)᪡ zᮡ ᖁ⩶⫭ȡᮥ í ࡹᨩ݅.
Type A ᪡E-Type B᮹݉⋉⦹᪡ḡၹᯕ᪥⦹ᵲŁ᪡᮹⫭ȡᇥ
ᕾᮥá☁⧕ᅙđŝType A᮹đᱶĥᙹ(R²)۵1ᯕŁE-Type
B ۵0.9999ಽᇥᕾࡹᨩᮝ໑, Type A۵ḡၹᯕ᪥⦹ᵲ=0.2709×
Table 11. Back Analysis of Rock Load Computation
Classification Type A E-Type B
= 4.7203
= 3.7455 Applied rock load
(Hp × F.S, m) 7.08 5.62
Fig. 14. Comparison of Rock Load
(a) Type A
(b) E-Type B
Fig. 15. Comparison of Rock Load by Various Estimation Methods in this Study
