* (ᵝ)ݡᬱ☁ḩ ᇡᰆ ([email protected])
Received February 14 2013, Revised May 8 2013, Accepted June 18 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͵͵ǤͶǤͳͷʹͻ Ǥ ǤǤ
㯓⢚㮖#⇍#⟖㐖㬲⛛ⴂ#㝳㬚#ቻ♪#⢚⡢㜚#ḛ⊺㡶ⴖ#⊲ᇓ㱦ኺ#⍂⛛
ଲ୍۴ ȵࣦଵ ȵକָ ȵ
Lee, Jea-Dug*, Kim, Byoung-Il**, Yoo, Wan-Kyu***, Han, Jin-Tae****
Evaluation on Reinforcing Effect of Inclined System Bolting by Model Tests and Numerical Analysis
ABSTRACT
Recent case studies in Japan have shown that rockbolts are commonly installed at an oblique angle to the excavation direction of the tunnel, instead of at a right angle, due to restriction of the working space. In particular, in the case of expansion in an existing tunnel, the working space can be very small, due to the large protective structures necessary to operate within an existing tunnel. In this case, where both the current use of the existing tunnel, and the reinforcement of the ground around the tunnel are required, the effects of installation angles and patterns of rockbolts are important factors in the design process. Therefore, in this study, a total number of 24 model tests are performed, to investigate the reinforcing effects of system bolting installed obliquely from the excavation direction of the tunnel, by changing the installation angle of bolts, longitudinal distance, and bonded length of bolts. The model test results indicate that the relaxed load ratio decreases, with the increase of both the bonded lengths and the number of the installed bolts, resulting in the decrease of the supported area by one bolt. Two-dimensional numerical analysis, which considered the reinforcement effect of inclined system bolting as the change of engineering properties near the tunnel, demonstrated that the deflection patterns at the tunnel crown in the numerical simulations, show a similar tendency to those measured in the model tests.
Key words : Inclined system bolting, Reinforcement effect, Laboratory model test, 2D numerical analysis
Ⅹಾ
↽ɝᨱᯝᅙ᮹Ŗᔍಡᨱ໕░ձ⪶ݡෝ᭥⧕ᅕ⪙Ŗ(⥥ಽ▮░)ᮥᖅ⊹⦹Łʑ᳕░ձᮥᔍᬊ⦹໕ᕽŖ⦹۵Ğᬑᨱ۵ಾᅝ✙ෝǕ₊ႊ
⨆ᨱᙹḢ⦹í┡ᖅ⧁ᙹᨧᨕᕽĞᔍḡí┡ᖅ⦹۵Ğᬑaᯩ݅. ᬕᬊᵲᯙ░ձᮥ⪶ݡŖ⦹۵Ğᬑᨱ۵᯲ᨦ᳑Õᯕๅᬑӹᒹʑভྙᨱಾ
ᅝ✙᮹➉▕(Ğᔍಾᅝ✙ᖅ⊹, ᔍᱥಾᅝ✙Ŗ, ಾᅝ✙ᱽ॒)ᨱݡ⦽á☁a⦥⦹݅. ᯕᩑǍᨱᕽ۵༉⩶⨹ᮥᯕᬊ⦹ᩍᯝၹᱢᮝಽ░
ձǕ₊ႊ⨆ŝᙹḢ⦹íᖅ⊹ࡹ۵ᜅ▽ಾᅝ✙᮹ᅕv⬉ŝ᪡░ձǕ₊ႊ⨆ᨱĞᔍḡíᖅ⊹ࡹ۵Ğᔍᜅ▽ಾᅝ✙᮹ᅕv⬉ŝෝእƱ⦹ᩡ
݅. ༉⩶ಾᅝ✙᮹ᖅ⊹bࠥ, ᖅ⊹eĊ, ᱶ₊ʙᯕ॒ᮥᄡ⪵⍽ⅾ24⫭᮹༉⩶⨹ᮥᙹ⧪⦹ᩡᮝ໑, ༉⩶⨹đŝ༉⩶ᅝ✙1}aᇡݕ⦹۵
໕ᱢᨱݡ⦽ᯕ᪥⦹ᵲၽᔾශᮡᇡݕ໕ᱢqᗭᨱqᗭ⦹۵äᮝಽӹ┡ԍ݅. ੱ⦽, ༉⩶ᅝ✙ᱶ₊ʙᯕᄡ⪵ᨱෙᯕ᪥⦹ᵲၽᔾශᮡᱶ
₊ʙᯕaʙᨕḩᙹಾqᗭ⦹۵Ğ⨆ᯕӹ┡ԍ݅. ⦽⠙░ձḡᅕᰍᖅ⊹⬉ŝෝᵝᄡḡၹ᮹Ŗ⦺ᱢ✚ᖒ᷾aಽeᵝ⦹۵ḡᅕᰍ༉⩶⪵ႊჶᨱ
᮹⦽2₉ᬱᙹ⊹⧕ᕾđŝa༉⩶⨹᮹ḱ᷾aపၽᔾĞ⨆ᮥᮁᔍ⦹íᩩ⊂⦹۵äᮝಽӹ┡ӹᅙ⧕ᕾʑჶᯕĞᔍᜅ▽ಾᅝ✙᮹ᅕv
⬉ŝෝᱢᱩ⯩༉ᔍ⧁ᙹᯩᮥäᮝಽ❱݉ࡽ݅.
áᔪᨕ Ğᔍᜅ▽ಾᅝ✙, ᅕv⬉ŝ, ༉⩶⨹, 2₉ᬱᙹ⊹⧕ᕾ
ࢢȇėॡ
Fig. 1. Model bolts
Fig. 2. Model bolts installation
1. ᕽು
ǎԕᨱᕽᅙĊᱢᯙ░ձŖᔍa᯲ࡽäᮡ40֥ᯕչᨩᮝ໑,
↽ɝ᮹ ░ձ Ŗᔍᨱ۵ ᵝಽ NATM(New Austrian Tunneling Method)Ŗჶᯕ ᱢᬊࡹŁ ᯩ݅. NATMᮡ ░ձ Ǖ₊ᨱ ᮹⦹ᩍ
ၽᔾ⦹۵ḡၹᄡ⩶ᮥ⨩ᬊ⧉ᮝಽ៉ၽ⭹ࡹ۵ḡၹ᮹ᦥ⋎⬉ŝᨱ
᮹⧕░ձᦩᱶᖒᮥ⪶ᅕ⦹۵Ŗჶᯕ݅. ᵝḡᅕᰍಽᕽ۵ᙰⓍญ
✙᪡ ಾᅝ✙a ᔍᬊࡽ݅. ಾᅝ✙۵ Ǖ₊ ᷪ Ŗ⦹ᩍ ᦵၹ᮹
ᯕ᪥ᮥⅩʑᨱႊḡ⦹Ł, ᇩᩑᗮ໕᮹⪽࠺ᮥᨖᱽ⦹ᩍḡ⦹Ŗ࠺
Ǖ₊ᨱᇩᦩᱶ⦽ᦵၹÑ࠺ᮥᨖᱽ⦽݅(Osgoui & Erdal, 2009).
əญŁಾᅝ✙۵ĞᱽᱢᯝᐱอᦥܩᖅĥᯱaŖ࠺᮹݉໕ᮥ
ᯱᮁíᖁ┾⧁ᙹᯩ݅۵ᰆᱱভྙᨱฯᯕᔍᬊࡽ݅(ᱶ⧕ᖒŝ
ྙȽ⩥, 1999).
ᜅ▽ᅝ❦ᮡ☖ᔢᱢᮝಽǕ₊ႊ⨆ŝᙹḢ⦹íǕḥᰆษ݅ᖅ
⊹⦹íࡹ۵ߑʑĥ⪵Ŗᮥ᭥⦽ᰆእ᮹ᬕᬊŖeᯕ⩲ᗭ⦹Ñӹ
ŖᩍÕᔢᅝ✙ᔞ᯦ᯕᨕಅᬕŔᨱᕽ۵Ṉᮡᅝ✙ෝᩑđ⦹ᩍ
ᔍᬊ⦹Ñӹ Ğᔍḡí ᖅ⊹⦹۵ Ğᬑa ᯩ݅. ʡ࠺Ƚ᪡ ᱶ⪙ᖎ (2007)ᯕၽ⢽⦽ၵᨱ໕↽ɝᨱᯝᅙᨱᕽ۵₉ప᮹ݡ⩶⪵, Ʊ☖ప ᷾a, ░ձ᮹ ʑ܆⨆ᔢ ॒᮹ ༊ᱢᮝಽ ᬕᬊᵲᯙ ░ձ᮹
⪶ݡŖᔍaฯᯕĥ⫮ࡹŁᯩ݅Ł⦽݅. əญŁᬊḡๅᙹ᪡ᯱᩑ⪹
Ğᩢ⨆॒ᨱݡ⦽ᔍ⫭ᱢᱽ᧞ŝʑ᳕ᯱᬱ᮹ᮁᬊ⦽⪽ᬊᯕ۵
šᱱᨱᕽᬕᬊᵲᯙ░ձ᮹⪶ݡŖᔍaᦿᮝಽ᷾aࢁäᮝಽᩩᔢ⦹
ᩡ݅. ੱ⦽ᕽĞᬱ॒(2008)ᮡᯝᅙ᮹ᝅᱽŖᔍಡᇥᕾᮥ☖⦹ᩍ
ᬕᩢᵲᯙ░ձ᮹⪶ݡŖᔍᨱᕽ۵░ձ᮹ݡᇡᇥᮥᅕ⪙Ŗ(⥥ಽ▮
░)ᯕ₉ḡ⦹ʑভྙᨱ░ձǕ₊ႊ⨆ᨱᙹḢ⦹íಾᅝ✙ෝ┡ᖅ⧁
ᙹᨧᨕᕽಾᅝ✙ෝĞᔍḡí┡ᖅ⦹۵Ğᬑaᯩ݅ŁᅕŁ⦹ᩡ݅.
ಾᅝ✙ᅕv⬉ŝᨱš⦽ᝅ⨹ᱢᯙᩑǍಽᔍḩ☁ḡၹᨱݡ⦽
݉ᙽᅕ ༉ߙ ༉⩶⨹ᮥ ᝅ⦹ᩍ ಾᅝ✙ᅕvᨱ ᮹⦽ ᬱḡၹ᮹
ᅕv⬉ŝෝ ᇥᕾ⦽ ྙᬦᵝ ॒(2005)᮹ ᩑǍa ᯩᮝ໑, ᙹ⠪ᱩญ
ᦵၹᨱ ݡ⦽ ݉ᙽᅕ༉ߙ༉⩶⨹ᮥ ᝅ⦹ᩍʕᰆಆᯕa⧕ḥ
ಾᅝ✙᮹ᅕv⬉ŝෝᇥᕾ⦽ᦩᱶ⪹ŝᯕᔢ(2009)᮹ᩑǍaᯩ݅.
ಾᅝ✙᮹Ñ࠺ᨱš⦽ᙹ⊹⧕ᕾᩑǍಽ۵ᱱᗭᖒ⧕ᕾᮝಽಾᅝ
✙aᖅ⊹ࡽḡ⦹Ǎ᳑ྜྷ᮹Ñ࠺ᨱݡ⦽ᩑǍ(᳑┽ḥŝᯕᱶᯙ, 1993; ᯕᩑȽ ॒, 1995; י⪹ ॒, 2004), 3₉ᬱ ᮁ⦽₉ᇥჶ
ᙹ⊹⧕ᕾ⥥ಽəఉᮥᯕᬊ⦹ᩍḡ⦹Ǎ᳑ྜྷ⩶ᔢᨱෙಾᅝ✙
ʙᯕᨱݡ⦽ᩑǍ(Goel et al., 2007) ၰ2₉ಽࠥಽ░ձ⢽ᵡ݉໕ᨱ
ݡ⦽3₉ᬱᙹ⊹⧕ᕾᮥ☖⦹ᩍಾᅝ✙᮹ᖅ⊹bࠥᄡ⪵ᨱෙ
ᩑǍෝᙹ⧪⦽ᔍಡ(ʡᬦǍ॒, 2010)aᯩ݅. ə్ӹĞᔍᜅ▽
ᅝ✙᮹ ᅕv⬉ŝᨱ ݡ⦽ ᩑǍ۵ ᦥḢ ฯḡ ᦫ݅Ł ⧁ ᙹ ᯩ݅.
ᯕᩑǍᨱᕽ۵ᔍḩ☁ᨱᕽĞᔍᜅ▽ᅝ✙᮹ᅕv⬉ŝෝ❭ᦦ
⦹ʑ᭥⦹ᩍ༉⩶ಾᅝ✙᮹ᖅ⊹eĊ, ᖅ⊹bࠥၰ☁⦝Łෝᄡ⪵⦹
۵༉⩶⨹ᮥᝅ⦽ᯕᰍ॒(2012)᮹ᩑǍđŝෝၵ┶ᮝಽ
༉⩶ಾᅝ✙᮹ᱶ₊ʙᯕᄡ⪵┉24case᮹༉⩶⨹ᮥᝅ⦹ᩡ
݅. ༉⩶⨹đŝಽ༉⩶ಾᅝ✙᮹ᱶ₊ʙᯕᄡ⪵ᨱෙĞᔍ
ᜅ▽ᅝ✙᮹ᅕv⬉ŝෝᇥᕾ⦹ᩡ݅.əญŁ2₉ಽࠥಽ░ձ᮹
ḡᅕ➉▕ᵲ░ձ݉ၰ⊂ᄞᇡᨱᜅ▽ᅝ✙aᱢᬊࡹ۵3┡᯦, 4┡᯦ၰ5┡᯦ᨱݡ⦹ᩍ2₉ᬱᮁ⦽₉ᇥჶᙹ⊹⧕ᕾᮥᝅ⦹ᩍ
əđŝෝ༉⩶⨹đŝ᪡እƱ⦹Ł, ⧕ᕾʑჶ᮹┡ݚᖒၰᱢᬊᖒ
ᮥ á☁⦹ᩡ݅.
2. ᝅԕ༉⩶⨹
2.1 ࡦ෴ਏॷ୍߹
ᯕᩑǍᨱᕽ۵ᯕᰍ॒(2012) ᩑǍෝₙŁ⦹ᩍᱥ໕ᱲ₊⩶
ಾᅝ✙ෝ༉⩶⪵⦹ᩡ݅. ༉⩶ಾᅝ✙۵əᬑ✙᪡༉⩶⪵ಾᅝ✙
᮹ᵝ໕ษₑಆᯕ∊ᇥ⯩ၽ⩥ࢁᙹᯩ۵ḢĞ10mm᮹ᱥᔑᅝ✙
(stud bolt)ෝᔍᬊ⦹ᩡ݅(Fig. 1). əᬑ✙ᰍഭ۵░ձ⢽ᵡႊ
Table 1. Soil properties of Jumunjin sand
Specific Gravity, Ƒ Unit Weight, ĹƂ(kN/m3) Relative Density,
Ɛ(%)
Soil Classification (USCS)
Cohesion Intercept, Ɓ(kPa)
Internal Friction Angle,ŋ(°)
2.62 16.14 80 SP 0 40.1
Fig. 3. Ground arch by installation angle of rock bolt ᕽෝₙ᳑⦹ᩍྜྷ-ູ✙እa45%ᯙູ✙⟹ᯕᜅෝᔍᬊ⦹ᩡᮝ
໑, ∊ᇥ⦽ vࠥa ၽ⩥⧁ ᙹ ᯩࠥಾ 28ᯝ ᧲ᔾ ⬥ ༉⩶⨹ᨱ
ᔍᬊ⦹ᩡ݅. əญŁ༉⩶ᙰⓍญ✙۵݅ᙹ᮹ၹᅖࡹ۵༉⩶⨹
ᝅࡹ۵ᱱᮥŁಅ⦹ᩍ⩥ᝅᱢᮝಽ≉ɪᯕᬊᯕ⦽ᰍഭᯙv❱(ࢱ
̹=8mm, ʙᯕ=1.5m, ⡎=20cm)ᮥ ᔍᬊ⦹ᩡ݅.
2.2 ࡦ෴ࢱ
༉⩶ḡၹᮡᯕᰍ॒(2012)᮹ᩑǍෝₙŁ⦹ᩍᵝྙḥ⢽ᵡᔍ
ෝᔍᬊ⦹ᩡᮝ໑, vᔍᰆ⊹ෝᯕᬊ⦹ᩍᔢݡၡࠥ(Ɛ) 80%ෝอ᳒
⦹۵Õ᳑݉᭥ᵲప(ĹƂ) 16.14 kN/⽎᮹༉⩶ḡၹᮥ⩶ᖒ⦹ᩡ݅.
ᔢݡၡࠥ80%ಽ᳑ᖒࡽ༉௹ഭᨱݡ⦽ᦶၡ-႑ᙹᔝ⇶ᦶ⇶⨹
(CD Test)ᮥᝅ⦽đŝᱥ݉ᱡ⧎bᮡ40.1°, ᱱ₊ᱩ⠙ᮡ0kPaᮝ ಽ ӹ┡ԍ݅(Table 1).
2.3 ࡦ෴ਏ࣡ࢫࢺ࣑
Rabcewicz(1964)᮹ᬱḡၹᦥ⊹ᯕುᨱ໕ಾᅝ✙᪡ᙰⓍ
ญ✙ෝ Ŗ⦹໕ 1⫭ Ǖḥᰆ᮹ 1/2 ׳ᯕอⓝ ░ձ᮹ ᳦ႊ⨆ŝ
⬂ႊ⨆ᮝಽᬱḡၹᦥ⊹a⩶ᖒࡽ݅. ə۵ಾᅝ✙᮹ʙᯕ᪡eĊᨱ
ݡ⦽Ğ⨹ᮥǕ₊ʙᯕᨱݡ⦹ᩍ(1)ŝzᯕᱽᦩ⦹ᩡ݅. əญ ŁᯕᩑǍᨱᕽ۵Rabcewicz᮹ᬱḡၹᦥ⊹ᯕುŝĞ⨹ᮥၵ┶
ᮝಽ༉⩶ಾᅝ✙᮹ᱶ₊ʙᯕෝđᱶ⦹ᩡ݅. ༉⩶ಾᅝ✙᮹ʑᵡ
ᖅ⊹eĊᮡ10.0×10.0cmᮝಽđᱶ⦹ᩡᮝ໑, ༉⩶ಾᅝ✙᮹ᱶ₊
ʙᯕ۵ḡၹᦥ⊹׳ᯕaʑᵡᖅ⊹eĊ᮹1/2(5.0cm) ᯕᔢᯕ⪶ᅕ
ࡹ۵ 12.0cmಽ đᱶ⦹ᩡ݅.
¥ƀ> ƒì © = ×íÒ¥ƀ (1)
ᩍʑᕽ, ¥ƀá ಾᅝ✙᮹ ʙᯕ(m) ƒ á ░ձ᮹ 1⫭ Ǖḥᰆ(m)
© á ಾᅝ✙᮹ eĊ(m)
░ձŖ᯲ᨦŖeᯕ⩲ᗭ⦹ᩍಾᅝ✙ෝǕ₊໕ŝᙹḢ⦹í
ᖅ⊹⦹ḡ༜⦹Łಾᅝ✙ෝĞᔍḡíᖅ⊹⦹໕ᅕvࡹ۵ᬱḡၹ᮹
ࢱ̹aqᗭ⦹íࡽ݅. ಾᅝ✙ᨱ᮹⦹ᩍᅕvࡹ۵ᬱḡၹ᮹ࢱ̹a
qᗭ⧉ᨱᕽ░ձǕ₊໕ᵝᄡḡၹᨱ⩶ᖒࡹ۵ᬱḡၹᦥ⊹᮹
ࢱ̹ࠥqᗭ⦹íࡽ݅. Fig. 3ᨱᕽ᳭⊂ᮡಾᅝ✙ෝĞᔍḡíᖅ⊹
⦽Ğᬑᨱ⩶ᖒࡹ۵ᬱḡၹᦥ⊹ᯕ໑, ᬑ⊂ᮡಾᅝ✙ෝᙹḢ⦹í
ᖅ⊹⦽Ğᬑᨱ⩶ᖒࡹ۵ᬱḡၹᦥ⊹ᯕ݅. Ğᔍᜅ▽ᅝ✙ᖅ⊹ಽ
ᯙ⦹ᩍಾᅝ✙᮹ᅕv⬉ŝaqᗭࡹ۵Ğᬑ, ಾᅝ✙ᖅ⊹eĊᮥ
qᗭ┅Ñӹಾᅝ✙ʙᯕෝ᷾a⍽ᕽ࠺ᯝ⦽ᅕv⬉ŝaၽᔾ
⧁ ᙹ ᯩࠥಾ ⦹ᩍ ⦽݅.
ᯕᩑǍᨱᕽ۵ᯕᰍ॒(2012)᮹ᩑǍđŝෝₙŁ⦹ᩍ༉⩶
ಾᅝ✙᮹ᱶ₊ʙᯕෝ᷾a┉༉⩶⨹ᮥᙹ⧪⦹ᩡ݅. ༉⩶ಾᅝ
✙᮹ᱶ₊ʙᯕ۵12cmᨱᕽ14cm ၰ16cmಽ᷾a⎑݅. ੱ⦽
༉⩶⨹ᄡᙹ۵༉⩶ಾᅝ✙᮹ᱶ₊ʙᯕ12cmᨱᕽ᮹༉⩶⨹đ ŝෝᇥᕾ⦹ᩍ☁⦝Ł۵60cm, ᖅ⊹bࠥ۵45°, 60°, 75°᪡90°,
⬂ႊ⨆ᖅ⊹eĊᮡ10.0cm əญŁ᳦ႊ⨆ᖅ⊹eĊᮡ10.0cm, 8.5cm ၰ 7.0cmಽ đᱶ⦹ᩡ݅. əญŁ ༉⩶⨹ᮡ ⅾ 24⫭ෝ
ᙹ⧪⦹ᩡ݅. Table 2۵ᯕᩑǍᨱᕽᙹ⧪⦽༉⩶⨹᳑Õ(☁⦝Ł
ၰ ༉⩶ᅝ✙᮹ ᖅ⊹eĊ)ᨱ ݡ⦹ᩍ ᱶญ⦹ᩍ ӹ┡ԙ äᯕ݅.
༉⩶⨹ᨱᕽᔍᬊ⦽⨹☁᳑⦹ᇡ۵༉⩶ಾᅝ✙ᅕvḡၹ᮹
ᄡ⩶ᯕၽᔾ⧁ᙹᯩࠥಾኩŖeᮝಽ⩶ᖒࡹᨕᯩᮝ໑, ༉⩶ಾᅝ✙
ᅕvḡၹ⩶ᖒᄡ⩶ၽᔾᮥᨖᱽ⧁ᙹᯩࠥಾᄥࠥᱽ᯲⦽ḱ
ᱽᨕᰆ⊹ෝᖅ⊹⦹ᩍv❱᮹ᄡ⩶ᮥᨖᱽ⦹ᩡ݅. ᩑḢ☁ᦶᮡFig.
4᪡zᯕ2}ḡᱱ(AḡᱱၰBḡᱱ)ᨱᕽ⊂ᱶ⦹ᩡᮝ໑, ᯕᩑǍᨱ ᕽ۵Bḡᱱᨱᕽ༉⩶ಾᅝ✙ᅕvḡၹ᮹ᄡ⩶ᱥŝ⬥᮹ᩑḢ☁ᦶ
⊂ᱶđŝෝᯕᬊ⦹ᩍ༉⩶ಾᅝ✙ᨱ᮹⦽ᅕv⬉ŝෝᇥᕾ⦹ᩡ݅.
əญŁᯱᖙ⦽༉⩶⨹ᙽᕽၰႊჶᮡᯕᰍ॒(2012)᮹ᩑǍ᪡
࠺ᯝ⦹݅.
Table 2. List of model test condition
Bonded length of bolts (cm) Longitudinal distance (cm) Installation angle of bolts (°) Soil Height (cm) Labeling method
12.0
10.0
90 60 B12-L10.0-2Line-A90-60
75 60 B12-L10.0-2Line-A75-60
60 60 B12-L10.0-2Line-A60-60
45 60 B12-L10.0-2Line-A45-60
8.5
90 60 B12-L8.5-2Line-A90-60
75 60 B12-L8.5-2Line-A75-60
60 60 B12-L8.5-2Line-A60-60
45 60 B12-L8.5-2Line-A45-60
7.0
90 60 B12-L7.0-2Line-A90-60
75 60 B12-L7.0-2Line-A75-60
60 60 B12-L7.0-2Line-A60-60
45 60 B12-L7.0-2Line-A45-60
14.0
10.0 75 60 B14-L10.0-2Line-A75-60
60 60 B14-L10.0-2Line-A60-60
8.5 75 60 B14-L8.5-2Line-A75-60
60 60 B14-L8.5-2Line-A60-60
7.0 75 60 B14-L7.0-2Line-A75-60
60 60 B14-L7.0-2Line-A60-60
16.0
10.0 75 60 B16-L10.0-2Line-A75-60
60 60 B16-L10.0-2Line-A60-60
8.5 75 60 B16-L8.5-2Line-A75-60
60 60 B16-L8.5-2Line-A60-60
7.0 75 60 B16-L7.0-2Line-A75-60
60 60 B16-L7.0-2Line-A60-60
Fig. 4. Schematic of model test
3. ༉⩶⨹đŝᇥᕾ
ᯕᰍ॒(2012)ᮡĞᔍᜅ▽ᅝ✙᮹ᅕv⬉ŝෝᱶపᱢᮝಽ
⪶ᯙ⦹ʑ ᭥⦹ᩍ Eq. (2)ෝ ᯕᬊ⦹ᩍ ᯕ᪥⦹ᵲ ၽᔾශ[ᄡ⩶ ᱥ
ᩑḢ☁ᦶ(ňÎ,ⅩʑᩑḢ☁ᦶ)ᨱݡ⦽ᄡ⩶⬥⦹ᵲ(ňÏ,ᯕ᪥⦹ᵲ)᮹
እ]ᮥᔑᱶ⦹ᩡ݅. əญŁᯕ᪥⦹ᵲၽᔾශᯕ᯲ᮥᙹಾ༉⩶ಾᅝ✙
ᖅ⊹ᨱ ᮹⦽ ᅕv⬉ŝ۵ ᬑᙹ⦽ äᮝಽ ⠪a⧁ ᙹ ᯩ݅.
«ÞÜß á ćňÎ ňÏ
Z Î×× (2)
ᩍʑᕽ, « á ᯕ᪥⦹ᵲ ၽᔾශ
ňÎá ᄡ⩶ ᱥ ᩑḢ☁ᦶ(Ⅹʑ ᩑḢ☁ᦶ) ňÏá ᄡ⩶ ⬥ ᩑḢ☁ᦶ(ᯕ᪥⦹ᵲ)
Fig. 5. Relationship between ratio of relaxed load and installation area per 1 bolt
Fig. 6. Relationship between installation angle and decreasing rate of installation area per 1 bolt
Fig. 7. Relationship between ratio of relaxed load and bonded length
Fig. 8. Relationship between installation angle and increasing rate of bonded length
3.1 ড౿Ԩܑऀۡୡݗࠛଲணࢳࠔ B12-2Line-60᮹༉⩶⨹ᨱᕽᇡݕ໕ᱢᨱෙᯕ᪥⦹ᵲၽᔾ ශᮡ Fig. 5᪡ z݅. b ᖅ⊹bࠥᨱᕽ ༉⩶ ಾᅝ✙ ᇡݕ໕ᱢŝ
ᯕ᪥⦹ᵲၽᔾශᮡᮁᔍ⦽ᔢššĥෝaḡ۵äᮝಽӹ┡ԍ݅.
bᖅ⊹bࠥᨱᕽʑᵡ⨹(B12-L10.0-2Line-A90-60)᮹ᯕ᪥⦹
ᵲၽᔾශᯕၽ⩥ࡹʑ᭥⦽ᇡݕ໕ᱢ(༉⩶ಾᅝ✙᮹᳦ႊ⨆eĊ×
⬂ႊ⨆eĊ, cm2)ᮡ༉⩶ಾᅝ✙᮹ᇡݕ໕ᱢŝᯕ᪥⦹ᵲၽᔾශ᮹
ᔢššĥᨱᕽ ᔑᱶ⧁ ᙹ ᯩᮝ໑, ə đŝ۵ Fig. 6ŝ z݅.
Fig. 5ᨱᕽӹ┡ӽäŝzᯕʑᵡ⨹᮹ᯕ᪥⦹ᵲၽᔾශᯕ
ၽ⩥ࡹ۵ᇡݕ໕ᱢqᗭᮉŝᖅ⊹bࠥ᮹ᔢššĥ۵እƱᱢᬑᙹ
⦽äᮝಽӹ┡ԍ݅. əญŁᯕᩑǍᨱᕽᙹ⧪ࡽ༉⩶⨹đŝᨱ
᮹⦽ ᔢššĥ۵ Eq. (3)᪡ z݅.
ƂƃƁƐƃƋƃƌƒÞÜß á ÔÐíÎÎÎ à ×íÕÎÏ Z (3)
ᩍʑᕽ, ƂƃƁƐƃƋƃƌƒ : ᅝ✙ ᇡݕ໕ᱢ qᗭᮉ(%)
: ᅝ✙᮹ ᖅ⊹bࠥ(°)
3.2 ড౿Ԩܑ୨చଲݗࠛଲணࢳࠔ Fig. 7ᮡᖅ⊹bࠥ 75°(L10.0-2Line-A75-60)᪡ 60°(L10.0- 2Line-A60-60)ᯙ༉⩶⨹ᨱᕽӹ┡ӽᯕ᪥⦹ᵲၽᔾශŝ༉⩶
ಾᅝ✙ ᱶ₊ ʙᯕ᮹ šĥෝ ӹ┡ԙ äᯕ݅. ᯕ᪥⦹ᵲ ၽᔾශŝ
ᱶ₊ʙᯕ᮹ᔢššĥ۵ᮁᔍ⦽äᮝಽӹ┡ԍ݅. əญŁᇥᕾࡽ
ᔢššĥෝᯕᬊ⦹ᩍʑᵡ⨹ŝ࠺ᯝ⦽ᯕ᪥⦹ᵲၽᔾශᯕၽ⩥
ࡹ۵༉⩶ಾᅝ✙᮹ᱶ₊ʙᯕෝᔑᱶ⦹ᩡ݅. əđŝ༉⩶ಾᅝ✙᮹
ᖅ⊹bࠥ75°᪡60°ᨱݡ⦹ᩍʑᵡ⨹ŝ࠺ᯝ⦽ᯕ᪥⦹ᵲᯕၽ⩥
ࡹ۵༉⩶ಾᅝ✙᮹ᱶ₊ʙᯕ۵14.2cm᪡15.9cmᯙäᮝಽӹ┡
ԍ݅.
Fig. 8ᮡʑᵡ⨹᮹ᯕ᪥⦹ᵲၽᔾශᯕၽᔾ⦹ʑ᭥⦽ᱶ₊
ʙᯕ᷾aᮉŝᖅ⊹bࠥ᮹ᔢššĥෝӹ┡ԙäᯕ݅. əญŁᯕ
ᩑǍ᮹ ༉⩶⨹ᨱᕽ ӹ┡ӽ ᔢššĥ۵ Eq. (4)᪡ z݅.
ƁƐƃƋƃƌƒÞÜß á Î××íÏÑÒ àÎíÎÎÑ Z (4)
ᩍʑᕽ, ƁƐƃƋƃƌƒ : ᅝ✙᮹ ᱶ₊ ʙᯕ ᷾aప(%)
Fig. 9. Relationship between increasing rate of deformation modulus and installation angle
Fig. 10. Schematic of support modeling
3.3 ࡦ෴ߧ࣮ൈԧড౿ܤ࣪Գࢱଭ࣡෴ծ
ᯕᩑǍᨱᕽ۵༉⩶ಾᅝ✙aᖅ⊹ࡽᅖ⧊ḡၹᮥ݉ᙽᅕಽaᱶ
⦹ᩍ༉⩶⨹ᮥᝅ⦹ᩡ݅. əญŁ॒ᇥ⡍⦹ᵲᯕ᯲ᬊ⦹۵݉ᙽ ᅕᨱᕽ۵݉ᙽᅕ᮹↽ݡ ḱపᔑᱶŖᮥᯕᬊ⦹ᩍ݉ᙽᅕ᮹
ᄡ⩶ĥᙹෝᔑᱶ⧁ᙹᯩ݅. ə్ӹ༉⩶⨹ᨱᕽ༉⩶⪵ࡽᅖ⧊ḡ ၹᮡᙰⓍญ✙༉⩶⪵ᰍഭ, ༉⩶ಾᅝ✙ၰ༉⩶ḡၹᮝಽ⩶ᖒࡹ໑, ᅖ⧊ḡၹ᮹ᄡ⩶ĥᙹ᮹ᔑᱶႊჶᮡbb᮹༉⩶⨹ᄡᙹᨱ
ᕽ ᄡ⪵ࢁ ᙹ ᯩ݅.
ᦩᱶ⪹ŝ ᯕᔢ(2009)ᮡ ʕᰆಆᮥ a⦹۵ ಾᅝ✙a ᖅ⊹ࡽ
ᙹ⠪ᱩญᦵၹᨱݡ⦹ᩍ݉ᙽᅕḡᱱǍ᳑ෝ⩶ᖒ⦽ᝅԕ༉⩶⨹
ŝᝅԕ༉⩶⨹ᮥ༉⩶⪵⦽3₉ᬱᙹ⊹⧕ᕾᮥᝅ⦹ᩡ݅. əญŁ
݉ᙽᅕḱŖᨱ᮹⦹ᩍᔑᱶࡽᄡ⩶ĥᙹෝᙹ⊹⧕ᕾᮝಽá᷾
⦽ đŝ, ݉ᙽᅕ ḱŖᨱ ᮹⦹ᩍ ᔑᱶ⦽ ᄡ⩶ĥᙹ۵ ∊ᇥ⦽
ᝁᖒᮥaḥ݅Łၽ⢽⦹ᩡ݅. ᕽᯕᩑǍᨱᕽ۵༉⩶ಾᅝ✙
aᖅ⊹ࡽᅖ⧊ḡၹ᮹ᄡ⩶ĥᙹෝ॒ᇥ⡍⦹ᵲᯕ᯲ᬊ⦹۵݉ᙽᅕ ᮹ ↽ݡ ḱప ᔑᱶŖᮥ ᯕᬊ⦹ᩍ ᔑᱶ⦹ᩡ݅.
ᯕᩑǍᨱᕽᙹ⧪ࡽ༉⩶⨹đŝᨱ᮹⦹໕ᩑḢ☁ᦶ᮹qᗭ⬉
ŝ۵℁❱ᔢᇡಽᇡ░12cm ḡᱱ(Aḡᱱ, Fig. 4)ʭḡၽᔾ⦹۵
äᮝಽӹ┡ԍ݅. ᕽ༉⩶⨹ᨱᕽӹ┡ӽᩑḢ☁ᦶqᗭჵ᭥
ෝ Łಅ⦹ᩍ ⧊ᖒᅕ(℁❱, ༉⩶ḡၹ ၰ ༉⩶ ಾᅝ✙)᮹ ࢱ̹۵
℁❱ᔢᇡ12cm ḡᱱʭḡᯙäᮝಽŁಅ⦹ᩡ݅. əญŁ⧊ᖒᅕᨱ
᯲ᬊ⦹۵॒ᇥ⡍⦹ᵲᮡ༉⩶ḡၹŝ℁❱᮹ᯱᵲᮝಽaᱶ⦹ᩡᮝ ໑, ⧊ᖒᅕ᮹ ᄡ⩶ĥᙹ۵ Eq. (5)ෝ ᯕᬊ⦹ᩍ ᔑᱶ⦹ᩡ݅.
ƁƍƋ áćÐÕÑ Z ĺƒƃƑƒZ ¢ƁƍƋ Ò Z ƕƒƃƑƒZ ƊÑ
(5)
ᩍʑᕽ, ĺƒƃƑƒ : b ༉⩶⨹ᨱᕽ ↽ݡ ⋉⦹ప ƕƒƃƑƒ: b ༉⩶⨹ ᄡᙹᨱ ᮹⦽ ᯱᵲ
ƁƍƋ : ⧊ᖒᅕ᮹ ᄡ⩶ĥᙹ
¢ƁƍƋ : ⧊ᖒᅕ᮹ ݉໕ᯕ₉༉ູ✙
Ɗ : ⧊ᖒᅕ᮹ ʙᯕ
ᔑᱶࡽ⧊ᖒᅕ᮹ᄡ⩶ĥᙹ۵༉⩶ಾᅝ✙aᖅ⊹ࡹḡᦫᮡ༉⩶
ḡၹ᮹ᄡ⩶ĥᙹ(¦ )᪡༉⩶ಾᅝ✙aᖅ⊹ࡽ༉⩶ḡၹ᮹ᄡ⩶ĥ ᙹ(¦)ಽǍᇥ⧁ᙹᯩ݅. ᔑᱶࡽᄡ⩶ĥᙹ᮹₉(¦«á ¦
à ¦ )۵༉⩶ಾᅝ✙ᅕv⬉ŝᨱ᮹⦹ᩍၽᔾ⦹۵⧊ᖒᅕ᮹ᄡ⩶
ĥᙹ᷾aపᯕ݅. Fig. 9۵༉⩶ಾᅝ✙ᖅ⊹ᨱ᮹⦹ᩍၽᔾࡽ༉⩶
ಾᅝ✙ᅕv⬉ŝᨱ⧕ݚ⦹۵ᄡ⩶ĥᙹ᪡ʑᵡ⨹᮹༉⩶ಾᅝ✙
ᅕv⬉ŝᨱ⧕ݚ⦹۵ᄡ⩶ĥᙹ᮹እಽᔑᱶ⦽ᄡ⩶ĥᙹ᷾aᮉŝ
ᖅ⊹bࠥ᮹ šĥෝ ӹ┡ԙ äᯕ݅. ᄡ⩶ĥᙹ ᷾aᮉᮡ ᖅ⊹bࠥ
ᄡ⪵ᨱ ᕽ 44.6%ⴇ56.5% ᷾a⦹۵ äᮝಽ ӹ┡ԍ݅.
4. 2₉ᬱᙹ⊹⧕ᕾ
4.1 ౿ැজԹ૬
ᯕᩑǍᨱᕽ۵2₉ಽࠥಽ░ձᨱĞᔍᜅ▽ᅝ✙aᱢᬊࡹ۵
Ğᬑᨱၽᔾ⦹۵░ձ᮹ᄡ⩶ᮥᇥᕾ⦹ʑ᭥⦹ᩍ2₉ᬱᙹ⊹⧕ᕾᮥ
ᙹ⧪⦹ᩡ݅. ⦽ǎࠥಽŖᔍᨱᕽᱽ⦽2₉ಽࠥಽ░ձ᮹⢽ᵡḡᅕ
➉▕ᨱ᮹⦹໕1┡᯦ᮡ߅ᅝ✙aᱢᬊࡹᨕᯩᮝ໑, 2┡᯦ᮡ░ձ ᮹݉ŝᨕˉᇡᨱᜅ▽ᅝ✙aᱢᬊࡽ݅. əญŁ3┡᯦, 4┡᯦
ၰ5┡᯦ᮡ░ձ᮹݉ŝ⊂ᄞᨱᜅ▽ᅝ✙aᱢᬊࡽ݅. ᕽ
ᯕᩑǍᨱᕽ۵ḡᅕ➉▕3┡᯦, 4┡᯦ၰ5 ┡᯦ᨱݡ⦹ᩍ༉⩶⨹ᨱ ᕽᔑᱶ⦽ᄡ⩶ĥᙹ᷾aᮉᮥᱢᬊ⦽2₉ᬱᙹ⊹⧕ᕾ(FLAC-2D)ᮥ
ᙹ⧪⦹ᩡᮝ໑, ᙹ⊹⧕ᕾ đŝෝ ༉⩶⨹ đŝ᪡ እƱ⦹ᩡ݅.
4.2 ౿ැজࢺ࣑
ᯝၹᱢᮝಽ ░ձ ḡᅕᰍಽ ᔍᬊࡹ۵ ಾᅝ✙, ᙰⓍญ✙ ॒ᮥ
ᙹ⊹⧕ᕾᨱᕽ༉⩶⪵⦹۵ႊჶᮡᩑᗮℕᗭಽ༉⩶⪵⦹۵ႊჶ, Ǎ᳑ᇡᰍಽ༉⩶⪵⦹۵ႊჶၰᵝᄡḡၹ᮹Ŗ⦺ᱢ✚ᖒᮥᄡ⪵
┅۵ႊჶᯕᯩ݅. ᯕᩑǍᨱᕽ۵ಾᅝ✙᪡ᙰⓍญ✙ෝǍ᳑ᇡᰍಽ
༉⩶⪵⦹۵ḡᅕᰍ༉⩶⪵ႊჶŝಾᅝ✙᮹ḡᅕ⬉ŝෝᵝᄡḡၹ ᮹ Ŗ⦺ᱢ ✚ᖒ ᄡ⪵ಽ ḡᅕᰍෝ ༉⩶⪵⦹۵ ႊჶᮥ ᔍᬊ⦹ᩍ,
Table 3. Support design by support system
Division Support System
3 4 5
Excavation Spacing (m) 2.0 1.5 1.2
Rock bolt
Length (m) 4.0 4.0 4.0
C.T.C (m) Longitudinal section 2.0 1.5 1.2 Cross section 1.5 1.5 1.5 Shotcrete Thickness (m) 0.08 0.12 0.16
Fig. 11. Numerical analysis section
Table 4. Ground properties by support system
Division Support System
3 4 5
Unit Weight(kN/m3) 25.0 23.0 21.0 Cohesion InterceptÞwß 700 300 100 Internal Friction Angle(°) 45.0 40.0 35.0 Deformation modulusÞtwß 500 250 100 Poisson’s ratioÞŃß 0.23 0.25 0.3 Coefficient of Lateral pressureÞr×ß 1.0 1.0 1.0 Table 5. Properties of shotcrete
Division Unit Weight (kN/m3)
Deformation modulus Þtwß
Poisson’s ratio ÞŃß
1st 24.0 5,000 0.2
2st 24.0 15,000 0.2
Table 6. Properties of rock bolt Division Unit Weight
(kN/m3)
Deformation modulus Þtwß
Poisson’s ratio ÞŃß
SD250, D25 78.5 210,000 0.3
Table 7. Load distribution ration by support system
Support System Load Distribution Ratio
Type 3 50%-25%-25%
Type 4 40%-30%-30%
Type 5 40%-30%-30%
b ႊჶ᮹ ┡ݚᖒ ၰ ᱢᬊᖒᮥ á☁⦹ᩡ݅(Fig. 10). ಾᅝ✙ᨱ
ݡ⦽Ǎ᳑ᇡᰍ༉⩶⪵ႊჶᮡಾᅝ✙ᖅ⊹bࠥa90°ᯙĞᬑᨱ
ᱢᬊ⦹ᩡᮝ໑, ᵝᄡḡၹ᮹Ŗ⦺ᱢ✚ᖒᮥᄡ⪵┅۵༉⩶⪵ႊჶ
ᮡಾᅝ✙ᖅ⊹bࠥa90°ᯙĞᬑ᪡Ğᔍḡíᖅ⊹ࡹ۵ಾᅝ✙ᨱ
ݡ⦹ᩍ ᱢᬊ⦹ᩡ݅.
4.3 ౿ැজۚࢫୡࢄন
ᙹ⊹⧕ᕾᩢᩎᮡḡၹ᮹Ğĥa⧕ᕾđŝᨱᩢ⨆ᮥၙ⊹ḡᦫࠥ
ಾ░ձ᮹᳭⊂, ᬑ⊂ၰ⦹ᇡᨱݡ⦹ᩍ4.5D(D : ░ձ⪹ᔑḢĞⴉ 10.18m) ᯕᔢᮝಽᖅᱶ⦹ᩡ݅. ੱ⦽░ձ݉ᨱᕽḡ⢽໕ʭḡ᮹
☁⦝Ł۵⢽ᵡḡᅕ➉▕3┡᯦, 4┡᯦ၰ5┡᯦(Table 3 ₙ᳑)ᨱ
ݡ⦹ᩍ bb 3D, 2D ၰ 1Dಽ ᖅᱶ⦹ᩡᮝ໑, 2₉ᬱ ᙹ⊹⧕ᕾ
݉໕ᮡ Fig. 11ŝ z݅.
bḡᅕ➉▕ᨱݡ⦽ḡၹ᳑Õᮡḡᅕ➉▕ᨱݡ⦽ᦵၹᇥඹᨱ
ᕽ3┡᯦ᮡᩑᦵᮝಽ, 4┡᯦ᮡ⣮⪵ᦵᮝಽəญŁ5┡᯦ᮡ
⣮⪵ᦵ ၰ ⣮⪵☁ಽ đᱶ⦹ᩡ݅. b ḡၹ᳑Õᨱ ݡ⦽ ྜྷᖒsᮡ
ࠥಽᖅĥ⠙௭(2010) ᱽ6⠙░ձᨱᱽࡽǎԕ░ձŖᝅᱢᨱ
᮹⦽ᦵၹ᮹ݡ⢽ྜྷᖒsᮥₙ᳑⦹ᩍTable 4᪡zᯕđᱶ⦹ᩡᮝ໑,
ḡၹ❭ƕ༉ߙᮡMohr-Coulomb᮹⧎ᅖʑᵡᮥᱢᬊ⦹ᩡ݅. əญ ŁᙰⓍญ✙᪡ಾᅝ✙ᨱݡ⦹ᩍᱢᬊ⦽ྜྷᖒsᮡTable 5 ၰTable 6ŝz݅. ੱ⦽ᙹ⊹⧕ᕾᨱᱢᬊ⦽᮲ಆᇥݕእ۵Table 7ŝz݅.
4.4 ฅॺԳন࣡ฃݗࠛ౿ැজէր(ߧ࣮ൈ֜ऀ୍
ැজ׆࣑)
2₉ᬱᙹ⊹⧕ᕾᮡ݉᭥⡎ᨱݡ⦽ᩑᔑᯕᙹ⧪ࡽ݅. ə్အಽ
ಾᅝ✙༉⩶⪵ᨱᕽ۵ಾᅝ✙᮹᳦ႊ⨆ᖅ⊹eĊᮥŁಅ⦹ᩍ⪹ᔑ vᖒᮥᔑᱶ⦹ᩍᱢᬊ⦹ᩍ⦽݅. əญŁಾᅝ✙ᖅ⊹bࠥa90°
ᯙĞᬑ, ⪹ᔑvᖒ᮹ᄡ⪵ಽಾᅝ✙᳦ႊ⨆ᖅ⊹eĊᄡ⪵ᨱݡ⦽
░ձ Ñ࠺ᮥ ᩩ⊂⧁ ᙹ ᯩ݅.
bḡᅕ➉▕ᨱᕽಾᅝ✙ᇡݕ໕ᱢqᗭᮉᄡ⪵ᨱෙᙹ⊹⧕ᕾ
ᮥᙹ⧪⦽đŝ, ಾᅝ✙⇶ಆ᷾aప(Fig. 13)ᮡᇡݕ໕ᱢqᗭ(ಾᅝ
✙᳦ႊ⨆ᖅ⊹eĊqᗭ)ᨱᕽ᷾a⦹۵äᮝಽӹ┡ԍ݅.
əญŁ3┡᯦ŝ4┡᯦ᨱᕽᇡݕ໕ᱢᯕqᗭᨱᕽᙰⓍญ✙
᮲ಆ(Fig. 14)ᮡ0.01MPaŝ0.02MPa qᗭ⦹۵äᮝಽӹ┡ԍ݅.
Fig. 12. Relationship between decrease of crown settlement and decreasing rate of installation area per 1 bolt
Fig. 13. Relationship between increase of rock bolt axial force and decreasing rate of installation area per 1 bolt
Fig. 14. Relationship between increase of shotcrete stress and decreasing rate of installation area per 1 bolt
(a) Type 3
(b) Type 4
(c) Type 5
Fig. 15. Relationship between crown settlement and deformation modulus
ə్ӹ5┡᯦ᨱᕽ۵ᙰⓍญ✙᮲ಆᯕ0.11MPa ᷾a⦹۵äᮝಽ
ӹ┡ԍ݅. ੱ⦽݉⋉⦹qᗭపᮡᇡݕ໕ᱢqᗭᨱ᷾a⦹Ł
ᯩᮝӹ ᯝᱶ⦽ Ğ⨆ᯕ ᨧ۵ äᮝಽ ӹ┡ԍ݅(Fig. 12). əญŁ
༉⩶⨹(☁⦝Ł=60cm, ᱶ₊ʙᯕ=12cm ၰ⬂ႊ⨆2ᩕ)᮹᳦ႊ
⨆ᖅ⊹eĊᨱᄡ⪵ᨱෙḱqᗭపŝእƱ⦽đŝ, ᙹ⊹⧕ᕾ᮹
݉⋉⦹qᗭపᄡ⪵Ğ⨆ᮡᮁᔍ⦽ᔢššĥෝ⩶ᖒ⦹ḡ༜⦹۵
äᮝಽ ӹ┡ԍ݅.
4.5 ச࣡ࢱ࣡෴ծ࣡ฃݗࠛ౿ැজէր(ߧ࣮ൈ
ଭࢱԳন࣡ฃැজ׆࣑)
ಾᅝ✙ᨱݡ⦽ḡᅕ⬉ŝ۵ᙰⓍญ✙ෝǍ᳑ᇡᰍಽ༉⩶⪵⦹Ł
ಾᅝ✙aᖅ⊹ࡹ۵ᩢᩎ᮹ḡၹᄡ⩶ĥᙹa᷾a⦹۵äᮝಽeᵝ
⦹ᩡ݅(Fig. 10). əญŁbḡᅕ➉▕ᨱᕽ᮹ḡᅕ⬉ŝᨱ⧕ݚ⦹۵
ᄡ⩶ĥᙹ۵ ݉⋉⦹పᮥ ʑᵡᮝಽ ᔑᱶ⦹ᩡ݅.
(a) Type 3
(b) Type 4
(c) Type 5
Fig. 16. Relationship between shotcrete stress and deformation modulus
Table 8. Deformation modulus around tunnel by rock bolt reinforcing effect
Division
Crown settlement
(mm)
Ground deformation modulus ( , MPa)
Deformation modulus around tunnel
(, MPa)
Type 3 13.00 500 518.44
Type 4 16.20 250 270.62
Type 5 17.45 100 113.93
Table 9. Decreasing rate of deformation modulus in model test
Division Installation angle of rock bolt(°)
90 75 60 45
Decreasing rate of installation area (%)
0 0 -4.11 -49.90 -54.23
15 22.20 17.11 -24.29 -34.34 30 31.34 23.49 -8.16 -13.28 ᵝᄡḡၹ᮹ ᄡ⩶ĥᙹ᪡ ░ձ᮹ ↽ݡ ݉⋉⦹ప šĥ۵ ░
ձ ᵝᄡḡၹ᮹ ᄡ⩶ĥᙹa ᷾a⧉ᨱ ᕽ ░ձ᮹ ↽ݡ ݉
⋉⦹పᯕ qᗭ⦹۵ äᮝಽ ӹ┡ԍ݅(Fig. 15). əญŁ ᙰⓍญ✙
᮲ಆᮡ ᄡ⩶ĥᙹ ᷾aᨱ ᕽ qᗭ⦹۵ äᮝಽ ӹ┡ԍ݅
(Fig. 16).
4.6 ߧ࣮ൈড౿Ԩܑࢫऀۡୡ࣡ฃݗࠛవۚಅ
߆ॺ୨էր(ߧ࣮ൈଭࢱԳন࣡ฃැজ׆࣑) Fig. 14᮹ᄡ⩶ĥᙹ᪡݉⋉⦹ప᮹šĥᨱᕽbḡᅕ➉▕ᨱ ᕽ⢽ᵡḡᅕᰍᖅ⊹ʑᵡᨱᕽӹ┡ӽ↽ݡ݉⋉⦹పᮥᯕᬊ⦹ᩍ
ಾᅝ✙᮹ḡᅕ⬉ŝᨱ⧕ݚ⦹۵ᄡ⩶ĥᙹෝᔑᱶ⦹ᩡ݅. ᄡ⩶ĥᙹෝ
ᔑᱶ⦽đŝ, ᜅ▽ಾᅝ✙ᖅ⊹ᨱ᮹⦽ḡᅕ⬉ŝ۵ᵝᄡḡၹ᮹
ᄡ⩶ĥᙹෝ13.39ⴇ20.62MPa(⠪Ɂ17.66 MPa) ᱶࠥ᷾a┅۵
⬉ŝᯙäᮝಽӹ┡ԍ݅(Table 8). əญŁTable 9ᮡ༉⩶⨹ᨱᕽ
༉⩶ಾᅝ✙ᅕv⬉ŝᨱ⧕ݚ⦹۵ᄡ⩶ĥᙹ(¦«)ෝᯕᬊ⦹ᩍᖅ⊹
bࠥ᪡ᇡݕ໕ᱢᄡ⪵ᨱݡ⦽ᄡ⩶ĥᙹ᷾aᮉᮥᔑᱶ⦽đŝᯕ݅.
ಾᅝ✙ḡᅕ⬉ŝᨱ᮹⦹ᩍ᷾aࡽ░ձᵝᄡḡၹᄡ⩶ĥᙹ()
᪡ ḡၹᄡ⩶ĥᙹ( )᮹₉۵ಾᅝ✙ḡᅕ⬉ŝᨱ⧕ݚ⦹۵ᄡ⩶ĥ ᙹ(«)ᯕ݅. ಾᅝ✙ḡᅕ⬉ŝᨱ⧕ݚ⦹۵ᄡ⩶ĥᙹᨱTable 9᮹
༉⩶⨹ᄡ⩶ĥᙹ᷾aᮉᮥŒ⦹໕ಾᅝ✙ᖅ⊹bࠥၰᇡݕ໕ᱢ
ᄡ⪵ᨱෙಾᅝ✙ḡᅕ⬉ŝᄡ⩶ĥᙹෝᔑᱶ⧁ᙹᯩ݅. Fig.
17ᮡ░ձᵝᄡḡၹᄡ⩶ĥᙹᄡ⪵᪡݉⋉⦹పšĥಽbḡᅕ➉
▕ᨱᕽಾᅝ✙ᖅ⊹bࠥ᪡ᇡݕ໕ᱢᄡ⪵ᨱෙ݉⋉⦹᷾aప
ᮥ ᔑᱶ⦽ đŝᯕ݅. Fig. 17ᨱᕽ ӹ┡ӹॐᯕ ݉⋉⦹ ᷾aప
ၽᔾĞ⨆ᮡ༉⩶⨹(☁⦝Ł=60cm, ᱶ₊ʙᯕ=12cm ၰ⬂ႊ⨆
2ᩕ)᮹ḱపၽᔾĞ⨆ŝᮁᔍ⦽äᮝಽӹ┡ԍ݅. ᕽᙹ⊹⧕
ᕾᨱᕽ༉⩶⨹᮹ᄡ⩶ĥᙹ᷾aᮉᱢᬊ⦹ᩍࠥ░ձÑ࠺ᮥ⠪a
⦹۵ߑ ᮁᬊ⦽ ႊჶᮝಽ ᔍᬊࢁ ᙹ ᯩ۵ äᮝಽ ❱݉ࡽ݅.
əญŁ༉⩶⨹ᨱᕽӹ┡ӽᖅ⊹bࠥ᪡ᇡݕ໕ᱢᨱෙḱ పᯕᙹ⊹⧕ᕾᅕ݅Ⓧíၽᔾ⦽ᯕᮁ۵ ༉⩶⨹ᨱᕽᙰⓍญ✙
ၰಾᅝ✙ෝ༉⩶⪵⦹ʑ᭥⦹ᩍᔍᬊ⦽ᰍഭ᮹vࠥ✚ᖒᯕ░ձ
ᙹ⊹⧕ᕾᨱᕽ༉⩶⪵⦽ᰍഭ᮹vࠥ✚ᖒŝᔢᯕ⦹ʑভྙᯙäᮝ ಽ ❱݉ࡽ݅.
(a) Type 3
(b) Type 4
(c) Type 5
Fig. 17. Relationship between crown settlement and installation angle
5. đು
ᯕᩑǍᨱᕽ۵ᯝၹᱢᮝಽ░ձǕ₊ႊ⨆ᨱᙹḢᮝಽᖅ⊹ࡹ۵
ᜅ▽ಾᅝ✙᮹ᅕv⬉ŝ᪡░ձǕ₊ႊ⨆ᨱĞᔍḡíᖅ⊹ࡹ۵
Ğᔍᜅ▽ಾᅝ✙᮹ᅕv⬉ŝෝእƱ⦹Łᯱ༉⩶⨹ŝ2₉ᬱ
ᙹ⊹⧕ᕾᮥ ᝅ⦹ᩡᮝ໑, ༉⩶⨹ŝ ᙹ⊹⧕ᕾᮥ ☖⦹ᩍ ᮡ
đುᮡ ݅ᮭŝ z݅.
(1) ༉⩶ ಾᅝ✙᮹ b ᖅ⊹bࠥᨱᕽ ༉⩶ ಾᅝ✙᮹ ᅕv⬉ŝ۵
ᇡݕ໕ᱢqᗭᮉᯕqᗭ⧉ᨱᕽ᷾a⦹۵äᮝಽӹ┡ԍ
݅. ੱ⦽ᱶ₊ʙᯕa᷾a⧉ᨱᕽ༉⩶ಾᅝ✙᮹ᅕv⬉ŝ a᷾a⦹۵äᮝಽӹ┡ԍ݅. əญŁbᖅ⊹bࠥᨱᕽᇡݕ໕ ᱢqᗭᮉၰᱶ₊ʙᯕᨱݡ⦽ᯕ᪥⦹ᵲၽᔾශᮡᮁᔍ⦽ᔢš šĥෝ ӹ┡ԍ݅.
(2) v❱ᔢᇡ12cm ḡᱱʭḡෝ⧊ᖒᅕᇡᰍಽŁಅ⦹Ł༉⩶ḡၹ
ၰv❱᮹ᯱᵲᯕ॒ᇥ⡍⦹ᵲᮝಽ᯲ᬊ⦹۵äᮝಽaᱶ⦹۵
Ğᬑ, ༉⩶ಾᅝ✙aᖅ⊹ࡽᅖ⧊ḡၹ᮹ᄡ⩶ĥᙹ۵݉ᙽᅕ᮹
ḱపᔑᱶᮥᯕᬊ⦹ᩍǍ⧁ᙹᯩ݅. ☁⦝Ł60cmᯝভ᮹
༉⩶ಾᅝ✙᮹ᖅ⊹bࠥᨱෙᄡ⩶ĥᙹ᷾aᮉŝᇡݕ໕ᱢ
qᗭᮉᮥእƱ⦽đŝ, ᄡ⩶ĥᙹ۵ᖅ⊹bࠥaqᗭᨱ
᯲ᦥḡ۵ äᮝಽ ӹ┡ԍ݅.
(3) ಾᅝ✙ෝǍ᳑ᇡᰍಽ༉⩶⪵⦹ᩍbḡᅕ➉▕ᨱᕽಾᅝ✙᮹
ᇡݕ໕ᱢqᗭᮉ(᳦ႊ⨆ᖅ⊹eĊᯕqᗭ) ᄡ⪵ᨱݡ⦹ᩍಾᅝ
✙᮹ ⪹ᔑvᖒᯕ ᄡ⪵⦹۵ 2₉ᬱ ᙹ⊹⧕ᕾᮥ ᙹ⧪⦽ đŝ,
ಾᅝ✙↽ݡ⇶ಆᮡᇡݕ໕ᱢᯕqᗭ⧉ᨱ᷾a⦹۵Ğ⨆
ᮥӹ┡ԩ݅. ə్ӹ݉⋉⦹పŝᙰⓍญ✙᮲ಆᮡᯝᱶ⦽
Ğ⨆ᮥᅕᯕḡᦫ۵äᮝಽӹ┡ӹಾᅝ✙ෝǍ᳑ᇡᰍಽ༉ᔍ
⦹Łಾᅝ✙ᖅ⊹eĊᄡ⪵ᨱෙ⪹ᔑvᖒᮥᱢᬊ⦹۵ᙹ⊹
⧕ᕾႊჶᮡ░ձ᮹Ñ࠺ᮥᩩ⊂⦹۵ߑᱢ⧊⦹ḡᦫᮡäᮝಽ
ၾ⩡Ჭ݅.
(4) ಾᅝ✙᮹ḡᅕ⬉ŝᨱݡ᮲⦹۵ᄡ⩶ĥᙹෝᱢᬊ⦹ᩍ░ձ᮹
݉ᄡ⩶ၽᔾపᮥᔑᱶ⦹Łᯕෝ༉⩶⨹ᨱᕽ⊂ᱶ⦽ḱ
ᄡ⩶ၽᔾపᮥእƱ⦽đŝ, ᙹ⊹⧕ᕾŝ༉⩶⨹᮹ᄡ⩶ప
ၽᔾĞ⨆ᮡᮁᔍ⦽äᮝಽӹ┡ԍ݅. ᕽḡᅕᰍ༉⩶⪵
ႊჶᮝಽ░ձḡᅕᰍᖅ⊹⬉ŝෝᵝᄡḡၹ᮹Ŗ⦺ᱢ✚ᖒ
᷾aಽeᵝ⦹۵ႊჶᮡ∊ᇥ⯩ᙹ⊹⧕ᕾᨱᱢᬊ⧁ᙹᯩ۵
äᮝಽ ӹ┡ԍ݅.
qᔍ᮹ɡ
ᯕᩑǍ۵ǎ☁⧕᧲ᇡÕᖅʑᚁ⩢ᝁᩑǍ}ၽᔍᨦ᮹ᩑǍእḡᬱ (ŝᱽჩ⪙: 11CCTI-C053463-03-000000, ŝᱽ: Ʊ☖ඹᅕ᳕⩶
░ձ݉໕ ⪶ݡ Ŗʑᚁ }ၽ)ᨱ ᮹⧕ ᙹ⧪ࡹᨩܩ݅.
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Osgoui, R. R. and Erdal, Ü. (2009). “An empirical method for de- sign of grouted bolts in rock tunnels based on the geological strength index(GSI).” Engineering Geology, Vol. 107, No. 3-4, pp. 154-166.
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