* (ᵝ)⦽⪵Õᖅ ☁༊⪹Ğᔍᨦᇡ ᔍᬱ, Ğ⯍ݡ⦺Ʊ ☁༊Ŗ⦺ŝ ᕾᔍ ([email protected])
Received January 2, 2013/ revised February 19, 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͵͵ǤͷǤʹͳʹͷ Ǥ ǤǤ
㔖㘪Ὢ㡶።ᦂ#⡪ᵖ⏊ⴖ#ᢢⲮ#⮮ቮ⌾#㣊ዲ#ሮᦗ
֫֜ন ȵୋહ ȵ୨জ
Kwon, Kusung*, Jang, Seung Yup**, Chung, Wonseok***
Fracture Behavior of Dowel Joint of Concrete Slab Track
ABSTRACT
Recently, an interest on joint behavior between adjacent concrete slab tracks has increasing due to large application of such track system. Dowel bars are widely used to improve load transfer capacity across the joints. Dowel bars reduce the deflections and stresses by transferring the load between the slabs. This study proposes the lumped shear spring model to efficiently model dowel joints of adjacent slabs. This model includes bearing stiffness between dowel bar and concrete as well as dowel gap. Strength of the proposed spring model is evaluated based on Concrete Capacity Design method under the assumption of shear failure mode in the joints.
Experiments are also performed up to failure to evaluate the accuracy of the proposed model. It has been observed that the proposed model is able to predict initial nonlinearity due to dowel gap, and capture material nonlinearity of the test slabs. Thus, it is recommended that the proposed model can be effectively applied to the dowel joints of concrete slab track.
Key words : Concrete track, Dowel, Anchor, Finite element analysis, CCD
Ⅹಾ
↽ɝ⎹Ⓧญ✙ȅࠥŖჶᯕ᷾a⧉ᨱᯙᱲ⦽ᜍ௹ቭෝᩑđ⦹۵ႊჶᨱݡ⦽šᝍᯕ׳ᦥḡŁᯩ݅. ᜍ௹ቭ᮹ᩑđᇡ۵⬉ŝᱢᯙ⦹ᵲᱥݍ, ᄡ⩶ᩑᗮ⪵, ᮲ಆᇥᔑᮥ᭥⧕ᕽ݅᭑ᜅ▽ᯕ݅ᙹᱢᬊࡽ݅. ᅙᩑǍᨱᕽ۵⎹Ⓧญ✙ᜍ௹ቭ݅᭑ᩑđᇡෝ⬉ᮉᱢᮝಽᯕᔢ⪵⧁ᙹᯩ۵ᩑ đᇡ᮹Ḳᵲᱥ݉ᜅ⥥ย(Lumped shear spring) ༉ߙᮥᱽᦩ⦽݅. ᱥ݉ᜅ⥥ย༉ߙ᮹vᖒᮡ݅᭑ၵ᮹vᖒŝᮁĊᮥŁಅ⦹ᩡᮝ໑, vࠥ۵
ᩑđᇡ᮹ᱥ݉❭ƕᨱɝÑ⦽Concrete Capacity Design(CCD) ႊჶᨱ᮹⧕ᔑᱶࡹᨩ݅. ⧕ᕾ༉ߙ᮹┡ݚᖒᮥá᷾⦹ʑ᭥⦹ᩍ݅᭑ಽᩑđ
ࡽᜍ௹ቭᝅ⨹ℕෝᱽ᯲⦹Łᰍ⦹ᝅ⨹ᮥᙹ⧪⦹ᩡ݅. ᱽᦩࡽ⧕ᕾ༉ߙᮡ݅᭑ŝ⎹Ⓧญ✙e᮹ᮁĊᮝಽᯙ⦽Ⅹʑእᖁ⩶ᖒၰ⎹Ⓧญ✙ᰍഭ
እᖁ⩶ᖒᮥ⧊ญᱢᮝಽၹᩢ⦹Łᯩ۵äᮝಽᇥᕾࡹᨩ݅. ᕽ⨆⬥ᜍ௹ቭ݅᭑᳑ᯙ✙ಽᩑđࡽ⎹Ⓧญ✙ȅࠥ᮹❭ƕʭḡ᮹እᖁ⩶Ñ
࠺ᮥ⧊ญᱢᮝಽᩩ⊂⧉ᮝಽ៉℁ࠥȅࠥ᮹ᖅĥ⬉ŝᱢᮝಽ⪽ᬊࢁᙹᯩᮥäᯕ݅.
áᔪᨕ ⎹Ⓧญ✙ȅࠥ, ݅᭑, ᧖⍅, ᮁ⦽ᗭ⧕ᕾ, CCD
1. ᕽು
ᜍ௹ቭȅࠥ᮹ᩑđᇡᨱ۵⬉ŝᱢᯙ⦹ᵲᱥݍᐱอᦥܩᄡ⩶ᩑᗮ⪵, ᮲ಆᇥᔑ॒ᮥ᭥⧕݅᭑ᜅ▽(Dowel system)ᯕᱢᬊࡽ݅.
ᖁ⧪ᩑǍ(Land Transport and Maritime Report, 2011) đŝ, ࠺ᯝ݉໕ᱢᯝĞᬑvᰍ݅᭑ၵ(Dowel bar)ෝ݅ᙹ႑⊹⦹۵äᯕ
⦹ᵲᱥݍ⬉ᮉ(Load Transfer Efficiency, LTE)ᯕaᰆᬑᙹ⦽äᮝಽ⠪aࡹᨩ݅. ᜍ௹ቭȅࠥᩑđᇡ᮹ᖅĥ, ᯕ్⦽݅᭑ᜅ▽ᨱ
ݡ⦽ ᖅĥ۵ ⦥ᙹᱢᮝಽ ḥ⧪ࡹᨕ ⧁ ŝᱶᯕ݅.
ߏʪėॡ
Fig. 1. Concept of Test Slab
Fig. 2. Test Setup
⧎Ŗʑ᮹Ŗʑᦶ, ᜍ௹ቭࢱ̹, ݅᭑ᮁĊ॒᮹݅᧲⦽ๅ}ᄡᙹෝ
ݡᔢᮝಽ⧕ᕾᱢᩑǍෝᙹ⧪⦹ᩍᄡ᭥ʑၹ᮹⦹ᵲᱥݍ⬉ᮉᮥᔑ ᱶ⦽đŝ, ᔢݚ⦽⦹ᵲᯕᯙᱲ⦽ᜍ௹ቭಽᱥݍࡹŁᯩᮝ໑✚⯩
⦹ᵲᯕ᯲ᬊ⦹۵ᇡᇥ᮹݅᭑ၵaǎᇡᱢᮝಽ95% ᯕᔢ᮹ᱥ݉ಆ
ᮥᱥݍ⦹۵äᮝಽᇥᕾࡹᨩ݅. Millard and Johnson (1984)ᮡ
݅᭑⬉ŝaḢᱲᱥ݉, እ✡ฝ, ⮉॒᮹3}᮹ີ⍅ܩ᷹ᮝಽǍᇥࢉ
ᮥၾ⩵݅. ੱ⦽⎹Ⓧญ✙vࠥavℕ᪡aʾí׳݅໕݅᭑ᮡ
Ḣᱲᱥ݉ŝእ✡ฝᨱ᮹⧕❭ƕaḡ႑ࡹ໑ၹݡಽ݅᭑ၵ᮹ᄡ⩶
ၽᔾᨱ⎹Ⓧญ✙ࠥᄡ⩶ᯕ⧉̹ၽᔾ⦽݅໕݅᭑ၵ᮹⮉ᯕŁಅ ݡᔢᯕࢉᮥᇥᕾ⦹ᩡ݅. He and Kwan (2001)ᮡ⬂ႊ⨆Ɂᩕᯕ
ၽᔾ⦽⎹Ⓧญ✙݅᭑ၵ᮹Ñ࠺ᮥ⧕ᕾŝᝅ⨹ᮥ☖⧕ᇥᕾ⦹ᩡ݅.
ᩑǍᨱ᮹⦹໕݅᭑ၵᨱa⧕ḡ۵⯹ŝၽᔾ⦹۵ᄡ᭥᪡᮹šĥ۵
ᝅ⨹ᮥ☖⧕ᅕᱶࡽᄡᙹॅᮥʑၹᮝಽ⦹۵“Beam on elastic foundation” ᯕುᮥʑⅩಽᱶ᮹ࢁᙹᯩᮝ໑ᯕෝᮁ⦽ᗭ⧕ᕾᨱ
ᱢᬊ⦹ᩍ℁ɝ⎹Ⓧญ✙Ǎ᳑ྜྷ᮹Ɂᩕ᧲ᔢ, ɚ⦽vࠥ, ᱥ݉Ñ࠺ᨱ ᕽ᮹⦹ᵲ-ᄡ᭥šĥෝᩩ⊂⧁ᙹᯩᮭᮥᇥᕾ⦹ᩡ݅. “Beam on elastic foundation” ᯕು᮹ĥᗮࡽᩑǍಽɁᩕ⎹Ⓧญ✙ᨱᕽ݅᭑ ၵ᮹Ñ࠺(El-Ariss, 2007)ᮡ᭥ᯕುᮥ໑ᯕ۵℁ɝ⎹Ⓧญ✙
Ǎ᳑ྜྷ᮹ᱥ݉Ñ࠺ᩩ⊂ᨱŁಅࡹᨕ⧁ᔍ⧎ᯥᮥၾ⩵݅. ੱ⦽
݅᭑ၵ᮹Ñ࠺ᮡ℁ɝ⎹Ⓧญ✙Ǎ᳑ྜྷ᮹ᩑᖒÑ࠺ᨱᵲ⦽ᗭ ಽ᯲ᬊࢁᙹᯩ۵äᮝಽᇥᕾ⦹ᩡ݅. Soroushian et al. (1987)ᮡ
⎹Ⓧญ✙ ḡᦶÑ࠺ᨱ š⦽ ⬉ŝෝ ᩑǍ⦹ʑ ᭥⧕ ℁ɝḢĞ ၰ
}ᙹ, ⎹Ⓧญ✙vࠥ, ⎹Ⓧญ✙ትಾ᮹⡎ၰʫᯕ॒ᮥᄡᙹಽ
⦹ᩍ ᝅ⨹ᮥ ᝅ⦹ᩡ݅. ᝅ⨹ᨱ ໕ ℁ɝḢĞᯕ qᗭ⦹Ł,
⎹Ⓧญ✙vࠥa᷾a⧉ᨱḡᦶvᖒᯕ᷾a⦹۵äᮝಽ⪶ᯙ
ࡹᨩᮝ໑ ᝅ⨹ᮥ ɝÑಽ ⦹ᩍ ᳑Õᨱ ෙ ḡᦶvᖒ ᝅ⨹ᮥ
ᱽᦩ⦹ᩡ݅.
ᅙ ᩑǍ۵ ȅࠥᜍ௹ቭ᮹ ݅᭑ ᩑđᇡ ᱥ݉Ñ࠺ ᩩ⊂ᮥ ᭥⦽
⧕ᕾ༉ߙᮥ ᱽ⦹Ł ᯕෝ ᝅ⨹ᱢᮝಽ á᷾⦽݅. ȅࠥᜍ௹ቭ۵
⦹໕ᨱיၹᯕᖅ⊹ࡹᨕ ᯩᮝအಽɝᅙᱢᯙᱥ݉Ñ࠺᮹ᯕ⧕ෝ
᭥⦽vࠥၰvᖒᩩ⊂ᯕᖅĥᨱ⦥⦹݅. ᯕෝ᭥⧕ᅙᩑǍᨱᕽ۵
⎹Ⓧญ✙ȅࠥᜍ௹ቭ݅᭑ᩑđᇡ᮹ḡᦶvᖒŝᮁĊᮥ⬉ᮉᱢᮝಽ
ᯕᔢ⪵⧁ᙹᯩ۵ᩑđᇡᱥ݉ᜅ⥥ย༉ߙᮥᱽᦩ⦽݅. ᱥ݉ᜅ⥥ย
༉ߙ᮹vࠥ۵ACI 318-08 (2008) ᇡಾD ၰ⎹Ⓧญ✙Ǎ᳑ᖅĥʑ
2. ᝅ⨹⥥ಽəఉ
⎹Ⓧญ✙ ȅࠥ ᜍ௹ቭ ᩑđᇡ᮹ ❭ƕÑ࠺ ᇥᕾᮥ ᭥⦹ᩍ Fig. 1 ŝzᯕᝅ⨹ℕෝᱽ᯲⦹Łᰍ⦹ᝅ⨹ᮥᝅ⦹ᩡ݅. ݅᭑ᜅ▽ᮡ
ḢĞ25mm vᰍ݅᭑ၵෝᔢᇡ᪡⦹ᇡᨱ6}ᦊⅾ12}ෝๅพʫᯕ
400mmಽᔞ᯦⦹ᩍᱽ᯲⦹ᩡ݅. ᅙםྙᨱᕽ۵ᜍ௹ቭᨱ݅᭑ၵa
ๅพࡹᨕᯩ۵ᜍ௹ቭෝŁᱶ⊂ᜍ௹ቭ(Fixed slab), ݅᭑ၵaᔞ᯦
ࡹᨕḡ۵ᜍ௹ቭෝa࠺⊂ᜍ௹ቭ(Movable slab)⋎⦹ᩡ݅.
Łᱶ⊂ᜍ௹ቭᨱ۵Łᱶ݉ḡə᪡⯭ḡḡəෝᖅ⊹⦹ᩡᮝ໑, a࠺⊂ᜍ௹ቭᨱ۵⯭ḡḡəෝFig. 2᪡zᯕᖅ⊹⦹ᩡ݅. ᯕ్⦽
ᝅ⨹ℕᖙ❦ᮡŁᱶ⊂ᜍ௹ቭᩑđᇡ᮹ᱥ݉❭ƕෝᮁࠥ⦹ʑ᭥⧉
ᯕ݅. ᝅ⨹ℕ᮹ ᖅ⊹ᙽᕽ۵ Fig. 3ŝ zᯕ Łᱶ݉ ḡə᪡ ⯭ḡ
ḡəෝᖅ⊹⦹ŁŁᱶ⊂ᜍ௹ቭෝḡəᨱŁᱶ⬥a࠺⊂ᜍ௹ቭෝ
Łᱶ⊂ ᜍ௹ቭ᪡ đ⧊⦹۵ ᙽᕽಽ ᖅ⊹⦹ᩡ݅.
(a) Installation of Fixed Jig (b) Installation of Hinged Jig
(c) Installation of Fixed Slab (d) Completed Test Setup
Fig. 3. Installation Process of Test Slab
(a) Position of Embedded Strain Gauges and Displacement Transducers (Front View)
(b) Position of Embedded Strain Gauges Installed at Dowels (Front View Of Fixed Slab with Dowel Bar) Fig. 4. Sensor Layout
ᜍ௹ቭᩑđᇡ᮹❭ƕÑ࠺ᝅ⨹ᮡActuator ᬊపᯕ2500kNɪ ᯙ aಆ ⥥౩ᯥᨱᕽ ᝅࡹᨩ݅. ⦹ᵲᮡ Fig. 2᪡ zᯕ a࠺⊂
ᜍ௹ቭԕ⊂600mm ḡᱱᨱᕽᰍ⦹ࡹᨩ݅. ੱ⦽ᝅ⨹ℕ᮹Ǎ᳑Ñ
࠺ ᇥᕾᮥ ⠪a⦹ʑ ᭥⧕ᕽ b ᝅ⨹ℕᨱ ĥ⊂ʑෝ ᖅ⊹⦹ᩡ݅.
Fig. 5. Concepts of Modeling (Version 6.71)ෝᔍᬊ⦹ᩍ⧕ᕾᮥᙹ⧪⦹ᩡ݅. ⎹Ⓧญ✙ᜍ௹ቭ۵
4ᱩᱱᱢ⊖ᚹᗭ(Layered Shell Element)ෝᯕᬊ⦹ᩍ༉ߙ⦹ᩡ
Ł, ᯙᱲᜍ௹ቭ᮹݅᭑ၵ۵ࢱᱩᱱᮥᩑđ⦹۵እᖁ⩶ᱥ݉ᜅ⥥ย
ᗭಽ ᯕᔢ⪵⦹ᩡ݅. ᷪ, ᅙ ᩑǍᨱᕽ۵ ʑ᳕᮹ ݅ᙹ ᩑǍ (Soroushian et al., 1987; Frantzeskakis and Theillout, 1989;
Martin-Perez and Pantazopoulou, 2001; He and Kwan, 2001;
El-Ariss, 2007)ᨱᕽᱢᬊ⦽ḡᦶvᖒ(Bearing stiffness)ᮥᯕᬊ
⦽ ݅᭑ၵ᮹ᝅᱽ ༉ߙยᮥ ݡᝁ⦹ᩍ݅᭑ၵ᮹ ༉ߙ ᨧᯕᔢ⪙
ᜍ௹ቭෝḲᵲᜅ⥥ยᗭ(Lumped spring element)ಽᩑđ⦹۵
e⠙⦹Ł ⬉ᮉᱢᯙ ༉ߙᮥ ᱽ⦽݅.
ᝅ⨹ℕ᮹❭ƕÑ࠺ᇥᕾᮥ᭥⦽ᰍഭ༉ߙᮡABAQUSᨱᕽᱽ Ŗ⦹۵ ༉ऩᮥ ᱢᬊ⦹ᩡ݅. ⎹Ⓧญ✙᮹ ᰍഭ እᖁ⩶ ༉ߙᮡ
“Concrete damaged plasticity” ༉ߙᮥᔍᬊ⦹ᩡ݅. ᯕ۵ᗱᔢ-ᗭ ᖒ ༉ߙಽᕽ Lubliner et al.(1989)ᨱ ᮹⧕ ᮭ ᱽᦩࡹᨩᮝ໑
Lee and Fenves(1998)ᨱ᮹⧕}ᖁࡽ༉ߙᯕ݅. ᭥༉ߙᮡ⎹Ⓧญ
✙᮹ᗱᔢÑ࠺ᮥᩩ⊂⦹۵ߑᱢ⧊⦽༉ߙಽǍᗮᦶಆᔢ┽᮹ᯙᰆ v⪵(Tension stiffening), ᦶ⇶ᩑ⪵(Compression hardening), v ᖒᗱᔢ(Damage parameter)ŝᗭᖒ➞(Inelastic strain)᮹✚ᖒ
ᮥ ⡍⧉⦹Ł ᯩ݅. ᜍ௹ቭ ᵝ℁ɝᮡ ABAQUSᨱᕽ ᱽŖ⦹۵
Plastic ᰍഭෝᯕᬊ⦹ᩍᦩᱥ⊂ᮝಽ᪥ᱥᗭᖒÑ࠺ᮥŁಅ⦹ᩡ݅.
⦹ᵲ᳑Õᮡᝅ⨹ŝ࠺ᯝ⦹ía࠺⊂ᜍ௹ቭԕ⊂600mm ḡᱱᨱ
ᰍ⦹⦹ᩡ݅. Łᱶ⊂ᜍ௹ቭ᮹⊂950mm ḡᱱᮡŁᱶ݉ᮝಽ, ԕ⊂600mm ḡᱱᮡa࠺݉ᮝಽᯕᔢ⪵⦹ᩡᮝ໑a࠺⊂ᜍ௹ቭ᮹
elastic foundation” ᯕುᨱ ɝÑ⦽݅.
ᅙᩑǍᨱᕽ۵݅᭑ၵෝWinkler᮹┥ᖒḡḡᅕಽ༉ᔍ⦹Łᅕ ᮹Ҿ݉⪚ᮡ݅᭑ၵ᮹Ҿ݉ᮥᄡłᱱᮝಽŁಅ⦹ᩡ݅. ᯕෝᮝಽ
⢽⩥⦹໕Eq. (1)ŝz݅. (He and Kwan, 2001; El-Ariss, 2007)
( 3 )
Vd = β EI Δ (1)
ᩍʑᕽβ = [dSKb/ 4EI]0.25, db۵݅᭑ၵ᮹ḢĞ, I۵݅᭑ၵ᮹
݉໕2₉༉ູ✙, E۵݅᭑ၵ᮹┥ᖒĥᙹᯕ݅. Vd۵ᱥ݉ಆ, ۵
ᱥ݉ᄡ᭥ᯕ݅. Kb۵ḡᦶvᖒᮝಽEq. (2)᪡zᯕ⢽⩥⧁ᙹᯩ݅.
(2)
ᩍʑᕽf 'c۵⎹Ⓧญ✙᮹ᦶ⇶vࠥ(Mpa ݉᭥)ᯕŁdb۵݅᭑ၵ ᮹ḢĞᮥ᮹ၙ⦹໑c1ᮡ℁ɝeĊᨱݡ⦽ᅕᱶĥᙹಽ25.4mm ᯕ⦹᮹ᙽ℁ɝeĊᨱݡ⧕ᕽ۵0.6᮹sᮥaḡŁ25.4mm ᯕᔢᨱ ᕽ۵ 1.0᮹ sᮥ w۵݅.
ᱽᦩ༉ߙ᮹ᱥ݉vᖒᮡᯥ᮹᮹eĊ(dj)ᮥࢱŁᖅ⊹ࡽᜍ௹ቭ ᮹Ñ࠺ᮥ☖⧕ᮁࠥࢁᙹᯩ݅. Fig. 6(a)᪡zᯕᜍ௹ቭᨱᱥ݉ಆ (Vd)ᯕ ᯲ᬊ⧁ Ğᬑ ݅᭑ ᩑđᇡᨱ ၽᔾ⦹۵ ᄡ᭥۵ ๅพ ⪚ᮡ
ᔞ᯦ࡹ۵ᇡᇥᨱᕽၽᔾ⦹۵ᄡ᭥1ŝי⇽ࡽᇡᇥᨱᕽၽᔾ⦹۵
ᄡ᭥2ಽӹڹᨕḥ݅. ᄡ᭥1ᮡᦿᕽᨙɪ⦽“Beam on elastic
(a) Behavior of the Slab with Dowel
(b) Behavior of Exposed Part in the Joint Fig. 6. Dowel Action Model
Fig. 7. Spring Model by Shear Stiffness
Table 1. Parameters of Shear Spring Model
Parameter Value Model description
©Ɨ 257,000 N Shear strength
ć¤Ƒ 61,470 N/mm Shear stiffness
ĺÎ 2 mm dowel gap
©Î 12,000 N dowel gap
ĺÏ 4 mm dowel gap
©Ï 48,000 N dowel gap
Table 2. Parameters for Shear Stiffness
Parameter Value
ć¤Ƒ 61,470 N/mm
¤ƀ 97.404
ĸ 0.02
200 GPa
¢ 19174.76
Ƃƈ 10 mm
foundation” ᯕುᨱ ᮹⧕ ᱶ᮹ࡹ໑ ᄡ᭥ 2۵ Fig. 6(b)᪡
zᯕŁᱶ݉ḡᱱŝa࠺እ⫭ᱥ݉ḡᱱ᮹Ñ࠺ᮝಽᯕᔢ⪵⧁
ᙹᯩ݅. ᩑđᇡᨱ᯲ᬊ⦹۵ᱥ݉ಆŝၽᔾ⦹۵ࢱᄡ᭥(1,
2)᪡᮹ šĥෝ ᱶญ⦹໕ ᱥ݉vᖒᮥ ᮁࠥ⧁ ᙹ ᯩŁ ᯕ۵
Eq. (3)ŝ z݅.
(3)
ᩍʑᕽE۵݅᭑ᩑđᰍഭ᮹┥ᖒĥᙹᯕ໑I۵݅᭑ᩑđᰍ᮹
݉໕2₉༉ູ✙ෝ᮹ၙ⦹໑dj۵Łᱶ⊂ᜍ௹ቭ᪡a࠺⊂ᜍ௹ቭ
ᔍᯕ᮹ eĊᮥ ᮹ၙ⦽݅.
ᦿᕽᨙɪ⦽ၵ᪡zᯕ⎹Ⓧญ✙᮹Ñ࠺✚ᖒ⊹ᯙⱖᨱ۵ḡᦶv ᖒᯕ⡍⧉ࡹᨕᯩ݅. ᱥ݉vᖒᮡ⎹Ⓧญ✙᮹Ñ࠺✚ᖒ⊹a⡍⧉
ࡹʑভྙᨱḡᦶvᖒੱ⦽ᱥ݉vᖒᨱ⡍⧉ࡽ݅Łᅝᙹᯩ݅.
ᕽḡᦶvᖒŝᱥ݉vᖒ༉ࢱ“Beam on elastic foundation”
ᯕುᨱ ɝÑ⧉ᮥ ⪶ᯙ⧁ ᙹ ᯩ݅.
a࠺⊂ᜍ௹ቭ᪡݅᭑ၵᔍᯕᨱ۵ᮁĊ(Gap)ᯕ᳕ᰍ⦽݅. ᯕ۵
ᝅ⨹ℕđ⧊ᮥᛞí⦹ʑ᭥⧕ᝅᱽ݅᭑ၵ᮹ḢĞᅕ݅Ⓧía࠺⊂
ᜍ௹ቭෝᱽ᯲⦹ᩡʑভྙᯕ݅. ᯕᔢᱢᮝಽ⢽໕ᯕˉҸ⦽ᮁĊᮡ
ᮁĊ᮹Ⓧʑอⓝvᖒᯕᨧ۵Ñ࠺ᮥ⦹íࡽ݅. ə్ӹᝅᱽa࠺⊂
ᜍ௹ቭ ᮁĊᮡᜍ௹ቭ đ⧊ ၽᔾ⦹۵ ❭ᗱŝ Ŗ᪅₉॒ᨱ
᮹⧕vᖒᮥwíࡽ݅. ᕽᩑđᇡእᖁ⩶ᜅ⥥ย᮹vᖒᮡ
Fig. 7ŝzᯕⅩʑᨱ۵݅ᵲḢᖁ᮹vᖒᮥaᱶ⦹ᩡ݅. ᅙᩑǍᨱ ᕽᔍᬊ⦽ ᱥ݉ᜅ⥥ย ༉ߙ᮹vᖒŝ aᱶ⦽ ݅᭑ᮁĊ᮹ sᮡ
Table 1ᨱᱽ⦹ᩡᮝ໑Table 2۵ᱥ݉ᜅ⥥ย༉ߙ᮹vᖒĥᔑᨱ
⦥⦽ ᄡᙹॅᮥ ᱶญ⦽ äᯕ݅.
3.2 ୢۚਆඹࠫԳܑ
ᜍ௹ቭᩑđᇡ᮹ᱥ݉ᜅ⥥ยvࠥ۵݅᭑ၵෝ⎹Ⓧญ✙᧖⍅ಽ
aᱶ⦹Łᖅĥʑᵡ(KCI, 2007)ᨱᕽᱽ⦽᧖⍅ᖅĥჶᮥᱢᬊ⦹
ᩍᔑᱶ⦹ᩡ݅. ⩥⧪᧖⍅ᖅĥჶᮡ᧖⍅᮹vࠥෝᅕ݅ᗱᛞí, əญŁᱶ⪶⯩⠪a⦹ʑ᭥⧕❭ƕᩎ⦺ᨱɝÑ⦽CCD(Concrete Capacity Design) ႊჶᨱ ɝÑෝ ࢱŁ ᯩ݅(Choi and Chun,
Ƃƍ 25 mm
ƁſÎ 360 mm
ƄƁƉ 43 MPa
ōƃƂì¯ 0.81
ōƁì¯ 1.2
ōƆì¯ 1
ōƃƁì¯ 1
ᩑšࡽvࠥ༉ࢱŁಅ⧕ᵝᨕ⦽݅. ᧖⍅᮹❭ƕ༉ऽ۵ᯙᰆ⦹ᵲ ᨱ᮹⦽❭ƕ᪡ᱥ݉⦹ᵲᨱ᮹⦽❭ƕಽӹڽ݅(KCI, 2007). ᜍ௹
ቭȅࠥᝅ⨹ℕ᮹Ñ࠺ᇥᕾđŝ, Łᱶ⊂ᜍ௹ቭ᮹݅᭑ၵ۵ᱥ݉⦹
ᵲᮥᱡ⧎⦹໑ᯕᨱෙ❭ƕ༉ऽ۵⎹Ⓧญ✙ᱥ݉❭ƕaḡ႑ᱢ ᯙäᮝಽ⪶ᯙࡹᨩ݅. ⎹Ⓧญ✙❭ƕ༉ऽᨱ᮹⦽᧖⍅ə൚᮹
Ŗ⋎ ⎹Ⓧญ✙ ❭ƕvࠥ(Vcbg)۵ Eq. (4)ෝ ෙ݅.
(4)
Eq. (4)ᨱᕽAvco۵݉ᯝ᧖⍅❭ƕ໕᮹↽ݡ⚍ᩢ໕ᱢᯕ໑, Avc۵
ᱥ݉vࠥᔑᱶᮥ᭥⦽݉ᯝ᧖⍅ੱ۵᧖⍅ə൚᮹⎹Ⓧญ✙❭ƕ໕
⚍ᩢ໕ᱢ, Ⱬed,V۵ᩑ݉Ñญᨱݡ⦽ᱥ݉vࠥ᮹ᙹᱶĥᙹ, Ⱬc,V۵
⎹Ⓧญ✙Ɂᩕၰᅕ᳑℁ɝ᮹ᮁྕᨱෙᱥ݉vࠥᨱݡ⦽ᙹᱶĥ ᙹ, Ⱬh,V۵⎹Ⓧญ✙ᨱๅพࡽ᧖⍅ᨱݡ⦽ᙹᱶĥᙹ, Ⱬec,V۵᧖⍅ə
൚ᯕ⠙ᝍ⦹ᵲᮥၼ۵Ğᬑ᮹ᱥ݉vࠥᨱݡ⦽ᙹᱶĥᙹᯕ݅. ੱ⦽
Vb۵ᱥ݉ᨱݡ⦽ʑᅙ⎹Ⓧญ✙᮹❭ƕvࠥಽᕽᯕ۵Eq. (5)᪡
z݅.
(5)
ᩍʑᕽle۵ᱥ݉ᨱݡ⧕᧖⍅aḡᦶᮥၼ۵ʙᯕ, do۵᧖⍅᮹
ḢĞ, fckᮡ⎹Ⓧญ✙ᦶ⇶vࠥᯕ݅. ca1ᮡ᧖⍅ᵲᝍᇡ░⎹Ⓧญ✙
݉ᇡʭḡ᮹ Ñญᯕ݅.
ᅙᩑǍᨱᕽŁಅ⦽ᜍ௹ቭᩑđᇡ᮹ᱥ݉vࠥ۵ᦿᕽʑᚁ⦽
CCDႊჶ᮹⎹Ⓧญ✙ᱥ݉❭ƕ༉ऽᱢᬊᨱ᧞257kNᮝಽ
ᔑᱶࡹᨩ݅. ᯕ۵ᅙᩑǍᨱᕽᱽᦩ⦽ᱥ݉ᜅ⥥ย᮹vࠥෝӹ┡ԙ
äᮝಽ Fig. 7᮹ Pyᨱ ⧕ݚࡽ݅. ᷪ, ᱽᦩ ༉ߙᮡ ᦿᕽ ʑᚁ⦽
ၵ᪡zᯕ ᱥ݉ᜅ⥥ย᮹vᖒ, ݅᭑᮹ ᮁĊᮥŁಅ⦽እᖁ⩶ᖒ, ᱥ݉vࠥෝŁಅ⦹ᩡ݅. Table 1ᮡᱽᦩ༉ߙᨱᕽᔍᬊ⦽᯦ಆ⊹ෝ
ᱶญ⦽äᯕ໑Table 3ᮡᩑđᇡ᮹ᱥ݉vࠥᔑᱶᮥ᭥⦽ᄡᙹ᮹
᯦ಆ⊹ෝ ᱶญ⦽ äᯕ݅.
4. đŝᇥᕾ
ᱽᦩࡽᜍ௹ቭᩑđᇡ༉ߙ᮹á᷾ᮥ᭥⧕ᜍ௹ቭᩑđᇡᝅ⨹ℕ
ෝᱽ᯲⦹Łᰍ⦹ᝅ⨹ᮥᙹ⧪⦹ᩡ݅. Fig. 8ᮡᝅ⨹ℕ᮹⦹ᵲ-ᄡ᭥
đŝෝࠥ⦽äᯕ݅. Łᱶ⊂ᜍ௹ቭ᮹ḱ(DT 2)ᮡ↽᳦ᰍ⦹⦹
ᵲᯙ᧞845kNʭḡᖁ⩶Ñ࠺ᮥᅕᩡᮝ໑⊂໕ᨱᕽ᮹ᝍb⦽Ɂᩕ
ᮡၽᔾ⦹ḡᦫᦹ݅. ၹ໕, a࠺⊂ᜍ௹ቭ᮹ḱ(DT 1)ᮡ⦹ᵲᰍ⦹
Ⅹʑᨱ۵݅᭑ၵ᪡a࠺⊂ᜍ௹ቭᮁĊ॒᮹ᩢ⨆ᮝಽ⦹ᵲ᷾a᪡
ḱᯕእᖁ⩶ᖒᮥᅕᯕ݅a᧞200kNᇡ░ᖁ⩶᮹šĥෝӹ┡ԕ ᨩ݅. a࠺⊂ᜍ௹ቭᨱᕽ۵᧞600kNᇡ░⊂໕ᨱɁᩕᯕၽᔾ⦹໕ ᕽᱥ݉❭ƕ⩶┽ಽḥ⧪ࡹᨩᮝ໑, ᧞870kNᨱᕽ⦹ᵲᱡ⧎܆ಆᮥ
ᔢᝅ⦹۵ äᮝಽ ᇥᕾࡹᨩ݅.
ᝅ⨹ℕ᮹ᰍ⦹ᝅ⨹⬥❭ƕ᧲ᔢᮡFig. 9᪡z݅. Łᱶ⊂ᜍ௹ቭ
݉໕ᮡ⬂ႊ⨆Ɂᩕᯕၽᔾ⦹ᩡᮝӹ, ⊂໕ᨱᕽ۵ᝍb⦽Ɂᩕᯕ
qḡࡹḡᦫᮡၹ໕, a࠺⊂ᜍ௹ቭ݉໕ᮡᝍb⦽⬂ႊ⨆Ɂᩕŝ
⊂໕᮹ᱥ݉Ɂᩕᯕḥᱥࡹ໕ᕽ❭ƕࡹ۵᧲ᔢᮥᅕᩡ݅. ᕽ
ᜍ௹ቭȅࠥ᮹⦹ᵲᱥݍ܆ಆᮡŁᱶ⊂ᜍ௹ቭ᮹݅᭑vࠥᅕ݅a࠺
⊂ ᜍ௹ቭ᮹ vࠥa ḡ႑ᱢᯙ äᮝಽ ᇥᕾࡹᨩ݅.
Fig. 10ᮡ Łᱶ⊂ ᜍ௹ቭ᪡ a࠺⊂ ᜍ௹ቭ᮹ ℁ɝᨱ ๅพࡽ
ᄡ⩶ශĥ᮹ĥ⊂ၰ⧕ᕾđŝᯕ݅. ᝅ⨹ŝ⧕ᕾŖ☖ᱢᮝಽŁᱶ⊂
ᜍ௹ቭ۵ᔢᇡaᦶ⇶ᔢ┽, ⦹ᇡaᯙᰆᔢ┽ᨱ᳕ᰍ⦹໑, a࠺⊂
ᜍ௹ቭ۵ᔢᇡaᯙᰆᔢ┽, ⦹ᇡaᦶ⇶ᔢ┽ᯥᮥ⪶ᯙ⧁ᙹᯩ݅.
ᝅ⨹ đŝ, Łᱶ⊂ ၰ a࠺⊂ ᜍ௹ቭ section B᪡ section C᮹
℁ɝᮡᯙᰆᔢ┽ᨱᕽ᧞500kN᮹⦹ᵲᨱ⧎ᅖ⦹۵äᮝಽᇥᕾࡹ
ᨩᮝӹ, ⧕ᕾᨱᕽ۵༉ु℁ɝᯕ⧎ᅖ⦹ḡᦫ۵äᮝಽᇥᕾࡹᨩ݅.
Fig. 11ᮡŁᱶ⊂ᜍ௹ቭᨱๅพࡽ݅᭑ၵᔢ໕᮹⦹ᵲ-ᄡ⩶ශ
Fig. 8. Load-Deflection Results of Test
(a) Cracks on Movable Slab
(b) Cracks on Fixed Slab Fig. 9. Cracks on Floating Slab
(a) Fixed Slab
(b) Movable Slab
Fig. 10. Strain Results of Embedded Reinforcements
Fig. 11. Strain Results in Dowel Joint šĥᯕ݅. əฝᨱᕽ᪡zᯕᔢᇡၰ⦹ᇡ݅᭑ၵa༉ࢱᯙᰆᔢ┽ᨱ
᳕ᰍ⦹ᩡ݅. Fig. 10ŝFig. 11᮹đŝෝ᳦⧊⦹ᩍᇥᕾ⦹໕Łᱶ⊂
ᜍ௹ቭ᮹ ݅᭑ၵ᮹ ᔢᇡ ᄡ⩶ශᯕ ᯙᰆ(᭥ಽ ᅝಾ)ᨱᕽ ᵲᦺᇡ
℁ɝᄡ⩶ශᯕᦥ௹ಽᅝಾᮝಽᄡ⪵⦹ŁᯩᮝအಽᄡłᱱᯕŁᱶ
⊂ ᜍ௹ቭᨱ ᳕ᰍ⦹۵ äᮝಽ ᇥᕾࡽ݅.
ᜍ௹ቭȅࠥᝅ⨹ℕ᮹❭ƕÑ࠺ᮥᙹ⊹⧕ᕾᱢᮝಽᇥᕾ⦹ʑ᭥
⦹ᩍᦿᕽʑᚁ⦽ၵ᪡zᯕእᖁ⩶ᮁ⦽ᗭ⧕ᕾᮥᙹ⧪⦹ᩡ݅.
Fig. 12۵ᝅ⨹ℕ᮹⦹ᵲ-ᄡ᭥⧕ᕾđŝෝᝅ⨹đŝ᪡⧉̹ࠥ⦽
äᯕ݅. Łᱶ⊂ᜍ௹ቭ᮹⧕ᕾḱᮡⅩʑᨱ۵ᖁ⩶Ñ࠺ᮥᅕᯕ݅
ᰍ⦹⦹ᵲᯕ᧞300kNᇡ░a࠺⊂ᜍ௹ቭ᮹Ɂᩕᨱ᮹⧕ၙᖙ⦽
እᖁ⩶Ñ࠺ᮥᅕᩡ݅. ᯕ۵Łᱶ⊂ᜍ௹ቭḱ(DT 2)᮹ᝅ⨹đŝ
᪡ᮁᔍ⦽sᯕ݅. a࠺⊂ᜍ௹ቭ᮹⧕ᕾđŝ, ḱᮡᦿᕽᨙɪ⦽
ၵ᪡zᯕᮁĊ᮹Ⓧʑ᪡vᖒᮥŁಅ⦽ᜅ⥥ยᗭෝᔍᬊ⦹ᩍ
⦹ᵲᰍ⦹Ⅹʑ᮹እᖁ⩶ᖒᯕǍ⩥ࡽ݅. ᖁ⩶Ǎeᮥḡӹ᧞530kN ᨱᕽ⮉Ɂᩕᨱ᮹⦽እᖁ⩶Ñ࠺ᯕ᯲ࡹ݅a᧞850kN᮹⦹ᵲᨱ ᕽᱥ݉ᜅ⥥ยᯕɚ⦽⊹ᨱᯕ໑⧕ᕾᯕ᳦ഭࡹᨩ݅. ɚ⦽⦹ᵲᮡ
Fig. 12. Load-Deflection Results of Test and Analysis
⧕ᕾ⊹᪡ᝅ⨹⊹a᧞1%᮹᪅₉ෝᅕᩍᬑᙹ⦽ᔢššĥෝӹ┡ԕ ᨩ݅. ᝅ⨹ℕ᮹ Ñ࠺ᮡ ❭ƕ ᨱ ᩑᖒÑ࠺ᮥ ӹ┡ԕŁ ᯩᮝӹ
⧕ᕾ༉ߙᮡḲᵲᜅ⥥ย ᗭaᱥ݉vࠥᨱᕽ⧎ᅖ⦹໕ᕽᱥℕ
⧕ᕾᯕ ᳦ഭࡹŁ ᯩᮭᮥ ⪶ᯙ⧁ ᙹ ᯩ݅.
ᅙᩑǍᨱᕽ۵ᱥ݉❭ƕෝaᱶ⦹ᩍCCDႊჶᨱɝÑ⦽ᱥ݉v
ࠥෝᔑᱶ⦹Łᯕෝᩑđᇡᱥ݉ᜅ⥥ยvࠥಽᱢᬊ⦹ᩍእᖁ⩶
ᮁ⦽ᗭ⧕ᕾᮥᝅ⦹ᩡ݅. ⧕ᕾđŝaᝅ⨹ℕ᮹Ñ࠺ŝᮁᔍ⦽
äᮝಽᇥᕾࡹ۵ၵ, ᅙᩑǍᨱᕽᱽᦩ⦽ᩑđᇡ⧕ᕾ༉ߙᮡ┡ݚ⦽
äᮝಽ ❱݉ࡽ݅. ੱ⦽ ᜍ௹ቭȅࠥ ݅᭑ᩑđᇡ۵ ᧖⍅ᖅĥჶᨱ
ɝÑ⦽CCD ႊჶᮝಽᖅĥvࠥෝᔑᱶ⦹ᩍࠥ⧊ญᱢᯙäᮝಽ
ᇥᕾࡽ݅.
5. ᧞ၰđು
ᅙᩑǍᨱᕽ۵݅᭑ၵෝḢᱲ༉ߙ⦹Ł݅ᙹ᮹ḡᦶvᖒᮥŁಅ
⦽ ᜅ⥥ยᗭෝ ᯕᬊ⦹۵ ʑ᳕᮹⧕ᕾ༉ߙᮥ ݡℕ⧁ ᙹᯩ۵
e⠙⦹໕ᕽࠥᱶ⪶ᖒᯕᬑᙹ⦽ᜍ௹ቭᩑđᇡ⧕ᕾ༉ߙᮥᱽᦩ⦹
ᩡ݅. ᱽᦩ༉ߙᮡ݅᭑ၵෝ༉ߙ⦹ḡᦫŁḲᵲᱥ݉ᜅ⥥ยᗭಽ
ݡℕ⦹۵ႊჶᯕ݅. ᱥ݉ᜅ⥥ย᮹vᖒᮡʑ᳕᮹Beam on elastic foundation ᯕುᨱɝÑ⦹Łᜍ௹ቭ᮹eĊᮥŁಅ⦹ᩍᔑᱶࡹᨩ ᮝ໑݅᭑᮹ᮁĊᮥŁಅ⦹ᩍⅩʑvᖒᮥđᱶ⦹ᩡ݅. ᱥ݉ᜅ⥥ย ᮹vࠥ۵⎹Ⓧญ✙ᱥ݉❭ƕෝaᱶ⦽CCD ႊჶᨱ᮹⧕ᔑᱶ⦹ᩡ
݅. ᱽᦩ༉ߙ᮹┡ݚᖒᮥ᯦᷾⦹ʑ᭥⧕ᝅ⨹ℕ᮹ᰍ⦹ᝅ⨹ᮥᝅ
⦹ᩡ݅. ᅙ ᩑǍᨱᕽ۵ ݅ᮭŝ zᮡ đುᮥ ᨩ݅.
(1) ᝅ⨹ᱢᩑǍđŝ, a࠺⊂ᜍ௹ቭ۵ᱥ݉⦹ᵲᯕ᧞870kNᨱᕽ
ᱥ݉❭ƕ⩶┽᮹Ɂᩕᯕḥᱥࡹ໑⦹ᵲᱡ⧎܆ಆᮥᔢᝅ⦹ᩡ݅.
Łᱶ⊂ᜍ௹ቭ۵↽᳦ᰍ⦹⦹ᵲʭḡᖁ⩶Ñ࠺ᮥᅕᩡ݅.
ᕽ, ᜍ௹ቭȅࠥ᮹⦹ᵲᱥݍ܆ಆᮡa࠺⊂ᜍ௹ቭ᮹vࠥa
äᮝಽ ❱݉ࡽ݅.
(4) ᱽᦩࡽ⧕ᕾ༉ߙᮡᜍ௹ቭ݅᭑᳑ᯙ✙ෝ⡍⧉⦽⎹Ⓧญ✙
⡍ᰆ, ⎹Ⓧญ✙ȅ॒ࠥ᮹❭ƕʭḡ᮹እᖁ⩶Ñ࠺ᮥ⧊ญᱢ ᮝಽᩩ⊂⧉ᮝಽ៉ࠥಽ⡍ᰆၰ℁ࠥȅࠥ᮹ᖅĥ⬉ŝᱢᮝ ಽ ⪽ᬊࢁ ᙹ ᯩ݅.
qᔍ᮹ɡ
ᯕᩑǍ۵ǎ☁⧕᧲ᇡၙ௹℁ࠥʑᚁ}ၽᔍᨦ᮹ᩑǍእḡᬱ(ŝ ᱽჩ⪙ 07₉ᖙݡŁᗮ℁ࠥA01)ᨱ ᮹⧕ ᙹ⧪ࡹᨩܩ݅.
References
ABAQUS, Inc. (2007). ABAQUS/Standard, Version 6.71. Pawtucket, R.I., USA.
ACI Committee 318. (2008). Building code requirements for structural concrete and commentary (ACI 318M-08), American Concrete Institute, Detroit, Mich.
Bhatti, M., Molinas-Vega, I. and Stoner, J. (1998). “Nonlinear analysis of jointed concrete pavements.” Transportation Research Record: Journal of the Transportation Research Board, Vol.
1629, pp. 50-57.
Choi, D. and Chun, S. (2007). “Anchoring to concrete.” Magazine of Korea Concrete Institute, Vol. 19, No. 4, pp. 41-44 (in Korean).
El-Ariss, B. (2007). “Behavior of beams with dowel action.” Engineering Structures, vol. 29, No. 6, pp. 899-903.
Frantzeskakis, C. and Theillout, J. N. (1989). “Nonlinear finite element analysis of reinforced concrete structures with a particular strategy following the cracking process.” Computers & Structures, Vol. 31, No. 3, pp. 395-412.
He, X. G. and Kwan, A. K. H. (2001). “Modeling dowel action of reinforcement bars for finite element analysis of concrete structures.”
Computers & Structures, Vol. 79, No. 6, pp. 595-604.
Kim, J. and Hjelmstad, K. (2003). “Three-dimensional finite element analysis of doweled joints for airport pavements.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 1853, pp 100-109.
Korea Concrete Institute (2007). Design code for concrete structures, Appendix , pp. 462-494 (in Korean).
Land Transport and Maritime R&D Report. (2011). Development of low vibration track (Floating slab track) and technology for improvement of performance of long-span bridges (in Korean).
Lee, J. and Fenves, G. L. (1998). “Plastic-damage model for cyclic loading of concrete structures.” Journal of Engineering Mechanics Division, ASCE, Vol. 124, No. 8, pp. 892-900.
Lubliner, J., Oliver, J., Oller, S. and Oñate, E. (1989). “A Plastic- damage model for concrete.” International Journal of Solids and Structures, Vol. 25, No. 3, pp. 299-326.
Martin-Perez, B. and Pantazopoulou, S. J. (2001). “Effect of bond,
aggregate interlock and dowel action on the shear strength degradation of reinforced concrete.” Engineering Structures, Vol.
23, No. 2, pp. 214-227.
Millard, S. G. and Johnson, R. P. (1984). “Shear transfer across cracks in reinforced concrete due to aggregate interlock and to dowel action.” Magazine of Concrete Research, Vol. 36, No. 126, pp. 9-21.
Soroushian, P., Obaseki, K. and Rojas, M. C. (1987). “Bearing strength and stiffness of concrete under reinforcing bars.” ACI Material Journal, Vol. 84, No. 3, pp. 179-184.
