* ᩑᖙݡ⦺Ʊ ᔍ⫭⪹Ğᜅ▽Ŗ⦺ᇡ ၶᔍŝᱶ ([email protected])
Received May 21, 2013/ revised June 25, 2013/ accepted August 7, 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͵͵ǤͷǤͳͻ͵ͷ
Ǥ ǤǤ
ᢦⴺ#㯂ⵣ㙾⛢ᾎᱛⴖ#≾ᢦ′#⍂⛛ⴂ#㝳㬚#㌚#Ꮾᨣ-ᾎᱛ#⽿ቻ␂#ⷚ⬆
୍ઽ ȵ୨ঃত ȵੲঃ
Kim, Jaeyoung*, Jeong, Sangseom**, Ahn, Sangyong***
Proposed Optimized Column-pile Diameter Ratio with Varying Cross-section for Bent Pile Structures
ABSTRACT
In this study, the behavior characteristics of bent pile structures with varying cross-section was examined through the measured results of field load test. A framework for determining the bending stress is calculated based on the stresses in the circumference of the pile using 3D finite element analysis. It is found that the bending stress near the pile-column joint changes rapidly and fracture zones occurs easily at variable cross-sections in bent pile structures. Also, the optimized column-pile diameter ratio was analyzed through the relationship between the column-pile diameter ratio and lateral crack load ratio. Based on this study, the optimized column-pile diameter ratio can be obtained near the inflection point of the curve between the column-pile diameter ratio and lateral crack load ratio. Therefore, a present study by considering the optimized variable cross-section condition would be improved bent pile structures design.
Key words : Bent pile structures, Variable cross-section, Finite element analysis, Optimized column-pile diameter ratio, Bending moment
Ⅹಾ
ᅙᩑǍᨱᕽ۵ᄡ݉໕݉ᯝ⩥ᰆ┡ᖅั૾᮹Ñ࠺✚ᖒᮥ⠪a⦹Łᯱ⩥ᰆᰍ⦹⨹ᔍಡෝᇥᕾ⦹ᩡᮝ໑, ੱ⦽3₉ᬱᮁ⦽ᗭ⧕ᕾᮥᯕᬊ⦹ᩍ
ั૾ԕᇡᨱᕽၽᔾ⦹۵᮲ಆᮥ☖⧕ᝍࠥᄥ⮉᮲ಆᮥᔑᱶ⦹ᩡ݅. ᇥᕾđŝ, ݉ᯝ⩥ᰆ┡ᖅั૾᮹ᄡ݉໕ᇡɝᨱᕽ⮉᮲ಆᯕḲᵲࡹᨕᰍഭ
❭ƕaၽᔾ⦹ʑaᰆᛍᬕäᮥᙹᯩᨩ݅. ᯕෝ☁ݡಽ, ݉ᯝ⩥ᰆ┡ᖅั૾᮹ʑࣆ-ั૾ḢĞእ᪡ᙹ⠪Ɂᩕ⦹ᵲእšĥෝ☖⧕↽ᱢ᮹ʑࣆ -ั૾ḢĞእෝᱽᦩ⦹ᩡ݅. ᩑǍđŝ, ↽ᱢ᮹ʑࣆ-ั૾ḢĞእ۵ʑࣆ-ั૾ḢĞእ᪡ᙹ⠪Ɂᩕ⦹ᵲእšĥłᖁ᮹ᄡłᱱᇡɝᨱᕽᔑᱶࡹᨩ ᮝ໑, ݉ᯝ⩥ᰆ┡ᖅั૾ᖅĥᨱ↽ᱢᄡ݉໕✚ᖒᮥŁಅ⦽݅໕}ᖁࡽᖅĥaᯕᨕḩᙹᯩᮥäᮝಽ❱݉ࡹᨩ݅.
áᔪᨕ ݉ᯝ⩥ᰆ┡ᖅั૾, ᄡ݉໕, ᮁ⦽ᗭ⧕ᕾ, ↽ᱢʑࣆ-ั૾ḢĞእ, ⮉༉ູ✙
1. ᕽು
⩥ᰍᰆݡƱప, ⅩŁ⊖Õྜྷ, ࠥಽၰĞᱥ℁॒᮹ݡȽ༉ÕᖅᔍᨦᨱᕽᔢᇡǍ᳑ྜྷ᮹ݡ⩶⪵·ᵲప⪵⇵ᖙ᪡ั૾ʑⅩ᮹ࠥᝍḡ
Ŗ ၽᔾࡹ۵ ᗭᮭ·ḥ࠺ ॒ᨱ ෙ ၝᬱ ᷾aಽ ʑ᳕ ⧎┡ั૾ ݡᝁ ⩥ᰆ┡ᖅั૾᮹ Ŗᯕ ᷾ݡࡹŁ ᯩ݅. ✚⯩ ⧕ᔢ Ʊప ၰ
ࠥಽƱ, Ğᱥ℁॒᮹Ǎ᳑ྜྷᮡᯝၹǍ᳑ྜྷᨱእ⧕⣮⦹ᵲၰḡḥ⦹ᵲ॒᮹ᙹ⠪⦹ᵲᨱၝq⦹ʑভྙᨱᙹ⠪⦹ᵲᮥŁಅ⦽ᖅĥa
ᵲ⦹Ł, Ǎ᳑⩶ᨱ ᯩᨕ ᔢᇡ ʑࣆŝ ⦹ᇡ ั૾᮹ ᯝℕ⪵ࡽ ᖅĥ ၰ ᩑǍa ⪽ၽ⯩ ᯕᨕḡŁ ᯩ݅. ᯕᨱ ↽ɝ ั૾⌂ᯕ ᨧᨕ
ᔢݡᱢᮝಽḡၹǕ₊ၰḡၹƱᯕᱢŁ, ⧎┡ั૾ᨱእ⧕ɝ᯦ᨱෙᗭᮭ·ḥ࠺ᮥ↽ᗭ⪵⧁ᙹᯩ۵݉ᯝ⩥ᰆ┡ᖅั૾(bent pile
ݓъėॡ
(a) Incheon Bridge
(b) Seohae Grand Bridge
Fig. 1. Application Examples of Bent Pile Structures
(a) T Type (b) 쨯GType
Fig. 2. Typical Types of Bent Pile Structures structures)ᯕ ኩჩ⯩ ᔍᬊࡹŁ ᯩ݅(Fig. 1).
Fig. 2᪡zᯕ, ݉ᯝ⩥ᰆ┡ᖅั૾ᮡᯝၹᱢᯙั૾ʑⅩ᪡ݍญ
ั૾⌂ᮥᖅ⊹⦹ḡᦫŁั૾ŝʑࣆᮥ⦹ӹ᮹ᯝℕ⪵ࡽᇡᰍಽ
ᯕᨕḥḢĞ1.0~3.0m᮹ั૾ʑⅩෝั⦽݅. ݅ෙʑⅩ⩶ᨱ
እ⧕ᔢᇡʑࣆŝ⦹ᇡั૾᮹ᵲeᨱั૾⌂ᯕᨧᯕʑࣆŝั૾ᯕ
ᯝℕ⪵ࡹᨕḡᔢᇡಽ࠭⇽ࡽǍ᳑ᱢᯙ✚ᖒᔢ, ᙹ⠪⦹ᵲᨱၝq⦹
ᩍᙹ⠪Ñ࠺ᨱݡ⦽á☁aᵲ⦹݅. ᯕ۵ḡᔢᇡಽ࠭⇽ࡽʑࣆ
ᰍഭaᙹ⠪⦹ᵲᨱݡ⧕ᗭᖒ݉ĥಽչᨕaíࢁᙹᯩᨕᰍഭ᮹
❭ƕ ີ⋕ܩ᷹ᮥ ❭ᦦ⧕ ⦹ʑ ভྙᯕ݅.
ᙹ⠪⦹ᵲᮥၼ۵ั૾ʑⅩ᮹⧕ᕾႊჶᮡᙹᝎ֥ᨱÙℱᩍ్
ႊჶॅᯕᱽᦩࡹᨩᮝ໑, ݡ⢽ᱢᯙ⧕ᕾႊჶᮝಽ۵Ğ⨹ᱢᯙႊჶ (Brinch Hansen, 1961; Broms, 1964), ᙹ⠪⦹ᵲᱥᯕჶ(Matlock, 1970; Reese and Wright, 1977; O'Neill and Gazioglu, 1984;
Jeong et al., 2004; Kim et al., 2011), ᮁ⦽ᗭჶ(Brown and Shie, 1991; Jeremic and Yang, 2002)ᯕᯩ݅. ↽ɝᩑǍđŝ
(Kim ॒, 2009)ᨱ᮹⦹໕, ᯕᵲᙹ⠪⦹ᵲᱥᯕჶੱ۵ᮁ⦽ᗭჶ ᯕḡၹ᮹እᖁ⩶ᖒŝᩑᗮᖒᮥŁಅ⧁ᙹᯩʑভྙᨱั૾ʑⅩ
⧕ᕾʑჶᮝಽᱢᱩ⦹݅ŁᅕŁࡹŁᯩ݅. ᮁ⦽ᗭჶᨱ᮹⦽ᙹ⊹
⧕ᕾᱢ༉ߙยʑჶᮡᰍഭ᮹እᖁ⩶ᖒŝั૾ŝḡၹ᮹Ğĥ໕
༉ߙย, əญŁ 3₉ᬱ Ğĥ ᳑Õ ॒᮹ ཹᔍa a܆⦹݅. ✚⯩,
ᮁ⦽ᗭ⧕ᕾჶᯱℕaᩑᗮℕ⧕ᕾᯕʑভྙᨱʑ┡ႊჶ(⦹ᵲᱥ ᯕ⧉ᙹჶ, ┥ᖒ⧕ᕾჶ॒)ॅᯕŁಅ⦹ʑᨕಅᬕḡၹ᮹ᩑᗮᖒᮥ
༉ᔍ⧁ᙹᯩ۵ᰆᱱᯕᯩ݅. ⦹ḡอ, ᮁ⦽ᗭ⧕ᕾᮥ☖⦽3₉ᬱ
ั૾-ḡၹ᮹༉ߙย᮹ᱶ⪶ᖒᮡḡၹŝั૾᮹ᰍഭ༉ߙၰྜྷᖒs ᨱ ݍḡအಽ ⩥ᰆ ᰍ⦹⨹ŝ᮹እƱ ॒ᮥ ☖⧕༉ߙย
á᷾ᯕ ᯝ₉ᱢᮝಽ ᯕᨕᲙ⦹۵ ݉ᱱࠥ ᯩ݅.
ǎᨱᕽ۵݉ᯝ⩥ᰆ┡ᖅั૾ᨱš⦽ᩑǍ(John, 2001; Kerop, 2001; Chai, 2002) ၰᱢᬊᔍಡa݅ᙹḥ⧪ࡹᨕ᪵݅. ⦹ḡอ, ǎԕ᮹Ğᬑ2004֥ᯖᔑ~ᰆᙹeŁᗮࠥಽ݉᧲Ʊᨱ⨹Ŗᮥ
ᝅ⦽äᯕᮭᯙอⓝᝅᱽᱢᬊࡽʑaʙḡᦫᦥᔢݡᱢᮝಽ
ŖᔍಡaฯḡᦫŁ, ᔢᇡʑࣆŝ⦹ᇡʑⅩ᮹Ğĥaᇩᇥ⦽
݉ᯝ⩥ᰆ┡ᖅั૾᮹Ǎ᳑ᱢ✚ᖒᔢǍ᳑⧕ᕾᮝಽǎ⦽⦹ᩍḡၹ Ŗ⦺⊂໕ᨱᕽ᮹ᩑǍ۵ၙእ⦽ᝅᱶᯕ݅. ⩥ᰍǎԕ݉ᯝ⩥ᰆ┡ᖅ
ั૾ᖅĥჶᮡࠥಽƱᖅĥʑᵡ(2004)ᨱᕽᱽ⦹۵ᖅĥႊჶᨱ
ᖅĥ⦹໑, ⦥ᨱ۵AASHTO(2002), FHWA(1987) ॒᮹
ǎʑᵡᮥᱢᬊ⧁ᙹᯩࠥಾࡹᨕᯩ݅. ݉ᯝ⩥ᰆ┡ᖅั૾ᨱ
š⦽ᩑǍಽ۵ᗱ⩢ᙹ॒(2005)ᮡᯙݡƱŁaƱǍe᮹ʑⅩ⩶
ᮝಽ ݉ᯝ ⩥ᰆ┡ᖅั૾ᮥ ᱢᬊ⦹ᩍ ⠪a⦹ᩡŁ, ᱶᔢᖍ ॒ (2005; 2006)ᮡᙹ⠪⦹ᵲᨱၝq⦽݉ᯝ⩥ᰆ┡ᖅั૾᮹ᙹ⠪Ñ࠺
✚ᖒᨱ š⦽ ᩑǍ ၰ P-ⱀ ⬉ŝෝ Łಅ⦽ ݉ᯝ ⩥ᰆ┡ᖅั૾᮹
Ñ࠺ᩑǍෝᙹ⧪⦹ᩡᮝ໑, ᗱ⩢ᙹ॒(2006)ᮡ݉ᯝ⩥ᰆ┡ᖅั૾
᮹ԕḥ⧕ᕾၰ℁ɝᖅĥᨱݡ⦽ᩑǍෝᙹ⧪⦹ᩡ݅. ੱ⦽, ↽ɝᨱ
۵ʡᔢȡ॒(2008)ᮡ݉ᯝ⩥ᰆ┡ᖅั૾᮹ᙹ⠪Ñ࠺✚ᖒᨱš⧕
ᇥᕾ⦹ᩡŁ, ᄡ݉໕݉ᯝ⩥ᰆ┡ᖅั૾᮹ᙹ⠪Ñ࠺ᇥᕾ(ᖒ℁Ƚ, 2008), ݉ᯝ⩥ᰆ┡ᖅั૾᮹ᗭᖒ⯭ḡෝŁಅ⦽↽ᱢᖅĥჶᱽᦩ (ᦩᔢᬊ, 2010) ၰ݉ᯝ⩥ᰆ┡ᖅั૾᮹e⠙⧕ᕾၰ↽ᗭ℁ɝእ
ᇥᕾ(ʡᰍᩢ॒, 2011) ॒᮹݉ᯝ⩥ᰆ┡ᖅั૾ʑⅩ᮹ᖅĥၰ
⧕ᕾႊჶᨱ š⦽ ᩑǍa ᙹ⧪ࡹᨩ݅.
݉ᯝ⩥ᰆ┡ᖅั૾᮹Ǎ᳑⩶ᮡⓍíᔢᇡʑࣆŝ⦹ᇡั૾᮹
ḢĞᯕ࠺ᯝ⦽ ⩶ŝ ḢĞᯕ݅ෙ ᄡ݉໕ ⩶ᮝಽǍᇥ⧁ ᙹ
ᯩ݅. ั૾ŝʑࣆ᮹ ḢĞᯕ࠺ᯝ⦽݉ᯝ ⩥ᰆ┡ᖅั૾᮹Ğᬑ,
(a)
(b)
Fig. 3. Typical Types of Bent Pile Structures and Bending Moment Distributions: (a) Type 1; (b) Type 2
↽ݡ⮉༉ູ✙۵ḡ⢽໕ᦥ௹᧞1~3D(D۵ั૾ḢĞ) ᱶࠥ᮹
ʫᯕᨱᕽၽᔾࡹ໑, ᯕ↽ݡ༉ູ✙᭥⊹ᨱᕽᗭᖒ⯭ḡaၽᔾࡹ۵
äᮝಽᅕŁࡹŁᯩ݅(Caltrans, 2006). ə్ӹᗭᖒ⯭ḡaḡᵲᨱ ᕽ ၽᔾࢁ Ğᬑ, ݉ᯝ ⩥ᰆ┡ᖅั૾᮹ Ǎ᳑ᱢᯙ ≉᧞ᇡෝ Ḣᱲ
⪶ᯙ⦹ʑᨕಖŁᮁḡšญaŅ⦹အಽᗭᖒ⯭ḡaḡᔢᇡᨱᮁ
ࠥ⦹ᩍ Ğᱽᱢᯙ ᖅĥෝ ࠥ༉⦹ʑ ᭥⦽ ႊᦩᯕ ᱽ⦹Ł ᯩ݅
(AASHTO, 2002). ᯕෝ᭥⧕ʑࣆḢĞᮥั૾ḢĞᅕ᯲݅í
ᖅĥ⦹Ñӹั૾ᔢ݉ᇡෝvšᮝಽᅕv⦹۵॒᮹ᄡ݉໕⬉ŝෝ
ᱢᬊ⦹ᩍ, ᗭᖒ⯭ḡෝᄡ݉໕ᮝಽᮁࠥ⦹Łᰍഭ᮹❭ƕaᄡ݉໕
ᇡɝᨱᕽၽᔾ⧁ᙹᯩࠥಾ⦹Łᯩ݅. ᯕ᪡zᯕ, ᄡ݉໕ᮥŁಅ⦽
݉ᯝ⩥ᰆ┡ᖅั૾᮹ᖅĥ۵ŖᖒၰĞᱽᖒᮥ࠺ᨱอ᳒⧁
ᙹᯩḡอ, ⦽⠙ᮝಽ۵ᄡ݉໕݉ᯝ⩥ᰆ┡ᖅั૾ᮡʑࣆŝั૾᮹
ḢĞᯕ࠺ᯝ⦽Ğᬑᨱእ⧕ᗭᖒ⯭ḡ᮹⩶ᖒʙᯕaእƱᱢṈᦥ
ᔢݡᱢᮝಽ≉ᖒᱢ(brittle) Ñ࠺ᯕᮁၽࡹအಽ(ᗱ⩢ᙹ॒, 2005;
ᱶᔢᖍ॒, 2006) ᄡ݉໕ᖅĥᨱݡ⦽ℕĥᱢᯕŁ⧊ญᱢᯙá☁a
Ǎࡽ݅. ⦹ḡอᦥḢʭḡᄡ݉໕ᮥᱢᬊ⧉ᨱᯩᨕᱢᱩ⦽ʑࣆ-ั
૾᮹ᄡ݉໕እᨱݡ⦽ᩑǍaၙእ⦹Łᯕᨱݡ⦽ʑᵡࠥษಉࡹᨕ
ᯩḡᦫᦥ, ᝅᱽŖݡᇡᇥᔢᇡʑࣆ-⦹ᇡั૾᮹݉໕ᮥ
࠺ᯝ⦹í Ŗ⦹Ł ᯩ۵ ᝅᱶᯕ݅.
ᯕᨱᅙᩑǍᨱᕽ۵ᄡ݉໕ᮥaḡ۵݉ᯝ⩥ᰆ┡ᖅั૾᮹Ñ࠺
✚ᖒᮥ⠪a⦹ʑ᭥⧕, ⩥ᰆ⨹ᔍಡෝᇥᕾ⧉ŝ࠺ᨱั૾ŝ
ḡၹ᮹3₉ᬱᱢᯙᔢ⪙᯲ᬊᮥᱢᱩ⯩༉ᔍ⧁ᙹᯩࠥಾᯝಉ᮹
3₉ᬱ ᮁ⦽ᗭ(finite element, FE)⧕ᕾᮥ ᙹ⧪⦹ᩡᮝ໑, ᯕෝ
☖⧕ั૾ԕ᮹3₉ᬱᱢᯙၽᔾ᮲ಆᮥၵ┶ᮝಽᙹ⠪᮲ಆᮥᔑᱶ⦹
ᩡ݅. ੱ⦽, ḡᵲᇡᨱᕽၽᔾ⦹۵ᗭᖒ⯭ḡ᮹᭥⊹(Ǎ᳑ᱢ≉᧞ᇡ)
ෝḡᔢᇡ᮹ᄡ݉໕ᇡɝᮝಽᮁࠥ⧉ᮝಽ៉݉ᯝ⩥ᰆ┡ᖅั૾᮹
ᮁḡᅕᙹaᬊᯕ⧕ḩᙹᯩ۵}ᖁࡽᖅĥჶᮥᱽ⦹Łᯱ, ᵝ
ᩢ⨆ᯙᯱෝŁಅ⦽݉ᯝ⩥ᰆ┡ᖅั૾᮹↽ᱢʑࣆ-ั૾ḢĞእෝ
ᱽᦩ⦹ᩡ݅.
2. ᄡ݉໕ᮥaḡ۵݉ᯝ⩥ᰆ┡ᖅั૾᮹Ǎ᳑✚ᖒ
⋹ญ⡍ܩᦥᩑႊࠥಽǎ(California department of transportation, Caltrans)ᨱᕽ᯲ᖒࡽseismic design criteria ver1.4(2006)ᨱ
໕݉ᯝ⩥ᰆ┡ᖅั૾᮹⩶ᮡFig. 3ŝzᯕ, ࠺ᯝ݉໕ŝᄡ݉
໕⩶ᮝಽǍᇥ⧁ᙹᯩ݅. ࠺ᯝ݉໕Ǎ᳑۵ᔢᇡʑࣆŝ⦹ᇡ
ั૾᮹ḢĞᯕ࠺ᯝ⦽Ǎ᳑ಽᕽ, Ǎ᳑ᱢᯙ≉᧞ᇡaḡၹԕᨱᕽ
ၽᔾ⦽݅. ᯕ۵ʑࣆŝั૾᮹݉໕ᯕ࠺ᯝ⦽݉ᯝ⩥ᰆ┡ᖅั૾ᮡ
ั૾ŝʑࣆ᮹vᖒ₉ᯕaÑ᮹ᨧʑভྙᨱ༉ູ✙ᇥ⡍a᪥อ⦹
໑ ↽ݡ ⮉༉ູ✙ ၽᔾ᭥⊹۵ ḡ⢽໕ ᯕ⦹ ั૾ḢĞ(D) 1~3႑
ᱶࠥʫᯕᨱᕽၽᔾ⦽݅ŁᅕŁࡹŁᯩ۵ߑ, ᯕ᪡zᯕ݉໕ಆᯕ
ᯝᱶ⦽Ğᬑᗭᖒ⯭ḡ(plastic hinge)᮹ၽᔾ᭥⊹۵↽ݡ⮉༉ູ✙
ၽᔾ᭥⊹aࡽ݅. ᕽ❭ƕaၽᔾ⦹ʑᛍᬕᗭᖒ⯭ḡ᭥⊹a
ḡᵲᨱ ၽᔾࡹ۵ Ğᬑ ᮁḡšญa Ņ⦽ ྙᱽᱱᯕ ᯩ݅. ᯕᨱ
↽ɝᨱ۵ᗭᖒ⯭ḡෝḡᔢᇡʑࣆᮝಽᮁࠥ⦹ʑ᭥⧕, Fig. 3(b)᪡
zᯕḡᔢᇡ ʑࣆ ḢĞᮥั૾ ḢĞᅕ݅ ᯲íᖅĥ⦹ᩍ ḡᔢᇡ
ʑࣆ᮹ ݉໕ಆᮥ ᯲í ⦹Ñӹ, ḡᵲᇡ ั૾᮹ ᔢ݉ᇡ᭥ෝ vš
॒ᮝಽᅕv⦹ᩍ݉໕ಆᮥ᷾a┅۵݉ᯝ⩥ᰆ┡ᖅั૾᮹Ŗ ᯕᯕᨕḡŁᯩ݅. ᯕ᪡zᮡᄡ݉໕ᮥaḡ۵݉ᯝ⩥ᰆ┡ᖅั૾
ᮡ ั૾ ḢĞᯕ ʑࣆ ḢĞᅕ݅ Ⓧʑ ভྙᨱ ั૾-ʑࣆ᮹ vᖒ
₉ᯕಽᯙ⦹ᩍั૾-ʑࣆᱲ⧊ᇡᨱᄡłᱱᯕ⩶ᖒࡹŁ↽ݡᇡᰍಆ ᯕ ᄡ݉໕ ᇡɝᨱᕽ ၽᔾ⦹ᩍ, ᄡ݉໕ ᇡɝᯕ aᰆ ≉᧞⧕ḱᨱ
(a) (b)
Fig. 4. Subsurface Soil Profile and Shaft Embedments of Field Load Test Site: (a) Subsurface Profile and Pile Embedment; (b) Pile and Column Configuration
Table 1. Material Properties in Field Load Test Site (Jeon et al., 2009)
Site Type Material Properties
Ĺ
t(kN/m3) cu(kN/m2) ŋ(deg) 쩌 fc(MPa) fy(MPa) K(MPa/m) E(MPa)Incheon (2009)
Pile
Concrete 24.5 - - 0.2 45.0 - - 26,000
Steel - - - 0.33 - 420.0 - 210,000
Casing - - - 0.33 - 420.0 - 210,000
Soil
Residual soil 16.7 0.5 22.0 0.30 - - 2.7 -
Silty sand 1 16.8 2.0 27.0 0.35 - - 6.79 -
Silty sand 2 16.7 2.1 28.0 0.45 - - 24.4 -
Weathered soil 3 19.4 2.2 27.0 0.45 - - 61.0 -
ᗭᖒ⯭ḡ۵↽ݡ⮉༉ູ✙aၽᔾ⦹۵ḡᵲᇡั૾ᯕᦥܭ
ḡᔢᇡʑࣆᇡ᭥ಽᯕ࠺⦽݅ŁᅕŁࡹŁᯩ݅. ᕽ↽ݡᇡᰍಆ ᯕḡᔢᮝಽᮁࠥࡹ໕, Ǎ᳑ᱢ≉᧞ᇡෝᮁḡᅕᙹ⦹۵ߑᬊᯕ⦹အ ಽᄡ݉໕Ǎ᳑᮹ᱢᬊᯕᮁญ⦹݅. ⦹ḡอ, ᔢݡᱢᮝಽᄡ݉໕
ᇡɝᨱᕽɪĊ⦽⮉༉ູ✙᮹ᄡ⪵ಽᯙ⧕࠺ᯝ⦽ḢĞ᮹ั૾ᨱ
እ⧕⎹Ⓧญ✙᮹ᦶ⇶❭ƕaዉญၽᔾ⦹ᩍᗭᖒ⫭ᱥ܆ಆᯕqᗭ
ࡹ໑, ᩑᖒ܆ಆᯕqᗭࡹᨕᔢݡᱢᮝಽ≉ᖒᱢ(brittle)ᯙÑ࠺ŝ
ⓑᄡ᭥aၽᔾ⧁ᙹᯩ݅. ə్ӹᄡłᱱ᮹ᮁྕӹᄡ݉໕ᨱෙ
ᗭᖒ⯭ḡ᮹᭥⊹ᄡ⪵ᨱݡ⦽ᩢ⨆ᮡᦥḢ᮹čᯕᇥᇥ⦽ᔢ┽(ᖒ℁
Ƚ, 2008; ᱶᔢᖍ॒, 2009)ಽᕽ, ݉ᯝ⩥ᰆ┡ᖅั૾᮹ᗭᖒ⯭ḡ
ၽᔾḡᱱᨱ ݡ⦽ ᔢᖙ á☁a ⦥⦽ ᝅᱶᯕ݅.
3. ⩥ᰆ⨹ᔍಡ᮹ᇥᕾᮥ☖⦽ᄡ݉໕✚ᖒᇥᕾ
3.1 ෮ୋਏԹ૬
ᅙᱩᨱᕽ۵Fig. 4᪡zᯕ, ᯙ00ḡᩎᨱᕽᱥĞᙹ॒(2009)ᨱ
᮹⧕ᙹ⧪ࡽ6ᅙ᮹݉ᯝ⩥ᰆ┡ᖅั૾(RC3~RC8)᮹ᙹ⠪ᰍ⦹
⨹ᔍಡෝ☁ݡಽᄡ݉໕݉ᯝ⩥ᰆ┡ᖅั૾᮹Ñ࠺✚ᖒᮥᇥᕾ⦹
ᩡ݅. Fig. 4(a)᪡ zᯕ, ᅙ ⨹ᨱ ᱢᬊࡽ ั૾ 6ᅙᮡ ᝅ✙ḩ
༉௹ၰ⣮⪵☁ಽǍᖒࡽḡၹᨱɝ᯦ࡹᨕᯩŁ, ั૾ḢĞ(Dp) 1,000mm, ʑࣆ ḢĞ(Dc) 850mm ੱ۵ 1,000mm, ั૾ ʙᯕ
11m~12mᯕ໑, ʑࣆʙᯕ۵4mಽ༉ࢱ࠺ᯝ⦹݅. ⨹ั૾ᵲ, RC5~RC8 ั૾ᮡᄡ݉໕✚ᖒᮥŁಅ⦹ʑ᭥⦽ั૾ᮝಽᱢᬊࡹ
ᨩᮝ໑, RC5᪡ RC6 ั૾᮹ ʑࣆ ḢĞ(Dc)ᮡ 850mmಽ ั૾
ḢĞᅕ݅ ᯲ᮡ ᄡ݉໕ Ǎ᳑ෝ aḡŁ ᯩ݅. ੱ⦽, RC7ŝ RC8
ั૾ᮡᙹ⠪⦹ᵲ᯲ᬊ↽ݡ⮉༉ູ✙aၽᔾ⦹۵ᗭᖒ⯭ḡ᭥⊹
(1~3Dp)ᨱࢱ̹ 12mm(ᇡ2mm Łಅ) ၰ ʙᯕ3.0m᮹vš
⍡ᯕᝒᮥŖ⦹ᩍᗭᖒ⯭ḡၽᔾḡᱱᮥḡᔢᇡಽᮁࠥ⧁ᙹᯩࠥ
ಾ⦹ᩡ݅. ᯕෝ☖⦹ᩍʑࣆḢĞ᮹ᄡ⪵ၰvš⍡ᯕᝒᅕvᨱ
ෙᄡ݉໕✚ᖒᮥǍ⩥⦹ᩍ݉ᯝ ⩥ᰆ┡ᖅั૾᮹ᙹ⠪Ñ࠺ᮥ
ᇥᕾ⦹ᩡ݅. ⨹ั૾ᨱᱢᬊࡽᙹ⠪⦹ᵲᮡb⦹ᵲ݉ĥษ݅15ᇥ eḡᗮ⦹ᩍၽᔾ⦹۵ᙹ⠪ᄡ᭥ෝ⪶ᯙ⦹ᩡᮝ໑, ᯕভᙹ⠪⦹ᵲ᮹
Ⓧʑ۵ั૾ᄥಽ↽ݡ300~500kNᮝಽᕽั૾ᰍഭ᮹❭ƕaᯝᨕ ӹʑʭḡ᮹ɚ⦽⦹ᵲᯕᦥܭ┥ᖒÑ࠺ᮥչᨕᗭᖒÑ࠺ᯕӹ┡ӹ
Fig. 5. Lateral Load-Deflection Curves in Field Load Tests ۵ ⦹ᵲ ჵ᭥ʭḡෝ ᱢᬊ⦹ᩡ݅. ᝍᇡ Ǎᗮ℁ɝᨱ ݡ⦽ ᩢ⨆ᮡ
Fig. 4(a)᪡ zᯕ ⬂ႊ⨆ ℁ɝ ႑ɝeĊᮥ ݍญ⦹ᩍ ᯕᨱ ෙ
Ñ࠺✚ᖒᮥᇥᕾ⧁ᙹᯩࠥಾ⦹ᩡᮝ໑, ᯕᨱRC3, RC5, RC7
ั૾᮹ĞᬑHD16ᮥ300mm eĊᮝಽӹᖁ⩶┽ಽᱢᬊ⦹ᩡᮝ໑, RC4, RC6, RC8 ั૾ᮡ 65mm eĊᮝಽ ℁ɝᮥ ႑ɝ⦹ᩡ݅.
ݡᔢ ḡၹᮡ 8m ʫᯕʭḡ ඹ☁ ၰ ᝅ✙ḩ ༉௹ಽ Ǎᖒࡹᨕ
ᯩᮝ໑, ə⦹ᇡᨱ۵⣮⪵☁⊖ᯕ᳕ᰍ⦽݅. ⧕ᕾᱢᬊࡽྜྷᖒᮡ
ᯝၹᱢᯙ⎹Ⓧญ✙ྜྷᖒŝ⩥ᰆḡၹ᳑ᔍđŝ(N⊹) ၰʑ᳕ྙ⨭ᨱ
ᱽࡹᨕᯩ۵sᮥ☁ݡಽݡ⢽ᱢᯙsᮥᔑᱶ⦹ᩡ݅. 6ᅙ᮹⨹
ั૾᮹ ᱽᬱ ၰ ⩥ᰆ ḡၹ᳑Õᮡ Table 1ᨱ ӹ┡ԕᨩ݅.
3.2 ෮ୋਏէրंজ
Fig. 5۵݉ᯝ⩥ᰆ┡ᖅั૾6ᅙ(RC3~RC8)᮹ᙹ⠪⦹ᵲ-ั૾
ࢱᇡ(ḡ⢽໕)᮹ᙹ⠪ᄡ᭥šĥෝӹ┡ԙ݅. RC3ŝRC4 ั૾ŝ
zᯕั૾ḢĞŝʑࣆḢĞᯕ࠺ᯝ⦹Łᗭᖒ⯭ḡᇡᇥᨱ⇵aᱢᯙ
ᅕvᯕ ᨧ۵ ᯝၹᱢᯙ ⩶┽᮹ Ğᬑ, ⦹ᵲ 350kN(ᙹ⠪ᄡ᭥ ᧞
70~90mm ᇡɝ)ᨱᕽᗭᖒÑ࠺ᯕᯝᨕԍᮭᮥᙹᯩᨩᮝ໑, ᝍᇡ
Ǎᗮ℁ɝᯕ᳑ၡ⦹íŖࡽRC4aRC3ᅕ݅ⓑ⦹ᵲᮥḡḡ⧁
ᙹ ᯩᮝӹ ə ᩢ⨆ᮡ Ⓧḡ ᦫ۵ äᮝಽ ӹ┡ԍ݅.
ʑࣆḢĞŝั૾ḢĞᯕ݅ෙᄡ݉໕Ǎ᳑ෝaḡ۵RC5᪡
RC6᮹Ğᬑ, Ⅹʑᙹ⠪⦹ᵲ-ᄡ᭥ʑᬙʑ۵ʑࣆ-ั૾ḢĞᯕ࠺ᯝ
⦽RC3 ၰRC4᪡Ñ᮹እ⦹ḡอ, ᅕ݅ԏᮡ⦹ᵲᯙ220kN ᱶࠥᨱᕽᗭᖒÑ࠺ᯕၽᔾ⦹۵äᮝಽӹ┡ԍ݅. ᯕ۵⦹ᇡั૾ᨱ
እ⧕ᔢᇡʑࣆ᮹݉໕ᱢᯕ᯲ᦥḡ໕ᕽǍ᳑ᱢ≉᧞ᇡaḡ⢽໕
ᇡɝ(ʑࣆ-ั૾Ğĥᇡ)ᮝಽᯕ࠺⧉ŝ࠺ᨱᯝᱶᯕᔢ᮹⦹ᵲ(┥
ᖒÑ࠺ᮥչᨕᗭᖒÑ࠺ᮥ⦹۵݉ĥ᮹⦹ᵲ)ᯕ᯲ᬊ⧁Ğᬑᨱ۵
ḢĞᯕ࠺ᯝ⦽RC3 ၰRC4ᅕ݅ᔢݡᱢᮝಽั૾ᰍഭ᮹ᇡᰍಆᯕ
qᗭ⦹ᩡʑ ভྙᯙ äᮝಽ ❱݉ࡽ݅.
⍡ᯕᝒᮝಽᗭᖒ⯭ḡᇡᇥ(↽ݡ⮉༉ູ✙᭥⊹)ᮥᅕv⦽RC7 ŝRC8᮹Ğᬑ, ᙹ⠪⦹ᵲ-ᄡ᭥ə௹⥥᮹Ⅹʑʑᬙʑa݅ෙ⨹
ั૾(RC3~RC6)ŝእ⦹ḡอ, ⦹ᵲ200kNᯕչᨕᗭᖒ݉ĥಽ
ḥ᯦⧁ᙹಾᱱ₉ᄡ݉໕ᮥaḡ۵⨹ั૾(RC5 ၰRC6)ŝእ
⦽ʑᬙʑෝᅕᯕ۵äᮝಽӹ┡ԍ݅. ੱ⦽᯲ᬊ⦹ᵲᨱෙั૾᮹
ᙹ⠪ḡḡಆᮡᯝၹᱢᯙ⩶┽᮹݉ᯝ⩥ᰆ┡ᖅั૾(RC3, RC4)ᅕ
݅݅ᗭ׳ᮡ500kNᨱᯕḡอ, ┥ᖒÑ࠺ᮥչᨕᗭᖒÑ࠺݉ĥෝ
ᅕᯕ۵ᱱᯕ݅ෙ⨹ั૾ᨱእ⧕ᇥ⦹íӹ┡ӹḡᦫᦹ݅.
ᯕ۵ ḡ⢽໕ ᯕ⦹ 3m ᱶࠥ ᅕvࡽ ⍡ᯕᝒᨱ ᮹⧕ ⮉༉ູ✙᮹
ᇥᔑᱶࠥa RC3 ၰ RC4 ั૾ᅕ݅ ݅ᗭ մᨕᲭʑ ভྙᯕŁ
❱݉ࡽ݅.
3.3 ౿ැজଡധ෮ୋਏॷߢंজ
ᅙ ᱩᨱᕽ۵ ݉ᯝ ⩥ᰆ┡ᖅั૾᮹ ᄡ݉໕ Ñ࠺ ✚ᖒᮥ ᅕ݅
ᔢᖙ⯩⠪a⦹Łᮁ⦽ᗭ⧕ᕾ༉ߙย᮹ᱶ⪶ᖒᮥá᷾⦹ʑ᭥⧕,
⩥ᰆ⨹đŝ᪡3₉ᬱᮁ⦽ᗭ⧕ᕾ(FEM)ᮥ☖⦽đŝෝእƱᇥ ᕾ⦹ᩡ݅. ᅙ⧕ᕾᨱᕽ۵ḡၹᔢᬊ3₉ᬱᮁ⦽ᗭ⧕ᕾ⥥ಽəఉ ᯙPLAXIS 3D Foundation(Ver. 2.2, 2008)ᮥᔍᬊ⦹ᩡ݅. ⧕ᕾ ᨱᔍᬊࡽḡၹၰั૾ྜྷᖒᮡ⩥ᰆ᳑Õŝ࠺ᯝ⦹íᱢᬊ⦹ᩡ݅.
Fig. 6ᮡ⩥ᰆ⨹᮹ᙹ⠪⦹ᵲ-ั૾ࢱᇡ(ḡ⢽໕) ᄡ᭥đŝsŝ
ᙹ⊹⧕ᕾᮥ☖⦽ᩩ⊂sᮥ እƱ⦹ᩍࠥ⦽äᯕ݅. እƱđŝ, ᱥၹᱢᮝಽ Ⅹʑ ┥ᖒ݉ĥ(᧞ 200~300kN)ෝ չᨕ ᗭᖒ݉ĥಽ
iᙹಾᙹ⊹⧕ᕾᮥ☖⧕ᔑᱶࡽᙹ⠪⦹ᵲ-ᄡ᭥łᖁđŝa⩥ᰆ
⨹đŝᅕ݅ḡḡಆᮥ݅ᗭⓍíᩩ⊂⦹۵äᮝಽӹ┡ӹ, ᙹ⊹⧕ᕾ
ᮥᯕᬊ⦽⧕ᕾᮡḡḡಆᮥŝݡ⠪a⦹۵äᮥᙹᯩᨩ݅. ✚⯩, Fig. 6(e)᮹všᮝಽᅕvࡽRC7 ั૾᮹Ğᬑ, ᝅᱽ⩥ᰆᰍ⦹⨹
ᨱᕽ۵ᗭᖒ݉ĥa૽ಘ⦹íӹ┡ӹḡᦫᦹḡอ, ᙹ⊹⧕ᕾđŝᨱ ᕽ۵ ᧞ 200kN᮹ ┥ᖒ݉ĥෝ չᨕ ᗭᖒ݉ĥa ӹ┡ӹ໕ᕽ ࢱ
đŝs᮹₉ᯕෝᅕᩡ݅. ə్ӹᯝၹᱢᮝಽḡၹᇥᨱᕽ۵ḡၹ ᨱእ⧕ั૾᮹vᖒᯕๅᬑⓍʑভྙᨱั૾ᰍഭ᮹❭ƕᅕ݅
ḡၹ❭ƕaຝᱡၽᔾ⦹íࡽ݅. ᕽั૾᮹ᙹ⠪Ñ࠺ᇥᕾᮥ
᭥⧕ᕽ۵ั૾ᰍഭอᮥŁಅ⦽⧕ᕾᯕᦥܭḡၹ-ั૾᮹ᔢ⪙᯲ᬊ
ᮥŁಅ⦽⧕ᕾᮥᙹ⧪⧕⦹໑, ั૾Ñ࠺⠪aั૾ᰍഭa
❭ƕࡹ۵ɚ⦽ᔢ┽ᅕ݅┥ᖒÑ࠺ੱ۵ᗭᖒÑ࠺ᮥᅕᯕ۵݉ĥʭ ḡෝŁಅ⦹۵äᯕᵲ⦹݅. ᯕᨱᙹ⊹⧕ᕾŝ⩥ᰆ⨹ᮥእƱ⦽
đŝ, ᅙᩑǍᨱᕽᱢᬊ⦽ᙹ⊹⧕ᕾႊჶᮡ݉ᯝ⩥ᰆ┡ᖅั૾᮹
Ñ࠺ᮥᨕ۱ᱶࠥᱢᱩ⯩ᩩ⊂⦹Łᯩ݅Ł❱݉ࡹᨩᮝ໑, ᕽ
4ᰆᨱᕽ۵PLAXISෝᯕᬊ⦹ᩍ⩥ᰆ⨹ᮝಽ۵ᔢᖙ⯩Łಅ⦹ʑ
ᨕಅᭁ݉ᯝ⩥ᰆ┡ᖅั૾᮹ᄡ݉໕ᨱݡ⦽ᩢ⨆ᮥᔢᖙ⯩⠪a
ෝ ⦹Łᯱ ⦽݅.
(a) Pile RC3 (b) Pile RC4 (c) Pile RC5
(d) Pile RC6 (e) Pile RC7 (f) Pile RC8
Fig. 6. Measured and Computed Lateral Load-Deflection Curves at Pile Head
4. ᮁ⦽ᗭ⧕ᕾᮥ☖⦽݉ᯝ⩥ᰆ┡ᖅั૾᮹ᄡ݉໕ᇥᕾ
ᅙᱩᨱᕽ۵ḡၹ-ั૾᮹ᔢ⪙᯲ᬊᮥŁಅ⦽ᮁ⦽ᗭ⧕ᕾ⥥ಽ əఉᯙPLAXISෝᯕᬊ⦹ᩍ݉ᯝ⩥ᰆ┡ᖅั૾᮹ʑࣆŝั૾
ḢĞᯕ ݅ෙ ᄡ݉໕ Ǎ᳑᮹ ᩢ⨆ᮥ ᔢᖙ⯩ ᇥᕾ⦹Łᯱ ⦹ᩡ݅.
ᅙ⧕ᕾᨱᱢᬊࡽ᳑ၡ⦽ᔍḩ☁ḡၹၰั૾ྜྷᖒᮡTable 2᪡
z݅.
4.1 ැজԹ૬ࢫୡࢄন
Fig. 7ᮡ⧕ᕾᨱᕽᔍᬊࡽݡ⢽ᱢᯙᮁ⦽ᗭີᛍၰĞĥ᳑Õ
ᮥᅕᩍᵝŁᯩ݅. ີᛍ᮹ᱥℕᱢᯙⓍʑ۵ั૾᮹Ñ࠺ᯕĞĥ໕᮹
ᩢ⨆ᮥၼḡᦫࠥಾ⦹ʑ᭥⦹ᩍ, մᯕႊ⨆ᮡั૾Ğĥಽᇡ░
ั૾ḢĞ(D)᮹10႑(10D), ʫᯕႊ⨆ᮡั૾ᖁ݉ᇡಽᇡ░ั૾
ʙᯕ(L)᮹0.5႑(0.5L)ෝᱢᬊ⦹ᩡ݅(Wallace et al., 2002). ⧕ᕾ ᨱᱢᬊࡽᗭ(element)۵15}᮹ᱩᱱᮝಽǍᖒࡽᡱʑ(wedge)
ᗭᯕ໑, ⅾᱩᱱᙹ۵᧞17,500}ᯕ݅. ḡၹŝั૾ᇡɝᨱᕽ۵
ࢱᰍഭe᮹ⓑvᖒ₉ᯕၰᙹ⠪⦹ᵲᮝಽᯙ⧕ᱥ݉ᄡ⩶ᯕᩩᔢࡹ
အಽ᳑ၡ⦽ີᛍෝᔍᬊ⦹ᩡŁ, ั૾ᮝಽᇡ░Ñญaມᨕḩᙹಾ
ີᛍ᮹ၡࠥෝqᗭ⎑݅. ᅙᮁ⦽ᗭ⧕ᕾᨱᕽั૾ᮡ┥ᖒ༉ߙ (linear-elastic)ᮥᱢᬊ⦹ᩡᮝ໑, ☁ᔍ⊖ᮡMohr-Coulomb༉ߙᮥ
ᔍᬊ⦹ᩡ݅. ⧕ᕾᨱ ᱢᬊ⦽ ᰍഭ ᱶᙹ۵ ݡ⢽ᱢᯙ ᳑ၡ⦽ ᔍḩ☁
ḡၹྜྷᖒᮥ☁ݡಽᔑᱶ⦹ᩡ݅. ั૾ŝḡၹᔍᯕ᮹Ğĥ໕(interface) ᨱ۵PLAXISᨱᕽᱽŖ⦹۵ᱲⅪᗭ(contact element)ෝ ᔍᬊ⦹ᩍ
ḡၹŝั૾ᔍᯕ᮹ၙҥ్ḱ(slip behavior) ၰั૾᮹aಆၹݡႊ
⨆ᨱᕽ ၽᔾ⧁ ᙹ ᯩ۵ ᯙᰆಆᨱ ᮹⦽ ḡၹ-ั૾ ᇥญ⩥ᔢ(gap behavior)ᮥ༉ߙย⦹ᩡ݅. Ğĥ໕᮹bᗭ۵3D quadrilateral 8-node ᗭᨱ᮹⧕Ǎᖒࡹᨩ݅. ᙹ⠪⦹ᵲᮥၼ۵ั૾᮹ั૾-ḡ ၹĞĥ໕༉ߙᮥᱢᬊ⦽ʑ᳕ᩑǍॅ(Won ॒, 2006; Jeong ॒, 2009)ᨱᕽᅕŁࡽၵ᪡zᯕ, ḡၹŝᱲ⧕ᯩ۵ั૾ᗭ᮹ᱩᱱᮡ
Coulomb ษₑᯕುᨱ᮹⧕ၙҥ్ḡíࡽ݅. Coulomb ษₑᯕುᮡ
Ğĥ໕ԕᨱᕽၽᔾ⦹۵ၙᗭᄡ⩶ᔢ┽᮹┥ᖒÑ࠺ŝᩢǍᄡ⩶
ᔢ┽᮹ᗭᖒÑ࠺ᮝಽǍᇥ⧁ᙹᯩ݅. ┥ᖒÑ࠺ᔢ┽ᨱᕽ᮹Ğĥ໕
ᗭ۵ᵝᄡḡၹၰǍ᳑ᗭ᪡࠺ᯝ⦹íÑ࠺⦹ḡอ, ┥ᖒÑ࠺
ᔢ┽ෝչᨕᕽ۵ᄡ⩶ᯕၽᔾ⦹íࡹ໕ᗭᖒÑ࠺ᔢ┽ಽᱥᯕࡹᨕ
Table 2. Material Properties for Numerical Analysis
Soil condition Load transfer analysis Ĺt(kN/m3) cu(kN/m2) ŋ(deg) K(kPa/m) 쩄50
Sand loose
O’Neill 18.1 - 32 10,000 -
dense 19.1 - 40 34,000 -
Clay Soft
O’Neill 17.6 40 - 20,000 0.02
Stiff 18.6 120 - 136,000 0.005
Bent pile structures concrete steel
Young's Modulus (kPa) 2.46×107 2×108
Unconfined compressive strength (kPa) 27,000 400,000
Steel rebar type - H32
Cross-section area of steel rebar (mm2) - 805
Thickness of steel rebar (mm) 125(outer) / 225(inner)
(a) (b) Fig. 7. Typical Idealized 3D Model for FE Analysis: (a) 3D View; (b) Plane View
Ğĥ໕ ᗭ᮹ ၙҥ్ḱ Ñ࠺(slip behavior)ᯕ ᯝᨕӹí ࡽ݅.
ᯕ۵ᱥ݉v॒ࠥ᮹Ğĥ໕ྜྷᖒqᗭಽǍ⩥⧁ᙹᯩᮝ໑, ᯕ్⦽
Ğĥ໕ᗭ᮹vࠥqᗭ۵ั૾ᵝᄡᇡ✚ᖒᮥၵ┶ᮝಽᔑᱶࡽ
vࠥ qᗭĥᙹ(Rinter)ෝ ᔍᬊ⦹ᩍ ݅ᮭŝ zᯕ ᔑᱶ⦽݅.
Ɓ
Ƈ ƌƒƃƐá «
Ƈ ƌƒƃƐƁ
ƑƍƇƊì ŋ
Ƈ ƌƒƃƐá «
Ƈ ƌƒƃƐŋ
ƑƍƇƊ (1)ᩍʑᕽ, cinter᪡Ⱪinter۵Ğĥ໕᮹ᱱ₊ಆŝษₑbᯕŁ, csoil᪡
Ⱪsoil۵ ḡၹ᮹ ᱱ₊ಆŝ ษₑbᯕ݅. Rinter۵ Ğĥ໕ qᗭĥᙹ (interface reduction factor)ಽ ᪥ᱥ⦽ rigid ᔢ┽ᨱᕽ۵ 1.0ᮥ, ၹݡ᮹Ğᬑ۵0ᮥᔍᬊ⦽݅. ᅙᩑǍᨱᕽ۵PLAXISᨱᕽᱽŖ⦹
۵ᯝၹᱢᯙჵ᭥᮹s(ᔍḩ☁0.7, ᱱᖒ☁0.5)ᮥᱢᬊ⦹ᩡ݅.
ᙹ⊹⧕ᕾᨱᕽ۵ั૾ၰḡၹྜྷᖒᮥ☁ݡಽ⦽Ⅹʑ᮲ಆᔢ┽ෝ
Ǎ⩥⦹ʑ ᭥⧕ ᬱḡၹ ᔢ┽(initial condition)ෝ Łಅ⦹۵ äᯕ
⦥⦹໑, ᕽⅩʑ⠪⩶ᔢ┽(initial equilibrium state)᮹ᔑᱶ ᯕๅᬑᵲ⦹݅. ᅙ⧕ᕾᨱᕽ۵ᰍഭ᮹ᯱᵲᮥŁಅ⦽Ⅹʑ᮲ಆ
Fig. 8. Cross-Section of Bent Pile Structures in the Horizontal Direction
(a)
(b)
Fig. 9. Behavior Characteristics of Bent Pile Structures with Variable Cross-Section: (a) Bending Stress Distribution; (b) Stress Contour of Bent Pile Structures with Variable Cross-Section ᇥ⡍ෝᔑᱶ⦹ᩡᮝ໑, Ⅹʑ݉ĥ(initial step)ᯕ⬥, ั૾ᨱa⧕ḡ۵
ᙹ⠪⦹ᵲᮡั૾ࢱᇡᨱ݉ĥᄥ᷾a⦹ᵲᮝಽ༉ߙย⦹ᩡ݅. ੱ⦽
ั૾᮹ɝ᯦ᨱ᮹⦽ᵝᄡḡၹ᮹᮲ಆᄡ⪵ӹั૾ᨱၽᔾ⦹۵ඹ
⦹ᵲ(residual-force) ॒ᮥᙹ⊹⧕ᕾᮝಽ⧕ᕾ⦹ʑ᭥⧕ᕽ۵ฯᮡ
eᯕ⦥⦹အಽ, ᅙᩑǍᨱᕽ۵ั૾᮹ɝ᯦⬉ŝ۵Łಅ⦹ḡ
ᦫᦹ݅.
4.2 ැজէրࠜധ࣡ۚছଭඌଦߚՑഠ
ᮁ⦽ᗭ⧕ᕾᮡᩑᗮᖒᯕŁಅࡽᩑᗮℕ⧕ᕾᯕʑভྙᨱ, Fig.
8ŝzᯕ3₉ᬱᱢᯙั૾ԕ᮲ಆᮥᔑᱶ⧁ᙹᯩ݅. ᕽᅙ
ᩑǍᨱᕽ᮹ ั૾ ԕ ᮲ಆᮥ ᱢᇥ⦹۵ ႊჶᮥ ᔍᬊ⦹ᩡ݅. ั૾
ԕᇡ᮹᮲ಆᮡั૾ԕGauss ᱩᱱᨱᕽ᮹ၽᔾ᮲ಆᮥᔍᬊ⦹ᩡᮝ ໑, ᯕ్⦽ႊჶᮥ☖⦹ᩍᙹ⠪⦹ᵲᮥၼ۵ั૾᮹᯦ℕᱢᯙ᮲ಆᮥ
❭ᦦ⧁ᙹᯩ݅. Fig. 8ᮡᙹ⠪⦹ᵲᯕx-ႊ⨆ᮝಽa⧕Ჭᮥভ᮹
ᯥ᮹᮹ᝍࠥᨱᕽ᮹ั૾᮹⧕ᕾ݉໕ᮥӹ┡ԕ໑, əฝ᮹ᱱᖁᬱᮡ
ั૾ԕᇡ᮹Gauss ᱩᱱᮥᯕᮡäᯕ݅. ั૾᮹݉᭥ʙᯕݚᙹ⠪᮲ ಆ(px)ᮡั૾ԕᇡᨱᕽ᯲ᬊ⦹۵᮲ಆ᮹x-ႊ⨆ᖒᇥॅᮥ☖⦹ᩍ
ᔑᱶ⧁ᙹᯩᮝအಽ, ᯥ᮹᮹ᝍࠥᨱᕽ᮹bၽᔾ᮲ಆᮥ݅ᮭŝ
zᯕ x-ႊ⨆ ᖒᇥᮝಽ ᱶญ⦹ᩡ݅.
ᩍʑᕽ, Tx۵x-ႊ⨆ᄂ░ᯕŁ, nx,ny,nz۵bႊ⨆᮹݉᭥ᄂ░ෝ
ӹ┡ԙ݅.
ᅙ⧕ᕾᨱᕽy-ႊ⨆ᮡḡ⢽໕ᨱᩑḢᯙʫᯕႊ⨆ᯕအಽny۵
0ᯕ݅. ᕽ, ᨕḥx-ႊ⨆᮲ಆsᮥၵ┶ᮝಽ, ݉᭥ʙᯕݚ
ᙹ⠪᮲ಆᮡ ᱱᖁᬱᮥ ݅ᮭŝ zᯕ ᱢᇥ⦹ᩍ ᔑᱶ⦽݅.
Ǝ
Ɩá
õ
ƖƂ¥
(3)ᩍʑᕽ, Lᮡ gauss ᱩᱱॅᮥ ᯕᮡ ᱱɝᬱ᮹ ᬱᵝ݅.
᭥᪡zᮡŝᱶᮥ☖⧕, Fig. 9(a)᪡zᯕᝍࠥᄥᙹ⠪᮲ಆᮥ
ᔑᱶ⦹ᩡ݅. ʑࣆŝั૾᮹ḢĞᯕ࠺ᯝ⦽Ğᬑ᪡۵ݍญ, ᄡ݉໕
Table 3. Material Properties and Geometries for Optimized Column-Pile Diameter Ratio
Condition Variables
Pile length (m) 10 / 30
Pile diameter (m) 2.0
Column length (m) 10
Column diameter (m) 1.5 / 1.75 / 2.0 Steel reinforcement ratio (%) 1.0 / 1.5 / 2.0
Soil condition Loose sand / Dense sand / Soft clay / Stiff clay
(a)
(b)
Fig. 10. Optimized Column-Pile Diameter Ratio: (a) Column-Pile Diameter Ratio Curve; (b) Bending Moment-Depth Distribution
݉ᯝ⩥ᰆ┡ᖅั૾ᨱᕽ۵ᄡ݉໕ᇡɝ(ḡ⢽໕)ᨱᕽ᮲ಆ᮹ᄡ⪵a
ⓑäᮥᙹᯩᨩ݅. ᯕ۵ʑࣆ᮹ḢĞᯕqᗭ⧉ᨱʑࣆ᮹
vᖒᯕqᗭ⦹íࡹᨕǍ᳑ᱢᮝಽᄡ݉໕ᯕaᰆ≉᧞⦹ʑভྙᯙ
äᮝಽ ❱݉ࡽ݅. ੱ⦽, Fig. 9(b)᪡ zᯕ, ⦹ᵲᮥ ၼ۵ ᄡ݉໕
݉ᯝ⩥ᰆ┡ᖅั૾ᨱᕽ۵ᄡ݉໕ᇡɝᨱaᰆⓑ᮲ಆᯕḲᵲࡹ۵
äᮥᙹᯩᨩ݅. ᕽ, ᄡ݉໕ᮥaḡ۵݉ᯝ⩥ᰆ┡ᖅั૾ᨱᕽ ۵ ↽ݡ ⮉༉ູ✙ ᭥⊹ಽ ᱶ᮹ࡹ۵ ᗭᖒ⯭ḡ᮹ ᭥⊹a ḡ⢽໕
ɝಽ ∊ᇥ⯩ ᯕ࠺⧁ ᙹ ᯩᮥ äᮝಽ ❱݉ࡽ݅.
5. ݉ᯝ⩥ᰆ┡ᖅั૾᮹↽ᱢʑࣆ-ั૾ḢĞእᱽᦩ
5.1 ౖୡ׆ܱ-࠱ތլणՍ
ᦿᕽʑᚁ⦽ၵ᪡zᯕ, AASHTO(2002)ෝእ⦽݉ᯝ⩥ᰆ┡
ᖅั૾᮹ ᖅĥ ʑᵡᨱᕽ۵ ḡᔢᇡ ʑࣆ᮹ ḢĞᮥ ḡᵲᇡ ั૾
ḢĞᅕ᯲݅íᖅĥ⦹ᩍ ḡᵲᇡᨱၽᔾ⦹۵ᗭᖒ⯭ḡෝḡ⢽໕
ᇡɝᮝಽᮁࠥ⧁ᙹᯩŁᯕෝ☖⧕ᮁḡᅕᙹaᬊᯕ⦹݅ŁᅕŁ⦹
Łᯩ݅. ⦹ḡอʑࣆ-ั૾᮹ᄡ݉໕ᮥŁಅ⦹ʑ᭥⧕ʑࣆ᮹ḢĞ
ᮥᇡᱢᱩ⦹íqᗭ┅۵ᖅĥ۵᪅⯩ಅᗭᖒ⯭ḡ᮹ḡᔢᇡᮁࠥ
aᯕᨕḡḡᦫŁ, ḡᵲᇡั૾᮹ḢĞᯕ⦥ᯕᔢᮝಽŝ݅⦹í
ᖅĥࡹ۵ ॒ ᩍ్ ྙᱽᱱᯕ ၽᔾ⧁ ᙹ ᯩ݅.
ᯕᨱᅙᱩᨱᕽ۵↽ᱢʑࣆ-ั૾ḢĞእෝᔑᱶ⦹ᩍ݉ᯝ⩥ᰆ
┡ᖅั૾᮹ ↽ᱢ ᄡ݉໕ ᳑Õ᮹ ᱽ⦹Łᯱ ⦹ᩡ݅. ᯕෝ ᭥⧕
ḡၹ᳑Õ(᳑ၡ⦽ᔍḩ☁, ۱ᜉ⦽ᔍḩ☁, čŁ⦽ᱱᖒ☁, ᩑ᧞⦽
ᱱᖒ☁), ั૾ ᖙᰆእ, ℁ɝእ ॒ ᩍ్ ᯙᯱෝ Łಅ⦹ᩍ ⧕ᕾᮥ
ᙹ⧪⦹ᩡ݅. ⧕ᕾᨱᱢᬊࡽ݉ᯝ⩥ᰆ┡ᖅั૾ᮡั૾ḢĞ(Dp)ᯕ
2,000mm, ʑࣆʙᯕ(Lc) 10mᯕ໑, ḡၹၰั૾ᰍഭྜྷᖒᮡᦿᖁ
Table 2᪡z݅. ੱ⦽, ↽ᱢʑࣆ-ั૾ḢĞእෝᔑᱶ⦹ʑ᭥⦽
ᄡᙹ᳑Õᮡ Table 3ŝ z݅.
ᅙ ⧕ᕾᨱᕽ۵ ݉ᯝ ⩥ᰆ┡ᖅั૾᮹ ᰍഭ ❭ƕa ၽᔾ⧁ ভ᮹
Ɂᩕ⮉༉ູ✙ၰɁᩕ⦹ᵲᮥᔑᱶ⦹ʑ᭥⦽ั૾݉໕⧕ᕾ⥥ಽəఉ
Response 2000ŝᄡ݉໕⬉ŝෝᱶ⪶⯩Ǎ⩥⦹ʑ᭥⦽FB-Multipier (Ver. 4, 2012) ⥥ಽəఉᮥ࠺ᨱᔍᬊ⦹ᩡ݅. ᯕভ, Ɂᩕ⮉༉ູ
✙᪡Ɂᩕ⦹ᵲᮡ݉ᯝ⩥ᰆ┡ᖅั૾ᰍഭ᮹❭ƕaḡ۵Łᮁ⦽
sᮝಽᕽ, ᯕෝ ᔑᱶ⦹ʑ ᭥⦽ ⧕ᕾŝᱶᮡ ݅ᮭŝ z݅.
(1) Response2000ᮥᯕᬊ⦹ᩍ݉ᯝ⩥ᰆ┡ᖅั૾ᰍഭ᮹݉໕
ၰྜྷᖒᄡ⪵ᨱෙmoment-curvature šĥෝǍ⦹Łᯕෝ
☖⧕ Ɂᩕ ༉ູ✙ෝ ᔑᱶ⦽݅.
(2) FB-Multipierෝᯕᬊ⦹ᩍᙹ⠪⦹ᵲᮥၼ۵݉ᯝ⩥ᰆ┡ᖅ
ั૾᮹ b ⦹ᵲᨱ ෙ ↽ݡ ⮉༉ູ✙ෝ ᔑᱶ⦹Ł, ᯕෝ
☖⧕ ⦹ᵲ-↽ݡ ⮉༉ູ✙ šĥᮥ Ǎ⦽݅.
(3) (1)݉ĥᨱᕽǍ⦽Ɂᩕ༉ູ✙a(2)݉ĥಽᇡ░ᔑᱶࡽ⦹ᵲ -↽ݡ⮉༉ູ✙šĥᨱᕽ⧕ݚ⦹۵᭥⊹ෝŁ, əভ᮹
⦹ᵲᮥᔑᱶ⦽݅. ᯕভᔑᱶࡽ⦹ᵲᮥɁᩕᙹ⠪⦹ᵲᯕŁ
⧁ ᙹ ᯩ݅.
↽ᱢʑࣆ-ั૾ḢĞእ᳑Õᮥᔑᱶ⦹ʑ᭥⧕, Fig. 10ŝzᯕ
ʑࣆ-ั૾ḢĞእ(Dc/Dp)᪡ᙹ⠪Ɂᩕ⦹ᵲእ(F/FDc=Dp)᮹šĥෝ
ᇥᕾ⦹ᩡ݅. ᯕভ, F۵ʑࣆ᮹ḢĞᯕqᗭ⧉ᨱᄡ݉໕ᮥ
(a) Loose Sand (b) Dense Sand
(c) Soft Clay (d) Stiff Clay
Fig. 11. Optimized Column-Pile Diameter Ratio Under Lateral Crack Load Ratio aḡ۵݉ᯝ⩥ᰆ┡ᖅั૾᮹ᙹ⠪Ɂᩕ⦹ᵲᮥ᮹ၙ⦹໑, FDc=Dp۵
ʑࣆŝั૾᮹ḢĞᯕ࠺ᯝ⦽݉ᯝ⩥ᰆ┡ᖅั૾᮹ᙹ⠪Ɂᩕ⦹ᵲᮥ
ӹ┡ԙ݅. ᕽʑࣆŝั૾᮹ḢĞᯕ࠺ᯝ⦽Ğᬑ(Dc/Dp=1.0), ᙹ⠪Ɂᩕ⦹ᵲእ(F/FDc=Dp)۵1.0ᯕࡽ݅. ⦹ḡอᗭᖒ⯭ḡෝḡ⢽
໕ᇡɝᮝಽᮁࠥ⦹ʑ᭥⧕ᕽʑࣆ-ั૾ḢĞእ(Dc/Dp)ෝqᗭ┅
໕, ᷪʑࣆ᮹ḢĞᯕqᗭ⦹íࡹ໕ʑࣆ᮹Ɂᩕ༉ູ✙۵qᗭ⦹í
ࡹŁ ᙹ⠪ Ɂᩕ⦹ᵲእ(F/FDc=Dp)۵ 1.0ᅕ݅ ᯲ᦥḡí ࡽ݅(Fig.
10(a)). ᯕ᪡zᯕ, ʑࣆ-ั૾ḢĞእ(Dc/Dp)aqᗭ⧉ᨱᄡ݉
໕݉ᯝ⩥ᰆ┡ᖅั૾᮹ᙹ⠪Ɂᩕ⦹ᵲ(F)ᮥᔑᱶ⦽⬥ᯕෝʑࣆŝ
ั૾᮹ḢĞᯕ࠺ᯝ⦽݉ᯝ⩥ᰆ┡ᖅั૾᮹ᙹ⠪Ɂᩕ⦹ᵲ(FDc=Dp) ಽᱶȽ⪵⦹໕Fig. 10(a)᪡zᯕᯕᵲḢᖁ⩶┽᮹łᖁᯕӹ┡ӽ݅.
ᯕভ, ʑࣆḢĞᯕqᗭ⦹ࠥᙹ⠪Ɂᩕ⦹ᵲእaᯝᱢᮝಽ
ᄡ⦹ḡᦫ۵ⅩʑǍe(F/FDc=Dp=1)ᯕၽᔾ⦹íࡹ۵ߑ, ᯕ۵ʑࣆ
ḢĞᯕqᗭ⧉ᨱෙᄡ݉໕ᱢᬊ᮹⬉ŝaᨧᯕ࠺ᯝ⦽ḢĞᮥ
w۵݉ᯝ⩥ᰆ┡ᖅั૾ŝษ₍aḡಽḡᔢᇡ ʑࣆᅕ݅ḡᵲᇡ
ั૾᮹❭ƕaຝᱡၽᔾ⦹۵Ǎeᮥӹ┡ԙ݅. ⦹ḡอ, ʑࣆḢĞᯕ
qᗭ⦹íࡹ໕ᙹ⠪Ɂᩕ⦹ᵲ(F)ᮡFDc=Dpᅕ᯲݅ᦥᲙḡᔢᇡ
ʑࣆ-ḡᵲᇡั૾᮹ᄡ݉໕᭥⊹ᨱᕽ❭ƕaaᰆຝᱡᯝᨕӹí
ࡹ໑, ᯕভෝᄡ݉໕⬉ŝaၽ⭹ࡹʑ᯲⦹۵ʑࣆ᮹↽ᱢḢĞ
(Dc.max)ᯕŁ⧁ᙹᯩ݅. ᕽʑࣆ-ั૾᮹ᄡ݉໕ᨱᕽ❭ƕa
ᯝᨕӹ۵ʑࣆ᮹↽ᱢḢĞ(Dc.max)ᮡʑࣆ-ั૾ḢĞእ(Dc/Dp)᪡
ᱶȽ⪵ࡽᙹ⠪Ɂᩕ⦹ᵲእ(F/FDc=Dp)šĥłᖁ᮹ᄡłᱱᯕ໑, ᯕ ಽᇡ░ ↽ᱢ᮹ ʑࣆ ḢĞ ᳑Õᮡ Dc.maxᨱᕽ ᔑᱶ⧁ ᙹ ᯩᮭᮥ
ᙹ ᯩ݅.
5.2 ࢱՍݗౖࠛୡ׆ܱ-࠱ތլण୪ੲ
Fig. 11ᮡḡၹ᳑Õ, ั૾ᖙᰆእ, ℁ɝእ॒ᮥŁಅ⦽ᄡ݉໕݉ᯝ⩥ᰆ┡ᖅั૾᮹↽ᱢʑࣆ-ั૾ḢĞእෝᔑᱶ⦽đŝෝӹ┡
ԙ݅. ᔍḩ☁ḡၹ᮹Ğᬑ, Fig. 11(a) ၰ(b)᪡zᯕ↽ᱢ݉໕
᳑Õᮡḡၹvᖒ(᳑ၡ⦽ᔍḩ☁, ۱ᜉ⦽ᔍḩ☁)ᨱⓑ₉ᯕa
ᨧ۵äᮝಽӹ┡ԍᮝ໑, ั૾ᖙᰆእ᮹ᩢ⨆ᮡᰆั૾(L=30m)᮹
Ğᬑ, ʑࣆŝ ั૾ᯕ ࠺ᨱ Ɂᩕ❭ƕa ၽᔾࡹ۵ ʑࣆ ḢĞእ (Dc.max/Dp)a0.84ಽᕽ0.85ᯙ݉ั૾(L=10m)ᅕ݅۵᯲ᮝӹə
⠙₉aⓍḡᦫᮡäᮝಽӹ┡ԍ݅. ੱ⦽, ʑࣆŝั૾᮹℁ɝపᯕ
࠺ᯝ⧁Ğᬑ, ʑࣆŝั૾ᯕ࠺ᨱɁᩕ❭ƕࡹ۵ʑࣆḢĞእ᮹
Ⓧʑ(Dc.max/Dp)۵℁ɝእ(As/A)᪡šĥᨧᯕÑ᮹ᯝᱶ⦽äᮝಽ
ӹ┡ԍ݅. ᩍʑᕽA۵ั૾݉໕ᱢᯕ໑, As۵℁ɝ᮹ⅾ݉໕ᱢᮥ
᮹ၙ⦽݅.
Fig. 11(c) ၰ(d)᪡zᯕ, ᱱᖒ☁ḡၹᨱᕽ۵ḡၹvᖒ(čŁ⦽
ᱱᖒ☁, ᩑ᧞⦽ᱱᖒ☁)ᨱ↽ᱢʑࣆ-ั૾ḢĞእaᔍḩ☁
ḡၹᅕ݅ ݅ᗭ ₉ᯕa ᯩ۵ äᮝಽ ӹ┡ԍᮝ໑, ᄡ݉໕ ᱢᬊᨱ
ෙ⬉ŝaၽ⩥ࡹʑ᭥⧕ᕽ۵čŁ⦽ᱱᖒ☁ᅕ݅ᩑ᧞⦽ᱱᖒ☁
ᨱᕽḢĞእaᬒ᯲ᦥࢉᮥᙹᯩ݅. ੱ⦽, čŁ⦽ᱱᖒ☁ᨱ ᕽ۵ั૾ᖙᰆእᨱෙ↽ᱢʑࣆ-ั૾ḢĞእǍe᮹ᩢ⨆ᯕ
ᔍḩ☁ᨱᕽอⓝⓍḡᦫᮡäᮝಽӹ┡ԍ݅. ə్ӹᩑ᧞⦽ᱱᖒ☁
ᨱɝ᯦ࡹᨕᯩ۵ᰆั૾᮹Ğᬑ, ʑࣆ-ั૾᮹ᄡ݉໕ᇡɝᨱᕽ
Ɂᩕ❭ƕaၽᔾࡹ۵↽ᱢʑࣆ-ั૾ḢĞእ(Dc.max/Dp)a0.8ᮝಽ ᕽ݉ั૾ᯝভ᮹0.95᪡እƱ⦹໕݅ᗭ₉ᯕaၽᔾ⦹۵äᮝಽ
ӹ┡ԍ݅. ᕽ, ᩑ᧞⦽ᱱᖒ☁ᨱᕽ۵↽ᱢʑࣆ-ั૾ḢĞእෝ
ᱢᬊ⧁Ğᬑᖙᰆእ᮹ᩢ⨆ᯕ᳕ᰍ⧉ᮥᙹᯩᨩᮝ໑, ↽ɝǎԕ
ᕽԉ⧕ᦩ᮹ᩑ᧞ᱱᖒ☁ḡၹᨱᄡ݉໕݉ᯝ⩥ᰆ┡ᖅั૾᮹Ŗ ᯕᯕᨕḡŁᯩᮭᮥŁಅ⧁ভ↽ᱢʑࣆ-ั૾ḢĞእෝᱢᬊ⧁
ᖙᝍ⦽ᵝ᮹a⦥⧁äᮝಽ❱݉ࡽ݅. ⦽⠙, ᱱᖒ☁ᨱᱢᬊࡽ
݉ᯝ⩥ᰆ┡ᖅั૾᮹↽ᱢʑࣆ-ั૾ḢĞእ۵℁ɝእᨱݡ⦽ᩢ⨆
ᯕ ᔍḩ☁ᅕ݅۵ Ⓧḡอ ə ₉ᯕ۵ ၙᗭ⦽ äᮝಽ ӹ┡ԍ݅.
6. đು
ᅙᩑǍᨱᕽ۵ᄡ݉໕ᮥaḡ۵݉ᯝ⩥ᰆ┡ᖅั૾᮹Ñ࠺✚ᖒ
ᮥ⠪a⦹ʑ᭥⧕, ⩥ᰆ⨹ᔍಡᇥᕾၰ3₉ᬱᮁ⦽ᗭ(finite element, FE)⧕ᕾᮥᙹ⧪⦹ᩡᮝ໑, ั૾ԕ᮹3₉ᬱᱢᯙၽᔾ᮲ಆ
ᮥၵ┶ᮝಽᙹ⠪᮲ಆᮥᔑᱶ⦹ᩡ݅. ੱ⦽, ḡᵲᇡั૾ᨱᕽၽᔾ⦹
۵ ᗭᖒ⯭ḡ᮹ ᭥⊹ෝ ᄡ݉໕ ᇡɝᮝಽ ᯕ࠺┅ʑ ᭥⧕, ᵝ
ᩢ⨆ᯙᯱෝŁಅ⦹ᩍḡၹ᳑Õᨱෙ↽ᱢʑࣆ-ั૾ḢĞእෝ
ᱽᦩ⦹ᩡ݅. ᅙ ᩑǍෝ ☖⦹ᩍ ᨕḥ đುᮡ ݅ᮭŝ z݅.
(1) ݉ᯝ⩥ᰆ┡ᖅั૾᮹ᄡ݉໕✚ᖒᮥ⠪a⦹ʑ᭥⦽⩥ᰆ⨹
ᔍಡᇥᕾၰ3₉ᬱᮁ⦽ᗭ⧕ᕾđŝ, ᄡ݉໕ᮥaḡ۵݉ᯝ
⩥ᰆ┡ᖅั૾ᮡั૾-ʑࣆ᮹vᖒ₉ᯕಽᯙ⦹ᩍᄡ݉໕ᨱᕽ
᮲ಆᯕ Ⓧí ᄡ⦹۵ äᮥ ᙹ ᯩᨩ݅. ᯕෝ ☖⧕, ᄡ݉໕
݉ᯝ⩥ᰆ┡ᖅั૾᮹Ǎ᳑ᱢ≉᧞ᇡ۵↽ݡ⮉༉ູ✙᭥⊹a
ᦥܭᄡ݉໕ᮝಽᯕ࠺⦹ʑভྙᨱᗭᖒ⯭ḡࠥḡᵲᇡั૾ᯕ
ᦥܭḡᔢᇡʑࣆᮝಽ∊ᇥ⯩ᮁࠥࢁᙹᯩ۵äᮝಽ❱݉ࡹᨩ݅.
(2) ݉ᯝ⩥ᰆ┡ᖅั૾᮹↽ᱢʑࣆ-ั૾ḢĞእ(Dc.max/Dp)ෝᱽ ᦩ⦹ʑ ᭥⧕, ʑࣆ-ั૾ ḢĞእ(Dc/Dp)᪡ ᙹ⠪ Ɂᩕ⦹ᵲእ
(F/FDc=Dp)᮹šĥෝᇥᕾ⦹ᩡ݅. ᇥᕾđŝ, ᄡ݉໕ᨱᕽ❭ƕ
a ᯝᨕӹ۵ ↽ᱢ ʑࣆ ḢĞ(Dc.max)ᮡ ʑࣆ-ั૾ ḢĞእ᪡
ᙹ⠪Ɂᩕ⦹ᵲእšĥłᖁ᮹ᄡłᱱᯥᮥᙹᯩᨩ݅. ᔍḩ☁
ḡၹ᮹Ğᬑ, ↽ᱢʑࣆ-ั૾ḢĞእ۵ḡၹvᖒၰᖙᰆእᨱ
ⓑᩢ⨆ᨧᯕ0.85 ᱶࠥಽᯝᱶ⦹íӹ┡ԍ݅. ⦹ḡอ, ᱱᖒ☁
ḡၹᨱᕽ᮹ ↽ᱢ ʑࣆ-ั૾ ḢĞእ۵ ᰆั૾ᯝ Ğᬑ 0.95,
݉ั૾ᯙĞᬑ0.8ಽӹ┡ӹᖙᰆእᨱ݅ᗭ⠙₉a᳕ᰍ⧉
ᮥᙹᯩᨩ݅. ᕽ݉ᯝ⩥ᰆ┡ᖅั૾᮹ᄡ݉໕ᮥᱢᬊ⧁
ᖙᰆእᨱݡ⦽ᖙᝍ⦽ᵝ᮹a⦥⧁äᮝಽ❱݉ࡹᨩ݅.
qᔍ᮹ɡ
ᯕםྙᮡ2012֥ࠥᱶᇡ(ၙ௹᳑ŝ⦺ᇡ)᮹ᰍᬱᮝಽ⦽ǎᩑ Ǎᰍ݉᮹ḡᬱᮥၼᦥᙹ⧪ࡽᩑǍ᯦ܩ݅(No. 2011-0030842).
ᩑǍ ḡᬱᨱ qᔍऽพܩ݅.
