Parametric Analysis on Ultimate Behavior of Cylindrical GFRP Septic Tank

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Received April 12 2013, Revised May 21 2013, Accepted June 17 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)

ǣǣȀȀǤǤȀͳͲǤͳʹ͸ͷʹȀǤʹͲͳ͵Ǥ͵͵ǤͶǤͳ͵͵͹ ǤǤǤ

Ⲏ㝳㯓#JIUS#ᇚⴶ㬖⟖#㉖Ὢ⢚⛢ⴖ#Ꮇ㬚ሮᦗ⮎#ᢾ㬚#ᾢᇚ≾⟖㬲⛛

׌ন࣪ȵ୺ֈ୪

Kim, Sung Bo*, Cho, Kwang Je**

Parametric Analysis on Ultimate Behavior of Cylindrical GFRP Septic Tank

ABSTRACT

The parametric analysis on ultimate behavior of buried cylindrical GFRP(Glass Fiber Reinforced Polymer) septic tank was presented.

Two kinds of F.E. analysis model(soil-spring model and 3D full model) was constructed. The ultimate behavior of septic tank was investigated according to the size of stiffened steel ring and properties of underground soil. Ramberg-Osgood model and Druker-Prager model were used for material nonlinear characteristics of GFRP septic tank and soil, respectively. The diameter and thickness of stiffened steel ring inside septic tank, elastic modulus and internal friction angle of soil were selected for parametric variables. The ultimate behavior of septic tank, load-displacement, axial and hoop strain, were calculated and investigated.

Key words : Cylindrical, GFRP, Septic tank, Soil spring, 3D precision analysis

Ⅹಾ

ᬱ☖⩶GFRP }ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ɚ⦽Ñ࠺ᨱݡ⦽ๅ}ᄡᙹ⧕ᕾᮥᙹ⧪⦹ᩡ݅. ḡၹᮥእᖁ⩶ᜅ⥥ยᮝಽݡℕ⦽⧕ᕾ༉ߙŝ3₉ᬱŁℕ᫵

ᗭෝ ᱢᬊ⦽ ࢱ aḡ ⧕ᕾ༉ߙᯕ ᯲ᖒࡹᨩ݅. ᅕvย᮹ ⩶┽᪡ ḡၹ᳑Õ᮹ ᄡ⪵ᨱ ঑ෙ }ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ ɚ⦽Ñ࠺ᯕ ᇥᕾࡹᨩ݅.

Ramberg-Osgood ༉ߙŝDruker-Prager ༉ߙᯕbbGFRP ၰḡၹ᮹እᖁ⩶ᖒᮥӹ┡ԕʑ᭥⦹ᩍᱢᬊࡹᨩ݅. ᬱ☖⩶}ᯙ⦹ᙹ⃹ญ᜽ᖅԕ ᇡᨱᖅ⊹ࡽvšᅕvย᮹ḢĞŝࢱ̹ၰḡၹ┥ᖒĥᙹၰԕᇡษₑb॒ᮥๅ}ᄡᙹಽ⦹ᩍ⦹ᵲ-ᄡ᭥šĥ, ⇶ႊ⨆ᄡ⩶ශၰ⬥⥥ႊ⨆ᄡ⩶

ශ॒ᯕᮁ⦽᫵ᗭ⧕ᕾᮥ☖⦹ᩍࠥ⇽ࡹᨩŁᩍ్ๅ}ᄡᙹॅᯕvšᮝಽᅕvࡽ}ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ɚ⦽vࠥᨱၙ⊹۵ᩢ⨆ॅᯕᇥᕾࡹᨩ݅.

áᔪᨕ ᬱ☖⩶, GFRP, }ᯙ⦹ᙹ⃹ญ᜽ᖅ, ḡၹᜅ⥥ย, 3₉ᬱᱶၡ⧕ᕾ

1. ᕽು

}ᯙ⦹ᙹ⃹ญ᜽ᖅᮡĞᱽᖒᰆŝ޵ᇩᨕᱥǎᱢᮝಽᱽ᳑ᝅᱢᯕⓍí᷾a⦹Łᯩᮝӹ, ᖅĥʑᵡ᮹ၙ⯂, ॒ಾʑᵡ᪥⪵॒ᩍ్aḡ

ᯕᮁಽ ᇡᝅ᜽Ŗ ᔍಡa ӹ┡ӹŁ ᯕᨱ ঑௝ ᙹḩ⪹Ğ ᅕᱥᮥ ᱡ⧕⦹۵ ྙᱽᱱᯕ ӹ┡ӹŁ ᯩ݅.

⩥⧪⦹ᙹࠥჶ᜽⧪Ƚ⊺ᨱ᮹⦹໕}ᯙ⦹ᙹ⃹ญ᜽ᖅᮡᬱ☖⩶ᚹǍ᳑⩶ᔢᯕŁǍ᳑ᰍഭಽᕽၶส᮹ᮁญᖍᮁv⪵⥭௝ᜅ❒(Glass Fiber Reinforced Polymer, ᯕ⦹GFRP)ᯕᔍᬊࡽ݅. ᅙ᜽ᖅᮡḡᵲᨱๅᖅࡹᨕᔢᇡ⦹ᵲᨱ᮹⦽ⓑ☁ᦶᮥḡḡ⦹ʑ᭥⦹ᩍᬱ☖⩶

ԕᇡᨱʙᯕႊ⨆ᮝಽ1.5m eĊᮝಽᅕvยᮥᖅ⊹⦹ࠥಾȽᱶࡹᨕᯩ݅. ⦹ḡอ⩥⧪ᖅĥʑᵡᮡᅕvย᮹ᰍഭaᬱ☖⩶ᚹǍ᳑᪡

࠺ᯝ⦽GFRPᯙĞᬑᨱอᱽ᜽ࡹŁᅕvย᮹᳦ඹᨱ঑ෙᖅĥᱩ₉a⪶พࡹḡᦫᦹ݅. ᐱอᦥܩ௝ḡၹᨱๅพࡽǍ᳑ᯥᨱࠥᇩǍ⦹Ł

ĵܓėॡ

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ᱢᬊࡹᨩ݅. všᅕvย᮹ḢĞŝࢱ̹ၰḡၹ┥ᖒĥᙹၰԕᇡษ ₑb॒ᮥๅ}ᄡᙹಽ⦹ᩍ⦹ᵲ-ᄡ᭥šĥ, ⇶ႊ⨆ᄡ⩶ශၰ⬥⥥ႊ

⨆ᄡ⩶ශ॒ᯕᮁ⦽᫵ᗭ⧕ᕾᮥ☖⦹ᩍࠥ⇽ࡹᨩ݅. ᩍ్ๅ}ᄡᙹॅ

ᯕvšᮝಽᅕvࡽ}ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ɚ⦽vࠥᨱၙ⊹۵ᩢ⨆ॅ

ᯕ ᇥᕾࡹᨕ }ᯙ⦹ᙹ ⃹ญ᜽ᖅ᮹ Ǎ᳑ᖒ܆ᮥ ⠪a⦹ᩡ݅.

2. }ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ᖅĥʑᵡ

⪹Ğᇡᨱᕽၽeࡽ⦹ᙹࠥჶ᜽⧪Ƚ⊺(⪹Ğᇡ, 2011)ᨱ᮹⦹໕, 1)~5)⧎᮹ ᖅĥʑᵡᮥ ໦ʑ⦹Ł 4)⧎ᨱ ᔍᬊࡽ ᄡᙹॅᨱ ݡ⦽

ᖅ໦ᮡ ᖅĥ ʑᵡ ⢽ʑ ᯕ⬥ᨱ ᱽ᜽⦹ᩡ݅.

1) ᪅ᙹ⃹ญ᜽ᖅႊඹᙹᙹḩʑᵡᮥḡ┍ᙹᯩ۵⃹ญ܆ಆᮥ

ᨕ᧝ ⦽݅.

3) Ǎ᳑ྜྷᅙℕ᮹ḢĞᯕӹ׳ᯕ۵3mෝⅩŝ⦹ᩍᕽ۵ᦩࡽ݅.

4) Ǎ᳑ྜྷᮥ ᬱ⩶ᮝಽ ᱽ᳑⦹۵ Ğᬑᨱ۵ Ǎ᳑ྜྷ᮹ ԕᇡᨱ

1.5mษ݅ᅕvยᮥǍ᳑ྜྷ᮹ᅙℕ᪡ᯝℕ⩶ᮝಽᖒ⩶⦹ᩍ

᧝⦹໑, ᅕvย᮹݉໕ᮡᦩᱥᖒᯕ1ᅕ᯲݅Ł, ⨩ᬊ᳭Ǖ⦹

ᵲᯕ݉᭥⡎ݚ⦹ᵲ᮹2႑ᯕᔢᯕࡹࠥಾ⦹ᩍ᧝⦽݅.

ćƄƁſ

Ƅ_Ɓ â ćƄƀſ

Ƅ_ƀ

= Î (1a)

©_ƁƐá ćÐ¢ > Ï©Ɛ^Ð (1b)

5) 4)᮹ᅕvยᮡᮁญᖍᮁv⪵⥭௝ᜅ❒ᮝಽᱽ᯲⦹ᩍ᧝⦹Ł, əᦩᱥᖒၰ⨩ᬊ᳭Ǖ⦹ᵲ᮹ĥᔑ᜾ᮡ݅ᮭŝz݅. ݅อ,

ᮁญᖍᮁv⪵⥭௝ᜅ❒᫙᮹ᰍḩᮥᔍᬊ⦹ಅ໕zᮡᙹᵡ

ᯕᔢ᮹ᅕvʑ܆ᯕᯩᨕ᧝⦹໑, ᇡ᜾॒ᮝಽᯙ⦽ᰍḩ᮹

᧞⪵aၽᔾࡹḡ ᦥܩ⦹ࠥಾႊ᜾⃹ญ ॒ᮥ⦹ᩍ᧝ ⦽݅.

☖⦹ᩍᙹ⧪ࡽ݅. ᅕvย᮹ᖅĥȽᱶ4)⧎᮹᜾(1a)ᨱᕽfc۵ᅕv ย᮹ᖅĥ⇶᮲ಆ, fca۵⨩ᬊ⇶᮲ಆ, fb۵ᖅĥ⮉᮲ಆ, fba۵⨩ᬊ

⮉᮲ಆᯕ݅. ੱ⦽᜾(1b)ᨱᕽPcrᮡᱶᙹᦶᮥၼ۵ᬱ⩶ย᮹᳭Ǖ⦹

ᵲᮝಽᕽE۵ᬱ☖⩶ᚹ⩶┽᮹}ᯙ⦹ᙹ⃹ญ᜽ᖅԕᇡᨱ1.5m eĊᮝಽᖅ⊹ࡽᅕvยᰍഭ᮹┥ᖒĥᙹ, I۵ᅕvย᮹݉໕2₉༉

ູ✙, rᮡ ᅕvย᮹ ᵲᝍ ၹĞᯕ໑ P۵ ݉᭥⡎ݚ ᖅĥ☁ᦶᮝಽ

⦹ᙹࠥჶ᜽⧪Ƚ⊺ᨱ© á Ñ×íÔÐƉƅƄîƁƋᮝಽȽᱶࡹᨕᯩ݅. ⦽⠙

࠺᜽⧪Ƚ⊺ᨱ᮹⦹໕GFRP ᰍḩ᮹ᅕvยᨱݡ⦽⨩ᬊ⇶᮲ಆ (_Ƅ_Ɓſ)ၰ⨩ᬊ⮉᮲ಆ(Ƅ_ƀſ)ᮡTable 1᮹sᮥᔍᬊ⦹ࠥಾᱽ᜽ࡹᨩ݅.

ੱ⦽, ᅙȽ⊺ᨱ᮹⦹໕ᔢᰍ⦹ᵲᮝಽᯙ⦽Ḣᔍb⩶݉໕ᮥ

w۵ᅕvยᨱၽᔾ⦹۵ᖅĥ⇶᮲ಆŝᖅĥ⮉᮲ಆᮥ᜾(2)ᨱ

᮹⦹ᩍ ĥᔑ⦹ࠥಾ ᱽ᜽ࡹŁ ᯩ݅.

Ƅ_Ɓá ć© Ɛ (2a) Ƅƀá ×íÕÑćƀƒ^Ï

ᩍʑᕽ, rᮡᅕvย᮹ᵲᝍၹĞ, A۵ᅕvย᮹݉໕ᱢ, b۵Ḣᔍ b⩶ ݉໕ᮥ w۵ ᅕvย᮹ ⡎, t۵ Ḣᔍb⩶ ݉໕᮹ ᅕvย᮹

ࢱ̹ᯕ݅. ᅕvย᮹ᖅĥ⇶᮲ಆၰᖅĥ⮉᮲ಆᨱݡ⦽᜾(2)ᮡ

ᅕvยᯕḢᔍb⩶݉໕᮹GFRP ᰍḩಽᱽ᯲ࡽĞᬑᨱอᱢᬊࡽ

݅. อᯝᬱ⩶᮹všᅕvยᮥᔍᬊ⦹۵ĞᬑGFRP᮹ᰍഭ✚ᖒ

ݡᝁᨱvᰍ᮹ᰍഭ✚ᖒᮥŁಅ⦹ᩍᖅĥ⇶᮲ಆᮥ݅ᮭŝzᯕ

ᙹᱶ⦹ᩍ᧝ ⦽݅.

ƄƁá ćƌ© Ɛ (3)

ᩍʑᕽ nᮡ vᰍ᮹ ┥ᖒĥᙹ᪡ GFRP᮹ ┥ᖒĥᙹ᮹ እಽᕽ

n=26ᯕ݅. əญŁ᜾(2b)۵Ḣᔍb⩶݉໕⩶┽᮹ᅕvยᨱݡ⦽

⮉᮲ಆᯕအಽᬱ⩶všᮝಽᰍ᯲ࡽᅕvย᮹ ⮉᮲ಆᮡ݅ᮭŝ

zᯕ ⪹ᔑ⦹ᩍ ӹ┡ԝ ᙹ ᯩ݅.

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Table 2. Design of circular stiffened ring[mm]

Diameter of cylindrical shell Diameter of steel pipe Thickness of steel pipe Stress ratio Buckling load ratio Stress check Buckling check

1500 43.7 2.3 0.7 2.8 O.K O.K

1700 43.7 2.3 0.9 1.9 O.K N.G

1700 43.7 2.5 0.8 2.0 O.K O.K

1700 48.6 2.3 0.7 2.7 O.K O.K

2000 48.6 2.5 0.9 1.7 O.K N.G

2000 48.6 2.8 0.8 1.9 O.K N.G

2000 48.6 3.2 0.7 2.1 O.K O.K

2500 48.6 3.2 1.1 1.1 N.G N.G

2500 60.5 2.3 0.9 1.6 O.K N.G

2500 60.5 3.2 0.7 2.2 O.K O.K

2500 60.5 4.0 0.6 2.6 O.K O.K

2800 60.5 3.2 0.9 1.5 O.K N.G

2800 60.5 4.0 0.7 1.8 O.K N.G

2800 76.3 2.8 0.6 2.9 O.K O.K

(a) front view

(b) section view

Fig. 1. Septic tank stiffened by steel pipe Ƅ_ƀá ×íÎÑć© Ɛƌ¬^Ï (4)

ᩍʑᕽ S۵ ᬱ⩶ vš ᅕvย᮹ ݉໕ĥᙹᯕ݅.

ᔢʑ᪡zᮡᖅĥ᳑Õᮝಽ}ᯙ⦹ᙹ⃹ญ᜽ᖅᨱݡ⦽ᖅĥෝ

ᙹ⧪⦹ᩍəđŝෝ Table 2ᨱӹ┡ԕᨩ݅. }ᯙ⦹ᙹ⃹ญ᜽ᖅ

ᅙℕ᮹᫙ᇡḢĞᮡ⩥⧪ᖅĥʑᵡᯙ3mᯕԕᨱᇡ⧊ࡹࠥಾᱢᬊ⦹

ᩡŁ, ᬱ⩶vš ᅕvย᮹ ḢĞ ၰ ࢱ̹۵ KSD 3556ᨱ ᱽ᜽ࡽ

vš᮹ ᱽᬱᮥ ᔍᬊ⦹ᩡ݅.

᜾(3)ŝ᜾(4)ಽᇡ░ᖅĥ⇶᮲ಆŝᖅĥ⮉᮲ಆᮥᔑᱶ⦹Ł

ᯕෝ᜾(1)ᨱݡ᯦⦹ᩍ᮲ಆá☁ၰ᳭Ǖ⦹ᵲá☁ෝᙹ⧪⦹ᩡ݅.

᜾ (1b)᮹ ᳭ᄡᨱ ᭥⊹⦽ ᯕುᱢᯙ ᳭Ǖ⦹ᵲ(©ƁƐ)ᯕ ᜾ (1b)᮹

ᬑᄡᨱ ໦ʑࡽ ݉᭥ ⡎ ݚ ᖅĥʑᵡ⦹ᵲ© á Ñ×íÔÐƉƅƄîƁƋ᮹

2႑ᯕᔢᯕࡹᨕ᧝⦽݅. ᷪ, Table 2ᨱᕽ᳭Ǖá☁۵᜾(1b)ᨱᕽ

©_ƁƐî© a 2ᅕ݅ Ⓧ໕ OKᯥᮥ ᮹ၙ⦽݅. ❱ᱶᮡ ᮲ಆá☁ ၰ

᳭Ǖá☁᮹ ᇡ⧊ᩍᇡෝ ӹ┡ԙ݅.

ᅙǍ᳑ྜྷ᮹᫙ᇡḢĞᯕ1.5m, 1.7m, 2.0m, 2.5m, 2.8mಽ

᷾a⧉ᨱ ঑௝ ᫵Ǎࡹ۵ ᬱ⩶vš ᅕvย᮹ ᫙Ğᮡ 43.7mm, 48.6mm, 60.5mm, 76.3mm ᯥᮥ᦭ᙹᯩ݅. ᷪ, ᅙℕ᮹ḢĞᯕ

⍅ḩᙹಾᅕvย᮹ḢĞᮡ↽ݡ16mmʭḡ⍅Კ᧝⦽݅۵äᮥ

᦭ᙹᯩ݅. ᅙℕ᮹᫙Ğᯕ2.0m, 2.5mᯝভᨱ۵᫵Ǎࡹ۵ᅕvย᮹

ࢱ̹۵࠺ᯝ⦹ŁḢĞᯕ12mm ₉ᯕӹḡอ, ᅙℕ᮹ḢĞᯕ2.8mᯝ

ভᨱ۵᫵Ǎࡹ۵ᅕvย᮹ḢĞᮡ᷾a⦹ḡอࢱ̹۵2.0m, 2.5m ᯙ Ğᬑᅕ݅ 4mm qᗭ⦹۵ äᮝಽ ᖅĥࡹᨩ݅.

ੱ⦽, ݡᇡᇥ᮹všᅕvย݉໕ᮥᔍᬊ⦽ᖅĥᨱᕽ᜾(1a)᮹

᮲ಆᨱݡ⦽ᦩᱥᖒᮥอ᳒⦹ḡอ, vš᮹݉໕ᯕ᯲ᮡĞᬑᨱ۵

᜾(1b)ᨱᱽ᜽ࡽ᳭Ǖᦩᱶᖒᮥอ᳒᜽┅ḡ༜⦹Łᅕvย᮹݉໕

ᮥⓍíᔍᬊ⦹ᩍ᧝᳭Ǖᨱݡ⦽ᖅĥ᳑Õ᜾ᮥอ᳒⦹Łᯩ݅.

ᷪ, ᅕvย᮹ᖅĥȽᱶ4)⧎᮹ࢱaḡ᜾ᨱᕽ᜾(1b)᮹᳭Ǖ᳑Õ᜾

ᯕ ᖅĥෝ đᱶ⦹۵ ᵲ᫵⦽ ᫵ᗭᯥᯕ ❭ᦦࡹᨩ݅.

3. ḡၹᜅ⥥ยᮥᱢᬊ⦽⧕ᕾ

ḡᵲᨱๅพࡽ}ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ɚ⦽Ñ࠺⧕ᕾᮥ᭥⧕Fig.

1ŝ zᯕ vš ᅕvยᮝಽ ᅕvࡽ }ᯙ⦹ᙹ ⃹ญ᜽ᖅᨱ ݡ⦹ᩍ

ჵᬊᮁ⦽᫵ᗭ⧕ᕾ⥥ಽəఉᯙABAQUSෝᔍᬊ⦹ᩍ⧕ᕾᮥᙹ⧪

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Fig. 2. F.E model of soil spring

Fig. 3. Ramberg-Osgood Stress-strain curve

Table 3. Material properties of soil spring model

Member Element Section Elastic Modulus [MPa] Poisson ratio Yiels stress [MPa] Hardening index Yield offset [%]

Cylindrical shell S4R5 t=9 7000 0.3 80 5 0.2

steel pipe B33 r=25

t=2.1 210000 0.3 240 - -

⦹ᩡ݅. ᅙℕǍ᳑ྜྷᮥ᭥⦹ᩍᮁ⦽᫵ᗭ⧕ᕾᨱᕽᔍᬊ⦽᫵ᗭ۵

4-ᱩᱱshell᫵ᗭෝᔍᬊ⦹ᩡŁ, Fig. 2᪡zᯕ⦹ᵲၰݡᔢǍ᳑ྜྷ

᮹ݡ⋎ᖒᮥŁಅ⦹ᩍᱥℕǍ᳑ྜྷ᮹ 1/4อᮥ༉ߙย⦹ᩡ݅. ᅕvย

ᮡŖeᅕ᫵ᗭෝᔍᬊ⦹ᩍshell ᫵ᗭᨱvℕᩑđ᜽⎑ᮝ໑ḡၹᨱ

ๅพࡽ☁ḩ᮹ᩢ⨆ᮥŁಅ⦹ʑ᭥⦹ᩍFig. 2᪡zᯕᬱ☖⩶ᚹ

Ǎ᳑᮹ ᱲᖁႊ⨆ŝჶᖁႊ⨆ᮝಽSPRINGA ᫵ᗭෝᔍᬊ⦹ᩡ݅.

ᮁ⦽᫵ᗭ⧕ᕾᨱ ᔍᬊ⦽ ᫵ᗭ᮹ ྜྷᖒ⊹۵ Table 3ŝ z݅.

ᅙℕǍ᳑ྜྷಽᔍᬊࡽGFRP᮹እᖁ⩶ᰍഭ✚ᖒᮥᱢᬊ⦹ʑ

᭥⦹ᩍRamberg-Osgood ༉ߙᮥᔍᬊ⦹ᩡ݅. Ramber-Osgood᮹

እᖁ⩶ ᮲ಆ-ᄡ⩶ශ šĥ᜾ᮡ ᜾ (5)᪡ z݅.

Ļ á ćň â¤Þ^ćňß^ƌ (5)

ᩍʑᕽ, Ļ : ᄡ⩶ශ

ň : ᮲ಆ

: ┥ᖒĥᙹ

¤ì ƌ : ᰍഭ ✚ᖒᨱ ঑ෙ ᔢᙹ

᜾(5)ᨱᕽᬑᄡ᮹ℌ⧎ᮡ┥ᖒᄡ⩶ᯕŁࢱჩṙ⧎ᮡᗭᖒᄡ⩶ᮥ

ӹ┡ԕ໑,¤᪡ƌᮡᰍഭ᮹Ğ⪵Ñ࠺ᮥӹ┡ԕ۵ᄡᙹᯕ݅. ᰍഭ᮹

⧎ᅖ᮲ಆň_×, əญŁ ᔩಽᬕ ๅ}ᄡᙹķෝ ᯦ࠥ⦹ᩍ ᱶญ⦹໕

Ramber-Osgood ༉ߙ᮹ ᄡᙹॅŝ᮹ šĥ᜾ᮡ ᜾ (6)ŝ z݅.

Ļ á ćň âķć ň_×

Þ^ć^ň^ň^×ß^ƌ (6) ᩍʑᕽ, ň× : ⧎ᅖ᮲ಆ

ķ ^: ⧎ᅖ offset ᄡᙹ

᜾ (6)ᨱᕽ ň á ň_×ᯝ ভ᮹ ᄡ⩶ශ Ļ á ÞÎ âķßň_×îᨱᕽ

ķÞň_×îß᮹sᮡFig. 3ᨱࠥ᜽ࡽၵ᪡zᯕ⧎ᅖoffset እᮉᮥ

᮹ၙ⦽݅. ƌᨱݡ⧕ᯝၹᱢᮝಽᔍᬊࡹ۵sᮡ5ᯕᔢᯕ໑, ᅕ݅

ᱶ⪶⦽ sᮡ ᅕ☖ ᯙᰆ ੱ۵ ᦶ⇶ ᝅ⨹ ߑᯕ░ᨱ ᮹⧕ ᨜ᮥ ᙹ

ᯩ݅. ķᨱ ݡ⦽ s ੱ⦽ ᝅ⨹ ߑᯕ░ᨱ ฿۵ ႊ᜾ᮝಽ ᖁᱶ⧁

ᙹ ᯩḡอ, ᯝᇡ ᰍഭ۵ offset እᮉᮥ aᱶ⦹ᩍ ⧎ᅖ offsetᮥ

ᔍᬊ⦽݅.

Fig. 4۵᜾(6)ᮥᔍᬊ⦹ᩍ⧎ᅖoffset(ķ),Ğ⪵ḡᙹ(ƌ), ⧎ᅖ᮲ ಆ(ň_×)ᮥ ᄡ⪵᜽⍽a໕ᕽ ӹ┡ԙ ᅙℕ Ǎ᳑ྜྷ᮹ GFRPᨱ ݡ⦽

᮲ಆ-ᄡ⩶ශ łᖁᯕ݅. Ğ⪵ḡᙹ۵ 5, 10, ⧎ᅖ᮲ಆᮡ 80MPa, 100MPa, 120MPaᮥᱢᬊ⦹ᩡᮝ໑, ķsᮡTable 4᪡zᯕ0.2%

᪡ 0.3%᮹ ⧎ᅖoffset እᮉᮥ ᱢᬊ⦽ sᮥ ᔍᬊ⦹ᩡ݅.

(5)

Fig. 5. Ramberg-Osgood model and Test results (a)ň_×=80MPa

(b)_ň_×=100MPa

(c) _ň_×=120MPa

Fig. 4. Stress-strain according to hardening parameter

Table 4. Hardening parameter(_ķ) according to yield stress and offset ratio

offset ratio

ň_×[MPa] 0.2% 0.3%

80 0.175 0.263

100 0.140 0.210

120 0.117 0.175

Fig. 4᮹đŝෝၵ┶ᮝಽᮁ⦽᫵ᗭ⧕ᕾᨱᔍᬊࡽGFRP ྜྷᖒ⊹

᮹ đŝෝ ᝅᱽ ᰍഭᝅ⨹đŝ(Jo and Kim, 2012)᪡ እƱ⦹ᩍ

Fig. 5ᨱӹ┡ԕᨩ݅. ⦹ᙹࠥჶᨱ໦᜽ࡽᖅĥʑᵡᨱ᮹⦹໕┥ᖒĥ ᙹ7845.3MPa, ⨩ᬊ⇶᮲ಆ41.2MPa, ⨩ᬊ⮉᮲ಆ68.6MPaᯕŁ

Fig. 5ᨱࠥ᜽ࡽၵ᪡zᯕᯙᰆᝅ⨹đŝ┥ᖒĥᙹ۵⠪Ɂ7,500MPa, ɚ⦽᮲ಆᮡ80ⴇ100MPa, ɚ⦽ᄡ⩶ශ(Ļ)ᮡ0.012ⴇ0.015ಽĥ⊂

ࡹᨩᮝအಽ, ᦩᱥᮉᯕ⮉ᨱݡ⦹ᩍ1.4ⴇ1.7, əญŁ⇶ಆᨱݡ⦹ᩍ

1.9ⴇ2.3ᯙᰍഭᯥᮥ᦭ᙹᯩ݅. ᯕ᪡zᮡᰍഭᝅ⨹đŝෝၹᩢ⦹

ᩍ, Ramberg-Osgood ༉ߙ(⧎ᅖ᮲ಆ80MPa, offset እᮉ0.2%, Ğ⪵ḡᙹn=5)ᮥᱢᬊ⦹ᩍᮁ⦽᫵ᗭ⧕ᕾᨱᔍᬊࡽGFRP᮹᮲ಆ- ᄡ⩶ࠥłᖁđŝෝFig. 5ᨱᕽӹ┡ԕᨩ݅. ⧕ᕾᨱᔍᬊࡽ᮲ಆ-ᄡ

⩶ශłᖁᯕᝅ⨹đŝ᮹ჵ᭥ԕᨱᇡ⧊⦹Łᯩᮭᮥ᦭ᙹᯩ݅.

ๅพࡽǍ᳑ྜྷᵝᄡ᮹ḡၹᮥᜅ⥥ย᫵ᗭಽ༉ߙย⦹ŁGFRP ᚹ᫵ᗭᨱᕽჶᖁႊ⨆᮹ᜅ⥥ยᔢᙹ᪡ᱲᖁႊ⨆᮹ᜅ⥥ยᔢᙹ۵

ḡၹၹಆĥᙹ᪡⧕ݚᚹ᫵ᗭ᮹໕ᱢᮥŒ⦹ᩍᱢᬊ⦹ᩡ݅. ḡၹŝ

Ǎ᳑ྜྷ ᔍᯕ᮹ḡၹၹಆĥᙹ۵Okeagu᪡Abdel-Sayed(1984)a

ᱽᦩ⦽᜾ŝJ. Oh(1999)aᗭ}⦽ᯝᅙ᮹ࠥಽ⩲⫭᜾ᮥᔍᬊ⦹ᩍ

ḡၹᜅ⥥ยᔢᙹෝᔑᱶ⦹ᩍᮁ⦽᫵ᗭ⧕ᕾᨱᱢᬊ⦹ᩡ݅. ᮁ⦽᫵

ᗭ⧕ᕾᨱᔍᬊ⦽ḡၹᜅ⥥ยᔢᙹsᨱݡ⧕ᕽ۵ᬱ⩶Ǎ᳑ྜྷ᮹ᱲ ᖁႊ⨆᮹ၹಆĥᙹ۵ჶᖁႊ⨆ၹಆĥᙹ᮹20%ಽᱽᦩ⦽Okeagu

᪡Abdel-Sayed᮹đŝෝ₥┾⦹ᩡŁᯙᰆಆᨱݡ⦽ḡၹᜅ⥥ย ᔢᙹ۵ᦶ⇶ಆᨱݡ᮲⦹۵ᜅ⥥ยᔢᙹ᮹10%᮹sᮥᱢᬊ⦹ᩡ݅.

ᬱ⩶všᮝಽᅕvࡽGFRP }ᯙ⦹ᙹ⃹ญ᜽ᖅᨱݡ⦽ᮁ⦽᫵

ᗭ⧕ᕾ đŝෝ⩥ᰆᰍ⦹ᝅ⨹(Jo and Kim, 2012)ŝእƱ⦹ᩡ݅.

Fig. 6ᮡᮁ⦽᫵ᗭ⧕ᕾđŝ᪡⩥ᰆᝅ⨹ᨱݡ⦽⦹ᵲ-ᄡ᭥ə௹⥥

ᯕ݅. ᮁ⦽᫵ᗭ⧕ᕾđŝ⦹ᵲᰍ⦹ᱱ⦹݉ᇡ᪡45° ᯕĊࡽ᭥⊹ᨱ ᕽ᮹⯹-ᄡ᭥ࠥ۵ᝅ⨹đŝ᪡እƱᱢᯝ⊹⧉ᮥ⪶ᯙ⧁ᙹᯩᮝ໑, ɚ⦽ᔢ┽ᨱᕽ᮹ᄡ᭥۵Okeagu᮹ᖅĥ᜾ᨱ᮹⦽đŝa᧞20%

ᱶࠥ ᯲í ⠪a⦹Ł ᯩ۵ äᮝಽ ӹ┡ԍ݅.

(6)

(a) Loading point

(b) 45° side

Fig. 6. Load-displacement of soil spring model

Fig. 7. 3D solid F.E. model

(a) full model (b) near shell and ring

(c) load plate Fig. 8. F.E. analysis model

4. 3₉ᬱᱶၡ⧕ᕾ

ḡၹᨱๅพࡽ}ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ɚ⦽Ñ࠺ᮥᅕ݅ᱶ⪶⯩

ᇥᕾ⦹ʑ᭥⦹ᩍḡၹᮥ ᜅ⥥ย᫵ᗭݡᝁᨱŁℕ᫵ᗭෝᔍᬊ⦽

3₉ᬱᱶၡ⧕ᕾᮥᙹ⧪⦹ᩡ݅. ḡၹᜅ⥥ย⧕ᕾŝ࠺ᯝ⦹í⦹ᵲ

ၰǍ᳑ྜྷ᮹ݡ⋎ᖒᮥŁಅ⦹ᩍFig. 7ŝzᯕᱥℕǍ᳑ྜྷ᮹1/4 อ Łಅ⦹ᩡ݅. ⧕ᕾ ༉ߙ᮹ Ⓧʑ۵ X⇶ᮝಽ 4.5m, Y⇶ᮝಽ

5.37m, Z⇶ᮝಽ 2.5m ᯕ݅.

Fig. 8(a)۵ᔾᖒࡽᱥℕ⧕ᕾ༉ߙᯕ݅. ḡၹᨱๅพࡽGFRP ᬱ☖⩶ᚹᮥᬱᵝႊ⨆ᮝಽ2°ᦊᇥ⧁⦹ᩍ180°ʭḡ4ᱩᱱᚹ᫵ᗭ ಽ ᯕᔑ⪵⦹ᩡ݅. Fig. 8(b)۵ ᅕvย ᵝᄡ᮹ ᫵ᗭ฾ᮥ ⪶ݡ⦽

əฝᮝಽᅕvยŝaʭᬕŔᮥᖙၡ⦹íᇥ⧁⦹ᩡᮝ໑, ᬱ☖⩶

ᚹ᮹ ᫙Ğᯕ 2mᯕŁ ๅพ ʫᯕa 0.37mᯥᮥ Łಅ⦹ᩍ ၹᬱ᮹

ᵲᝍᨱᕽ1.37m ᯕᔢਉᨕḥŔᇡ░Mesh᮹Ⓧʑෝ᷾a᜽┅໕ᕽ

༉ߙย⦹ᩡ݅. Fig. 8(c)۵50mm ࢱ̹᮹v❱ᨱḲᵲ⦹ᵲᯕᰍ⦹

ࡹ۵ ᇡᇥᮝಽᕽ Plate᫵ᗭෝ ᔍᬊ⦹ᩍ ᰍ⦹❱ᮥ Łಅ⦹ᩡ݅.

ḡၹᮡABAQUSᨱᕽᱽŖࡹ۵Drucker-Prager ༉ߙᮥᔍᬊ

⦹ᩡᮝ໑, GFRP ᰍḩ᮹ᬱ☖⩶ᚹᮡRamberg-Osgood ༉ߙᮥ, všᅕvยᮡ┥ᖒ-᪥ᱥᗭᖒᯥᮥaᱶ⦹ᩡ݅. Ğĥ᳑Õᮝಽḡၹ ᮹ ᫙Şᮡ ḡၹ᮹ ᮁ࠺ᖒᮥ Łಅ⦹ᩍ bb X⇶ŝ Z⇶ᨱ ݡ⧕

Ǎᗮ᜽⎑ᮝ໑, ↽⦹݉ᇡ۵༉ࢱǍᗮ⦹ᩡ݅. 1/4 ༉ߙยᮝಽᯙ⧕

ᱥℕᱢᯙǍ᳑ྜྷŝݡ⋎ᯕࡹ۵ᇡᇥᨱݡ⧕ᕽ۵ABAQUSᨱᕽ

ᱽŖࡹ۵ݡ⋎᳑ÕᯙXSYMMŝZSYMMᮥᔍᬊ⦹ᩡ݅. ᅕvย ᮹ Ğᬑ ᩎ᜽ ZSYMMᮥ ᔍᬊ⦹ᩍ ༉ߙย⦹ᩡ݅.

⦹ᵲ᳑Õᮡ⮺᮹ࡹີᬑʑෝŁಅ⦹ᩍຝᱡᱥℕᱢᯙ༉ߙᨱ

ᵲಆᮥa⦹ᩡŁ, እᖁ⩶ḡၹ⧕ᕾ᮹ᙹಕᖒᮥ᭥⦹ᩍHelwany (2007)a ᱽᦩ⦽äŝzᯕᗮࠥ⦹ᵲᮥᱢᬊ⦹ᩡ݅. ᯕভ࠺ᱢ⬉ŝ

(7)

Table 5. Material property of 3D solid model

Member Element Type

Density ćÞƋƋîƑ^ÏßÞƋƋ^Ðß

§

Elastic Modulus (MPa)

Poisson ratio Soil Solid C3D8R 1.85e-9 410 0.25

GFRP Shell S4R5 1.7e-9 7000 0.3

Table 6. Boundary conditon of 3D soild model

Supporting points U1 U2 U3 UR1 UR2 UR3

 Fix Free Free Free Free Free

 Free Free Fix Free Free Free

 Fix Free Free Free Fix Fix

 Free Free Fix Fix Fix Free

 Fix Fix Fix Fix Fix Fix

 Displacement Increase Load

+BQBO3PBE"TTPDJBUJPO +BQBO3PBE"TTPDJBUJPO

(a) 4MPa (b) 6MPa

+BQBO3PBE"TTPDJBUJPO +BQBO3PBE"TTPDJBUJPO

(c) 8MPa (d) 10MPa

Fig. 9. Load-displacement curve aၽᔾ⦹ḡᦫࠥಾᝅᱽ⦹ᵲᯕ᯲ᬊ⦹۵ᰍ⦹❱ᨱݡ⦹ᩍᱡᗮ᮹

0.1mm/secᦊ⦹⨆᮹ᄡ᭥ෝ᷾a᜽┅۵⦹ᵲ᳑Õᮥᔍᬊ⦹ᩡ݅.

b⧕ᕾ ݉ĥᄥಽᝅᱽᰍ⦹ࡹ۵⦹ᵲ᮹Ⓧʑ۵⦹݉ᇡᨱᕽၽᔾ⦹

۵ḡᱱၹಆᮥ⧊ᔑ⦽⬥ᨱᯕෝᝅᱽ⦹ᵲᮝಽ⪹ᔑ⦹ᩍĥᔑ⦹ᩡ

݅. GFRP᪡ ᅕvย᮹ ྜྷᖒ⊹۵ Table 5᪡ zŁ Ğĥ᳑Õ ၰ

⦹ᵲ᳑Õᮡ Table 6ŝ z݅.

Drucker-Prager ༉ߙᮡ ᯝၹᱢᮝಽ Mohr-Coulomb ༉ߙŝ

⧉̹᫙ᦶ᮹᳕ᱢእ┥ᖒÑ࠺ᮥᅕᯕ۵ḡၹᨱݡ⧕ᵝಽᔍᬊࡹŁ

ᯩ۵እ┥ᖒᰍഭ༉ߙᯕ݅. ᅙ༉ߙ᮹ᯙᯱᵲᨱḡၹ┥ᖒĥᙹ᪡

ḡၹ᮹ԕᇡษₑb(ŋ)ᮥᄡ⪵᜽┅໕ᕽ⧕ᕾᮥᙹ⧪⦹ᩡᮝ໑ḡၹ ᮹ԕᇡษₑbᨱ঑ෙABAQUSᨱᕽᱽŖࡹ۵᯦ಆᄡᙹĸ᪡᮹

šĥ᜾ᮡ ᜾ (7)ŝ z݅.

ĸ á ćÐ à ŋÓŋ (7)

Fig. 9۵⦹ᵲᰍ⦹ᱱ⦹݉ᇡᬱ☖⩶GFRP ᚹ᮹⯹-ᄡ᭥ə௹⥥

ᯕ݅. ḡၹ┥ᖒĥᙹ۵4MPa, 6MPa, 8MPa, 10MPaŝԕᇡษₑb (_ŋ) 20°, 27°, 30°ᨱ঑ෙᄡ᭥᮹ᄡ⪵ෝᅕᩍᵝŁᯩ݅. ┥ᖒĥᙹ

ၰ ԕᇡษₑbᯕ ᯲ᮥᙹಾ ⦹ᵲᨱ ݡ⧕ ᄡ᭥a Ⓧí ӹ┡ӹ۵

äᮥᅝᙹᯩ݅. ᷪ, ԕᇡษₑbᯕ20°ᯙĞᬑḡၹ᮹┥ᖒĥᙹa

4MPaᨱᕽ10MPaಽ2.5႑᷾a⧉ᨱ঑௝ɚ⦽⦹ᵲᮡ80kNᨱᕽ

(8)

(a) 4MPa (b) 6MPa

(c) 8MPa (d) 10MPa

Fig. 10. Axial strain at loading point

110kNᮝಽ1.4႑᷾a⦹ᩡ݅. ⦽⠙, ḡၹ᮹┥ᖒĥᙹa᯲ᮡĞᬑ

ԕᇡษₑb᮹Ⓧʑᄡ⪵ᨱ঑ෙ⯹-ᄡ᭥ɚ⦽Ñ࠺᮹₉ᯕ۵Ⓧḡ

ᦫᮝӹḡၹ᮹┥ᖒĥᙹa⍅ḩᙹಾə₉ᯕa⪶ᩑ⧕ḡŁᯩ݅.

ᷪ, ḡၹ᮹ ┥ᖒĥᙹa 4MPaᯙ Fig. 8(a)ᨱᕽ ԕᇡษₑbᯕ

20°~30°ಽ ᄡ⪵⧁ ভ, 20mm᮹ ᄡ᭥ෝ ၽᔾ᜽┅۵ ⦹ᵲᮡ

75kN~80kNᮝಽᕽ 5kN᮹ ⡎ᮥ ᅕᯕḡอ, ḡၹ᮹ ┥ᖒĥᙹa

10MPaᯙFig. 8(d)ᨱᕽ۵100kN~160kNᮝಽᕽ60kN᮹ⓑᄡ࠺

⡎ᮥ ᅕᯕŁ ᯩ݅.

ੱ⦽, ḡၹᜅ⥥ย⧕ᕾŝ3₉ᬱᱶၡ⧕ᕾᨱݡ⧕⦹ᵲᰍ⦹ᱱ

⦹݉ᨱᕽ᮹ᄡ᭥ෝእƱ⦹ᩡᮥ Ğᬑḡၹ᮹┥ᖒĥᙹa4MPa, ԕᇡษₑbᯕ20°ᯝভእƱᱢᯝ⊹⦹Łᯩᮭᮥᅕᯕ۵ߑ, ᯕ۵

ḡၹᜅ⥥ยᔢᙹෝᱢᬊ⧁ভᩑ᧞⦽ᔍḩ☁ᨱaʭᬕḡၹᮥᱢᬊ

⦹ᩡʑ ভྙᯕ݅.

Fig. 10ᮡ⯹-ᄡ⩶ශə௹⥥ಽᕽ⦹ᵲᰍ⦹ᱱ⦹ᇡᨱᕽ᮹ᬱ☖⩶

ᚹ᮹⇶ႊ⨆ᄡ⩶ශə௹⥥ᯕ݅. ⯹-ᄡ⩶ශə௹⥥ᩎ᜽┥ᖒĥᙹa

ԏᮥᙹಾ, ԕᇡษₑbᯕ᯲ᮥᙹಾᄡ⩶ශᯕ᷾a⧉ᮥ⪶ᯙ⧁ᙹ

ᯩ݅. ⦽⠙, ⯹-ᄡ᭥šĥ᪡ษ₍aḡಽḡၹ᮹┥ᖒĥᙹa᯲ᮡ

Ğᬑ ԕᇡษₑb᮹ Ⓧʑ ᄡ⪵ᨱ ঑ෙ ⯹-ᄡ⩶ශ Ñ࠺᮹ ₉ᯕ۵

Ⓧḡᦫᮝӹḡၹ᮹┥ᖒĥᙹa⍅ḩᙹಾᄡ⩶ශ᮹ᄡ࠺⡎ᯕ᷾a

⦹Łᯩ݅. ੱ⦽ḡၹ᮹ԕᇡษₑbᯕ20^oᱶࠥಽ᯲ᮝ໕ɚ⦽⦹ᵲ

ᇡɝᨱᕽᄡ⩶ශᯕḡᗮᱢᮝಽ᷾a⦹Łᯩḡอ, ḡၹ᮹ԕᇡษₑ bᯕ20^oᯕᔢ᮹Ğᬑɚ⦽⦹ᵲᇡɝᨱᕽᄡ⩶ශ᮹᷾ᇥᯕᮭᮝಽ

ᄡ⪵⦹໑ᯕ్⦽⩥ᔢᮡḡၹ᮹┥ᖒĥᙹ᪡ ྕš⦹íӹ┡ӹŁ

ᯩ݅.

Fig. 11ᮡ ᬱ☖⩶ᚹ᮹ ᬱᵝႊ⨆ ᄡ⩶ශᨱݡ⦽ ə௹⥥ᯕ݅.

⇶ႊ⨆ᄡ⩶ශŝ۵ᔢᯕ⦹íḡၹ᮹ԕᇡษₑbᯕ20^oᯙĞᬑᨱ

ɚ⦽⦹ᵲᇡɝᨱᕽᄡ⩶ශ᮹᷾ᇥᯕᮭᮝಽᄡ⪵ࡹŁᯩᮭᮥ᦭

ᙹ ᯩ݅.

vš ᅕvย᮹ ၹḡ෥ŝ ࢱ̹᮹ ᄡ⪵ᨱ ঑ෙ ᬱ☖⩶ GFRP ᚹ᮹ᄡ᭥᪡ᄡ⩶ශ᮹šĥෝ᦭ᦥᅕʑ᭥⦹ᩍ}ᯙ⦹ᙹ⃹ญ᜽ᖅ ᮹᫙Ğᮡ2mಽ࠺ᯝ⦹í⦹Łᅕvย᮹ၹḡ෥ŝࢱ̹ෝᄡ⪵᜽⍽

ᮁ⦽᫵ᗭ⧕ᕾᮥḥ⧪⦹ᩡ݅. ᅕvย᮹ၹḡ෥ᮥ21.85mm, 24.3mm ᯙ Ğᬑ᪡ ᅕvย᮹ ࢱ̹ෝ 2.3mm, 2.5mm, əญŁ 3.2mmᯙ

Ğᬑᨱ ݡ⧕ ḡၹԕᇡษₑbᮥ 27°ಽ Łᱶ᜽┅Ł ┥ᖒĥᙹෝ

4MPa, 6MPa, 8MPa, 10MPaಽ ᄡ⪵᜽⍽ a໕ᕽ ɚ⦽⧕ᕾᮥ

ᙹ⧪⦹ᩡ݅.

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(a) 4MPa (b) 6MPa

(c) 8MPa (d) 10MPa

Fig. 11. Hoop strain at loading point

(a) r=21.85mm, t=2.3mm (b) r=24.3mm, t=2.5mm (c) r=24.3mm, t=3.2mm Fig. 12. Load-displacement according to ring size

Fig. 12۵ᅕvย᮹ၹḡ෥ŝࢱ̹ᨱݡ⦽ḡၹ᳑Õ᮹ᄡ⪵ᨱ

঑ෙ⦹ᵲᰍ⦹ᱱ⦹݉ᇡ᮹⯹-ᄡ᭥ə௹⥥ᯕ݅. ᅕvย᮹ၹḡ෥ŝ

ࢱ̹a᯲ᮥᙹಾ, ┥ᖒĥᙹa᯲ᮥᙹಾᄡ᭥aⓍíၽᔾ⦹۵äᮥ

᦭ᙹᯩ݅. ၹḡ෥ŝࢱ̹a࠺ᯝ⦽Ğᬑḡၹ┥ᖒĥᙹ᮹ᄡ⪵ᨱ

঑௝4MPaᯙĞᬑa10MPaᅕ݅᧞1.8႑ᄡ᭥aฯᯕၽᔾ⦹۵

äᮥ᦭ᙹᯩᮝ໑, ┥ᖒĥᙹa࠺ᯝ⦽Ğᬑᨱ۵ၹḡ෥ᯕ21.85mm, ࢱ̹a 2.3mmᯙ Ğᬑa ၹḡ෥ᯕ 24.3mm, ࢱ̹a 3.2mmᯙ

Ğᬑᅕ݅᧞1.15႑ᄡ᭥aฯᯕၽᔾ⦹۵äᮥ⪶ᯙ⧁ᙹᯩ݅.

Fig. 13ᨱᕽ⦹ᵲᰍ⦹ᱱ⦹݉ᇡᨱᕽ᮹⇶ႊ⨆ᄡ⩶ශᮥࠥ᜽⦹

ᩡ݅. ᅕvย᮹ၹḡ෥ၰࢱ̹a᯲ᮥᙹಾᄡ⩶ᯕⓍíၽᔾ⦹۵

äᮥ ⪶ᯙ ⧁ ᙹ ᯩ݅. ੱ⦽ ɚ⦽⦹ᵲ ɝ⃹ᨱ ࠥݍ⦹໕ ⇶ႊ⨆

ᄡ⩶ශ᮹᷾ᇥᯕᮭᮝಽᄡ⦹۵äᮥ⪶ᯙ⧁ᙹᯩ۵ߑᅕvย᮹

Ⓧʑa᯲ᮥᙹಾᯕ్⦽Ñ࠺ᯕ⪶ᩑ⯩ӹ┡ԍ݅. ᯕ۵⦹ᵲᰍ⦹

Ⅹʑᨱ۵všᅕvย᮹ᩢ⨆ᮝಽGFRP ᬱ☖⩶ᚹǍ᳑a⇶ႊ⨆

ᮝಽᮭ᮹łශಽ⭹ᨕḡ݅aɚ⦽⦹ᵲᨱ ࠥݍ⦹໕⇶ႊ⨆ᮝಽ

᧲᮹ łශಽ ⮉ᄡ⩶ᯕ ᄡ⪵⦹ʑ ভྙᯕ௝Ł ❱݉ࡽ݅.

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Fig. 13. Axial strain according to ring size

(a) r=21.85mm, t=2.3mm (b) r=24.3mm, t=2.5mm (c) r=24.3mm, t=3.2mm Fig. 14. Hoop strain according to ring size

Fig. 14۵⦹ᵲᰍ⦹ᱱ⦹݉ᇡ᮹ᬱ☖⩶GFPR ᚹ᮹⬥⥥ႊ⨆

⯹-ᄡ⩶ශə௹⥥ᯕ݅. ⦹ᵲᰍ⦹Ⅹʑ݉ĥᨱᕽ۵⦹ᵲ᮹᷾a᪡

⧉̹ᱱḥᱢᮝಽᬱᵝႊ⨆ᮝಽᯙᰆ᮹ᄡ⩶ශᯕ᷾a⦹݅aɚ⦽

⦹ᵲ ɝ⃹ᨱ ࠥݍ⦹໕ ᄡ⩶ශ᮹ ᷾aa ᱱ₉ qᗭ⦹Ł ᯩ۵ߑ, ᯕ۵⦹ᵲᰍ⦹❱᮹Ⓧʑ⬉ŝಽᯙ⦹ᩍ⦹ᵲᰍ⦹ᱱḢ⦹ᇡ᮹ᬱ☖

⩶ᚹ᮹ᬱᵝႊ⨆ᄡ⩶ᮡⅩʑ⦹ᵲᰍ⦹݉ĥᨱᕽ۵᧲᮹łශ᷾a a૽ಘ⦹ḡอɚ⦽⦹ᵲᨱᱲɝ⧁ᙹಾłශ᮹᷾aᨧᯕᙹḢᄡ᭥

a ᷾a⦹ʑ ভྙᯕ௝Ł ❱݉ࡽ݅. ੱ⦽, ⬥⥥ႊ⨆᮹ ᄡ⩶ශᮡ

ḡၹ┥ᖒĥᙹa ࠺ᯝ⦽ Ğᬑᨱ۵ ၹḡ෥ᯕ 21.85mm, ࢱ̹a

2.3mmᯙĞᬑaၹḡ෥ᯕ24.3mm, ࢱ̹a3.2mmᯙĞᬑᅕ݅

᧞ 3.3႑ Ⓧí ၽᔾ⦹۵ äᮥ ⪶ᯙ⧁ ᙹ ᯩ݅.

⩥⧪}ᯙ⦹ᵲ⃹ญ᜽ᖅ᮹ᅕvย᮹ᖅĥȽᱶᮡ, ᔢᰍ⦹ᵲᨱݡ

⦽ ᮲ಆ᮹ ᦩᱥᖒᨱ ݡ⦽ ᳑Õ᜾ (1a) ၰ ᱶᙹᦶᮥ ၼ۵ ᬱ⩶

ย᮹᳭Ǖᨱݡ⦽Ƚᱶ᜾(1b)ᯕ໑Table 2᮹ᖅĥđŝᨱ᮹⦹໕

ݡᇡᇥ ᮲ಆ᮹ ᦩᱥᖒᮡ อ᳒⦹ḡอ ᳭Ǖ ᦩᱶᖒ ᳑Õᯕ ᝅᱽ

ᖅĥෝ᳭ᬑ⦹Łᯩ݅. ⦹ḡอ, ᝅᱽݡᇡᇥ᮹}ᯙ⦹ᙹ⃹ญ᜽ᖅᮡ

ᅙםྙᨱᕽ⧕ᕾ⦽ၵ᪡zᯕḡၹᨱ30~40cm᮹᧶ᮡʫᯕಽ

ๅพࡹᨕᯩᮝ໑ᔢᰍ⦹ᵲᮡḡၹᮥ☖⦹ᩍᬱ☖⩶ᚹ᮹↽ᔢ݉

ᇡᇥᨱ Ḳᵲ⦹ᩍ ᯲ᬊ⦽݅. ঑௝ᕽ ᫙ಆ᮹ ᷾a᪡ ⧉̹ ᬱ☖⩶

ᚹᅙℕၰvšᅕvยᮡḡᗮᱢᮝಽ⮉ᄡ⩶ᯕၽᔾ⦹໑᫙ᦶᮥ

ၼ۵ᬱ⩶ย᮹᳭ǕÑ࠺ᮡӹ┡ӹḡᦫ۵݅. ə్အಽ⩥⧪}ᯙ⦹

ᵲ⃹ญ᜽ᖅ᮹ᅕvย᮹᳭ǕᖅĥȽᱶᨱݡ⦽ᅕ᪥ᯕ᫵Ǎࡽ݅Ł

❱݉ࡽ݅.

5. đು

ᅙםྙᨱᕽ۵⩥⧪}ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ᖅĥʑᵡᨱᇡ⧊ࡹ۵

ᬱ⩶všᮝಽᅕvࡽḡᵲๅᖅ⩶GFRP }ᯙ⦹ᙹ⃹ญ᜽ᖅᮥᖅĥ

⦹Ł ᮁ⦽᫵ᗭ⧕ᕾᮥ ᙹ⧪⦹ᩍ ɚ⦽Ñ࠺ᮥ ᇥᕾ⦹ᩡ݅. ḡၹᮥ

እᖁ⩶ᜅ⥥ยᮝಽݡℕ⦽⧕ᕾ༉ߙŝ3₉ᬱŁℕ᫵ᗭෝᱢᬊ⦽

ࢱaḡ⧕ᕾ༉ߙᮥᯕᬊ⦹ᩍ, ᅕvย᮹⩶┽᪡ḡၹ᳑Õ᮹ᄡ⪵ᨱ

঑ෙ}ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ɚ⦽Ñ࠺ᨱݡ⦽ๅ}ᄡᙹ⧕ᕾᮥᙹ⧪

⦹ᩡ݅.

3₉ᬱᱶၡ⧕ᕾᮥ☖⧕ḡၹ᳑Õᨱ঑௝ๅพࡽᬱ☖⩶ᚹǍ᳑

᮹ɚ⦽vࠥaᔢᯕ⦹íӹ┡ԍ݅. ḡၹ᮹┥ᖒĥᙹa2.5႑ᄡ⪵

⧉ᨱ঑௝ɚ⦽ᄡ᭥a᧞1.8႑Ⓧíၽᔾ⦹ᩡ݅. ḡၹԕᇡษₑb ᮹ᄡ⪵ᨱ঑ෙɚ⦽ᄡ᭥۵Ⅹʑ┥ᖒǍeᨱᕽ۵ⓑ₉ᯕaᨧḡอ,

⦹ᵲᯕa⧕ḩᙹಾḡၹԕᇡษₑbᯕ᯲ᮥᙹಾⓍíၽᔾ⦹ᩡ݅.

ੱ⦽, ݡᇡᇥ᮹}ᯙ⦹ᙹ⃹ญ᜽ᖅᮡḡၹᨱ᧶ᮡʫᯕಽๅพࡹᨕ

ᯩᨕᕽ ᫙ಆ᮹ ᷾a᪡ ⧉̹ ᬱ☖⩶ ᚹ ᅙℕ ၰ vš ᅕvยᮡ

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ḡᗮᱢᮝಽ⮉ᄡ⩶ᯕၽᔾ⦹໑⩥⧪ᖅĥȽᱶᮝಽᔍᬊࡹŁᯩ۵

᫙ᦶᮥၼ۵ᬱ⩶ย᮹᳭ǕÑ࠺ᮡၽᔾ⦹ḡᦫᮭᮥ⪶ᯙ⦹ᩡ݅.

ᷪ, ḡၹᨱๅพࡽ}ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ɚ⦽Ñ࠺ᨱᵲᩍ⦽ᩢ⨆

ᮥᵝ۵ᯙᯱ۵ḡၹ᳑Õᯕḡอ⩥⧪ᖅĥ᳑Õᨱ۵ḡၹ᮹ᩢ⨆ᮥ

ྕ᜽⦹Łᯩʑভྙᨱ}ᯙ⦹ᙹ⃹ญ᜽ᖅ᮹ᖅĥȽᱶᨱݡ⦽ᅕ᪥

ᯕ ᫵Ǎࡽ݅Ł ❱݉ࡽ݅.

qᔍ᮹ɡ

ᅙᩑǍ۵⦽ǎᩑǍᰍ݉᮹ᯝၹᩑǍᯱḡᬱᔍᨦ(No. 2012R1 A1A2044646)᮹ᩑǍእḡᬱᮝಽᙹ⧪ࡹᨩᮝ໑, ᱡᯱ۵ᩑǍእ

ḡᬱᨱ qᔍऽพܩ݅.

References

Drucker, D. C. and Prager, W. (1952). “Soil mechanics and plastic analysis for limit design.” Quarterly of Applied Mathematics, Vol. 10, No. 2, pp. 157-165.

Jo, K. J. and Kim, S. B. (2012). “Design of high strength underground FRP septic tank stiffend by circular steel pipe.” J. Korean Society of Civil Engineering, 32(3A), pp. 171-181 (in Korean).

Ministry of Environment. (2011). Standard of structural and material performance of underground septic tank, Code of sewerage 58 (in Korean).

George Abdel-Sayed. (1978). “Stability of flexible conduits embedded in soil.” Canadian J. Civil Eng., 5(33), pp. 324-334.

Helwany, Sam. (2007). Applied soil mechanics with ABAQUS applications, John Wiley & Sons.

Medhat Ghobrial and George Abdel-Sayed. (1985). “Inelastic buckling of soil-steel structures.” Transportation Research Board, pp. 7-14.

Oh, J. H. (1999). Design and construction of soil retaining, Engineers (in Korean).

Okeagu, B. N. and Abdel-Sayed, G. (1984). “Coefficients of soil reaction for buried flexible conduits.” Journal of Geotechnical Engineering, ASCE, Vol. 110, pp. 908-922.

Ramberg, W. and Osgood, W. R. (1943). “Description of stress- strain surves by three parameters.” Technical Note No.902, National Advisory Committee For Aeronautics, Washington DC.

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