高温下におけるコンクリートの爆裂発生指標とリング拘束試験方法

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Title

高温下におけるコンクリートの爆裂発生指標とリング拘束

_{試験方法( 本文(Fulltext) )}

Author(s)

谷辺, 徹

Report No.(Doctoral

Degree)

博士(工学) 甲第460号

Issue Date

2014-09-30

Type

博士論文

Version

ETD

URL

http://hdl.handle.net/20.500.12099/50385

※この資料の著作権は、各資料の著者・学協会・出版社等に帰属します。

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㧗 ୗ࡟࠾ࡅࡿࢥࣥࢡ࣮ࣜࢺࡢ

⇿⿣Ⓨ⏕ᣦᶆ࡜ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲ

Ring restraining testing and spalling index

of concrete at high temperature

ᖹᡂ

26 ᖺ 9 ᭶

ᒱ㜧኱Ꮫ኱Ꮫ㝔

ᕤᏛ◊✲⛉༤ኈᚋᮇㄢ⛬

⏕⏘㛤Ⓨࢩࢫࢸ࣒ᕤᏛᑓᨷ

㇂㎶ ᚭ

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┠ḟ

┠ ḟ

➨㸯❶ ᗎㄽ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 1 㸯㸬㸯 ◊✲ࡢ┠ⓗ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 1 㸯㸬㸰 ◊✲ࡢ⫼ᬒ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 1 㸯㸬㸰㸬㸯 ࢥࣥࢡ࣮ࣜࢺࡢ⪏ⅆᛶ⬟↷ᰝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 1 㸯㸬㸰㸬㸰 ࢥࣥࢡ࣮ࣜࢺࡢ⪏ⅆᑐ⟇ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 3 㸯㸬㸱 ㄽᩥࡢᵓᡂ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 6 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 9 ➨㸰❶ ࢥࣥࢡ࣮ࣜࢺࡢ㧗 ≉ᛶ࡟㛵ࡍࡿ᪤ ࡢ◊✲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 10 㸰㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 10 㸰㸬㸰 ࢥࣥࢡ࣮ࣜࢺࡢ໬Ꮫⓗᛶ㉁㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 10 㸰㸬㸱 ࢥࣥࢡ࣮ࣜࢺࡢ≀⌮ⓗᛶ㉁㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 13 㸰㸬㸱㸬㸯 ᐦᗘ㸦density㸧㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 13 㸰㸬㸱㸬㸰 ẚ⇕㸦specific heat㸧㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 14 㸰㸬㸱㸬㸱 ⇕ఏᑟ⋡㸦thermal conductivity㸧㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 16 㸰㸬㸱㸬㸲 ⇕ᣑᩓ⋡㸦thermal diffusivity㸧㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 17

㸰㸬㸱㸬㸳 ⇕⭾ᙇಀᩘ㸦coefficient of thermal expansion㸧㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 17

㸰㸬㸲 ࢥࣥࢡ࣮ࣜࢺࡢຊᏛⓗᛶ㉁㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 18 㸰㸬㸲㸬㸯 ᅽ⦰ᙉᗘ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 19 㸰㸬㸲㸬㸰 ᙎᛶಀᩘ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 21 㸰㸬㸲㸬㸱 ᛂຊ㸫ࡦࡎࡳ㛵ಀ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 22 㸰㸬㸳 ࢥࣥࢡ࣮ࣜࢺࡢࡦࡎࡳᛶ≧ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 26 㸰㸬㸴 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 28 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 29 ➨㸱❶ ࢥࣥࢡ࣮ࣜࢺࡢ⇿⿣Ⓨ⏕࣓࢝ࢽࢬ࣒࡟㛵ࡍࡿ᪤ ࡢ◊✲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 31 㸱㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 31 㸱㸬㸰 ⇿⿣⌧㇟ࡢ◊✲ྐ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 31 㸱㸬㸰㸬㸯 ᡃࡀᅜ࡟࠾ࡅࡿ⇿⿣⌧㇟ࡢ◊✲ྐ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 31 㸱㸬㸰㸬㸰 ᾏእ࡟࠾ࡅࡿ⇿⿣⌧㇟ࡢ◊✲ྐ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 33 㸱㸬㸱 ࢥࣥࢡ࣮ࣜࢺࡢ⇿⿣⌧㇟ࡢ࣓࢝ࢽࢬ࣒ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 34 㸱㸬㸱㸬㸯 ࢥࣥࢡ࣮ࣜࢺࡢ⇿⿣⌧㇟ࡢ≉ᚩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 34 㸱㸬㸱㸬㸰 ࢥࣥࢡ࣮ࣜࢺࡢ⇿⿣⌧㇟ࡢศ㢮㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 35 㸱㸬㸱㸬㸱 ⇿⿣Ⓨ⏕࣓࢝ࢽࢬ࣒ࡢ◊✲ࡢ⌧≧ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 36 㸱㸬㸲 ࢥࣥࢡ࣮ࣜࢺࡢ⇿⿣ホ౯᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 36 㸱㸬㸲㸬㸯 Ỉ⵨Ẽᅽࡢホ౯ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 37 㸱㸬㸲㸬㸰 ⇕ᛂຊࡢホ౯ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 40 㸱㸬㸳 ⇿⿣ᢚไ᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 44

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┠ḟ 㸱㸬㸳㸬㸯 ⪏ⅆ⿕そᮦࢆタ⨨ࡍࡿ᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 44 㸱㸬㸳㸬㸰 ྜᡂ⧄⥔㸦PP ⧄⥔㸧ࢆῧຍࡍࡿ᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 47 㸱㸬㸴 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 49 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 50 ➨㸲❶ ࢥࣥࢡ࣮ࣜࢺࡢ⇕ᛂຊィ ᪉ἲ࡟㛵ࡍࡿ᪤ ࡢ◊✲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 53 㸲㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 53 㸲㸬㸰 Connolly ࡟ࡼࡿ⇕ᛂຊࡢィ ᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 53 㸲㸬㸰㸬㸯 ⇕ᛂຊࡢィ ᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 53 㸲㸬㸰㸬㸰 Ỉ⵨Ẽᅽࡢィ ᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 55 㸲㸬㸰㸬㸱 ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 56 㸲㸬㸱 ෇⟄⌮ㄽ࡟ࡼࡿ⭾ᙇᅽࡢィ ᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 57 㸲㸬㸲 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 58 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 59 ➨㸳❶ ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲ࡟ࡼࡿ⡆᫆࡞⪏⇿⿣ᛶホ౯ᡭἲࡢᥦ᱌ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 60 㸳㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 60 㸳㸬㸰 ᥦ᱌ࡍࡿࣜࣥࢢᣊ᮰ヨ㦂᪉ἲࡢᴫせ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 60 㸳㸬㸰㸬㸯 ⇕ᛂຊࡢィ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 61 㸳㸬㸰㸬㸰 Ỉ⵨Ẽᅽࡢィ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 62 㸳㸬㸱 ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲࡢጇᙜᛶ᳨ドヨ㦂㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 64 㸳㸬㸱㸬㸯 ౪ヨయᴫせ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 64 㸳㸬㸱㸬㸰 ຍ⇕ヨ㦂㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 65 㸳㸬㸱㸬㸱ほᐹ࠾ࡼࡧィ㡯┠ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 65 㸳㸬㸱㸬㸲 ⇿⿣≧ἣほᐹ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 66 㸳㸬㸱㸬㸳 ᗘィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 66 㸳㸬㸱㸬㸴 Ỉ⵨Ẽᅽィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 67 㸳㸬㸱㸬㸵 ᣊ᮰ࣜࣥࢢࡦࡎࡳィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 68 㸳㸬㸱㸬㸶 ౪ヨయኚ఩ィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 68 㸳㸬㸱㸬㸷 ⇕ᛂຊࡢ⟬ฟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 69 㸳㸬㸱㸬㸯㸮 ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲࡢጇᙜᛶ᳨ドヨ㦂⤖ᯝࡢ⪃ᐹ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 71 㸳㸬㸱㸬㸯㸯 ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲࡢㄢ㢟㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 72 㸳㸬㸲 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 72 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 73 ➨㸴❶ ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲࡢ᭱㐺໬ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 74 㸴㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 74 㸴㸬㸰ヨ㦂ᴫせ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 75 㸴㸬㸰㸬㸯ヨ㦂Ỉ‽ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 75 㸴㸬㸰㸬㸰 ౪ヨయᴫせ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 75

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┠ḟ 㸴㸬㸰㸬㸱 ᐃホ౯㡯┠ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 78 㸴㸬㸰㸬㸲 ຍ⇕ヨ㦂㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 79 㸴㸬㸱ヨ㦂⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 80 㸴㸬㸱㸬㸯 ࡦࡎࡳࢤ࣮ࢪࡢ✀㢮࠾ࡼࡧ㍈᪉ྥࡦࡎࡳࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 80 㸴㸬㸱㸬㸰 ࣜࣥࢢẁᩘࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 83 㸴㸬㸱㸬㸱 ࣜࣥࢢእᚄࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 84 㸴㸬㸱㸬㸲 ࣜࣥࢢཌࡳࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 87 㸴㸬㸱㸬㸳 ᅽຊఏ㐩፹యὀධ᪉ἲࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 93 㸴㸬㸲 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 94 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 96 ➨㸵❶ ⇿⿣Ⓨ⏕࣓࢝ࢽࢬ࣒ࡢ௬ㄝ࡜⇿⿣Ⓨ⏕ᣦᶆࡢᥦ᱌ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 97 㸵㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 97 㸵㸬㸰 ⇿⿣Ⓨ⏕࣓࢝ࢽࢬ࣒ࡢᥦ᱌ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 97 㸵㸬㸰㸬㸯 ◚ቯࣉࣟࢭࢫ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 97 㸵㸬㸰㸬㸰 ⇿⿣ࣉࣟࢭࢫ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 98 㸵㸬㸱 ⇿⿣Ⓨ⏕ᣦᶆࡢᥦ᱌ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 99 㸵㸬㸲 ⇿⿣Ⓨ⏕ᣦᶆࡢ᳨ドヨ㦂㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 101 㸵㸬㸲㸬㸯 ౪ヨయ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 101 㸵㸬㸲㸬㸰 ຍ⇕ヨ㦂㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 102 㸵㸬㸲㸬㸱ホ౯㡯┠ _{㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃} ₁₀₂ 㸵㸬㸳 ᗘィ ⤖ᯝ࡜⪃ᐹ _{㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃} ₁₀₃ 㸵㸬㸳㸬㸯 ࢥࣥࢡ࣮ࣜࢺ ᗘ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 103 㸵㸬㸳㸬㸰 ᣊ᮰ࣜࣥࢢ ᗘ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 103 㸵㸬㸴 ⇿⿣≧ἣほᐹ⤖ᯝ࡜⪃ᐹ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 103 㸵㸬㸴㸬㸯 ⇿⿣≧ἣࡢほᐹ _{㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃} ₁₀₃ 㸵㸬㸴㸬㸰 ⇿⿣つᶍ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 104 㸵㸬㸴㸬㸱 ⇿⿣῝ࡉ࡜⤒㐣᫬㛫ࡢ㛵ಀ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 105 㸵㸬㸵 Ỉ⵨Ẽᅽࡢィ ⤖ᯝ࡜⪃ᐹ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 105 㸵㸬㸵㸬㸯 Ỉ⵨Ẽᅽ࡜⤒㐣᫬㛫ࡢ㛵ಀ _{㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃} ₁₀₅ 㸵㸬㸵㸬㸰 Ỉ⵨Ẽᅽ࡜㣬࿴⵨Ẽᅽࡢ㛵ಀ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 105 㸵㸬㸵㸬㸱 Ỉ⵨Ẽᅽ࡜ᘬᙇᛂຊࡢ㛵ಀ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 106 㸵㸬㸵㸬㸲 Ỉ⵨Ẽᅽࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 106 㸵㸬㸶 ᣊ᮰ᛂຊࡢ⟬ฟ⤖ᯝ࡜⪃ᐹ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 106 㸵㸬㸶㸬㸯 ᣊ᮰ᛂຊࡢ⟬ฟ _{㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃} ₁₀₆ 㸵㸬㸶㸬㸰 ᩿㠃ෆࡢᣊ᮰ᛂຊศᕸࡢ᥎ᐃ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 107 㸵㸬㸷 ᘬᙇࡦࡎࡳ◚ቯᣦᩘࡢ㐺⏝ᛶࡢ᳨ド㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 108 㸵㸬㸷㸬㸯 ᘬᙇࡦࡎࡳ◚ቯᣦᩘࡢ᳨ド᮲௳ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 108 㸵㸬㸷㸬㸰 ᘬᙇࡦࡎࡳ◚ቯᣦᩘ᳨ド⤖ᯝ _{㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃} ₁₀₈ 㸵㸬㸯㸮 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 109 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 110

(6)

┠ḟ ➨㸶❶ ㉸㧗ᙉᗘ⧄⥔⿵ᙉࢥࣥࢡ࣮ࣜࢺ࡛ࡢ⇿⿣Ⓨ⏕ᣦᶆࡢ㐺⏝ᛶホ౯ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 111 㸶㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 111 㸶㸬㸰ヨ㦂ᴫせ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 111 㸶㸬㸰㸬㸯ヨ㦂Ỉ‽ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 111 㸶㸬㸰㸬㸰 ౪ヨయ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 111 㸶㸬㸰㸬㸱 ࢥࣥࢡ࣮ࣜࢺ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 112 㸶㸬㸰㸬㸲 ຍ⇕᮲௳ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 113 㸶㸬㸱 ⇿⿣≧ἣほᐹ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 114 㸶㸬㸱㸬㸯 ⇿⿣≧ἣ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 114 㸶㸬㸱㸬㸰 ᩿㠃ほᐹ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 115 㸶㸬㸲 ᣊ᮰ᛂຊィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 119 㸶㸬㸳 Ỉ⵨Ẽᅽィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 120 㸶㸬㸴 ᘬᙇࡦࡎࡳ◚ቯᣦᩘ࡟ࡼࡿホ౯ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 122 㸶㸬㸵 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 124 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 125 ➨㸷❶ ྛ✀⇿⿣ᙳ㡪ᅉᏊࡢ⇿⿣Ⓨ⏕ᣦᶆ࡟ࡼࡿホ౯ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 126 㸷㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 126 㸷㸬㸰ヨ㦂ᴫせ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 127 㸷㸬㸰㸬㸯ヨ㦂Ỉ‽ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 127 㸷㸬㸰㸬㸰 ౪ヨయ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 127 㸷㸬㸰㸬㸱 ࢥࣥࢡ࣮ࣜࢺ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 127 㸷㸬㸰㸬㸲 ຍ⇕᮲௳ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 129 㸷㸬㸰㸬㸳ィ㡯┠ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 129 㸷㸬㸱 ⢒㦵ᮦ✀㢮࠾ࡼࡧᙉᗘࣞ࣋ࣝࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 130 㸷㸬㸱㸬㸯ヨ㦂Ỉ‽ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 130 㸷㸬㸱㸬㸰 ⇿⿣≧ἣほᐹ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 131 㸷㸬㸱㸬㸱 ౪ヨయ ᗘィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 134 㸷㸬㸱㸬㸲 Ỉ⵨Ẽᅽィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 135 㸷㸬㸱㸬㸳 ᣊ᮰ᛂຊィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 137 㸷㸬㸱㸬㸴 ᘬᙇࡦࡎࡳ◚ቯᣦᩘ࡟ࡼࡿ⇿⿣῝ࡉ᥎ᐃ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 138 㸷㸬㸱㸬㸵 ⢒㦵ᮦ✀㢮࠾ࡼࡧᙉᗘࣞ࣋ࣝࡢᙳ㡪ࡢࡲ࡜ࡵ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 140 㸷㸬㸲 PP ⧄⥔ࡢῧຍࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 141 㸷㸬㸲㸬㸯ヨ㦂Ỉ‽ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 141 㸷㸬㸲㸬㸰 ⇿⿣≧ἣほᐹ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 141 㸷㸬㸲㸬㸱 ౪ヨయ ᗘィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 146 㸷㸬㸲㸬㸲 Ỉ⵨Ẽᅽィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 147 㸷㸬㸲㸬㸳 ᣊ᮰ᛂຊィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 148 㸷㸬㸲㸬㸴 ᘬᙇࡦࡎࡳ◚ቯᣦᩘ࡟ࡼࡿ⇿⿣῝ࡉ᥎ᐃ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 150 㸷㸬㸲㸬㸵 PP ⧄⥔ࡢῧຍࡢᙳ㡪ࡢࡲ࡜ࡵ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 152 㸷㸬㸳 ຍ⇕᮲௳࠾ࡼࡧ㣴⏕᮲௳ࡢᙳ㡪㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 153

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┠ḟ 㸷㸬㸳㸬㸯 ౪ヨయ✀㢮㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 153 㸷㸬㸳㸬㸰 ⇿⿣≧ἣほᐹ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 153 㸷㸬㸳㸬㸱 ౪ヨయ ᗘィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 157 㸷㸬㸳㸬㸲 Ỉ⵨Ẽᅽィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 159 㸷㸬㸳㸬㸳 ᣊ᮰ᛂຊィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 160 㸷㸬㸳㸬㸴 ᘬᙇࡦࡎࡳ◚ቯᣦᩘ࡟ࡼࡿ⇿⿣῝ࡉ᥎ᐃ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 162 㸷㸬㸳㸬㸵 ຍ⇕᮲௳࠾ࡼࡧ㣴⏕᮲௳ࡢᙳ㡪ホ౯ࡢࡲ࡜ࡵ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 164 㸷㸬㸴 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 165 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 166 ➨㸯㸮❶ ⪏ⅆ⿕そᮦࢆ㐺⏝ࡋࡓ⇿⿣ᢚṆຠᯝࡢ᳨ド㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 167 㸯㸮㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 ₁₆₇ 㸯㸮㸬㸰ヨ㦂ᴫせ㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 167 㸯㸮㸬㸰㸬㸯ヨ㦂Ỉ‽ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 167 㸯㸮㸬㸰㸬㸰 ౪ヨయ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 168 㸯㸮㸬㸰㸬㸱 ࢥࣥࢡ࣮ࣜࢺ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 169 㸯㸮㸬㸰㸬㸲 ⪏ⅆ⿕そᮦ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 170 㸯㸮㸬㸰㸬㸳 ຍ⇕᮲௳ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 171 㸯㸮㸬㸰㸬㸴ィ㡯┠ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 171 㸯㸮㸬㸱 ⇿⿣≧ἣほᐹ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 172 㸯㸮㸬㸲 ౪ヨయ ᗘィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 176 㸯㸮㸬㸳 Ỉ⵨Ẽᅽィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 177 㸯㸮㸬㸴 ᣊ᮰ᛂຊィ ⤖ᯝ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 178 㸯㸮㸬㸵 ᘬᙇࡦࡎࡳ◚ቯᣦᩘ࡟ࡼࡿホ౯ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 179 㸯㸮㸬㸶 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 181 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 182 ➨㸯㸯❶ ⤖ㄽ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 183 㸯㸯㸬㸯 ࡣࡌࡵ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 183 㸯㸯㸬㸰 ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 183 㸯㸯㸬㸱 ⇿⿣Ⓨ⏕࣓࢝ࢽࢬ࣒࡜⇿⿣Ⓨ⏕ᣦᶆ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 184 㸯㸯㸬㸲 ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲ࡜⇿⿣Ⓨ⏕ᣦᶆࡢ㐺⏝ᛶホ౯ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 185 㸯㸯㸬㸳 ⪏ⅆ⿕そᮦࢆ㐺⏝ࡋࡓ⇿⿣ᢚṆຠᯝࡢ᳨ド㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 185 㸯㸯㸬㸴 ⇿⿣✀㢮࡜Ⓨ⏕ࣉࣟࢭࢫࡢ࢖࣓࣮ࢪ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 186 㸯㸯㸬㸵 ࣜࣥࢢᣊ᮰ヨ㦂᪉ἲࡢ௒ᚋࡢᒎ㛤㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 187 㸯㸯㸬㸵㸬㸯 ࢥࣥࢡ࣮ࣜࢺࡢ㓄ྜタィ࡬ࡢᒎ㛤㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 187 㸯㸯㸬㸵㸬㸰 ᵓ㐀㒊ᮦࡢ⪏ⅆᛶ↷ᰝ࡬ࡢᒎ㛤㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 188 㸯㸯㸬㸶 ࠾ࢃࡾ࡟ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 188 ཧ⪃ᩥ⊩ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 189 ㅰ㎡㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 190 Ⓨ⾲ㄽᩥ 㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃㺃 191

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PP

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2009 1 17 80N/mm2 2013 2 2.13 80N/mm2 1.1 2012 3 5 20mm 2012 3 4 4.2 80N/mm2 50 100N/mm2 RABT 4 80 N/mm2 ₅ ₆ 1.1 2 1 2 3

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1

JASS6 2007 7 11

1.2 JASS6

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2 6 8 9 RABT 4 10 RABT 9 11 12 1.1 1.2 13 1.1 13 1.2 13

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3 PP 14 1.1 PP 2kg/m3 170 PP PP 1.1

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1.2 Eurocode2 Eurocode4 1952 1854 1 300 8 50mm 2 300 8 100mm 2

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UFC HSC PP UFC 100 0.3 PP PP PP 6

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PP

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[1] JASS 5 2009.

[2] 2013.

[3] 2012

[4] ZTV-TUNNEL Zusaetzliche Technische Vertragasbed-ingungen und Richtlinien fuer den Bau von Strassentunneln Teil 1 Geschlossene Bauweise, Bundesministerium fuer Verkehr, 1995.

[5] Vol. 41 No. 1 pp. 38-42 2003.1. [6] RC Vol.24 No. 1 pp. 1719-1724 2002. [7] JASS 6 2007. [8] 60 5 pp. 843-844 2005. [9] Vol. 31 No. 1 pp. 1567-1572 2009. [10] 63 pp. 151-162 2004. [11] 61 5 pp. 795-796 2006. [12] 62 5 pp. 1211-1212 2007. [13] 2012.5. [14] pp. 98-109 2009.

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1 4

CEN (European Committee for Standardization) Eurocode2

5 Eurocode4 6

RILEM International Union of Laboratories and Experts in Construction Materials Systems and Structures

4 7 8 2.1 2.2 30 600 600 700 C-S-H 1100 1200 570 600 900

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2.1 7 8 30 120 100 ( ) 30 300 ( ) C S H 100 130 100 160 180 250 270 50 150 200 300 (C4A3S) CaO (CaSO4 2H2O) 130 160 (Ca(OH)2) 450 500 Ca(OH)2 CaO+H2O 120 600 570 ( ) 600 700 C-S-H -C2S 600 900 (CaCO3 CaO+CO2) SiO 1100 1200 1200 1200 1060 1700

(19)

2.2 8 CaSO4 2H2O 130 160 CaCO3 750 900 CaO CaO Ca(OH)2 C S H 100 300 C S H Ca(OH)2 450 500 CaO 300 400 (AFt)C3A3CSH32 100 100 160 180 250 270 (AFm)C3ACSH12 DTA 50 150 200 300 (C4A3S) CaO C4AHX C4AHX 20 C3AH6 50 100 12 110 170 7 300 4 700 0 C4A3 CaO C3AH6 C3AH6 20 C4AHX C2AHX CAHX 270 330 4.5 550 C12A7 CaO CAHX CAHX CAH10 20 C3AH6 CAH10 200 500 2 600 C2AHX C2AHX C2AH9 20 C3AH6 C2AH6 300 11 C5S6H5 100 160 250 260 9 C6S6H5 180 790 800 830 900 1000

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density kg/m3 2,000 2,500kg/m3 100 600 900 600 Eurocode2 5 20 115 20 20 115 1,200 12 2.3 2.1 Eurocode2 600 2.3 Eurocode2 5 kg/m3 ( ) = (20°C) 20°C 115°C ( ) = (20°C) × 1 – 0.02( - 115) 85 115°C 200°C ( ) = (20°C) × 0.98 – 0.03( - 200) 200 200°C 400°C ( ) = (20°C) × 0.95 – 0.07( - 400) 800 400°C 1200°C ( ) 2.1 Eurocode2 5 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200 2,300 2,400 2,500 0 200 400 600 800 1000 1200 2300kg/m3 _3% Eurocode2

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specific heat K kJ/kg K 0.8 1.0 kJ/kg K 500 Eurocode2 5 400 9 2,300kg/m3 8 1 Eurocode2 Eurocode2 0 1.5 3.0 1.47 kJ/kg K 2.02kJ/kg K 2.4 2.2 2.4 Eurocode2 5 kJ/kg K cp( ) = 900 10-3_20°C _100°C cp( ) = (900 + ( - 100)) 10-3_100°C _200°C cp( ) = (1000 + ( - 200) 2) 10-3_200°C _400°C cp( ) = 1100 10-3_400°C _1200°C cp( ) 2.2 Eurocode2 5 2 9 2.5 2.3 2,300kg/m3 ₈ 0.0 0.5 1.0 1.5 2.0 2.5 0 200 400 600 800 1000 1200 0% 1.5% 3%

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2.5 9 kJ/kg K (kg/m3₎ _(%) cp( ) = ( 6.73×10-4_× 2_{+1.23× +692) 10}-3 _{2,300 8} ALC cp( ) =( 2.0×10-4_× 2_{+0.12× +1330) 10}-3_{510 10 14} cp( ) =( 2.0×10-4_× 2_{+0.12× +1330) 10}-3_{1,550 1,760 6 8} cp( ) =( 5.49×10-4_× 2_{+1.63× +516) 10}-3_{1,870 2,150 12} cp( ) 2.3 9 3 Eurocode2

Eurocode2 EC2 AIJ

2.4 EC2 100 200 AIJ 8% AIJ EC2 100 400 2.4 Eurocode2 5 9 0.0 0.5 1.0 1.5 2.0 2.5 0 200 400 600 800 1000 1200 ALC 0.0 0.5 1.0 1.5 2.0 2.5 0 200 400 600 800 1000 1200

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thermal conductivity /m m2 ₁ W/m K Eurocode2 5 2.5 9 GHP 2.6 2.6 Eurocode2 EC2 AIJ 2.7 700 2.5 Eurocode2 5 2.6 9 W/m K (kg/m3₎ _(%) k( ) = 4.42×10-6_× 2 _5.58×10-3_× _{2.49 2,300}₈ ALC k( ) = 2.15×10-7_× 2 _9.0×10-6_× _{0.151 510}_{10 14} k( ) = 3.11×10-6_× 2 _3.4×10-3_× _{1.54 1,550 1,760 6 8} k( ) = 2.47×10-6_× 2 _3.24×10-3_× _{1.78 1,870 2,150 12} k( ) 2.6 9 0.0 0.5 1.0 1.5 2.0 2.5 0 200 400 600 800 1000 1200

Upper limit Lower limit

0.0 0.5 1.0 1.5 2.0 2.5 0 200 400 600 800 1000 1200 ALC

(24)

2.7 Eurocode2 5 9 thermal diffusivity

m2_/sec

500

coefficient of thermal expansion

80 90 110 7 12 10-6_/ ₃ _2.7 10 2.7 10 ×10-6_/ _×10-6_/ _×10-6_/ 2.2 9.5 10.1 14.4 7.7 6.1 11.7 6.1 7.2 3.6 8.1 7.4 4.1 8.3 6.5 9.7 6.8 8.1 7.2 8.5 8.1 10.1 6.1 0.9 17.5 11.3 7.4 -1.6 4.5 0.0 0.5 1.0 1.5 2.0 2.5 0 200 400 600 800 1000 1200

(25)

2009 3 Eurocode2 5 Eurocode4 6

RILEM International Union of Laboratories and Experts in Construction Materials Systems and Structures 2.8 11

Recommendation of RILEM TC200-HTC mechanical concrete properties at high temperatures – modeling and applications

2009 3 2012 4

RILEM

2.8 RILEM 3 4

[11 21]

Part 1: Introduction – General presentation Materials and Structures, Vol. 40, 2007, _pp.841-853 Part 2: Stress-strain relation Materials and Structures, Vol. 40, 2007, _pp.855-864 Part 3: Compressive strength for service and _{accident conditions} Materials and Structures, Vol. 28, 1995, _pp.410-414 Part 4: Tensile strength for service and accident _conditions Materials and Structures, Vol. 33, May _{2000, pp.219-223} Part 5: Modulus of elasticity for service and _{accident conditions} Materials and Structures, Vol. 37, March _{2004, pp.139-144} Part 6: Thermal strain Materials and Structures, Supplement _{March 1997, pp.17-21} Part 7: Transient creep for service and accident _conditions Materials and Structures, Vol. 31, June _{1998, pp.290-295} Part 8: Steady-state creep and creep recovery for _{service and accident conditions} Materials and Structures, Vol. 33, _{January-February 2000, pp.6-13} Part 9: Shrinkage for service and accident _conditions Materials and Structures, Vol. 33, May _{2000, pp.224-228} Part 10: Restraint stress Materials and Structures, Vol. 38, 2005, _pp.913-919 Part 11: Relaxation Materials and Structures, Vol. 40, 2007, _pp.449-458

(26)

2009 AIJ 3 Eurocode2 5 AIJ Eurocode2 1 AIJ 2009 3 AIJ Fc(T) Fcr(Tr) Fc c(T) cr(Tr) -2.1 -2.2 2.9 2.8 AIJ W/B W/B Fc(T) Fc c(T) ( -2.1) 3 Fcr(Tr) Fc cr(Tr) ( -2.2) 3 Fc Fc(T) T c(T) T Fcr(Tr) Tr cr(Tr) Tr 2.9 AIJ 3 T,Tr( ) c(T) cr(Tr) 0 1.00 1.00 100 0.80 0.94 200 0.33×W/B + 0.76 0.87 300 0.36×W/B + 0.71 0.80 400 0.45×W/B + 0.56 0.64 500 0.39×W/B + 0.41 0.48 600 0.47×W/B + 0.20 0.32 700 0.44×W/B + 0.11 0.16 800 0.15 0 W/B

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2 Eurocode2 5 Eurocode2 Fc(T) Fc c(T) 2.10 2.8 AIJ W/B NWC HSC NWC 2 HSC Class1 Class3 3 2.10 Eurocode2 5 T( )

Normal Weight Concrete High Strength concrete

c(T) c(T)

Class1 Class2 Class3

20 1.00 1.00 1.00 1.00 1.00 50 1.00 1.00 1.00 100 1.00 1.00 0.90 0.75 0.75 200 0.95 0.97 0.70 250 0.90 300 0.85 0.91 0.85 0.65 400 0.75 0.85 0.75 0.75 0.45 500 0.60 0.74 0.30 600 0.45 0.60 0.25 700 0.30 0.43 800 0.15 0.27 0.15 0.15 0.15 900 0.08 0.08 1000 0.04 0.04 1100 0.01 0.01 1200 0 0 0

Class1 C 55/67 C 60/75 Class2 C 70/85 C 80/95 Class3 C 90/105

2.8 3 5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 200 400 600 800 1000 1200 AIJ -W/B20% AIJ -W/B40% AIJ -W/B60% AIJ EC2-EC2-Class1 EC2-Class2 EC2-Class3

(28)

2009 AIJ 3 AIJ E(T) Er(Tr) 20 E(20) e(T) er(Tr) -2.3 -2.4 2.11 2.9 AIJ 1/3 14 70 100 200 600 Eurocode2 E(T) E(20) e(T) ( -2.3) 3 Er(Tr) E(20) er(Tr) ( -2.4) 3 E(20) 20 E(T) T e(T) T er(Tr) Tr 2.11 AIJ 3 T,Tr( ) e(T) er(Tr) 20 1.00 1.00 100 0.80 0.85 200 0.68 0.70 300 0.57 0.50 400 0.45 0.30 500 0.35 0.15 600 0.25 0.08 700 0.15 0.04 800 0.075 0.00 900 0 0.00

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2.9 3 2009 AIJ 3 Eurocode2 5 1 AIJ cu(T) cur(Tr) 20 cu(20) cu(T) cur(Tr) -2.5 -2.6 2.12 2.10 Eurocode2 cu(T) AIJ 20 cu(20) cu(T) 2.13 2.11 Eurocode2 AIJ Eurocode2 2 50 min cu(T) cu(20) cu(T) ( -2.5) 3 cur(Tr) cu(20) cur(Tr) ( -2.6) 3 cu(20) 20 cu(T) T cu(T) T cur(Tr) Tr cur(Tr) Tr 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 200 400 600 800 1000

(30)

2.10 AIJ 3 2.12 AIJ 3 T,Tr( ) cu(T) cur(Tr) 20 1.00 1.00 100 1.00 1.00 200 3.7×10-3_{× T-200 +1.1} 3.8×10-3_{× T} r-200 +1.0 300 400 500 600 700 800 4.3 2.13 Eurocode2 5 T( ) cu T cu(T) 20 0.0025 1.00 100 0.0040 1.60 200 0.0055 2.20 300 0.0070 2.80 400 0.0100 4.00 500 0.0150 6.00 600 0.0250 10.00 700 0.0250 10.00 800 0.0250 10.00 900 0.0250 10.00 1000 0.0250 10.00 1100 0.0250 10.00 0 2 4 6 8 10 12 0 200 400 600 800 1000

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AIJ-2.11 Eurocode2 5 2 Eurocode2 5 Popovics 22 -2.7 c(T) 2.10 cu T 2.13 Eurocode2 -2.7 n n=3 -2.8 n=2.5 Eurocode4 6 20 Fc 20 Eurocode4 -2.8 20 Fc 20 -2.9

AIJ Eurocode2 Eurocode4

( -2.7) 22 0 2 4 6 8 10 12 0 200 400 600 800 1000

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EC2-( -2.8) 5 6 ( -2.9) 5 6 T T T 20 T T 2.12 Eurocode 5 6 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.01 0.02 0.03 0.04 0.05 20 400 600 800

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2009 3

2012 4 Eurocode2 5 2.13

2.13 4

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2.13 23 24 25 23 24 25 Eurocode2 5 Siliceous aggregates : ( -2.10) 5 ( -2.11) 5 Calcareous aggregates : ( -2.12) 5 ( -2.13) 5 2.14 Eurocode2 4 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 16,000 0 200 400 600 800 1000 1200 Tc

(35)

1 4

CEN (European Committee for Standardization)

Eurocode2 5 Eurocode4 6

RILEM International Union of Laboratories and Experts in Construction Materials Systems and Structures

4

1

2

RILEM

(36)

[1] 2002.6. [2] 2004.10. [3] 2009.3. [4] 2012.5.

[5] European Committee for Standardization (CEN) Eurocode2 Design of concrete structures Part1-2 General rules Structural fire design EN1992-1-2 2004.12.

[6] European Committee for Standardization (CEN) Eurocode4 Design of composite steel and concrete structures Part 1-2 : General rules - Structural fire design EN1994-1-2: 2005 (E)

[7] Schneider U 1983.

[8] 2001.6.

[9] 2008.

[10] Vol. 22 No. 3 1984.3.

[11] RILEM Technical Committee: Recommendation of RILEM TC 200 HTC: Mechanical concrete properties at high temperatures modelling and applications: Part 1: Introduction General presentation, Materials and Structures, Vol. 40, pp. 841 853, 2007.

[12] RILEM Technical Committee: Recommendation of RILEM TC 200 HTC: Mechanical concrete properties at high temperatures modelling and applications: Part 2: Stress strain relation, Materials and Structures, Vol. 40, pp. 855-864, 2007.

[13] RILEM DRAFT RECOMMENDATION 129 MHT TEST METHODS FOR MECHANICAL PROPERTIES OF CONCRETE AT HIGH TEMPERATURES: Compressive strength for service and accident conditions, Materials and Structures, Vol. 28, pp. 410-414, 1995.

[14] RILEM TC 129 MHT: Test methods for mechanical properties of concrete at high temperatures Recommendations: Part 4: Tensile strength for service and accident conditions, Materials and Structures, Vol. 33, pp. 219-223, 2000.5.

[15] RILEM TC 129 MHT: Test methods for mechanical properties of concrete at high temperatures: Modulus of elasticity for service and accident conditions Materials and Structures, Vol. 37, pp. 139-144 March.2004.

[16] RILEM TC 129 MHT: TEST METHODS FOR MECHANICAL PROPERTIES OF CONCRETE AT HIGH TEMPERATURES: Recommendations: Part 6 Thermal strain, Materials and Structures, Supplement, pp. 17-21, 1997.3.

[17] RILEM TC 129 MHT: TEST METHODS FOR MECHANICAL PROPERTIES OF CONCRETE AT HIGH TEMPERATURES: Recommendations: Part 7: Transient creep service and accident conditions, Materials and Structures, Vol. 31, pp. 290-295, 1998.6.

[18] RILEM TC 129 MHT: Test methods for mechanical properties of concrete at high temperatures Recommendations: Part 8: Steady-state creep and creep recovery for service and accident conditions, Materials and Structures, Vol. 33, pp. 6-13, Jan.-Feb.2000.

(37)

[19] RILEM TC 129 MHT: Test methods for mechanical properties of concrete at high temperatures Recommendations: Part 9: Shrinkage for service and accident conditions, Materials and Structures, Vol. 33, pp. 224-228, 2000.5.

[20] RILEM Technical Committee: Recommendation of RILEM TC 200 HTC: Mechanical concrete properties at high temperatures modelling and applications: Part 10: Restraint stress, Materials and Structures, Vol. 38, pp. 913-919, 2005.12.

[21] Schneider, U. : RILEM Technical Committee: Recommendation of RILEM TC 200 HTC: Mechanical concrete properties at high temperatures modelling and applications: Part 11: Relaxation, Materials and Structures, Vol. 40, pp. 449-458, 2007.

[22] Sandor Popovics : A numerical approach to the complete stress-strain curve of concrete, Cement and Concrete Research, Vol. 3, pp. 583-599, 1973.9.

[23] Anderberg, Y, et al. : Stress and deformation characteristics of concrete at high temperatures, Lund institute of technology Lund Sweden 1976 division of stractural mechanics and concrete construction, 1976.8.

[24]

pp. 106-109 1997.5.

[25] Khoury, G.A. , et al, : Strain of concrete during first heating to 600 under load, Magazine of Concrete Research, Vol. 37, No. 133, pp. 195- 215, 1985.

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1950 1850 1 2 3 5 6 7 1956 8 1952 27 PS 5 3.1 3.2 PS 3.1 PS 8

(39)

1955 15cm 3.3 1 3 PS 3.2 PS 2 8 (1) (2) (3) PS PS PS PS 1956 PS 1966 1 RC PS PS 3.3 8

(40)

R. Jansson 9

1854 Barrett

10 1911 Gary

11 13 1972 Mayer-Ottens

Aggregate Spalling Surface Spalling Corner Spalling Explosive Spalling

4 14 Connolly 15 19 20 150 1956 100

Aggregate Spalling Surface Spalling

(41)

Corner Spalling Explosive Spalling

3.5 2 15

(42)

Gary 11 13 Mayer-Ottens 14 Aggregate Spalling Surface Spalling Corner Spalling Explosive Spalling 4

17 2 3.1 6 17 3.1 17 Aggregate spalling 7 30min H A S D W Corner spalling 30 90min / T A ft R Surface spalling 7 30min H W P ft Explosive spalling 7 30min H A S fs G L O P Q R S W Z Sloughing off spalling / T fs L Q R Post cooling spalling / W1 AT A D fs ft G H L O AT P Q R S T W Z W1

(43)

1 Harmathy 1965 2 3.1 Moisture Clog 2 3 2 1966 1 3.1 3 3 5 Moisture Clog 3 3.1 1 6

(44)

1

18 20 21 22

RILEM Technical Committee 227 HPB

3.2 A E 5 3 20 23 26 3.2 3 20 23 26 Type A Type B Type A Type C Type B Type D Type E Type A 2 0.1Mpa 4MPa 374 22MPa 18 3.3 100MPa 500 500 150 300 500mm 5.0

(45)

5.4 0 3 JIS A 1304 40mm Type E 0.17MPa 40mm 3.3 18 19 3.4 80MPa 3 1200 8mm 5 Type E 3.5 3.4MPa Moisture Clog 12mm 15mm

(46)

3.4 19 3.5 19 Kalifa 20 Kalifa 91.9MPa 2.95% 3.6 600 6 10 20 30 40 50mm 3.7 3.7MPa 50mm 250 3.7MPa 3.7

(47)

3.6 20 3.7 20 1 Ulm 27 Khoury 28 2 RC 29 80 200MPa 350 350mm 400 400mm RC ISO834 30 3.8 PP 3.6

(48)

3.8 29 3.6 RC 29 RC 31 3.9 RC RABT 32 PP PP 3.7 PP

(49)

RC

3.9 31

(50)

33 35 33 34 3.10 200 400 600 800 3.11 3.10 33 34 el pl 3.11 33 34

(51)

Connolly 3.12 2 15 3.12 15 36 41 PP 4 42 47 80MPa 48 36 37 38 41 39 RC RC RABT 32 3.13 200 350 425 500 4 8 Loading arm Water cooled load cell Concrete

specimen Stiff _connection Steel support rod Hydraulic rams Stiff restraint frame Access for thermo-couple

(52)

50mm 500 3.8 350 425 200 350 350 3.14 3.15 40 3.13 RC 39 3.8 500 39

(53)

3.14 40 3.15 40

RABT

mm

0

20

40

60

80

0

20

40

60

80

100

200

300

500

400

0

100

200

300

500

400

0 T=1792t-0.6752

R2=0.9841

RWS

0

20

40

60

80

0

20

40

60

80

100

200

300

500

400

0

100

200

300

500

400

0 mm

T=8164t-1.0168

R2=0.9769

(54)

PP PP 4 42 47 PP 2kg/m3 3.16 PP 170 PP 3.17 PP 47 Kalifa 43 PP 0 3kg m3 _100MPa ₆ 600 6 10 20 30 40 50mm PP 3.18 4MPa 3kg m3 _PP _1MPa 3.16 PP 43 3.17 PP 47

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(56)

1950 1850 1 2 3 5 6 1 1950 2 5 24 27 Connolly 2 3 PP

(57)

[1] Vol. 15 No. 2 pp. 23 30 1966.

[2] Harmathy, T. Z. : Effect of moisture on the fire endurance of building elements, ASTM special technical publication, No. 385, pp. 74 95, ASTM 1965.

[3] Consolazio, G.R., McVay, M.C., Rish III, J. W. : Measure-ment and prediction of pore pressures in saturated cement mortar subjected to radiant heating, ACI Materials Journal, Vol. 95, M50, pp. 525-536, 1998.

[4] Zeiml, M, Leithner, D, Lackner, R, Mang, H.A. How do polypropylene fibers improve the spalling behavior of in-situ concrete? Cement and Concrete Research, Vol. 36, pp.929 942, 2006.

[5] Vol. 45 No. 9 pp. 87

91 2007.

[6] Anderberg, Y. : Spalling phenomena of HPC and OC. International Workshop on Fire Performance of High Strength Concrete, Maryland, NIST Special Publication, Vol. 919, pp. 13 14, 1997.

[7] 2004

pp. 385 388 2004.

[8] PS No.40 pp. 34 42 1956.

[9] R. Jansson Fire spalling of concrete – A historical overview, Concrete Spalling due to Fire Exposure: Proceedings of the 3rd International Workshop, Volume 6, 2013.9.

[10] Barret On the French and other methods of constructing iron floors, Civil Engineering and Architect’s Journal, Vol XVII, pp 94,1854.

[11] Gary, M. Brandproben an Eisenbetongbasuten (in German), Deutcher Ausschlutss für Eisenbetong, Heft 11, Berlin, Germany, 1911.

[14] Meyer-Ottens C. Zur Frage der Abplatzungen an Betonbauteilen aus Normalbeton bei Brandbeanspruchung, PhD-thesis, Braunshweig, Germany, 1972.

[15] Connolly R.J. The spalling of concrete in Fires PhD thesis submitted to Aston University 1995.

[16] pp.98-108 2009.3. [17] 2012.5. [18] Vol.18 No.1 pp. 657 662 1996. [19] Vol. 29 No. 1 pp. 753 758 2007.

[20] Kalifa, P., Menneteau, F. D., Quenard, D. : Spalling and pore pressure in HPC at high temperatures, Cement and Concrete Research, Vol. 30, pp. 1915-1927, 2000.

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[21]

Vol. 32 No. 1 pp. 1151 1156 2010.

[22] RC

Vol. 34 No. 1 pp. 1162 1167 2012.

[23] Schneider, U. M. C. Alonso, P. Pimienta, R. Jansson : Physical properties and behaviour of high-performance concrete at high temperatures, Proceeding of Sixth Inter-national Conference on Structures in Fire., USA, Michigan, pp. 800 816, 2010.

[24] Jansson, R., L, Boström : The influence of pressure in the pore system on fire spalling of concrete, Fire Technology 46, No. 1, pp. 217 230, 2010.

[25] Ko, J., Ryu, D., Noguchi, T. : The spalling mechanism of high strength concrete under fire, Magazine of Concrete research, Vol. 63, No. 5, pp. 357 370, 2011.

[26] L.T. Phan, : Pore pressure and explosive spalling in concrete, Materials and Structures, Vol. 41, pp. 1623 1632, 2008.

[27] Ulm, F. J., Coussy, O., Bamnt, Z. P. : The chunnel fire. Analysis of concrete damage, Journal of Engineering Mechanics, pp. 283 289, Vol. 126, No. 3, 1999.

[28] Koury.G.A, Majorana C.E, Pesavento F. and Schrefler B.A Modeling of heated concrete Magazine of Concrete Research Vol.54 No.2.pp.77 1101 2002.

[29] 80 200N/mm2

75 648 pp.461 468 2010.

[30] ISO 834-1 1999 Fire resistance tests Elements of building construction Part1 General requirements, International Organization for Standardization.

[31]

Vol.62 No.4 pp.844 854 2006.

[33] 621 pp.169 174 2007. [34] 73 623 pp.143 147 2008. [35] 100N/mm2 75 648 pp. 453 460 2010. [36] pp. 263 264 1980.9 [37] Vol. 19 No. 1 pp. 631 636 1997. [38] 145 pp. 45 55 2003 . [39] RC

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Vol. 24 No. 1 pp. 1719 1724 2002.

[40] CONCRETE

JOURNAL Vol. 45 No. 9 pp. 111 114 2007. [41]

pp. 405 406 2005.

[42] Khoury, G. A., Willoughby, B. : Polypropylene fibres in heated concrete. Part 1 : Molecular structure and materials behavior, Magazine of Concrete Research, Vol. 60, No. 2, pp. 125 136, 2008.

[43] Kalifa, P., Chéné, G., Gallé, C. : High-temperature behaviour of HPC with polypropylene fibres From spalling to microstructure, Cement and Concrete Research, Vol. 31, pp. 1487 1499, 2001. [44]

No. 544 pp. 171 178 2001. [45]

Vol. 30 No. 1 pp. 339 344 CD-ROM 2008.

[46] Watanabe, K., Mugume, R.B., Horiguchi, T. : Effect of elevated temperatures on flexural behaviour of hybrid fibre reinforced high strength concrete, Journal of Structural Fire Engineering, Vol. 1, No. 1, Multi - Science Publishing Co Ltd, pp. 17 28, 2010.

[47]

Vol. 34 No. 1 pp. 1126-1131 2012.

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RILEM Technical Committee 227 HPB 1 4 Connolly 5 6 8 Connolly 5 4.1 4 4.1 4 4.2 300 50 100mm W/C 0.3 0.4 0.5 0.6 0 10 20 30MPa 2 Heat Flux 80 110 140KW/m2

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4.1 5 3.12 4.1 5 4.2 5 Loading arm Water cooled load cell Concrete

specimen Stiff _connection Steel support rod Hydraulic rams Stiff restraint frame Access for thermo-couple

(62)

Connolly 4.2 2 Formed void 4.2 5 4.1 0.1 6.6MPa 9.7 33.1MPa Connolly

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4.1 5 Reference W/C Ratio Heat kW/m2 Load N/mm2 Final Load N/mm2 Notes A94/237/5 0.3 80 10.5 16.0

A94/237/7 0.3 80 30.3 31.9 Surface spalling

A94/237/4 0.3 110 30.4 33.1 Release* spalling

A94/237/3 0.3 140 10.3 16.9

A94/237/5 0.3 140 10.5 16.0

A94/237/2 0.3 140 20.5 25.5 Release* spalling

A94/237/2 0.3 140 25.0 27.8

*) Spalling on release of load after test

Connolly 4.3 4.3 150mm 20 200mm 4.2 1 2 4.3 5

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4.2 5

Depth mm One sided heating Two sided heating 20 Surface spalling Explosive spalling 30 No spalling Explosive spalling

50 No spalling No spalling 100 No spalling No spalling 200 No spalling No spalling 6 8 -4.1 -4.4 -4.1 -4.2 4.4 8 -4.3 E -4.4 -4.3 -4.4 -4.2 4.4 8

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( -4.1) ( -4.2) ( -4.3) ( -4.4) Connolly 5 6 8 1 Connolly 2

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[1] Schneider, U., Alonso, M. C., Pimienta, P., Jansson, R. : Physical properties and behaviour of high-performance concrete at high temperatures, Proceeding of Sixth Inter-national Conference on Structures in Fire., USA, Michigan, pp. 800-816, 2010.

[2] Jansson, R., Boström, L. : The influence of pressure in the pore system on fire spalling of concrete, Fire Technology, Vol. 46 ,No. 1, pp. 217-230, 2010.

[3] Ko, J., Ryu, D., Noguchi, T. : The spalling mechanism of high strength concrete under fire, Magazine of Concrete research, Vol. 63, No. 5, pp. 357-370, 2011.

[4] Phan, L.T. : Pore pressure and explosive spalling in concrete, Materials and Structures, Vol. 41, pp. 1623-1632, 2008.

[5] Connolly, R.J. The spalling of concrete in Fires PhD thesis submitted to Aston University 1995. [6] 226 pp. 67-72 1974.6. [7] No. 478/ -21 pp. 91-100 1993.11. [8] Vol. 33 No. 1 pp. 437-442 2011.

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5 1 RABT 1 ISO 2 2 3 4 5 2 3 2

(68)

Connolly 1 5.1 2 2 -5.1 -5.2 3 4 5 3 -5.3 -5.4

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5.1 ( -5.1) ( -5.2) ( -5.3) ( -5.4) 1

RILEM Technical Committee 227 HPB

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5.3

2

-5.4

5.2 6 9 3.2

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5.4 5mm 2mm 2 6 2 1 300 50 8mm 2 300 100 8mm 2 5.1 2 5.2 20 5.4 5.1 kg m3 W/C 1 15mm 2 25mm SP. 0.3 132 440 814 524 524 8.8 1.64% 2.56g/cm3 1 1.42% 2.58g/cm3 2 1.34% 2.52g/cm3 SP.

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5.2 1 5.1 900mm ISO834 RABT RWS 2 5.5 RABT30 5 1200 1200 30 110 5.1 5.5 RABT30 1 2 K 5 10 20 30 40 50mm 6 25 75mm 2 3 10MPa 10mm 20mm 2

(MPa) (GPa) (MPa) (%)

(73)

4 80 25 75mm 2 5 1000 mm 25 75mm 2 6 3 4 10 4 10 2 2 1 1 5.6 5.7 RABT30 5.6 5.7 0 200 400 600 800 1000 1200 0 20 40 60 80 100 120 140 (min) RABT30 0 200 400 600 800 1000 1200 0 1 2 3 4 5 6 7 8 9 10 (min) RABT30 4min 10min

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2 5.8 5.8 3 5.9 10 25mm 75 75mm 25 80 5.9 5.10 10mm 20mm 10mm 0.2MPa 20mm 0.3MPa 20mm 10mm 1 5.11 Kalifa 10 0 200 400 600 800 1000 0 1 2 3 4 5 6 7 8 9 10 (min) 5mm 10mm 20mm 30mm 40mm 50mm 4min 10min 0 20 40 60 80 100 0 1 2 3 4 5 6 7 8 9 10 (min) 25mm 75mm 4min 10min

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5.12 25mm 10 500 75mm 3 10 100 5.12 5.13 (a) 25mm 5 0.06mm 5.13 (b) 6 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 1 2 3 4 5 6 7 8 9 10 (min) 10mm 20mm 4min 10min 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0 20 40 60 80 100 120 140 160 180 200 10mm 20mm 10mm 4.15min 20mm 4.15min 6.05min( 20mm) 0 100 200 300 400 500 0 1 2 3 4 5 6 7 8 9 10 (min) 25mm 75mm 4min 10min 5.10 5.11

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(a) (b) 5.13 1 -5.5 5.14 10 25mm 6MPa 75mm 1.5MPa ( -5.5) 5.14 2 -5.4 5 5 25mm 3MPa 5.10 10mm 0.1MPa 20mm -5.4

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3 5 25mm 3MPa ADINA 2 5 5.3 5.15 5.16 a 5 50mm 520 Eurocode 2 11 12 5.3 RABT30 W/m K 51.91-5.03×10-5_× 2 J/m3 _{K 7.85 0.482 7.995×10}-7_× 2 3.1 W/m K 2-0.24 /120 0.012 /120 2 J/m3 _{K 2300 900 80 /120} _{4 /120} 2 W/m2 _K 150 5 25mm 3MPa 39 5.16 b Eurocode 5.16 b 5 10mm

11MPa 42MPa 54MPa

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5.15 a b 5.16 1 2 3 4 5 25mm

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1 2 3 4 5 6 7 1 2 3

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[2] ISO 834-1 1999 Fire resistance tests Elements of building construction Part1 General requirements, International Organization for Standardization

[3] 226 pp. 67-72 1974.6. [4] No.478/Vol. 21 pp. 91-100 1993.11. [5] Vol. 33 No. 1 pp. 437-442 2011.

[6] Schneider, U., Alonso, M. C., Pimienta, P., Jansson, R. : Physical properties and behaviour of high-performance concrete at high temperatures, Proceeding of Sixth Inter-national Conference on Structures in Fire., USA, Michigan, pp. 800-816, 2010.

[7] Jansson, R., Boström, L. : The influence of pressure in the pore system on fire spalling of concrete, Fire Technology, Vol. 46 ,No. 1, pp. 217-230, 2010.

[8] Ko, J., Ryu, D., Noguchi, T. : The spalling mechanism of high strength concrete under fire, Magazine of Concrete research, Vol. 63, No. 5, pp. 357-370, 2011.

[9] Phan, L.T. : Pore pressure and explosive spalling in concrete, Materials and Structures, Vol. 41, pp. 1623-1632, 2008.

[10] Kalifa P Menneteau F.D Quenard D Spalling and pore pressure in HPC at high temperatures Cement and Concrete Research, Vol. 30, pp. 1915-1927, 2000.

[11] European Committee for Standardization (CEN) Eurocode2 Design of concrete structures Part1-2 General rules Structural fire design EN1992-1-2 2004.12

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5

1

RABT 1 ISO 2

2

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6.1 6.1 No. _mm ( ) (mm) (mm) * ** *** 1 300 8 100 5 284 100 A N,H Ci S 2 284 100 A N Ci S 3 300 0.5 100 2 299 100 B N Ci P 4 300 8 100 2 284 100 B N Ci,Ax P 5 300 18 100 2 264 100 B N Ci P 6 520 8 100 2 504 100 B N Ci P 7 300 8 100 2 284 100 C N Ci SA *) N 80 H 300

**)Ci Circumference Ax Axial

***) S Syringe P Pump

SA 0.05MPa Syringe & Remove Air

1 2 5 2 50mm 2 5 15 10 10 15 50mm 5 300 520mm 0 0.5 8 18mm 0mm 0.5mm 8 18mm 6.1 1mm 6.1 2 5

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2 0.3 6.2 6.4 300 2 300 5 520 2 6.1 6.2 kg m3 W/C kg m 3 1 2 A,B 0.3 150 500 744 406 611.6 4.0 (A) 3.5 (B) C 0.3 150 500 718 417.6 624.4 5 6.3 3.15g/cm3 1.64% 2.60 g/cm3 1 2010 0.98% 2.61 g/cm3 2 1505 1.64% 2.61 g/cm3

(84)

6.4

(cm)

mm

% (MPa) (GPa) (MPa) (%)

A 22.5 525 490 508 0.9 23.0 76.8 43.2 6.6 3.8 2 B 780 700 740 1.9 15.0 91.2 42.6 5.6 4.4 4 C 745 670 708 1.8 13.4 92.5 43.9 4.2 4.0 6 3 N 80 H 300 Circumference Axial 3 5 6.1 Ci Ax 4

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S Syringe

P Pump

0.05MPa SA Syringe & Remove Air 45 0.05MPa 1 20mm 2 K 3 80 300 -6.1 -6.4 ( -6.1)( -5.1) ( -6.2) ( -5.2) ( -6.3) ( -5.3) ( -6.4)

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5 10MPa 6 1000 /mm -6.5 ( -6.5) 1 900mm 5.1 2 RABT30 1 5.5 3 6.2 1

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6.2 6.5 2 6.5 No. _mm ( ) (mm) (mm) 1 300 8 100 5 284 100 A N,H Ci S 4 300 8 100 2 284 100 B N Ci,Ax P 1 H 300 n 5 6.3 2 1 2 1 H P P 300 284 A A B B

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6.3 H N H -6.6 6.4 300 ( -6.6) ( -5.5) -1 -2 -1 -2 6.4 0 1 2 3 4 5 6 0 2 4 6 8 10 min N-1 N-10 N-20 N-30 N-40 0 1 2 3 4 5 6 0 2 4 6 8 10 min N-2 N-10 N-20 N-30 N-40 0 1 2 3 4 5 6 0 2 4 6 8 10 min H-1 H-10 H-20 H-30 H-40 0 1 2 3 4 5 6 0 2 4 6 8 10 min H-2 H-10 H-20 H-30 H-40

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8 10 2 Circumference Axial 3 5 2 Ci Ax -6.6 -6.7 6.5 ( -6.7) 6.5 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 min 10mm-Ci 10mm-Ax 25mm-Ci 25mm-Ax 40mm-Ci 40mm-Ax

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6.6 5 A B 2 2 1 6.6 No. _mm ( ) (mm) (mm) 1 300 8 100 5 284 100 A N,H Ci S 4 300 8 100 2 284 100 B N Ci,Ax P 1 6.6 6.7 5 5 -A 2 5 6.6

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2 5 6.7 RABT30 2 5 10 10mm 5 60 2 10mm 40mm 6.8 6.8 6.8 10mm 5 2 5 2 5 2 6.7 300mm 520mm 2

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6.7 No. _mm ( ) (mm) (mm) 4 300 8 100 2 284 100 B N Ci,Ax P 6 520 8 100 2 504 100 B N Ci P 1 20mm 6.9 6.10 6 520-8 300-8 300-8 8 520-8 12 300-8 25mm 65mm 2 300-8 8 520-8 6.9 6.10

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2 6.11 6.13 520-8 300-8 25mm 40mm 520-8 520-8 300-8 6.11 300-8 6.12 520-8-A 6.13 520-8-B

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3 10mm 25mm 6.14 6.15 10mm 300-8 520-8 300-8 8 520-8 300-8 520-8 6.14 10mm 6.15 25mm 6.8 0.5mm 8mm 18mm 4 6.8 No. _mm ( ) (mm) (mm) 2 284 100 A N Ci S 3 300 0.5 100 2 299 100 B N Ci P 4 300 8 100 2 284 100 B N Ci,Ax P 5 300 18 100 2 264 100 B N Ci P 1 6.9 6.16 4 5 8 2 6

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2 6.9 6.17 6.1 8mm 26mm 2mm 8mm 8mm 300-8 18mm 300-18 6.9 300-0 300-0.5 300-8 300-18 (min) 1 3.43 4.00 2.18 3.83 2 3.65 3.57 4.33 3.54 3.78 4.08 (min) 1 5.00 5.50 8.18 7.50 2 7.33 5.00 7.33 6.17 5.25 7.42 (min) 1 1.57 1.50 6.00 3.67 2 3.68 1.43 3.00 2.62 1.47 3.33 (mm) 1 11.0 5.0 24.0 25.0 2 11.0 11.0 27.0 11.0 8.0 26.0 (mm) 1 3.1 0.7 7.4 7.4 2 2.6 2.5 6.8 2.8 1.7 7.1 6.16 0 1 2 3 4 5 6 7 8 9 300-0 300-0.5 300-8 300-18 0 5 10 15 20 25 30 300-0 300-0.5 300-8 300-18

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300-0 300-0.5 300-8 300-18 6.17 a) 300-0 b) 300-0.5 c) 300-8 d) 300-18 6.1

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3 6.18 4 5mm 10mm 8mm 18mm 25mm a) 300-0 b) 300-0.5 c) 300-8 d) 300-18 6.18 4 -6.6 6.19 10mm 4 300-8 300-18 6 8

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a) 10mm b) 25mm 6.19 5 8mm 300-8 18mm 300-18 -6.8 10 25mm 10 25mm ( -6.8) 0 1.0 mm mm -6.7 10mm 25mm 3 10 6.20 300-0 25mm 3 5 10 300-0.5 0.3 0.4 300-8 300-18 1 0.8 0.9 10mm 25mm 3 10mm 0.6

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10mm 25mm 6.20 -6.8 5 10 10mm 25mm 6.21 6.21 8mm 18mm 8mm 1 0.8 0.9 18mm 8mm a) 5min 10mm b) 5min 25mm c) 10min 10mm d) 10min 25mm 6.21 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 12 14 16 18 mm 3min-10mm 5min-10mm 10min-10mm 0.0 0.2 0.4 0.6 0.8 1.0 0 2 4 6 8 10 12 14 16 18 mm 5min-25mm 10min-25mm y = 35.004x - 3.2414 R² = 0.9987 y = 11.343x - 1.9442 R² = 0.9643 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 5min-10mm y = 21.524x + 7.1336 R² = 1 y = 7.012x + 1.3966 R² = 0.9759 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 5min-25mm y = 31.152x - 3.724 R² = 0.9985 y = 10.212x - 2.1873 R² = 0.9866 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 10min-10mm y = 30.147x - 3.2001 R² = 0.9975 y = 9.9006x - 2.0293 R² = 0.9892 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 10min-25mm

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6.10 3

S Syringe P Pump

0.05MPa SA Syringe & Remove Air 6.10 No. mm ( ) (mm) (mm) 1 300 8 100 5 284 100 A N,H Ci S 5 300 18 100 2 264 100 B N Ci P 7 300 8 100 2 284 100 C N Ci SA 6.22 6.24 0.05MPa SA 3 5 10mm 4MPa 25mm S P SA 6.22 S

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6.23 P 6.24 SA 1 2 0 2 4 6 8 10 0 2 4 6 8 10 12 14 16

SA-1

P5 P10 P25 P40 0 2 4 6 8 10 0 2 4 6 8 10 12 14 16

SA-2

P5 P10 P25 P40

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3 100mm 2 5 2 300-8 8 520-8 300-8 520-8 8mm 18mm 8mm 1 0.8 0.9 18mm 8mm 4 0.05MPa SA 3 5 10mm 4MPa 25mm S P SA 300 8 50mm 2 80 SA

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[2] ISO 834-1 1999 Fire resistance tests Elements of building construction Part1 General requirements, International Organization for Standardization.

[3] 226 pp. 67-72 1974.6. [4] No.478/Vol. 21 pp. 91-100 1993.1. [5] Vol. 33 No. 1 pp. 437-442 2011. [6] Vol. 45 No. 9 pp. 87-91 2007.

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1 2 3 5 7.1 6 1 xy 7.2 7 xy z 7.1 1 6

(105)

7.2 7 2 P f Kalifa 8 91.9MPa 2.95% 10mm 50mm 6 600 2MPa 3.7MPa 50mm 250 -7.1 ( -7.1)( -5.4)

(106)

7.3 7.3 2 P f 7.3 1 7.4 7.3 f PP PP PP

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2 -7.2 -7.3 f -7.4 f 7.4 ( -7.2) ( -7.3) ( -7.4) ( -7.5) f f I-f z t-f I-lim 1

I

_-f

I

_-lim YES NO NO YES

(108)

3 300 50 8mm 2 300 100 8mm 5mm 2mm 2 6 1 2 2 6.2 7.1 7.2 7.3 2 100 200mm 50 100mm JIS A 1476 20 7.1 kg m3 W/C 1 2 0.3 132 440 814 524 524 8.8 7.2 3.15g/cm3 1.64% 2.60 g/cm3 1 1.42% 2.58g/cm3 2 1.34% 2.52g/cm3 7.3

(MPa) (GPa) (MPa) (%)

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1 900mm 5.1 2 RABT30 9 5.5 3 1 6.2 1 2 K 5 10 20 30 40 50mm 25 75mm 6.2 2 20mm 3 10MPa 10mm 20mm 2 4 80 6.2 25 75mm -7.6 ( -7.6)( -6.5)

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7.5 7.6 NO.1 NO.2 NO.1 NO.2 200 310 140 340 140 340 7.5 NO.1 7.6 NO.2 7.7 7.8 80 NO.1 NO.2 10 80 7.5 80 NO.1 NO.2 10 25 45 80 8 10 7.7 NO.1 7.8 NO.2 7.4 4 10 6 0 50 100 150 200 250 300 350 400 0 1 2 3 4 5 6 7 8 9 10 min NO.1 5mm 10mm 20mm 30mm 40mm 50mm 0 50 100 150 200 250 300 350 400 0 1 2 3 4 5 6 7 8 9 10 min NO.2 5mm 10mm 20mm 30mm 40mm 50mm 0 20 40 60 80 100 0 1 2 3 4 5 6 7 8 9 10 min NO.1 25mm 75mm 0 20 40 60 80 100 0 1 2 3 4 5 6 7 8 9 10 min NO.2 25mm 75mm

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7.4 7.9 7.10 7.1 100mm 61 70mm 6 7 20 Z 2 7.4 NO. min mm NO.1 3.8 10.0 6.2 70.0 17.7 20.1 NO.2 3.8 10.2 6.4 61.0 17.6 19.8 3.8 10.1 6.3 65.5 17.6 19.9 7.9 NO.1 7.10 NO.2 7.1 (NO.2)

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7.11 NO.1 NO.2 10mm 7.11 7.12 NO.2 10mm 3.5 20mm 10mm 2 4 10mm 0.05MPa 20mm 0.3MPa 7.13 SVP 10mm 20mm SVP Kalifa 8 7.12 7.13 0 10 20 30 40 50 60 70 0 2 4 6 8 10 12 min NO.1 NO.2 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 1 2 3 4 5 6 7 8 9 10 min NO.2 10mm 20mm 4 10 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0 25 50 75 100 125 150 NO.2 10mm 20mm 6min 20mm 4min 20mm 4min 10mm

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2 SVP 10 f 0.1 0.2 f 0.05MPa 7.4 7.14 -7.6 25mm 4 5 2 3MPa 3 75mm 10 1MPa 5 25mm 3MPa 10mm 0.1MPa 7.14 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 0 1 2 3 4 5 6 7 8 9 1011121314151617181920 min NO.1-25mm NO.1-75mm NO.2-25mm NO.2-75mm 4 10

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25mm

3 5

-7.7 7.15

7.18 3 25mm 2MPa

5mm NO.1 NO.2 6MPa

10MPa 5 5mm NO.1 NO.2

14MPa 30MPa ( -7.7) z mm (MPa) 25 mm (MPa) z mm ( ) 25 mm ( ) 7.15 NO.1 7.16 NO.1 7.17 NO.2 7.18 NO.2 0 10 20 30 40 50 0 50 100 150 200 250 300 350 400 Tc NO.1 3min 5min 0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 MPa NO.1 3min 5min 0 10 20 30 40 50 0 50 100 150 200 250 300 350 400 Tc NO.2 3min 5min 0 10 20 30 40 50 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 MPa NO.2 3min 5min

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-7.2 -7.5 f -7.5 1 7.19 11 12 30 200 400 0.14 0.30 0.15 0.20 0.25 0.30 4 f 200 400 200 500 200 300 400 500 4 7.6 140 350 200 400 7.19 12 7.20 NO.1 NO.2 40mm 20mm NO.2 500 5mm 10mm 200 400 0.15 0.30 R² = 0.9993 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 200 400 600 800 1000 ( )

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4 10 NO.1 =0.2 NO.1 f =200 NO.2 =0.2 NO.2 f =200 7.20 1 2 3 4 5 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 (min) NO.1( 0.2) t-f 200 t-f 300 t-f 400 t-f 500 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 (min) NO.1(_t-f 200 ) 0.15 0.20 0.25 0.30 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 (min) NO.2( 0.2) t-f 200 t-f 300 t-f 400 t-f 500 0 10 20 30 40 50 60 70 80 0 2 4 6 8 10 12 (min) NO.2(t-f 200 ) 0.15 0.20 0.25 0.30

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[1] Vol. 15 No. 2 pp. 23-30 1966.

[2] Harmathy, T. Z. : Effect of moisture on the fire endurance of building elements, ASTM special technical publication, No. 385, pp. 74-95, ASTM 1965.

[3] Vol. 45 No. 9 pp. 87-91

2007.

[4] Consolazio, G.R., McVay, M.C., Rish III, J. W. : Measure-ment and prediction of pore pressures in saturated cement Mortar subjected to radiant heating, ACI Materials Journal, Vol. 95, M50, pp. 525-536, 1998.

[5] Zeiml, M, Leithner, D, Lackner, R, Mang, H.A. How do polypropylene fibers improve the spalling behavior of in-situ concrete?, Cement and Concrete Research, Vol. 36, pp. 929-942, 2006.

[6] Anderberg, Y., : Spalling phenomena of HPC and OC. International Workshop on Fire Performance of High Strength Concrete, Maryland, NIST Special Publication 919, pp. 13-14, 1997.

[7]

143 pp. 28-35 1967.7.

[8] Kalifa, P., Menneteau, F. D., Quenard, D., : Spalling and pore pressure in HPC at high temperatures, Cement and Concrete Research, Vol. 30, pp. 1915-1927, 2000.

[10] A2 pp. 247-248, 1999.9. [11] pp.63-65 2009.3. [12] 621 pp.169-174 2007.

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2 f f 1 1 f f

200MPa UFC 100MPa

HSC UFC PP

8.1 100MPa

HSC 200MPa UFC PP

4 100AS 100ASP 200UFC 200UFCP

8.1 300 50 8mm 2 300 100 8mm 5mm 2mm 5 10 25 40mm 4 80 5 10 25 40mm 2 8 1 2

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8.1 PP

vol% HSC UFC

100MPa 0 RABT30 100AS

0.2 RABT30 100ASP

200MPa 0 RABT30 200UFC

0.5 RABT30 200UFCP

8.1

100AS 200UFC PP

100AS 100ASP 200UFC 200UFCP 4 8.2

8.3 8.4 8.5 100AS 100 200mm UFC 50 100mm 20 8.2 NO. W/C kg m 3 W C Pre1 Pre2 S1 G1 G2 SP.1 SP.2 PPF StF 100AS 0.3 150 500 718 418 626 5.0 100ASP 0.3 150 500 718 418 626 5.0 1.82 200UFC 158 1322 932 22 157 200UFCP 158 1322 932 22 4.55 157

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8.3 C 3.15g/cm3 Pre1 UFC 1 Pre2 UFC 2 S1 1.64% 2.60 g/cm3 G1 2010 0.98% 2.61 g/cm3 G2 1505 1.64% 2.61 g/cm3 SP.1 SP.2 UFC PPF 12mm 43 m 0.91g/cm3 StF 15mm 0.2mm 8.4 NO. % SL mm FL* mm _Tc** 100AS 1.8 745 670 708 13.4 100ASP 1.8 14.1 15.6 200UFC 310 300 305 12.7 200UFCP 180 150 165 14.6 *FL 100AS UFC 0 ** Tc 8.5 NO.

(MPa) (GPa) (MPa) (MPa) (%)

100AS 92.5 43.9 4.2 3.8

100ASP 95.7 43.8 6.0 3.7

200UFC 209.2 56.3 35.3 0.6

200UFCP 188.5 56.1 37.2 0.6

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20mm 8.6 8.2 8.3 8.7 8.8 PP 100ASP PP 200UFCP PP PP 200UFC PP 100AS 40 1 30 200UFCP 35mm 100AS PP 100ASP 100AS 200UFC PP 200UFCP 200UFC 8.6

100AS 100ASP 200UFC 200UFCP

(min) 1 4.7 4.3 2.3 3.2 2 4.3 3.8 3.3 3.2 4.5 4.1 2.8 3.2 (min) 1 6.9 5.8 48.2 67.0 2 11.9 6.5 40.2 62.5 9.4 6.2 44.2 64.8 (min) 1 2.2 1.5 45.8 63.8 2 7.6 2.7 36.9 59.3 4.9 2.1 41.4 61.6 (mm) 1 15.0 14.0 15.0 38.0 2 17.0 13.0 20.0 33.0 16.0 13.5 17.5 35.5 (mm) 1 2.8 3.4 4.6 10.8 2 5.5 3.6 4.1 9.0 4.2 3.5 4.3 9.9

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8.2 8.3 8.1 8.8 100AS 5mm 200UFC 1mm 50mm 1 0 10 20 30 40 50 60 70

100AS 100ASP 200UFC 200UFCP

0 5 10 15 20 25 30 35 40

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8.7 100AS 100 AS -1 100 AS -2 100 ASP -1 100 ASP -2

(124)

8.8 200UFC 200 UFC -1 200 UFC -2 200 UFCP -1 200 UFCP -2

(125)

8.1 100AS-1 8.3 100ASP-1

8.2 100AS-1 8.4 100ASP-1

8.5 200UFC-1 8.7 200UFCP-1

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80 8.1 2 5 10 25 40mm 8 -8.1 3 5 8.4 8.11 5 10mm 10 10 12MPa 25mm 6MPa 40mm 2MPa ( -8.1) ( -6.5) 8.4 100AS-1 8.5 100AS-2 8.6 100ASP-1 8.7 100ASP-2 8.8 200UFC-1 8.9 200UFC-2 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 min 100AS-1 r-5 r-10 r-25 r-40 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 min 100AS-2 r-5 r-10 r-25 r-40 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 min 100ASP-1 r-5 r-10 r-25 r-40 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 min 100ASP-2 r-5 r-10 r-25 r-40 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 min 200UFC-1 r-5 r-10 r-25 r-40 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 min 200UFC-2 r-5 r-10 r-25 r-40

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8.10 200UFCP-1 8.11 200UFCP-2 5 10 25 40mm 5mm 2mm 10MPa 8.12 8.19 2 7MPa 5 10mm 4 25 40mm 10 100AS 10 40mm 100ASP-1 40mm 4MPa 1 200UFC 25 40mm 5 10mm 30 30 1mm 30 3.1 Sloughing - off spalling 200UFCP PP 200UFC 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 min 200UFCP-1 r-5 r-10 r-25 r-40 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 min 200UFCP-2 r-5 r-10 r-25 r-40

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8.12 (100AS-1) 8.13 (100AS-2) 8.14 (100ASP-1) 8.15 (100ASP-2) 8.16 (200UFC-1) 8.17 (200UFC-2) 8.18 (200UFCP-1) 8.19 (200UFCP-2) 0 10 20 30 40 0 2 4 6 8 0 10 20 30 40 50 60 70 min 100AS-1 P-5 P-10 P-25 P-40 0 10 20 30 40 0 2 4 6 8 0 2 4 6 8 10 0 10 20 30 40 0 2 4 6 8 0 10 20 30 40 50 60 70 min 100AS-2 P-5 P-10 P-25 P-40 0 10 20 30 40 0 2 4 6 8 0 2 4 6 8 10 12 0 10 20 30 40 0 2 4 6 8 0 10 20 30 40 50 60 70 min 100ASP-1 P-5 P-10 P-25 P-40 0 10 20 30 40 0 2 4 6 8 0 2 4 6 8 10 0 10 20 30 40 0 2 4 6 8 0 10 20 30 40 50 60 70 min 100ASP-2 P-5 P-10 P-25 P-40 0 10 20 30 40 0 2 4 6 8 0 2 4 6 8 10 0 10 20 30 40 0 2 4 6 8 0 10 20 30 40 50 60 70 min 200UFC-1 P-5 P-10 P-25 P-40 0 10 20 30 40 0 1 2 3 4 0 2 4 6 8 10 0 10 20 30 40 0 2 4 6 8 0 10 20 30 40 50 60 70 min 200UFC-2 P-5 P-10 P-25 P-40 UFC-2 0 10 20 30 40 0 1 2 3 4 0 2 4 6 8 10 0 10 20 30 40 0 2 4 6 8 0 10 20 30 40 50 60 70 min 200UFCP-1 P-5 P-10 P-25 P-40 0 10 20 30 40 0 2 4 6 8 0 2 4 6 8 10 0 10 20 30 40 0 2 4 6 8 0 10 20 30 40 50 60 70 min 200UFCP-2 P-5 P-10 P-25 P-40 0 10 20 30 40 0 2 4 6 8 0 2 4 6 8 10

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-8.2 -8.5 I-f -8.5 1 I-lim 7.19 1 z-f 6 0.15 0.30 z-f 200 500 0.30 z-f 100 150 200 8.20 8.27 ( -8.2) ( -7.2) ( -8.3) ( -7.3) ( -8.4) ( -7.4) ( -8.5) ( -7.5) 100AS 200UFC 200UFC 40 60 100AS 80 PP 100AS I-f 0.3 z-f 100 PP 100ASP 200

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8.20 100AS-1 8.21 100AS-2 8.22 100ASP-1 8.23 100ASP-2 8.24 200UFC-1 8.25 200UFC-2 8.26 200UFCP-1 8.27 200UFCP-2 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 min 100AS-1 100-0.3 150-0.3 200-0.3 0 10 20 30 40 0 5 10 15 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 min 100AS-2 100-0.3 150-0.3 200-0.3 0 10 20 30 40 0 5 10 15 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 min 100ASP-1 100-0.3 150-0.3 200-0.3 0 10 20 30 40 0 5 10 15 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 min 100ASP-2 100-0.3 150-0.3 200-0.3 0 10 20 30 40 0 5 10 15 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 min 200UFC-1 100-0.3 150-0.3 200-0.3 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 min 200UFC-2 100-0.3 150-0.3 200-0.3 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 min 200UFCP-1 100-0.3 150-0.3 200-0.3 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 min 200UFCP-2 100-0.3 150-0.3 200-0.3

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100MPa HSC

100AS 200MPa UFC 200UFC PP

1 100AS 200UFC

100

2 200UFC

3 PP 100ASP 0.2 vol% 200UFC 0.5 vol%

UFC 100ASP 200 4 1 5 5 10mm 4 25 40mm 10 MPa 6 200UFC 30 30 1mm Sloughing - off spalling