Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 171 (2017) 121 – 130 6XVWDLQDEOH&LYLO(QJLQHHULQJ6WUXFWXUHVDQG&RQVWUXFWLRQ0DWHULDOV6&(6&0 2QWKHFRQILQHGKLJKVWUHQJWKFRQFUHWHDQGQHHGRIIXWXUHUHVHDUFK $QWRQLXVD ,VZDQGL,PUDQEDQG3UDERZR6HWL\DZDQD b a Department of Civil Engineering, Universitas Islam Sultan Agung, Semarang-Indonesia Structural Engineering Research Group, Department of Civil Engineering, Institut Teknologi Bandung, Bandung- Indonesia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© 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license 7KH$XWKRUV3XEOLVKHGE\(OVHYLHU/WG (http://creativecommons.org/licenses/by-nc-nd/4.0/) 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKHRUJDQL]LQJFRPPLWWHHRI6&(6&0 Peer-review under responsibility of the organizing committee of SCESCM 2016 Keywords:+LJKVWUHQJWKFRQFUHWH VWUHQJWK FRQVWLWXWLYHHTXDWLRQV FRQILQHPHQWPRGHO ,QWURGXFWLRQ ,QIUDVWUXFWXUH GHYHORSPHQW UHTXLUHV H[FHOOHQW PDWHULDO TXDOLW\ DQG GXUDEOH VR PDQ\ LQQRYDWLRQV WR SURGXFH D PDWHULDOWKDWKDVDKLJKTXDOLW\KDYHEHHQLQWHQVLYHO\FRQGXFWHG+LJKVWUHQJWKFRQFUHWH f’c03D KDVVXSHULRU PHFKDQLFDO SURSHUWLHV DQG GXUDELOLW\ FRPSDUHG ZLWK QRUPDOVWUHQJWK FRQFUHWH EHFDXVH RI WKH KDUGQHVV RI WKH EUHDNGRZQRIDKLJKDQGDORZHUSRURVLW\+RZHYHUKLJKVWUHQJWKFRQFUHWHPDWHULDOLVEULWWOHOHVVGXFWLOHDQGPRUH VHQVLWLYHWRDVSHFWVRIWKHSODQQLQJDQGH[HFXWLRQRIFRQVWUXFWLRQFRPSDUHGZLWKPDWHULDOVPDGHRIQRUPDOVWUHQJWK &RUUHVSRQGLQJDXWKRU7HO ID[ E-mail address:DQWRQLXV#XQLVVXODDFLG 1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of SCESCM 2016 doi:10.1016/j.proeng.2017.01.318 122 Antonius et al / Procedia Engineering 171 (2017) 121 – 130 FRQFUHWH +LJKVWUHQJWK FRQFUHWH PDWHULDO¶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o WRWKHFRQFHQWULFD[LDOORDGLVGHWHUPLQHGE\WKHHTXDWLRQEHORZ Po = Į fc’ (Ag – Ac) + As fy (TXDWLRQ GRHVQRWWDNHLQWRDFFRXQWWKHHIIHFWRIFRQILQHPHQW61,>@WRVWLSXODWHWKHYDOXHRIĮLV HTXDOWRIRUYDULRXVFRQFUHWHFRPSUHVVLYHVWUHQJWK1=6>@DOVRVHWVWKHYDOXHRIĮRILQWKH HTXDWLRQDERYHEXWDSSOLHVIRUFRQFUHWHFRPSUHVVLYHVWUHQJWKXSWR03D,IWKHFRQFUHWHFRPSUHVVLYHVWUHQJWKLV KLJKHUWKHQ Į f’c 7KHĮYDOXHLVOLPLWHGWRQROHVVWKDQ(TXDWLRQ VKRZVWKDW1=6KDVEHHQDFFRPRGDWLQJWKHGHFUHDVHRI WKHFROXPQD[LDOFDSDFLW\ZKHQXVLQJKLJKVWUHQJWKFRQFUHWH 1H[WWKHDERYHHTXDWLRQDFFXUDF\ZLWKH[SHULPHQWDOUHVXOWVRIKLJKVWUHQJWKFRQFUHWHFROXPQDJDLQVWFRQFHQWULF ORDGZKLFKKDVEHHQGRQHE\VHYHUDOUHVHDUFKHUVKDYHHYDOXDWHG>@)LJXUHVKRZVWKHUHODWLRQVKLSEHWZHHQȡs.fs/f'c DQGWKHUDWLREHWZHHQWKHD[LDOORDGWHVWUHVXOWV Pexp WRWKHD[LDOFDSDFLW\RIFROXPQVE\61, (TXDWLRQ )URP WKHVHUHODWLRQVKLSVVKRZWKDWWKHFRQILQLQJUHLQIRUFHPHQWUDWLR ȡs VLJQLILFDQWUROHLQLQFUHDVLQJWKHFDSDFLW\RIWKH D[LDOFROXPQ7KHKLJKHUWKHUDWLRRIWKHLQVWDOOHGFRQILQLQJUHLQIRUFHPHQWWKHPRUHLQFUHDVHWKHD[LDOFDSDFLW\ZLOO EH*HQHUDOO\IURPWKHLPDJHLWLVDOVREHVHHQWKDWWKHYDOXHRIĮLVTXLWHVDIHLQWKHYDOXHRIZKHQWKHYDOXH ȡs.fs/f'cLVKLJKHUWKDQ&RQYHUVHO\ZKHQWKHUDWLRȡs.fs/f'cORZHUHYHQEHORZWKHQLWLVTXLWHULVN\ZKHQXVLQJWKH IDFWRULQWKHFDOFXODWLRQRIWKHFROXPQD[LDOFDSDFLW\7KHUHVXOWVVKRZWKDWĮ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ntonius et al / Procedia Engineering 171 (2017) 121 – 130 )LJXUH$[LDO&DSDFLWLHVRIFROXPQV>@ $QWRQLXV &XVVRQ 3DXOWUH İspall/e'co f'c 03D )LJXUH5HODWLRQEHWZHHQFRQFUHWHVWUHQJWKDQGYVİVSDOOݶFR &RQVWLWXWLYHHTXDWLRQVRIFRQILQHGKLJKVWUHQJWKFRQFUHWH ,WLVNQRZQWKDWWKHGHVLJQSKLORVRSK\RIFRQILQLQJUHLQIRUFHPHQWLVWKDWZKHQLWUHFHLYHVDVHLVPLFORDGWKHFROXPQ D[LDOIRUFHDIWHUWKHFRYHUVSDOOLQJUHPDLQVZHOOSUHVHUYHG9ROXPHWULFUDWLRRIFRQILQLQJUHLQIRUFHPHQWUHTXLUHGLQ WKHFROXPQLVGHWHUPLQHGE\WKHPDJQLWXGHRIWKHLQFUHDVHLQWKHVWUHQJWKRIFRQILQHGFRQFUHWHRUKYDOXH(TXDWLRQ KYDOXHXSWRQRZKDVEHHQZLGHO\SURSRVHGDQGJHQHUDOO\DGDSWHGWRWKHFRQGLWLRQVLQHDFKUHVHDUFKHUV¶FRXQWU\ 124 Antonius et al / Procedia Engineering 171 (2017) 121 – 130 3.1 Strength enhancement of confined concrete (K) 3.1.1 Model by Muguruma et al 0XJXUXPD HW DO >@ SURSRVHG D K YDOXH HTXDWLRQ EDVHG RQ H[SHULPHQWDO UHVXOWV RQ WKH FRQFUHWH ZLWK WKH FRPSUHVVLYHVWUHQJWKRI03D7KHUHIRUHWKHPRGHOFDQEHDSSOLHGWRQRUPDODQGKLJKVWUHQJWKFRQFUHWH,WLV UHSRUWHG WKDW WKH PRGHO FDQ EH XVHG WR DQDO\]H WKH FRQFUHWH ZLWK FRQILQHPHQW WKDW KDYH D QRUPDO DQG KLJK \LHOG VWUHQJWKVWUHQJWK KYDOXHHTXDWLRQLVPDWKHPDWLFDOO\ZULWWHQ Vm Cc K f c Cc U I \K Đ s à ă wạ IF â Cc FRHIILFLHQW GHSHQGV RQ WKH UDWLR RI FRQILQLQJ UHLQIRUFHPHQW ȡ \LHOG VWUHVV RI FRQILQLQJ UHLQIRUFHPHQW fyh FRPSUHVVLYH VWUHQJWK RI FRQFUHWH f'c VSDFHG FRQILQLQJ UHLQIRUFHPHQW s DQG WKH FRUH FURVVVHFWLRQDO DUHD RI UHLQIRUFHPHQW w 7KHDERYHHTXDWLRQGRHVQRWWDNHLQWRDFFRXQWWKHHIIHFWRIWKHFRQILJXUDWLRQRIWKHUHLQIRUFHPHQW &RQILQLQJUHLQIRUFHPHQWDVVXPHGKDVEHHQ\LHOGHGDWWKHWLPHRISHDNUHVSRQVH 3.1.2 Model by Diniz & Frangopol 'LQL] )UDQJRSRO>@GHYHORSHGDFRQVWLWXWLYHPRGHOWKDWFDQEHDSSOLHGWRFRQFUHWHFRPSUHVVLYHVWUHQJWKRI 03DKYDOXHLVGHWHUPLQHGE\WKHIROORZLQJHTXDWLRQ K f cc f c Đ Ã f le ăă f c áạ f c â (TXDWLRQ LQXQLWVRISVL&RQILQHPHQWLQGH[LVFDOFXODWHGE\WKHIRUPXOD Ash f yt f lat d e s p LQZKLFKAsh = O Ast (TXDWLRQ VKRZVWKDW'LQL]FRQVLGHUVWKHFRQILQLQJUHLQIRUFHPHQWKDVEHHQ\LHOGHGDWWKHWLPHRIPD[LPXP UHVSRQVHȜIRUPIDFWRULVWKHUHLQIRUFHPHQWFRQILJXUDWLRQCfIDFWRULVXVHGWRFRUUHFWWKHYDOXHRIWKHVWUHVVVXSSOLHG E\FRQILQLQJUHLQIRUFHPHQWE\WKHIROORZLQJHTXDWLRQ s Cf dc 6RWKDWWKHHIIHFWLYHODWHUDOVWUHVVLV fle = Cf flat. 3.1.3 Model by Legeron & Paultre /HJHURQ 3DXOWUH>@SURSRVHGDPRGHORIFRQILQHPHQWWKDWFDQEHDSSOLHGWRQRUPDODQGKLJKVWUHQJWKFRQFUHWH KYDOXHLVFDOFXODWHGE\ f cc K I f c c &RQILQHPHQWLQGH[I'eIRUPXODWHG f le I e f c 125 Antonius et al / Procedia Engineering 171 (2017) 121 – 130 :KHUHf'leLVWKHHIIHFWLYHODWHUDOVWUHVV7KHVWUHVVRQWKHFRQILQLQJUHLQIRUFHPHQWLVREWDLQHGE\FDOFXODWLQJWKHILUVW VWUDLQRIFRQILQHPHQWDWWKHWLPHRIWKHFRQFUHWHUHLQIRUFHPHQWVWUHVVUHDFKHVDPD[LPXPDQGWKHQFDOFXODWHWKHVWUHVV WKDWFRUUHVSRQGVWRWKHVWUHVVRQWKHVWUHVVVWUDLQGLDJUDP/HJHURQPRGHOKDVEHHQXVHGDVWKHPDLQUHIHUHQFHWRORZHU WKHGHVLJQHTXDWLRQUHLQIRUFHPHQWRIFRQILQHPHQWZLWKUHJDUGD[LDOORDGOHYHODVZHOODVLQWKHGHVLJQRIFRQILQLQJ UHLQIRUFHPHQWDJDLQVWVHLVPLFORDGV>@ 3.1.4 Model by Antonius et al $QWRQLXVHWDO>@SURSRVHGDKLJKVWUHQJWKFRQFUHWHFRQILQHPHQWPRGHOEDVHGRQH[SHULPHQWDOUHVXOWVRIFRQFUHWH FRQFHQWULFURXQGFURVVVHFWLRQRIWKHORDG6WUHQJWKHQKDQFHPHQWRIWKHFRQILQHGFRQFUHWHLVEHORZ K f cc f co Đ f à ăă áá â f co f2LVDHIIHFWLYHODWHUDOVWUHVVZKHUHWKHFRHIILFLHQWRIFRQILQHPHQWHIIHFWLYHQHVVIRUVTXDUHVHFWLRQZKRDGRSWWKH HTXDWLRQSURSRVHGE\0DQGHU>@5HVXOWVRILQYHVWLJDWLRQVFRQGXFWHGE\$QWRQLXVVWUHVVRIFRQILQLQJUHLQIRUFHPHQW DWWKHWLPHRISHDNUHVSRQVHLVQRWDOZD\V\LHOGKHQFHWKHVWUHVVWRDVTXDUHFURVVVHFWLRQFROXPQLVFDOFXODWHGE\WKH HTXDWLRQEHORZ fs ẵ ê s d c E s đ OQ ô ằ ắ ơô U s f c ẳằ 3.2 Validation of K equations to the experimental results 7KHKHTXDWLRQVDERYHZLOOWKHQEHYDOLGDWHGZLWKGDWDIURPH[SHULPHQWVFRQGXFWHGE\$QWRQLXV ,PUDQ>@RQ WKHWHVWLQJRIFRQILQHGQRUPDODQGKLJKFRQFUHWHZLWKVTXDUHFURVVVHFWLRQ 7DEOH 7DEOH([SHULPHQWDOGDWDRIVTXDUHVHFWLRQXQGHUFRQFHQWULFORDGLQJV>@ &RQILQLQJVWHHO 6SHFLP f’c HQ 03D &RQI VSDFLQJ Us $/ ± $0 ± $ $+ ± %/ ± %0 ± % %+ ± &/ ± &0 ± & &+ ± ± '/ '0 ± ' '+ ± Pmax f’cc N1 03D K 126 Antonius et al / Procedia Engineering 171 (2017) 121 –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fc ĐH à f cc ăă c áár â H cc ĐH à r ăă c áá © H cc ¹ r fc f cc H c H cc f cc H c H cc )XUWKHUPRUHWKHSDUDPHWHUVVWUDLQDUH Hco’ f’co 127 Antonius et al / Procedia Engineering 171 (2017) 121 – 130 H cc H co > K @ 6WUHVVRIFRQILQLQJUHLQIRUFHPHQWLVGHWHUPLQHGE\HTXDWLRQ )XUWKHUPRUHWKHPRGHOPRGLILFDWLRQPDGHLVWKH YDOXHHTXDWLRQRIKGXFWLOLW\SDUDPHWHUV İc HIIHFWLYHODWHUDOVWUHVVDQGUHVLGXDOVWUHVV fr 4.1 Strength enhancement of confined concrete (K) and residual stress (fr) 7KHKHTXDWLRQEDVHGRQWULD[LDOWHVWVRIKLJKVWUHQJWKFRQFUHWHKDVEHHQGHYHORSHGE\,PUDQHWDO>@XVLQJ 2WWRVHQFULWHULDZKLFKLVDGRSWHGWRHVWLPDWHWKHVWUHQJWKLQFUHDVHLQQRUPDODQGKLJKVWUHQJWKFRQFUHWHFROXPQVGXH WRFRQILQHPHQW7KHKHTXDWLRQLV K f cc f co Đ fl à f ăă ¸¸ l f f co â co $QGIRUWKHUHVLGXDOVWUHQJWKHQYHORSH fr f co Đ fl à f ăă ¸¸ l f f co © co ¹ )DLOXUHVWUHQJWKHQYHORSHVKRZQLQILJXUHVWDWHVWKDWWKHYDOXHHTXDWLRQKSURSRVHGLQWKLVPRGHOKDVDQRQOLQHDU VKDSHDQGWHQGWREHHTXDOWRWKHYDOXHHTXDWLRQKRI0DQGHUHWDO>@;LHHWDO>@DQG$QVDUL /L> @7KHK YDOXHHTXDWLRQLVDOVRGHULYHGIURPWKHWULD[LDOWHVWLQJLQZKLFKHDFKXVHV\LHOGFULWHULD$QRWKHUSKHQRPHQRQWKDWLV YLVLEOHLQWKHSLFWXUHLVWKHYDOXHHTXDWLRQKE\5LFKDUW>@DQGLVWKHEDVLVIRUGHWHUPLQLQJWKHYROXPHWULFUDWLRRI FRQILQLQJUHLQIRUFHPHQWE\61,LVXQGHUHVWLPDWLRQRIODWHUDOORZVWUHVV XSWRf2f'coa FRPSDUHGZLWKRWKHU HTXDWLRQV )LJXUH)DLOXUHVWUHQJWKHQYHORSHRIKPRGHOV 128 Antonius et al / Procedia Engineering 171 (2017) 121 – 130 4.2 Ductility parameter ,QWKHYDOXHRIKLQWKHDERYHHTXDWLRQDIIHFWVWKHEHKDYLRURIFRQILQHGFRQFUHWHGXFWLOLW\7KHGDWDRIWHVWUHVXOWV URXQGFURVVVHFWLRQFROXPQE\$QWRQLXV>@DQGDVTXDUHFURVVVHFWLRQFROXPQWHVWGDWDE\$QWRQLXV ,PUDQWREH VXEVHTXHQWO\FRPELQHGWRGHWHUPLQHWKHSDUDPHWHUVRIWKHQHZGXFWLOLW\5HVXOWVRIUHJUHVVLRQ\LHOGVWKHHTXDWLRQ VHH )LJXUH H85c = H’cceK 4.3 Effective lateral stress ,W KDVEHHQ REVHUYHG WKDWIRU FRQILQHG FRQFUHWH ZLWK VTXDUH VHFWLRQV WKDW IRU VSDFLQJVRI WLHV JUHDWHUWKDQ OHDVW GLPHQVLRQRIWKHFROXPQWKHFRQILQLQJHIIHFWVDUHQHJOLJLEOH>@WKHUHIRUHWKHODWHUDOVWUHVVIRUVTXDUHVHFWLRQZLWKD FRUUHFWLRQIDFWRUSURSRVHGE\'LQL] )UDQJRSRO>@LVDGRSWHG § s ·§ U H85c = H’cc à f k ă s f e ă â ă d c áạâ s H85c=Hcc K )LJXUH5HJUHVVLRQRIH85cHTXDWLRQ &RUURERUDWLRQZLWKWKHH[SHULPHQWDOUHVXOWV 7KH PRGLILHG VWUHVVVWUDLQ UHODWLRQVKLS IRU FRQILQHG FRQFUHWH LV WKHQ XVHG WR VLPXODWH H[SHULPHQWDO UHVXOWV RI UHLQIRUFHGFRQFUHWHFROXPQVLQ7DEOHDERYH7KHFRPSDULVRQVRIWKHPRGLILHGPRGHOZLWKVSHFLPHQVIRUVTXDUH VHFWLRQVVKRZHGLQ)LJXUHWKURXJK ,WFDQEHVHHQIURPWKRVHILJXUHVWKDWWKHPRGLILHGPRGHOVLPXODWHWKHVWUHVV VWUDLQRIFRQILQHGQRUPDODQGKLJKVWUHQJWKFRQFUHWHRQWKHSUHDQGSRVWSHDNUHVSRQVHVDWLVIDFWRULO\ 129 Antonius et al / Procedia Engineering 171 (2017) 121 – 130 )LJXUH0RGLILHGPRGHOYVH[SHULPHQWDOUHVXOWVIRU$FRQILJXUDWLRQ &RQILQHGFRQFUHWHVWUHVV IFF 03D )LJXUH0RGLILHGPRGHOYVH[SHULPHQWDOUHVXOWVIRU%FRQILJXUDWLRQ 0RGLILHG0RGHO ȡV V PP I\ 03D ȡV V PP I\ 03D ([S [PP 0RGLILHGPRGHO ([S [PP &/ I F 03D &0 I F 03D &+ I F 03D '/ I F 03D '0 I F 03D '+ I F 03D &RQFUHWHD[LDOVWUDLQ )LJXUH0RGLILHGPRGHOYVH[SHULPHQWDOUHVXOWVIRU&FRQILJXUDWLRQ )LJXUH 0RGLILHGPRGHOYVH[SHULPHQWDOUHVXOWVIRU'FRQILJXUDWLRQ &RQFUHWHD[LDOVWUDLQ &RQFOXVLRQ )XUWKHUVWXGLHVRQFDOFXODWLRQRID[LDOFDSDFLW\RQKLJKVWUHQJWKFRQFUHWHFROXPQVDUHQHHGHGZKHUHWKHFRHIILFLHQW Į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ntonius et al / Procedia Engineering 171 (2017) 121 –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¶FRXQWU\ 124 Antonius et al / Procedia Engineering 171 (2017) 121 – 130 3.1 Strength enhancement of confined concrete (K) 3.1.1 Model by Muguruma et al 0XJXUXPD... 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the. .. DWWKHWLPHRISHDNUHVSRQVHLVQRWDOZD\V\LHOGKHQFHWKHVWUHVVWRDVTXDUHFURVVVHFWLRQFROXPQLVFDOFXODWHGE\WKH HTXDWLRQEHORZ fs ẵ ê s d c E s đ OQ ô ằ ắ ơô U s f c ẳằ 3.2 Validation of K equations to the experimental results