Determination of tensile crack bridging of PCM-concrete interface subjected to fatigue loading by means of bending test

Transcription

1 Journl of Struturl nginring Vol.55A Mrh 9 JSC Dtrmintion of tnsil rk briging of -onrt intrf subjt to ftigu loing by mns of bning tst Di Zhng *, Hitoshi Furuuhi **, Akihiro Hori ***, Fujim Siji ****, Tmon U ***** * Lb of nginring for Mintnn Systm, Division of Built nvironmnt, Hokkio Univrsity, M.. **Lb of nginring for Mintnn Systm, Division of Built nvironmnt, Hokkio Univrsity, Dr.. *** Spil Aitivs Dpt., DKA Chmils GmbH, Sls Mngr, Dr.. **** Hrlo Proution & Thnil Support Stion, Dnki Kgku Kogyo CO..Lt., Assistnt Mngr. *****Lb of nginring for Mintnn Systm, Division of Built nvironmnt, Hokkio Univrsity, Dr.. In this ppr, simpl n hny tst mtho for trmintion of th tnsil rk briging l of -onrt intrf is propos. Bs on th ftigu filur mhnism of -onrt intrf tht is govrn by rk propgtion s th rsult of intrf briging grtion, th J-intgrl mtho propos for trmining th tnsion softning rltion of onrt unr stti loing is moifi to trmin th -onrt intrf tnsil strss grtion rltion. Th riv grtion rltion is ompr to tht of norml onrt unr yli unixil tnsil tsts, n it n b foun tht th -onrt intrf hs highr grtion rt so tht mor ttntion shoul b pi to th -onrt intrf uring th sign of rtrofitt struturs unr ftigu loing. Kyors: -onrt intrf, Ftigu bning tst, strss grtion l, nrgy quivln. BACKGROUD Polymr mnt mortr ovrly mtho rtrofitting mtho is us to inrs th lo pity n nvironmntl rsistn of brig ks. In light of th k bon strngth of norml mnt bs mtrils, offrs goo ompromis in trms of ost n bhvior. Th rtrofitt highy or brig k r xpt to rsist millions of yls of rpt xl los from pssing trffi uring thir srvi lif. Subsquntly, bs rpirs hv somtims pos problm u to thir boning. Dboning n strt from ny isontinuity bounry, joints or rk utting th ovrly, oftn ith lifting of th gs of th bon r. This inus n rks hih lrt th mg pross, n n rpir ork is n. As rsult, thr is inrsing intrst in bttr knolg to prit th bhvior of -onrt intrf unr yli loing n to fin solutions to nsur thir urbility. Although thr r mny stuis rporting th improvmnt in th mhnil proprtis of n th filur mhnism of thm unr stti n yli loing onitions r prsnt, thr hv bn f stuis rlt to -onrt intrf proprtis n filur mhnisms unr ftigu loing onition. Ftigu lif prition n th sign of rpir struturs n so fr only b prform through n mpiril pproh. Th invstigtions on th ftigu proprtis n filur mhnisms of -onrt intrf r nssry for proposing propr rpir mtho. This ls to th nssity of th vlopmnt of n nlytil tool tht is pplibl to th prition of intrf ftigu prformn n to th sign of struturl rpirs in th futur. Vrious pprohs hv bn us in th ftigu lif ssssmnt of struturl lmnts. A ily pt pproh for nginring prti is bs on mpirilly riv S- igrms, lso knon s Wöhlr urvs. This pproh provis rltion btn mximum strss or strss mplitu n th numbr of lo yls to filur. Hovr, it os not llo us to srib th softning bhvior of mtril bus of th ppli for ontrol, hih onsquntly ls to unstbl rk propgtion. Th formtion ontroll unixil tnsil tst on noth onrt prism is mor irt y to invstigt th mtril proprty unr yli loing onition. Hovr, suh tst prour rquirs vry spifi n pris y to rry out in omprison ith bning tst, hih is normlly ppli to provi t for th vrifition of th mtril l. Rntly, ftigu nlysis mtho ombining th briging strss grtion l unr yli lo n FM nlysis is ris by Prpong t l 3. In this mtho, th S- rltion from th bning tsts is introu ith th ftigu nlysis mol to trmin th ftigu briging strss grtion -86-

2 rltion n th volution of mi-spn fltion is slt for th vrifition. Th xprimnts r sir to b onut but th nlysis prour my tk tim. Strting ith th J-intgrl bs mtho by Li t l 4, sris of mthos bs on nrgy bln hv bn propos for trmining th tnsion softning urv of onrt: th n J-intgrl bs mtho 5, th moifi J-intgrl mtho 6, n n mtho propos by i 7. By using J-intgrl mtho, th tnsion softning igrms n b trmin from singl bm spimn. Only th lo, th lo point isplmnt n th rk opning t th noth tip r nssry to b msur. It hs bn prov tht th J-intgrl mtho is pplibl to stti tnsion softning rltion of onrt intrf. In this stuy, th J-intgrl mtho bs on lo ontroll bning tsts togthr ith briging grtion thory r introu to trmin th briging strss grtion rltion of -onrt intrf.. FATIGU MODL. Mhnism of ftigu rk groth in onrt intrf For -onrt ol-joint intrf, th mtril phss n broly b lssifi s mnt in onrt or pst n ggrgts, s ll s th intrfs btn ggrgt n hyrt mnt pst. Th ftigu loing uss ths physil phss to unrgo mirosopi hngs, suh s opning n groth of bon rks, hih xist t th intrfs btn ors ggrgt n hyrt mnt pst vn prior to th pplition of lo 8. Ths mirosopi hngs in turn us trimntl hngs in mrosopi mtril proprtis. Typilly, th ggrgt briging for rss ith numbr of yls bus of th intrfil mg or ggrgt brkg 9. Subsquntly, th rk propgts both by inrsing lngth n ith ith th inrs of ppli loing yls until th quilibrium nnot b stisfi ith furthr rk propgtion. At this momnt, th strutur fils, n it fins th ftigu lif. This mhnism is so ll Briging Strss Dgrtion n th -onrt intrf grtion l is onsir th ssntil us of rk propgtion n ns to b lrifi. Bs on th bov isussions, som bsi ssumptions for ftigu moling n b stt:. Aftr ominnt ftigu rk is rt, th briging bhvior ithin th frtur zon is govrning th rt of ftigu rk vlopmnt.. Th strss t th rk tip rmins onstnt n is qul to th mtril tnsil strngth. 3. Mtril proprtis outsi th frtur zon r unhng uring ftigu loing. Th J-intgrl mtho ombins th fititious rk mol propos by Hillrborg ith nrgy quivln ssumptions n hs bn ppli to stti nlysis prours. In th vlopmnt of th ftigu nlysis mtho, th filur of orinry mntitious mtrils, suh s plin onrt n -onrt intrf, unr ftigu flxur or ftigu tnsion is govrn by th initition n th propgtion of singl loliz rk; thrfor, th fititious rk is pproprit n nough for rprsnting th rk n th filur mhnism. In orr to orrlt th J-intgrl mtho n ftigu nlysis through nrgy quivln onpts n to prit th rk vlopmnt in -onrt intrf, th folloing itionl ssumptions my b not: 4. Th nrgy ppli for th inrmnt of fltion t loing point is totlly bsorb for th fititious rk propgtion synhronously. 5. Th rk propgtion unr ftigu loing is rgr s slo rk propgtion unr stti loing. Only th nrgy ppli uring th fltion inrmnt orrsponing to th inrmnts of rk lngth n ith is tkn into ount, ignoring th nrgy orrsponing to th ovrlpp prt btn jnt hystrti loops s Fig... Briging mol of -onrt intrf unr tnsion ftigu Monotoni tnsion Th roughnss of th joint surf, th mix proportions of substrt onrt n th onstrution mtho r th min ftors ffting th bon proprtis of -onrt intrf. In th prsnt invstigtion, n mpiril mol bs on th J-intgrl mtho propos by Zhng ill b opt. In this mol th -onrt intrf tnsion softning rltion is xprss s funtion of th intrf roughnss, substrt onrt omprssiv strngth n th rk mouth opning isplmnt CMOD bs on th nlysis of xprimntl t. 3 { }xp f ti.46 fi f ' 5.4G f ti 9.4R.3R fi.5mm 4.74R G mm.8.8 if f' if f' < f' f' 3 xp hr f ti is intrf splitting tnsil strngth, R is th intrf roughnss lult bs on JIS Stnr, is tkn s 6.93 n is funtion of R, orrspons to th rk opning hn th strss hs ropp to zro, G fi is th intrfil frtur nrgy xprss s funtion of omprssiv strngth of n intrf roughnss. -86-

3 st. n st n b. n st n Cyli tnsion Dgrtion of ggrgt briging of onrt unr yli unixil tnsion hs bn stui by rsrhrs in lst to s 9, 5, 6, 7. By nlyzing th xprimntl t, it is onlu tht th briging strss grtion rltion of mntitious mtrils pns on to min prmtrs orrsponing to mximum rk opning s th mximum rk ith orrsponing to th zro lo, n numbr of yls,. It n b xprss s: for k k for k k k k log log < log. n Fig. Prour of ftigu rk nlysis hr n rprsnt briging strss t -th yl n first yl, rsptivly. is givn by q.; n k n k r grtion ftors, hih rflts th rt of ggrgt briging grtion. 3. PROCDUR OF FATIGU AALYSIS Th prour of ftigu lif nlysis is shon by simpl support omposit bm subjt to ftigu lo. For givn mximum n minimum flxurl ftigu lo lvl, P mx n P min, uring th loing pross in th first yl, rk initits ith mximum lngth mx n ith mx, n th fltion xprins th mximum vlu mx s shon in Fig.. Th briging l ithout strss grtion togthr ith numril intgrtion mtho n b us to lult th unit nrgy onsumption of fititious rk s:

4 During th unloing pross, prt of th xtrnl nrgy umult in othr portions bsis th fititious rk ill b rls n thr is rsiul fltion min in th fully unlo stt. Thrfor, to proprly vlut th nrgy onsum in th fititious rk, th mount of lsti nrgy rls must b xlu. Th nrgy ppli for th fititious rk inrsing from zro to ith mx uring th first yl is lult s: min mx P 4 hih quls to th r S of th hystrti loop of first yl s shon in Fig.. Whn th rk xprins th son yl of lo, th trnsfrr strss ross th rk rus u to th triortion of mtril onstitunt on th rk pln. Th quilibrium n not b mintin ith th gr briging strss istribution of th rk r hn CMOD rhs mx. Thrfor, th xisting rk propgts ith itionl lngth to mx n itionl ith to mx, n th fltion inrss from mx to mx. Th briging ls ith n ill b us in th ol frtur zon n th nly vlop frtur zon, rsptivly. Th unit nrgy onsumption of ol frtur rk zon n b xprss s: 5 Th nrgy onsum for th CMOD inrsing from mx to mx is lult s: Δ min min P P 6 hih rprsnts th r S s shon in Fig.b. At this stg, th totl nrgy onsum for CMOD inrsing from zro to mx is lult s mx mx Δ 7 hih is qul to umultion r of S n S. Th prour ill b ontinu ith th xtnsion of rk pros until th lo pity strts to rop ith inrsing rk lngth. At this stg, th omposit bm is onsir to hv fil in ftigu. Aoring to this prour, for th -th lo yl, th frtur history zon ill b ivi into stions ith iffrnt ftigu history, rnging from to yls. Th totl nrgy onsum for CMOD inrsing from zro to mx orrspons to th r nlos by nvlop urvs of lo-formtion igrm n th unloing urv of lst yl ith horizontl oorint xis. Th unit nrgy onsumption of fititious rk uring this pross n b xprss s:... 8 hr,,.. - rprsnt th history of rk ith t h yl. As init in Fig.., hn th fititious rk lngth is n th fititious CMOD is y, th folloing rltion n b obtin. y y y / / 9 Thn, th nrgy hih is onsum in this portion ftr yls of lo n b lult s follos: y y y b... b... b... From q., th folloing rltionship n b riv... b -864-

5 Thn furthr onuting th first n son orr rivtiv in both si of q., th folloing to qutions n b riv rsptivly:... ' b... b 3 hr i n i i,.. rprsnt unit nrgy onsumption n briging strss of fititious rk stion hih xprins ftigu lo for i yls, sprtly. If furthr ssumption is m tht t ny quilibrium stt, th strss vlu t th point of intrstion btn h stion is ontinuously istribut, hih mns tht th folloing rltion is obtin: i i for i,,.. 4 Thn finlly th qution n b rrng s: 5 b hr b is th ith of omposit bm. Substitut th q. into q. 5. Th fititious rk lngth i, rk mouth opning isplmnt CMOD n nrgy ppli by xtrnl lo i i,.. ftr i yls of lo n b obtin from xprimnt obsrvtion. Th vlus of prmtr k n k oul obtin bs on t fitting. 4. XPRIMTAL OVRVIW 4. Mtrils n spimns Th / rtio n strngth proprtis of onrt n us in this stuy n b foun in Tbl.. Th us in this stuy is prmix PA polyrylt i str por rsin n vlop s splying mortr for rpiring of ross stion of struturs. It hs hrtristis of high nsity, high bon strngth n lo ontrtion. Th omprison of urbility Mtril Tbl. Mtril Proprtis Wtr Comprssiv mnt strngth rtio MP Young s Moulus GP Conrt 63% %* *th vlu of /ompoun Tbl. Comprison of Durbility btn n orml Mortr Durbility Mortr W/C5% xmintion W/ompoun3.4% Rltiv ynmi Rltiv ynmi Frzing lsti Moulus lsti Moulus n f86.4% 3 f98.5% 3 Thing yl yl Crbontion Dry shrinkg Chlori ion pntrtion pth Crbont thiknss 7.4mm 8 ys mm 8 ys Crbont thiknss.7 mm8 ys mm 8 ys bhviors btn n norml mortr is shon in Tbl.. Th onrt substrts surfs r trt by tr jt WJ mtho. Spil ttntion s pi to provi qut moistur on th substrt onrt surf. Th substrt onrt s pl in tr for 48hrs n fr tr s rmov bfor sting. Th onnt intrf is sprt ith oon tringulr prism to inu th noth n th g of spimn t tsting is t lst thr months so s to llvit th fft of initil hyrtion vlopmnt. 4.. Apprtus n tst prour Splitting tnsil tst Th splitting tnsil tst is us orli to msur th tnsil strngth of onrt. It s first propos by Lobo Crniro n Brllos uring th Fifth Confrn of th Brzilin Assoition for Stnriztion in n s ltr opt s stnr tst. Rmy n Strikln 4 us th ASTM C496 stnr tst mtho s gnrl gui n vlop splitting tst for omposit ylinrs, onstrut ith on-hlf onrt n on-hlf rpir mtril. Thir tst sho tht th ylinril splitting tnsil gv onsistnt rsults. In this stuy, splitting tnsil tst s shon in Fig. s onut to vlut th tnsil strngth of th onrt intrf. To prvnt lol filur in omprssion t th loing gnrtors, to thin strips m of plyoo r pl btn th loing pltns n th spimn to istribut th lo. A noth ith siz of.75 x m t h si is inu uring th sting prour. Th ontt r btn th onrt substrt n th is -865-

6 oth x x lngth x ith x pth P Conrt P 7 Fig. Splitting tnsil tst stup unit:mm 5.5 m. Th mximum tnsil strss n b lult by th folloing qution: P mx 6 πa hr mx is th mximum tnsil strngth in th spimn hn th ppli lo is P, A is th r of ontting surf. Thr point bning tst Th 5k pity f bk ontroll loing mhin is mploy in this stuy. For stti tst, th tsts r rri out unr isplmnt ontrol onition n th loing sp s.mm/min. hil th ftigu tsts r unr lo ontrol onition. Thr point ftigu bning tsts r onut both unr stti loing n ftigu loing. Th til of xprimnt st-up of stti tst n b foun in th rfrn 8. Th xprimntl st-up of ftigu tst is shon in Fig. 3. Stti flxur tsts r onut bfor ftigu flxur tsts to trmin th stti flxur strngth. Bs on th vrg flxur strngth, th mximum ftigu strss r trmin for h lvl. Sin tst t of h yl is us s input, th tim n lultion ffiint option is to hoos highr vlu of strss lvl. In this stuy, to lvls of S mx.9 n S mx.85, ith on spimn for h lvl, hih th ftigu lif r only in hunrs, r onut. Ftigu loing s ontroll ith onstnt mplitu btn mximum n minimum lo lvls. A frquny of 5 Hz s hosn ith sin v form. Th vlu of.5k orrsponing to th prlo s hosn for th minimum lo in orr to voi ny slip of spimns tht n our unr totl unloing in th ftigu tst. 4.3 Dt olltion For ftigu loing tst, Linr Vribl Diffrntil Trnsurs LVDTs r introu to msur th fltion t th mi-spn of spimns from both sis of Lo Cll Disp. trnsur π Gg For lo ll For π Ggs n LVDTs Conrt For strin ggs A/D hngr bor PC 36 Oil ylinr Whtston brig Amplifir Con strin gug st-up Fig.3 Tst st-up of ftigu bning tst unit: mm

7 Tbl.3 Strngth of Stti Loing Tst Sris 3 Avrg Flxurl Strngth MP Tnsil Strngth MP spimns. To obtin th CMOD s ll s rk propgtion pross t th lst filur yl, four on irtionl π gugs ith ury of.mm r rrng ith th sm istn from th position of noth tip to th top of omposit bm. To vlut th propgtion of th fititious rk in th ligmnt portion, th longituinl strin istribution of th noth bm s msur. Strin gugs ith lngth of 5mm r provi long th ligmnt portion. For th purpos of obtining s mny msur t s possibl to vlut th fititious rk propgtion, svn strin gugs r pl on th ligmnt portion. h strin gug s st mm prt s shon in Fig.3. Th Hz smpling systm ADRC onsisting of Whtston brig, mplifir, A/D hngr bor n prsonl omputr s us for roring th t. smpls oul b msur for son by using this systm. Th st-up of this systm is shmtilly shon in Fig XPRIMTAL RSULTS AD AALYSIS Th xprimntl rsults unr both stti n ftigu loing r illustrt n isuss in this stion. 5.. Rsults unr stti loing Th rltion btn lo n mi-spn fltion of thr stti spimns of omposit bm r shon in Fig. 4. Th ultimt tnsil strngth n flxurl strngth of omposit spimns is shon in Tbl 3. Th vrg Lo K F-LS-3 F-LS- F-LS-.5.5 Dfltion. mm Fig.4 Lo-fltion rltion unr stti loing flxurl strngth is us to trmin th ftigu strss in th ftigu tst. 5.. Rsults unr ftigu loing Ftigu tst rsults r us for trmining th briging strss grtion rltion. In th lulting prour, svrl ssntil mtril rltions, th onstitutiv rltion unr stti loing, th nrgy ppli by xtrnl lo n th vlopmnt of fititious rk n ntrl fltion bs on xprimntl rsults, r introu s input in th qution. Dmg hrtristis Th progrssiv ftigu filur is srib by illustrtion of inrs in CMOD ginst th numbr of yls s shon in Fig. 5. It n b sn tht th filur hrtristis of onrt intrf is similr to thos of mntitious mtril lik onrt n n b ivi into to istint stgs. Th first stg is th lrtion stg, hr th rt of mg of spimn rss s th rk gros t smll numbr of loing yls. Th son stg is n lrtion stg, hr thr is sty inrs in th rk groth rt right up to filur. On rtin gr, th filur hrtristis of.35 3 Crk ith mm Smx.9 Smx.85 Lo K umbr of Lo yl Fig.5 Crk volution urv.5..5 Cntrl fltion mm Fig.6 Lo-Dfltion rltion unr ftigu loing S mx

8 Crk lngth mm Tnsil strss MP from q. Smx.9 Smx.85 nrgy Consum *m Crk CMOD ith mm mm Fig.7 Crk lngth n CMOD rltion Smx Crk ith mm Fig.8 CMOD mm CMOD rltionship S mx.9 -onrt intrf obsrv in this tst furthr monstrts th vliity of ssumption tht onrt intrf prforms lik mntitious mtrils. Lo-fltion urvs Fig.6 xhibits typil lo-fltion urv until totl filur of spimn s obtin from flxurl ftigu tst. It n b noti tht by using ADRC systm, th lo-fltion rltion of h yl n b ror. 3 Fititious rk propgtion Th rk opning lult from th output from svn strin gugs ispos t th ligmnt portion is ssum to b fititious CMOD. Th tip of fititious rk t mximum lo of h yl orrspons to th point t hih th strin is zro n th lngth of fititious rk n b obtin n plott ginst CMOD in Fig Implmnttion n Disussion In this stion, th briging grtion l is lult using th prour of ftigu nlysis isuss in Chptr 3. Th lultion prour onsists of to stgs: In th first stg, th lultion of th nrgy ppli by th xtrnl lo ftr rtin numbr of yls of ftigu loing is prform. Th rsult is shon in Fig.8. Tnsil strss MP Crk CMOD ith mm mm Fig.9 Tnsil strss-cmod rltionship Smx.9 Smx umbr of Lo yl Fig. Strss-umbr of yl rltion In orr to voi th influn of t flutution, th rltion btn nrgy onsum n CMOD is firstly rprsnt by mthmtil xprssion bs on t fitting mtho. Thn th first orr n son orr rivtiv lultion is onut togthr ith input of fititious CMOD n lngth obtin from tst rsults to trmin th vlu on th right si of q.5. Th lultion rsult is plott ginst CMOD n numbr of loing yls in Fig.9 n Fig. rsptivly. It n b sn from Fig. 9 tht for th sm CMOD, th tnsil strss hn Smx.85 is smllr thn tnsil strss hn Smx.9. This is bus it xprins mor lo yls to rh th sm CMOD n subsquntly hs mor strss grtion. In th son stg, th briging grtion l s shon in q. is substitut into lft si of q.5 n th vlu of k n k n b obtin through to-prmtr nonlinr fitting mtho. Th finl grtion rltion riv from ombin t of to strss lvls for -onrt intrf is shon blo: log for.6mm..log for >.6mm

9 In orr to ompr th strss grtion rltion btn norml onrt n -onrt intrf, th strss grtion rltion of onrt obtin by yli unixil tnsil tsts 7 is quot in this stuy n xprss s follos:.8 4log for.6mm.4.log for >.6mm 8 It is noti tht th offiint k n k in th grtion l of -onrt intrf r similr to tht of norml onrt hn rk ith is smllr thn.6mm, hil k for -onrt intrf is lrgr thn for norml onrt hn rk ith is lrgr thn.6mm. This implis tht -onrt intrf xhibits th highr rt of briging strss grtion thn tht of ggrgt briging in norml onrt, n shoul b rgr s th ky issu of rtrofitt struturs spilly subjt to ftigu loing. 6. COCLUSIOS A ftigu nlysis mtho of -onrt omposit bm unr ftigu flxur hs bn propos by pplying th onpt of briging fft grtion n fititious rk bs on thory of nrgy quivln. Th nlytil mtho hs bn vlop bs on th ftigu filur mhnism of -onrt intrf tht is govrn by rk propgtion s th rsult of intrf briging grtion. Th J-intgrl mtho propos for trmining th tnsion softning rltion of onrt unr stti loing is moifi to trmin th -onrt intrf tnsil strss grtion rltion. This mtho hs th folloing fturs: Thortilly spking, th tnsil strss grtion rltion n b trmin from singl bm spimn. Only th lo, th lo point isplmnt, th rk lngth n opning ith r nssry to b msur or trmin. Mnhil, th ftigu bning tst is sir to b prform thn th unixil tnsil ftigu tst. 3 Th mtho propos in this stuy n b us for othr mntitious mtrils or omposit intrfs s long s th thory of fititious rk n nrgy quivln r tnbl. 4 Th -onrt intrf strss grtion rltion s obtin bs on th mtho mntion bov n ompr ith tht of rk in norml onrt. It n b foun tht th -onrt intrf hs highr grtion rt so tht mor ttntion shoul b pi to th -onrt intrf uring th sign of -rtrofitt struturs unr ftigu loing. ACKOWLDGMT Th surf WJ trtmnt ork srib in this ppr s rri out t Hokusi Knstsu Co.Lt. Th uthors r grtful to thir ollbortion. RFRCS Trn, Q. T., Toumi, A. n Turtsinz, A., Molling of boning btn ol onrt n ovrly: ftigu loing n ly ffts, Mtrils n Struturs, DOI.67/s y. Ohm, Y., Rnt progrss in Conrt-Polymr omposits, Avn Cmnt Bs Mtrils, Vol.5, o., pp. 3-4, Prpong, S. n Tkshi, M., Fibr briging grtion bs ftigu nlysis of CC unr flxur, Journl of Appli Mhnis Vol.6 pp August 3. 4 Li, V.C. n Wr, R.J.:, A novl tsting thniqu for post-pk tnsil bhvior of mntitious mtrils, Frtur Toughnss n Frtur nrgy, Blkm, 83-95, Rokugo, K., Is, M., Sko, S. n Koyngi, W., Tnsion softning igrms of stl fibr rinfor onrt, Frtur of Conrt n Rok, lsvir, 53-5, Uhi, Y., Rokugo, K. n Koyngi, W., Dtrmintion of tnsion softning igrms of onrt by mns of bning tst. Journl of Mtrils, Conrt Struturs n Pvmnts of JSC, o.46/v-4, 3-, i, J.,Sumrnnih n Tntrmisirikul, S.: Mtho to Dtrmin th Tnsion Softning Curv of Conrt, Frtur Mhnis of Conrt Struturs. Proings of FRAMCOS-3, Vol., , vill, A. M, n Brooks, J.J, Conrt thnology, Longmn Sintifi & Thnil, Lonon. 9 Zhng, J., Stng, H., n Li, V.C, xprimntl stuy on rk briging in FRC unr unixil ftigu tnsion, J. Mt. In Civ. ngrg., ASC,, 66-73, Fbrury. Hillrborg, A., Mor, M. n Ptrsson, P Anlysis of rk formtion n rk groth in onrt by mns of frtur mhnis n finit lmnts, Cmnt n Conrt Rsrh, Vol.6. pp , 976. Di, Z., Furuuhi, H., Hori, A., Fujim, S. n U, T., Influn of intrf roughnss on -onrt intrfil frtur prmtrs, Proings of th thir ACF Intrntionl Confrn, -3 ovmbr 8, HCM City. JIS B 6:Gomtril Prout Spifitions GPS - Surf txtur: Profil mtho- Trms, Dfinitions n surf txtur prmtrs, JIS,. 3 Lobo Crniro, F. Brllos, A., Rsistn l Trtion s Btons, Int. Asso. Tst. Rs. Lb. Mtr. Strut. RILM Bull Rmy, G.., Strikln, A.M., An xprimntl vlution of rpi stting pthing mtrils us in th rpir of onrt brigs n pvmnts, Albm -869-

10 Highy Rsrh, Projt 93-3, Prt II, 984, pp Goplrtnm, V.S., n Shh, S.P., Softning rspons of plin onrt in irt tnsion. ACI J., 83, Rinhrt, H. W., Cornlissn, A. W., n Horijk, D.A., Tnsil tsts n filur nlysis of onrt, J, Strut. ngrg., ASC,, Horijk, D.A., Tnsil n tnsil ftigu bhviour of onrt, xprimnts, moling n nlyss, Hron, 37,- 77,99. 8 Di, Z., Furuuhi, H., Hori, A. n U, T., Mo I Frtur Bhviors of -onrt Intrfs, Proings of JCI, Vol.3, o.,