Relation of roughness parameters and tension softening diagram of concrete-to-concrete interface
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- Ursula Austin
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1 Fraur Mhani Cnr Cnr Sruur - An Durabiliy Mnirg rig Cnr Sruur- B. H. Oh al. (d) 2 Kra Cnr Iniu Sul ISBN la rughn parar n ng diagra nr--nr ra A. Sah K. Yaada S. Ihiyaa & T. Ha Akia Prural Univriy Yurihnj Akia apan ABSTACT: Thi papr labra rla rughn parar n ng diagra nr--nr ra. Spin ih igh yp plag j hr yp nlihi n r plyd r valua n ng diagra (TSD) lld by ura brva ligan ar raur. ughn parar r aurd hih lud axiu high n raurd ura (P) ih 3-dinal rughn analyzr. Th auhr alulad ky ar hih i rai raurd par xludg dahd par n ura dividd by al ligan ara. Th auhr aud n rughn parar a a rprnaiv high dl prpd a pull-u dl dl. Th dl dl an drib ipran ap hih appard TSD pin ih plag j. INTOODUCTION. Cnr--nr raial ura Evry nr ruur ha viably nr-nr raial ura uh a plag j ag addial nr r rpair rrn. In day hadg ard raal ruural dign nial nru r ar lag nd r akg nhann adh prran pibl hrugh pl undrg adh hani hih i a pi hi papr..2 Prviu udi Thr ar any liraur ha udid ay nhang rngh plag j xprinally bgng a vry arly da (Kkubu 95). Th n rul i pild r niug any rul r plag nr rrig xig nr ruur (AI 29). Thugh knldg abu praial ran r nr ra i prvailg undanal knldg abu bai hani nr--nr ra i lil. Th auhr hav bn ndug bai udi ra nr hially hanially (Sah al a 28b). On rul i ha axiu high raurd ura ha an ia rla ih raurd ara ura xludg dahd par (Sah.al. 28b). Th hani prdug rla i parabl n bn high ui xn ara una. A i knn r ar yp ura rughn parar aurabl ih auad quipn r han axiu high (IS B 6 2). lahip bn rughn parar hanial prran ra i n knn ar..3 Purp rarh Thi papr u n grag knldg ura rughn nr--nr raial ura ih hanial prpri ahivd by TSD (n ng diagra) plyg la analyi quipn. 2 EXPEIMENT 2. Spin Th auhr prpard igh yp pin ih varid yp plag j ad r dirn rughng r urd ih dirn ld n. Al hr yp nlihi pin ih a varid iz axiu aggrga r ad r a rrn. Tabl h aribu pin Tabl 2 ix prpr nr. Th nubr pin a hr r ah a hih hav a by a lngh 4. Ar 24 hur r a nr hal par ld j ura a rughnd a. Thn nr a a rad hal ld a d-
2 = D ( hfigur T ) h. Th pin r urd apid () r a 2ºC r 28 day ar al a nr. 5 dph nh a id a ThA prpraliy i D(hT) i nr alld pin br raur ughn. iur prabiliy i i a nnlar un rlaiv huidiy h praur T (Bažan Tabl. Aribu pin. & Najjar 972).Th iur a balan rquir ha varia i ar a pr uni vlu nr (ar nn ) b qual divrgn iur lux = (2) (3) hr / h i lp rp/drp ir (al alld iur apaiy). Th gvrng qua (EquaCa3)arard u b pld Ca prviuly by apprpria bundary iial ndi. Th. rla bn aun vaprabl Figur Typial dail pin (p) hd r prdug (b). ar pin rlaiv huidiy i alld adrp ir i aurd ih rag rlaiviy huidiy ng drp ir ppi 2.2 Tn diagra a. Nglg ir dirn (Xi al. 994) Fraur ughn a xudill ih llg rp ir b brvg ud ih ILEM 985). Lad rrn rnda bh rp (ILEM drp ndi. rakay uh png diplan By i hyri (CMOD) iur r aurd ladg. T ir uld nuuly b akn durg aun dirn anl dad igh pin ba rla vaprabl ar v rlaiv huidiy ua gd ardg pri aurn a unr b ud ign variaigh ad l a glud ah nd rlaiviy huidiy. Tha hap pin. rp Srv yprladg ud parar g highir HPC iquipn lunda by any pd rpn ih hlp d-bak y pially h ha lun xn ra quipn. hial ra urn dr pr TSD a lad-cmod urv ruur ahivd pr izr diribu (ar--n pin ih plyg uli-lar apprxiarai n hial pi SF nn hih a praur ardizdix by addiiv CI (CI urghd i hd 24). nrgy variu i nud nrgy an durg.). InFraur liraur rula b raur a ligan diplayd ara und drib rp ir a an nral nld y-axihvr TSD prn graph nr ih (Xi x-axi al. 994). hih i abbrviad a F. Th i n npapr i-pirial xpr prpd by g iial Mjrnll r hih i ia a nil rnghi Nrlg (997) adpd bau Prdg FraMCS-7 May Th ar nn an b xprd a u vaprabl ar (apillary ar ar vapr adrbd ar) nn-vaprabl (hially bund) ar n (Mill 966 Panazpul & Mill 995). I i ranabl au haprpr vaprabl ar i a un Tabl 2. Mix nr. rlaiv huidiy h dgr hydra dgr ilia u ra i.. =(h) = ag-dpndn rp/drp ir (Nrlg Mjnll 997). Undr hi aup by ubiug Equa Equa 2 n ba L=4 h h= Ligan & + & + (Tran Dh h) = &=5 + n h ura Nh xpliily r hn vlu hydra Wr iaun a rak idh lad b zr rarak idh). SF nn. Thi rp ir (riial rad 2.3 Obrva ih analyzg quipn Ar raur ughn raurd ara liga (h a ) = ( ) + n brvd d harar ra. (g )h a ba ir ura raurd ligan (4) rvd ih lar 3-D aurg ah a lv )h 2 dpi (g Figur l rval; K2µ µ. ( ) ra ypial xapl parar rughn IS B aurd 3-D daa hih a ardizd by 6 (IS B 6 2). Fr aurn hr hr lngh ir (Lr) ra(gl ir) rprn rrn (r 2µ rval) phyially (adrbd)ar nd r 5 (rbund µ rval) daa r prd ir) rprn apillary ar hr(apillary ndi hr u valu avar. Thi xpr i valid nly r l nn lngh (λ) ar Th rprnih aun SF. Thparar i valuad rughn r an abvar pr uni vluavlngh hld hr gl pra % nd ra av rlaivdu huidiy i a an xludd. b xprd high undula (Fig.(Nrlg 2) Th Mjrnll 997) a undula i lng av hih xd ra avlngh. auhr u a apl quar r (5) ( ) = k + k Th ah vg pin. vg Ar plau parg ura n i SEM (anng lrn irp) brva parar. apl afr plad kin ar arial hra kvgdn. vg addi dgi bn lid gla r. Quaniaiv axiu aun ar pr uni vlu ha an analyi Ca apillary Si r pr dn ihgl ug EPMA ill all pr (bh pr) n (Elrn prb a nanalyzr). ba an alula Kir K ( ) = g h g h (6) Th arial parar kvg kvg g an b alibrad by ig xprinal daa rlvan r (vaprabl) ar nn nr a variu ag (Di Luzi & Cuai 29b). Figur 2. Typial rughn parar ura. 2.2 Tpraur vlu 8.ha a arly ag hial ra N 7. aiad ih n hydra N-3 SF ra - ar 6. xri praur ild i -3 n unir FS r 5. nn-adiabai y vn i nvirnnal SP- an b praur i nan. Ha ndu dribd nr a la r praur n 3. xdg C (Bažan & Kaplan 996) by Furir 2. la hih rad ) a P M ( r r u l C q.. = λ T (7).8. hr q i.2 ha.4lux.6 T icrak ablu idh () praur λ i ha nduiviy; Figur 3. Tn ng diagra pin. hi
3 Tabl 3. Mhanial prpri pin. lund by ndi = D ( h T ) hran j. Th par raurd ligan r laiid iv yp hih Th ar r prpraliy (A) (E) i Tabl 4. D(hT) Typ (A) i la iur ura prabiliy dahd par i i lik a nnla ura pin-. rlaiv Typ huidiy (B) i h raial praur ran zn (ITZ) & Najjar n ura 972). Th aggrga. iur Typ a balan (C) i dahd par ha pin varia plag i j r ar a han pin-. Typ vlu (D) i nr raurd (ar ura nn xlud-g ITZ j pin divrgn (E) i iur ha nlihi lux b q n. Th daa Tabl 4 ar avrag valu aurd a µ rval ih lar 3-D aurg ah. = 3 ESULTS 3. uld hanial prpri Figur 3 Tabl 3 h ahivd TSD hanial prpri pin rpivly. Th ruld F ar rangg r.2n/ (pin ).5 N/ (pin ) ih a rrn rul.n/ r pin N. Cpriv rngh i 42.7 MPa. 3.2 ughn parar Th auhr laiid ura raurd ligan yp ar raur ughn. On i a raurd par r i a dahd par hih ar dribd blak par hi par Figur 4 rpivly. Th raurd par a hararizd by xpd aggrga r rugh par hr high i grar han.2. Figur 5 h diribu high n raurd ura a nr ligan hih r aurd a 2 µ rval ih lar 3-D aurg ah. Figur 6 rprn rlahip bn P hr i a rai raurd par xludg dahd par n ura dividd by al ligan ara P i axiu high n raurd ura ih aurd rg. Th graph ll ha r i a rrla bn P. W an al brv ha valu i dirn r ah r Th ar nn an b xprd a vaprabl ar (apillary a vapr adrbd ar) nn- (hially bund) ar n (Mil (a) Spin (b) Spin SP Panazpul & Mill 995). I i ra Figur 4. Sapl laiid ligan raurd par (blak) dahd au n (hi). ha vaprabl ar i a u rlaiv huidiy h dgr hydra dgr ilia u ra i.. = = ag-dpndn rp/drp (Nrlg Mjnll 997). Undr hi au by ubiug Equa N-3 Equai ba h = h h -3 SP- -3 & + & + Figur 5. Diribu high n raurd ura. hr / h i lp rp/ ) 8. ir (al alld iur apa ( gvrng qua (Equa N 3) u b P N95 6. by apprpria bundary iial ndii N236 Th rla bn aun ar rlaiv huidiy 4. E i alld ir i aurd ih rag huidiy drp SPir h 2. a. Nglg ir dirn PW (Xi al. llg rp ir ill b FS rrn bh rp drp..2 By.4.6 ay.8 i. hyri Figur 6. lahip ir bn uld P. b akn aun rla vaprabl ar v rlaiv hui b ud ardg ign varia Tabl 4. Faur rughn parar ypially laiid ura. rlaiviy huidiy. Th hap ir r HPC i lund by any p pially h ha lun xn hial ra urn dr ruur pr iz diribu (arrai n hial pi SF urg i hd praur ix.). In liraur variu rulai und drib rp ir nr (Xi al. 994). Hvr h papr i-pirial xpr pr Nrlg Mjrnll (997) i adpd b Prdg FraMCS-7 May
4 = In D ( Tabl h T ) 4 h n an naurally raliz ha () avrag high () n dahd par ((A) - (C)) i lr Th han prpraliy n n raurd i par D(hT) ((D) (E)). i alld I i rhy iur prabiliy n ha vn i i a a nnlar (A) hih un i ura rlaiv j huidiy ad h ih praur h gla T ld (Bažan i & nidrd Najjar 972). b Th al iur la a rughn balan rquir () i 6.3µ ha (rrn varia lngh i i.25). ar a pr uni vlu Th valu nr B/C r (ar nn z ) b abl qual i abu.5 divrgn ( a ha iur λ.25 lux.8) llg ha rughn i.5 i largr a (B) han n a (C) vn r a = dahd par. I ay ugg ha par (2) (B) hih i ITZ arund ar aggrga an nribu Th ar nn hanial an prran b xprd vn a highr u han par vaprabl (C). Thn ar dahd par (C) ay b (apillary ar ar r vapr han adrbd ITZ hr ar) ui nn-vaprabl adh ay hav (hially urrd. bund) ar n (Mill 966 Panazpul On r & h Mill i 995). par I i ranabl rughn parar au ha bh vaprabl raurd ar par (D) i a un (E) an rlaiv ha huidiy h z dgr ar al hydra a a valu dgr E/D ilia i al u ra. all a λ (r i.. = (h ).25 = ag-dpndn 2.5). Thi rp/drp a i ipran bau ir i i (Nrlg rlad Mjnll prviu 997). Undr udy (Sah hi aup. al. 28b) hih by ubiug ld ha raurd Equa par Equa ligan 2 nribud n ba raur nrgy (F) a a ra a nlihi n rgardl j yp. Inrg dg i ha hil z bh dahd h raurd par ar gg largr = & + & + & n (3) alng h ih λ h ndny grg ra ar dirn. I an ha grg ra ( all a λ) r dahd par i abu 2. hr / h i lp rp/drp hra n r raurd par i vr 5. uggg undula i dan a ir (al alld iur apaiy). Th gvrng qua (Equa 3) u b pld raurd by apprpria par pard bundary iial dahd ndi. par. Th rla bn aun vaprabl 3.3 ar Obrva rlaiv by huidiy SEM i EPMA alld adrp ir i aurd ih rag rlaiviy Figur 7(a) h SEM ph a apl r huidiy drp ir ppi pin-n hr n an brv a rugh ura a. any Nglg aggrga ir dirn hal-bddd (Xi al. 994) i. In a llg pin- rp (Fig. ir 7(b)) n ill an b ud brv ih h rrn bran bh rp aly ad drp Ca(OH) ndi. 2. By Figur ay 8 dpi i Ca/Si hyri ap hih iur auhr pd ir uld r analyzg b akn aun dirn dirn pha r rla niun vaprabl nr ar (Sah v rlaiv. al. huidiy 28a). u Th ap b ud h ardg hr lr ign rprng varia gradd a rlaiviy rai huidiy. Ca dividd Th by hap Si r rul rp quaniaiv ir r analyi HPC lund Ca by Si any ih parar EPMA. In pially ap gray h zn ha rprn lun CSH xn gl hr ra rai hial i bn ra. 3. blak urn zn dr rprn pr Ca(OH) 2 hr rai i vr 3. hi zn ruur pr iz diribu (ar--n rprn aggrga aly ni SiO 2 r priy rai hr n hial rai i bl pi.. SF nn urg In Figur i 8 hd an d praur pii diribu ix addiiv Ca(OH).). In 2. Th liraur dahd variu par rula pin-a - an ha b hik und blak drib layr ang rp ha ir n ar nral ad nr Ca(OH) (Xi 2. Fraurd al. 994). ura Hvr pin- prn ha n uh papr blak layr i-pirial hugh Ca/Si xpr i high arund prpd by aggrga Nrlg Mjrnll Figur (997) 8(). In i hi adpd ap al bau all i xpliily par an aun b aud r b vlu CSH gl bau hydra gray ra zn i abundan SF nn. llg Thi rp rughg. ir I rad an b aid ha Ca/Si ap rval ak layr Ca(OH)2 hih play a priary rl n rak pah. ( h ) = ( ) + ( g ) h ( g ) h K ( ) hr ir r (gl ir) rprn phyially (a) bund Fraurd (adrbd) ura ar pin-n nd r (apillary ir) rprn apillary ar. Thi xpr i valid nly r l nn SF. Th i rprn aun ar pr uni vlu hld gl pr a % rlaiv huidiy i an b xprd (Nrlg Mjrnll 997) a ( ) = k + k vg vg (4) (5) (b) Dahd ura pin- Figur hr 7. ksem Obrva n ura. vg k vg ar arial parar. Fr axiu aun ar pr uni vlu ha an ill all pr (bh apillary pr gl pr) n an alula K a n ba K ( ) = g h g h (6) (a) pin-a (b) pin- () pin- Figur Th 8. arial Ca/Si ap parar r id k vg ra. k vg g an b alibrad by ig xprinal daa rlvan r (vaprabl) ar nn nr a 4 variu DISCUSSION ag (Di Luzi & Cuai 29b) Inlun Tpraur vlu aggrga n raurd ura Th N auhr ha a prp arly ag a dl dpid hial Figur ra 9 hr aiad ih aggrga n ar hydra aud SF b ra phr h ar xri diar i l praur (l i liknd ild i ibr n unir lngh) bad r nn-adiabai n SEM y ph (Fig. vn 7(a)). i nvirnnal praur ivn r i i nan. h Ha layr ndu n an pa b arund dribd aggrga nr by a all a la r aggrga praur ar dld n xdg l a C a (Bažan rval. & Th Kaplan prj 996) lngh by Furir aggrga la hih i aud rad b l/4 hih i analgu avrag ibr lngh ibr rrn ry. q = λ Thn ar raur r appar a raurd T ura ha lk lik n dpid Figur 9. (7) Th r (D) Tabl 4 ll i abu 7 µ hr hn q λ i i 2.5 ha n lux T diar i ablu aggrga praur i alulad λ i b.39 ha nduiviy; i hi b 94µ bad n rlahip dpid Figur Prdg FraMCS-7 May
5 9. Thi rul (94µ) i diu valu z Tabl 4. Th a rlahip i brvd hn λ i.8 (hr i 22µ) iz aggrga i alulad b.2 i b 6µ hih ar n valu ih dl prdid Figur 9. Mrvr vn hn λ i.25 hih i vry all rg pard rdarily iagd aggrga iz ny dl i rgnizd; i.. a i 6µ aggrga iz i 4µ n i 8µ. Thugh an all aggrga (abu µ r allr) Figur 7 dl i n ih a ra rg.. Fr aggrga iz ix prpr ud udy nubr aggrga an b alulad. Th nubr aggrga a ra vlu hr n pi axiu iz aggrga (2) upi ar va (6p. r.6 23p. r.3 p. r.5 bl.5). Th nubr ar ralii r brva Figur 7 Figur 8. A ura rughn i dply rlad hanial prran (Sah. al. 28b) ipran vry all-izd aggrga huld b phaizd. On nrary a dahd par ITZ dpndny rughn n λ i n lar. Fr xapl (A) (C) Tabl 4 i allr hn λ i 2.5 han hn λ i.25. Th alulad aggrga iz i 4µ r allr n dahd ura bad n a dl dpid Figur 9. Th all aggrga ay n b aggrga bu kd ixur Ca(OH) 2 aggrga r brva Figur 8(b). Figur 9. Mdl r drg rla bn aggrga iz rughn parar. 4.2 Pull-u dl dl Th abv nd dl an b aily vlvd nil dl dl hih auhr prpd liraur (Sah. al. 29). In hi dl xrag r aga rak prpaga ar rakg i nly ad by any iz aggrga. Th aggrga a a dl hih hav dirn lngh. Br rakg nil rngh ra i drd by rai pi Ca(OH) 2 CSH. (Fig. 8) In Figur a hr ibr (dl) i a dl a givn iz aggrga. Aug ha xrag r = D ( dl h T ) ll h ibr rrn ry hih Naaan prpd (Naaan 989) llg Equa Th prpraliy ar lad. Th i Naaan D(hT) Mdl drib iur a rlahip prabiliy bn xrag i i a nnla r xrad diplan rlaiv huidiy r l h ibr praur a ll. & Najjar 972). Th iur a balan ha varia i ar a 2λl ax vlu ( ) nr (ar nn ) b q P = () 2λl λl λ ( V)( divrgn + ) + 2V iur lux λ l Pξ ( ) = = (2) λl λ ( + ) Th ar nn an b xprd a hr P i axiu vaprabl xrag ar r (apillary i a diplan vapr a P V i adrbd rai ar) ara ibr nn- dividd by al (hially ara ax i bund) harg ar r n (Mil pr lngh upprd Panazpul by a dl & Mill ( 995). uliplid I i ra valu τ ax (raial au harg ha r) vaprabl irurn lngh ψ) rlaiv l i huidiy bddd h dgr lngh. Th hydra ar i a u nan λ i drd dgr by ilia xrag u ra rigidiy k i.. = hih i harg = ag-dpndn r pr uni diplan. rp/drp Th Equa () (Nrlg (2) Mjnll ar 997). rul Undr r a gl ibr. Thn by xrag ubiug r Equa r ulipl i- Equai hi au br i dribd ba qua (3). = (3) P A N ( l ) P ( l ) l h h = h hr P(l) i P r givn lngh l N(l) i nubr hr ibr givn / h i lngh lp l. rp/ Th nubr ir dl i (al lkd alld ha iur aggrga hi dl. gvrng Thn i qua vlu (Equa aggrga 3) u b apa ah iz i by a apprpria N(l) i bundary prpral iial ndii valu l -3. Naurally P(l) Th rla i r bn ara aun ibr hih i ar prpral rlaiv huidiy valu l 2. Thn i alld ally P A i prpral ir i valu aurd l -. ih rag Figur 2(a) h huidiy lad-diplan drp ir rlahip dl a. h Nglg lngh ir i l dirn r 2l bad (Xi al. h n abv nd dl. llg In rp igur PMA ir rpr-iln rngh rrn ak arix bh rp PMB i drp b rngh rng By arix. ay A i i diud hyri pr-viu udy (Sah ir al. 29) uld hih b akn i diplayd aun Figur rngh rla vaprabl ra ar v dph rlaiv hui FPZ hav l rlahip. b ud ardg I dph ign FPZ varia arix (A) i hall rlaiviy dph huidiy. raurd Th hap arix nd b hall ir hih r HPC hr i dl lund ar by -anludd. On nrary pially i h dph ha lun FPZ arix xn p (B) i dp dph hial raurd ra arix nd urn b dr dp hih lng ruur dl ar pr ludd. iz diribu Thi dl (arrai rphlgial n aur hial TSD pi a i SF larly h dpid Figur urg 2(b). i Mrvr hd praur dp FPZ ix nd raur id.). rg In liraur arix hih variu ak rulai raur ura und id n drib akg rp larg. ir Th dl al nr xpr (Xi ran al. 994). hy Hvr i rlad nil rngh papr i-pirial TSD. Th ran xpr r i pr h i a ll. Tnil Nrlg rngh Mjrnll (997) i u i adpd b & + & + Prdg FraMCS-7 May
6 = D ( h T )arix h rngh xra r dl.() A a i bh rngh arix lngh dl ar rlad i a diud Th prpraliy D(hT) i abv. alld Thn i rlad nil rngh. iur prabiliy i i a nnlar un rlaiv huidiy h praur T (Bažan & Najjar 972). Th iur a balan rquir ha varia i ar a pr uni vlu nr (ar nn ) b qual divrgn iur lux =. Mdld dl r aggrga. Figur h = h h & + & + &n (2) (3) hr / h i lp rp/drp ir (al alld iur apaiy). Th gvrng qua (Equa 3) u b pld by (a) apprpria bundary iial ndi. Tnil r arix xra dl Th rla bn aunr vaprabl ar rlaiv huidiy i alld adrp ir i aurd ih rag rlaiviy huidiy drp ir ppi a. Nglg ir dirn (Xi al. 994) llg rp ir ill b ud ih rrn bh rp drp ndi. By ay i hyri iur ir uld b akn aun dirn rla vaprabl ar v rlaiv huidiy u b ud ardg ign varia rlaiviy (b)huidiy. Th hap dl rp Cbd r arix Figur 2. lahip bn TSD dl ir r HPC i lund by any dl. parar pially h ha lun xn ra Th dl al drib ran hy aggrhial ra urn dr pr ga lun Wriz diribu TSD. Th ran r i i a ruur pr (ar--n ll. Th rng ra hih ha high rarai n hial pi SF nn ur id rg hr lng dl (larg agurg i hd praur ix addiiv grga) larg riial.). In ar ludd liraur hih variulad rula an b idh TSDhra ra hih und Wr drib rpak ir nral ha l raur narr rg hr hr nr (Xi al. 994). Hvr prn dl (all aggrga) ar ludd hih lad papr i-pirial xpr prpd by all Wr. S rng ra brg bh high i Nrlg Mjrnll (997) i adpd bau Prdg FraMCS-7 May rughn parar (hrlahip ) = ( ) + Th bn hanial prpri (g i)h dpid rughn parar raur ura (4) Figur 3(a)-(). (gwr )P h Figur Th rlahip bn ( ) K iz hih 3(a) rl axiu aggrga Th ar nn an b xprd a u vaprabl ar (apillary ar ar vapr adrbd ar) nn-vaprabl (hially bund) ar n (Mill 966 Panazpul & Mill 995). I i ranabl au ha vaprabl ar i a un rlaiv huidiy h dgr hydra dgr ilia u ra i.. =(h) Figur. Fraur rg rp/drp dph lund by ir rngh = ra ag-dpndn prpry: ak ra (l piur) (Nrlg Mjnll 997). Undr hi auprng n (righ piur). by ubiug Equa Equa 2 n ba xpliily aun r vlu hydra larg Wr gr rulg high raur nra SFFnn. Thi by rp ir rgy F bau i lund bh Wr. rad 4.3 lahip bn hanial prran i naural bau P i lkd lngh dl. A Figur 6 hd P ar lly rhrthi iir (gl bau ir) lad. alr naural P rprn i parabl phyially (adrbd) ar nd high bund una hra i parabl r (apillary rprn apillary rang ir) una. ar. Thi xpr i valid nly r l nn ).25Th i rprn aun SF. ar (r pr uni vlu hld gl pr Na % rlaiv (Nrlg.2 huidiy i an b xprd N95 W N236 Mjrnll 997) a E + k (. ) = k (5) vg vg SP PW.5 hr kvg kvg ar arial parar. Fr FS-3528 axiu. aun ar pr uni vlu ha an.5 ill all pr. (bh 2. apillary 4. pr 6. gl 8. pr) n P () an alula K a n ba (a) lahip bn P Wr g h N + N95.8 N236 (6) K ( ) =.6 g h E i a SP Th arial parar kvg kvg PWg an A.2 b alibrad by ig xprinal daa rlvan r (vaprabl) ar nn nr a.ag (Di Luzi & Cuai 29b). FS-3528 variu Tpraur vlubn (b) lahip. N ha a arly ag hial ra N aiad ra.8 ih n hydra SF N95 ar xri praur ild i nn236 unir r nn-adiabai y vn i nvirnnal.6 praur i nan. Ha ndue an b.4 nr a la r praur SP n dribd PW by xdg C (Bažan & Kaplan 996) A.2 Furir la hih rad F i a =. λ T. FS-3528 (7). hr q i() lahip ha bn lux T i F ablu Figur 3. lahip bn rughn parar praur λ i ha nduiviy; hi hanial prpry. q
7 Ar all i lly rlad P. I i urly uppd ha P i lly rlad z r ll knn a ha nr ha a naur raal hararii n i raurd ura (Mihahi 993). Thn ur parar ( P z) hav a r: i.. dl a. Figur 3(b) rprn rlahip bn hih h ha i baially drd by. Bu vn dahd par prdu hih riga r hial adh hih prdu pin- h i zr. A F i nld ara ih TSD x-axi y-axi n F i rngly ad by Wr. S ally F ar prpral a Figur 3() h. Thn i gr F al gr. 5 CONCLUSIONS Th auhr ndud raur hani igh dirn yp nr pri hih hav a vrial plag j hr yp nlihi n hih hav dirn iz aggrga. Th dg ar a ll.. Thr ar hr ypial valu rughn parar r raurd par dahd par raial rani zn. 2. Dl dl a prpd hih an b ud diu rlahip bn rughn parar rphlgial aur TSD. 3. Th hani hih gvrn rlahip bn rughn parar ( z P) hanial prpri ( F Wr) i rvald. ACKNOWLEDEMENTS Thi udy a anially upprd by ran-aid r SPS ll (ran N r DC-) by SPS hih auhr graully aknldg. EFEENCES = ) D ( h T h AI. 29. apan arhiural ard piia rd nr rk ASS 5. Tky: AI. Th prpraliy i D(hT) CI. 24. T hd iur r raur prabiliy nrgy pla i nr i a nnla (Dra). In Izui I. (d.) rlaiv CI ard. huidiy Tky: h CI. praur IS B rial & Najjar Prdu 972). Th Spiia iur (PS) a - balan Sura xur: ha Pril hd- varia Tr i di ar a ura xur parar. vlu Tky: nr IS. (ar nn ) b q Kkubu M. 95. A udy n plag j bn ld divrgn iur lux n nr. Tran. SCE: Mihahi H. Uka S. & Miura S Fundanal udy n analyi raurd ura niiu arial. = Tran. AI: Naaan A.E. Naur. Naj H. & Alan Bnd Mhani Fibr rd Cn Bad Cpi pr N. UMCE Th 89-9 ar Ann nn Arbr: Dp. an Civil b Eng. xprd a Univ. Mih. vaprabl ar (apillary a ILEM Dra vapr nda adrbd Dra ar) nn- Fraur Enrgy (hially Mrar bund) Cnr by ar Man n (Mil Thr-p bnd Panazpul T n Nhd & Ba. Mill Ma. 995). & Sru.: I i ra 8(6) au ha vaprabl ar i a u Sah A. Yaada K. & Ihiyaa S. 27. A Diu n Tn Sng rlaiv Chararii huidiy Fraur h dgr Pr hydra Cnr Pri ih dgr a Vrial ilia Plag u. ra Pr. AI Thku hap.: = ag-dpndn rp/drp i.. = Sah A. Yaada (Nrlg K. & Ihiyaa Mjnll S. 28a. 997). Fragraphi Undr hi au Diu n Vrial Cnru Ca ih Fr by ubiug Equa Equai Dirn Marial Cnr Pri. Pr. AI Thku hap.: 7-8. ba Sah A. Yaada K. & Ihiyaa S. 28b. A Diu n Fraur Enrgy Vrial Cnr. Pr. 7 Eur. Cn. Fra.: h = & + & + Sah A. Yaada K. & hihiyaa S. 29. h Diu n r- lahip bn rngh duiliy ra b- n n ld nr plyg n-ngdiagra pull-u hr dl / h dl. i Tran. lp AI: 74(637) rp/ ir (al alld iur apa gvrng qua (Equa 3) u b by apprpria bundary iial ndii Th rla bn aun ar rlaiv huidiy i alld ir i aurd ih rag huidiy drp ir h a. Nglg ir dirn (Xi al. llg rp ir ill b rrn bh rp drp By ay i hyri ir uld b akn aun rla vaprabl ar v rlaiv hui b ud ardg ign varia rlaiviy huidiy. Th hap ir r HPC i lund by any p pially h ha lun xn hial ra urn dr ruur pr iz diribu (arrai n hial pi SF urg i hd praur ix.). In liraur variu rulai und drib rp ir nr (Xi al. 994). Hvr h papr i-pirial xpr pr Nrlg Mjrnll (997) i adpd b Prdg FraMCS-7 May
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