Australian Journal of Basic and Applid Scincs, 5(12): 2761-2767, 211 ISSN 1991-8178 hrmal and Structural Analysis of Rollr Compactd Concrt (R.C.C) Dams by Finit Elmnt Cod 1 Rahimi, A. and Noorzai, J. 1 Instructor, Dpartmnt of Watr Scinc Enginring, Sanandaj Branch, Islamic Azad Univrsity, Sanandaj, Iran. 2 Associat Profssor, Dpartmnt of Civil Enginring, Univrsiti Putra Malaysia. Abstract: h prsnt invstigation dals with th finit lmnt formulation of th fild problm with rspct to valuation of th hat gnratd in th body of th dam during and aftr construction of th rollr compactd concrt dams. So, a two dimnsional finit lmnt cod has bn dvlopd for prdicting th tmpratur and strsss in rollr compactd, concrt dam. Finally th application of this softwar has bn illustratd by thrmal and structural analysis of a rollr compact concrt dam. Ky words: Rollr compactd concrt dam, hrmal modling, Finit lmnt formulation. INRODUCION h largst volumtric chang in rollr compactd concrt dams rsults from th chang in tmpratur. h rat of chang in tmpratur is du to cmnt hydration, which introducs tmpratur gradints in th rollr compactd concrt dam body. In th strss analysis of a rollr compactd concrt dam, th valuation of strss is considrd to b mor complx than normal gravity dam. his is du to fact that in th rollr compactd concrt dam thr is a tndncy to construct th dam without joints and mostly continuously. Hnc, thrmal loading is of major concrn sinc th dam must carry th inducd strss causd by a constantly changing tmpratur during th construction phas and th following cooling priod. h two- dimnsional analysis of concrt gravity dams during its construction phas was analyzd Araujo t al., (1998) by using th finit lmnt mthod. Satta t al. (1995) prsntd th strss-strain analysis of concrt structurs xposd to tim and spac variabl thrmal loads by using th finit lmnt tchniqu. Also, for th thrmal analysis of mass concrt with finit lmnt mthod, Ishikawa, (1991) suggst th considration of th following two conditions: 1. h valu of th lastic modulus of concrt should tim dpndnt. 2. Finit lmnts should b addd according th casting schdul of concrt. h aim of this rsarch was to valuation of application and dvlopmnt of finit (limitations) lmnt softwar for tmpratur distribution in rollr compactd concrt dams. Finit Elmnt Formulation im Dpndnt Hat Problms: h bi dimnsional hat transfr problm is govrnd by th diffrntial quation (Fourir s law): ( k x ) ( k x ) Q c (1) x x y y t =mpratur at tim t and x, y coordinats k x & k y = hrmal conductivity for th x and y dirctions c=spcific hat cofficint, = Spcific mass Q=Hat sourc (rat of intrnal hat gnration du to hydration raction of cmnt) In th finit lmnt mthod th tmpratur valus at th nods ar xprssd as: [ N ] { } (2) [N] = Shap functions {} = mpratur vctors Corrsponding Author: Rahimi, A., Instructor, Dpartmnt. of Watr Scinc Enginring, Sanandaj Branch, Islamic Azad Univrsity, Sanandaj, Iran. E-mail: abobakrr@hotmail.com, a.rahimi@iausdj.ac.ir 2761
h gnral procdur for analyzing Eq. (1) is to valuat th Galrkin rsidual intgral with rspct to th spac coordinats for a fixd instant of tim.h Galrkin rsidual intgral is in th form of Sgrlind (1984): 2 2 { R} [ N] ( kx k ) [ ] [ ] 2 y d 2 c N d N Qd (3) x y t Intgrating by parts th first trm of Eq. (3) using Fouris s law for hat transfr by conduction and using Eq. (2), th following systm of linar diffrntial quations ar obtaind: [ c ]{ } [ k t ]{ } { F t } (4) t Whr [ c ] is usually calld th capacitanc matrix which is xprssd as: [ c ] c [ N ] [ N ] d (4-a) and [ k t ] [ k k ] [ k m ] (4-b) Whr [ k k ] is stiffnss matrix for fild problms and [ k m ] is boundary stiffnss matrix for fild problms? [ k ] [ B ] [ D ][ B ] d (4-c) k kx [ D] ky [ N ] [ B] x [ N ] y [ k m ] u h [ N ] [ N ] du (4-d) (h) is thrmal convction, and { F t } { } { F } { F s } (4-) F Is th lmnt forc vctor and { F } is th lmnt forc vctor in boundary condition s { F } Q [ N ] d (4-f) { Fs } u nv h [ N ] du (4-g) nv Is th tmpratur of th surrounding nvironmnt? Equation (4) can b intgratd in tim by using and algorithm in gnraliz finit diffrnc mthod which lads to Sgrlind (1984): [ c] t [ k ] { } [ c] (1 ) t [ k ] t b t((1 ){ Ft } a { Ft } b ) { } b and { F t } b ar {} and { F t } { } a, { F t } a ar {} { F t } at tim a. 1 and is a scalar at tim b { } a (5) 2762
Araujo (1998) indicats that it is convnint to tak 1 in ordr to avoid spurious oscillations. hn it taks following form: ([ c ] t [ k t ] ) { } b [ c ]{ } a t { F t } b (6) 3. hrmal ransint and Strss Strain Analysis: o valuat th strss - strain stat and th displacmnt fild Du to any distribution loads, som hypothss can b assumd Zinkiwicz and aylor, (1991): Uncoupld tmpratur and strss fild. Infinitsimal strains and displacmnts. Linar lastic bhavior of matrial. h first assumption allows solving at a fixd tim th thrmal transint, thn onc th tmpratur fild is known, th strss-strain stat can b stimatd.as soon as th tmpratur associativ distribution in concrt mass is known at vry tim t, th rsulting tnsion ij within concrt can b asily obtaind through th hypothsis of th matrial s linar lastic bhavior.ij is convrtd into quivalnt nodal thrmal forcs Own and Hinton (1984). h tmpratur that appars rapidly in ach lifts about 3 days aftr concrt casting has bn assumd to b th initial tmpratur valu Satta t al., (1995). Also a simulation formula is xprssd by Zhu, t al. (1999): p r f (7) p is placing tmpratur of concrt, r is tmpratur ris du to hat of hydration f is th final stabl tmpratur of th dam p + r rprsnts th maximum tmpratur of concrt, which th strss lvl is zro. h linar lastic bhavior of matrial can b dscribd as: { } [ D ]{ } (8) {} is strain du to thrmal xpansion, xprssd by Satta t al., (1995): { } (1 ) ({ } { }) (9) is tmpratur in corrspondnc with thrmal strain lvl zro and is cofficint of thrmal xpansion. [D] is lasticity matrix which dpnds up typ of problms (Zinkiwicz, O.C., 1983). Howvr, whil gnrating th [D], th lasticity young s modulus of concrt at ag t ( E t ) is xprssd as tim dpndnt (Dungar, R. and Kahir, 1988): E E t t E E.44 ( ) max t max t for th for th t t t t and (1) E is maximum lasticity and t max is th tim at days (i.. whn t is days). 4. Dvlopmnt Of Finit Elmnt Softwar For mpratur Analysis: Basd on th abov tmpratur formulation, a two dimnsional finit lmnt cod has bn writtn and its validity has bn vrifid against som standard bnch mark problms, Noorzai t al. (21). h softwar consists of two main blocks namly: Hmastr Block: his blocks valuats th tmpratur distribution at diffrnt stag of construction. h dtail computational stratgis ar prsntd ls whr, Noorzai, (21). 2763
Strmastr Block: In this block, th thrmal distribution in th body of th dam convrtd in to quivalnt nodal forc. hn usual strss- strain analysis of th problms has bn workd out. hs two blocks along with major subroutin ar shown in Fig1. MAIN GDAAA LDAA SIFM FRON SRS S R M A S R H M A S R INPU SIFPS GLOBAL FRON Fig. 1: Flow Chart of Finit Elmnt Cod for hrmal and Structural Analysis in R.C.C Dams. Analyzd R.C.C Dam: Problm Dfinition: his dam is supposd to b constructd in th provinc of Baluchistan, southrn ast part of Iran, whil th matrial proprtis ar prsntd in tabl1. abl 1: mpratur and matrial proprtis of R.C.C, mass concrt and rock ground. Matrial Hat Conduction Hat Convction Spcific Hat Elasticity Modulus Poisson Ratio Coff. Kcal/marc Coff. Kcal/m^2 hr c Kcal/Kg /m^2 Rock Ground 2.3.3.6E+6.3 Mass Concrt 2.4.3 2.3E+6.3 R.C.C Concrt 2.4.3 1.65E+6.3 h concrt is cast in 5 cm thick horizontal lifts, ach layr bing placd in 3 days. In th Fig 2 was showd that th finit lmnt modl of th complt dam sction undr plan strain condition, four nods isoprimtric typ, with on dgr frdom at ach nod for tmpratur analysis and two dgr frdom pr nod for thrmal strss - strain analysis has bn considrd. Fig. 2: Finit Elmnt Modling of th Dam - Foundation Systm otal numbr of lmnts = 2372; otal numbr of nods = 2546. Paramtrs Involvd: Clarification Proprty of Concrt: h clarification proprty of concrt (hydration) can b dscribd as th following quation of Ishikawa, (1991): max (1 Exp ( t )) (11) Whr is th tmpratur of concrt undr an adiabatic condition, max is th maximum tmpratur of concrt undr an adiabatic condition, is a paramtr which prsnts a hat gnration rat and t is tim (hr) in th prsnt study, max = 17 c, and =.138 is adoptd for this simulation purpos (Dungar, t al., 1988). 2764
mpratur(c) h=.m 25. 15.. 7. mpratur(c) 45. 35. 25. 15. h=4.m. 7. mpratur(c) h=8.m. 7. mpratur(c) 46. h=m 34. 28. 22. 16. 8. 18. 28. 38. 48. 58. mpratur(c) 64. 56. 48. 32. 24. 16. h=28.m 15. 25. 35. 45. mpratur(c) h=34.m 12. 18. 24. 36. 42. 48. mpratur(c) h=36.m 15. 25. 35. mpratur(c) h=39.5m 15. 25. 35. Fig. 3: mpratur distribution at lift no11. Initial mpratur Of Rock Ground: Bfor calculating th tmpratur of concrt, w must know th tmpratur distribution in th rock ground just bfor th start of th casting of th concrt. It may b difficult to masur th tmpratur within th rock mdia. Usually th tmpratur distribution with in rock is obtaind through calculation. As a mthod to calculat, it is assumd that th initial tmpratur of all nods corrsponding to th rock ground is th sam (27.6 C). Changing th atmosphric tmpratur for two yars with incrmnt of 48 hours (total 365 incrmnts) obsrvd data, thn th hat transfr is analyzd btwn th atmosphric tmpratur and th rock ground. RESULS AND DISCUSSION mpratur Prdiction: o study tmpratur distribution in th dam body,15 stags of construction hav bn considrd.h schdul of construction phas of th dam with rspct to No. of lifts, hight of th dam,thicknss of ach lift and tim (in days) plannd by th consultant for th construction of ach lift is prsntd in Fig. 4. h rspons of th dam is valuatd for15 stag of construction. Du to spac limitation only final stag of construction ar discussd hr. Figur 3 illustrat h tmpratur variation at diffrnt hight at lift No.11 of th dam.it is obvious from ths plots that thr is drop in tmpratur at both D/S and U/S facs of th dam du to ffct of atmosphric tmpratur,whil th intrior portion coold at lowr rat. Morovr th ffct of gallry in rducing th tmpratur is clarly shown in th abov plot (h=4m). 2765
Hight of th dam 7 6 5 4 3 2 1 Fig. 4: Construction Phas of th dam. Hight of dam(m) 1 2 3 4 5 6 7 8 9 1 11 12 13 14 15 No.of stag im at nd of lift(day) 8 7 6 5 4 3 2 im at nd of lift Structural Analysis: In prsnt study, mainly th bhavior of th R.C.C dams during construction stag has bn considrd. h structural rspons of th dam for th lift No. 15 of construction stag has bn discussd by applying th dad wight plus thrmal loads. h tmpratur of all th nodal points with rspct to tim t has bn dtrmind for a particular lift. Now, basd on th work prsntd by Zhu t al., (1999), th dtrmind by using quation (7). h variation of th principal strsss at th nd of vry lift is valuatd and only for th 15 th stag of construction, in th sction of th dam is plottd in Fig5. hs plots ar mad for h=7.6 and 42.66 mtrs rspctivly. It can b sn from ths plots that in th convntional concrt mostly thr is tnsil strss appars whil th cor undrgos comprssiv strsss.but th comprssiv strsss ar with in thir limit. Principal Strsss 5 45 4 35 3 25 2 15 5-5 - -15-2 -25-3 Maximum Principal strss Minimum Principal strss 2 12 22 32 42 52 h=7.6m Principal Strsss Maximum Principal strss 4 35 Minimum Principal strss 3 25 2 15 5-5 12 17 22 27 32 - -15 h=42.66m -2-25 -3 Fig. 5: Variation of principal strsss (t/m^2) for lift No.15. Conclusion: Finit lmnt softwar for th thrmal and structural analysis in R.C.C dams xposd to tim variabls paramtrs has bn dvlopd. his softwar is a gnralizd two dimnsional finit lmnt cod can prdict th tmpratur distribution in th problms of plan strss, plan strain simulation usual calculatd th strss in th dam body. Disassociating th variation of th thrmal charactristics of concrt with rspct to strss-strain stat of th matrial allows th study of th problm in a simplifid uncoupld way. h proposd numrical procdur for thrmal transint analysis and thrmal strss analysis in th R.C.C gravity dam was shown to b ffctiv and practical in prdiction of th tmpratur lvl by thrmal transints in dam body. Morovr, it is possibl to considr nvironmntal conditions variability in tim, intrnal hat gnration (hydration) and th variability of th gomtry during th analysis.nsil strss appars in th skin of th dam, which is at a lowr tmpratur, whil th cor undrgos comprssiv strsss. ACKNOWLEDGEMENS Currnt study has bn supportd financial through th rsarch projct by Grants No. 222, NRCI, of National Rsarch Projct Schm of Iran, also th support of National Rsarch Council of Islamic Rpublic of Iran. 2766
REFERENCES Araujo, J.M and A.M. Awruch, 1998. Craking safty valuation on gravity concrt dams during th construction phas, Intrnational Journal Computrs and Structurs, 93-14. Dungar, R. and Kahir, 1988. II R.C.C Concrt dam, Motor-Columbus Eng. Inc., unpublishd rport. Ishikawa, M., 1991. hrmal strss analysis of concrt Intrnational Journal of computrs and Structurs, 347-352. Noorzai, J., M. Mhrdadi, J.H. Zargani, 21. hrmal and structural Analysis of R.C.C dams Intrnational Journal of Finit Elmnt in Analysis Dsign. U.S.A. Own, D.R.J. and E. Hinton, 1984. Finit lmnts in plasticity, thory and practic, pin ridg Ltd. Swansa, U.K. Satta, A., R. Scotta, R. Vitalinai, 1995. Strss analysis of concrt structurs subjctd to variabl thrmal loads, Jnl. of Structural Enginring, 446-457. Sgrlind, L.J., 1984. Applid finit lmnt analysis, John Wily and Sons, Nw York. Zhu, B., P. Xu and S. Wang, 1999. hrmal strsss and tmpratur control of R.C.C gravity dams, Jnl. of Hydropowr and Dams., 65-77. Zinkiwicz, O.C. and R.L. aylor, 1991. h finit lmnt mthod, McGraw - Hill, Inc., NwYork. Zinkiwicz, O.C., R.L., 1983. h finit lmnt mthod in Enginring and Scinc, McGraw Hill, Nw Dlhi. 2767