Finite Element Simulation of Prevention Thermal Cracking in Mass Concrete

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1 In. J. of Compung Scence and Mahemacs 1 Fne Elemen Smulaon of Prevenon Thermal Crackng n Mass Concree Junca Xu 1, Zhenzhong Shen 1, Song Yang 2, Xn Xe 3, Zhengyu Yang 3 1. College of Waer Conservancy and Hydropower Engneerng, Hoha Unversy, Nanjng, Chna 2. College of Waer Conservancy, Yunnan Agrculural Unversy, Kunmng, Chna 3. Deparmen of Elecrcal and Compuer Engneerng, Norheasern Unversy, Boson, USA Absrac: Mass concree srucures play a very mporan role n cvl engneerng. The crackng of concree s regarded as one of he bgges engneerng problems. Therefore, s very necessary for he crackng of mass concree o do he conrol analyss. Some facors should be consdered n mass concree crack conrol analyss, manly ncludng he hea releases model of concree, he mechancal model o he concree, he process of emperaure conrol n he ppe model. Dfferenal evoluon algorhm and equvalen algorhm are adoped o solve he coeffcen of adabac emperaure and cool waer effec. In he paper, sress feld calculaon, back analyss calculaons, and coolng ppe processng creae secondary developmen based on he ABAQUS sofware plaform. The second developmen of he code s used o reasonably solve he problem wh one acual aqueduc n hydraulc engneerng. Keywords: mass concree; dfferenal evoluon algorhm; equvalen algorhm; crack conrol Bographcal noes: Junca Xu s senor engneer n Hoha Unversy, Nanjng Cy, Chna. Hs curren research neress nclude nfrasrucure healh monorng and compuaonal mechancs of concree srucures. xujc@hhu.edu.cn Zhenzhong Shen s professor n Hoha Unversy, Nanjng, Chna. Hs curren research neres s hydraulc srucure safey evaluaon. zhzhshen@hhu.edu.cn Song Yang s assocae professor n Yunnan Agrculural Unversy, Kunmng Cy, Chna. Hs curren research neres s cvl engneerng. ysclff007@sna.com Xn Xe receved hs Ph.D. degree a Norheasern Unversy, Boson n Hs research neress are MEMS, Mcro Acuaors, Mcrofludcs, and Self- Assembly. xe.x@husky.neu.edu Zhengyu Yang s a Ph.D. canddae a Norheasern Unversy, Boson. Hs research area s manly on Cloud Compung, SSD FTL Desgn, Flash Resource Managemen, Cachng Sorage Sysem, Deduplcaon, Vrualzaon, VM Mgraon, and Performance Smulaons. yang.zhe@husky.neu.edu Copyrgh 201x Inderscence Enerprses Ld.

2 J. Xu, Z. Shen, S. Yang, X. Xe, Z. Yang 1 Inroducon The hydraulc secor has always been plagued by cracks formed by hermal sress n mass concree consrucon. These cracks are caused by he key echncal problems, whch mus be solved durng mass concree consrucon. Many scenss proposed some dfferen mehods o solve hs problem. P. Fusch proposed he fve-parameer numercal negraon model for concree (P. Fusch e al., 1994). Sprngenschmd R suded he hermal crackng n concree a early ages and provded he prevenon mehod for hs work (Sprngenschmd e al., 1998). Clough menoned he exenson of classcal elemen o solve praccal nonlnear problems assocaed wh creep, crackng closng, hea ransfer ec (Clough e al., 1999). De Schuer used degree of hydraon o smulae he hermal crackng n massve hardenng concree elemens (G. Schuer e al., 2002). Hael J H also proposed one numercal model o predc he hermo-mechancal condons durng hydraon of early-age concree (Hael e al., 2003). Lourenço Valdaed gave one analycal and connuum numercal mehod o esmae he compressve srengh of masonry (Lourenço e al., 2006). Inyeop Chu appled he hermal sress devce for predcon of sresses n mass concree (Inyeop Chu e al., 2013). Sress has been nvesgaed n oher relaed engneerng work (Bofang Z. e al., 1989). Wh he esablshmen of new nverson algorhms, such as dfferenal evoluon, and an colony algorhms, hese algorhms ouperform radonal ones by provdng a faser and more accurae mehod o solve he problem of emperaure conrol back analyss (Prce KV. e al., 1999). Due o he connuous mprovemen of compuer hardware levels and soluon algorhms, s no longer a problem ha he prevous hgh nonlnear consuve calculaon s used on personal compuers. In he presen work, a new mehod, DE (dfferenal evoluon), s nroduced o oban nverson emperaure feld calculaon parameers, based on he calculaon of he emperaure feld hea ransfer heory and he sress feld of sold mechancs. Ths mehod can be used o realze he emperaure and sress couplng calculaon, and smulae he emperaure and sress feld durng he mass concree consrucon perod n ABAQUS plaform o reduce he workloads of exploaon, whch can be appled n praccal engneerng o verfy he feasbly of he skech. Maeral sress has been nvesgaed n oher relaed engneerng work (Xe X. e al., 2014, 2017; Yang C. e al., 2016, 2017; Zhengyu Y. e al., 2016; Jank B. e al., 2017; Jake R. e al., 2014). 2 The calculaon prncple of emperaure feld 2.1 The ransen hea conducon heory Based on he hea balance prncple, he recursve equaons of concree emperaure feld calculaon can be obaned as follows by usng he fne elemen mehod n he spaal doman, and he backward dfference mehod o he me doman, combnng wh he exreme condons of funconal, based on he concree emperaure feld of las momen {T n}, we can derve he emperaure feld of nex me {T n+1}.

3 Fne Elemen Smulaon of Prevenon Thermal Crackng n Mass Concree 1 1 [ H ] [ R] { Tn 1} [ R]{ Tn} { Fn 1} 0 (1) n n where H s hermal conducon marx, R s hermal resdual marx, T n and T n+1 s emperaure marx, s me sep, F n+1 s hermal load. 2.2 Thermodynamc parameers nverson A ceran quany of hea s produced when concree s poured and hydraon reacon occurs. Feedback should also be consdered for he analyss of he coeffcen of adabac emperaure as well as oher coeffcens o oban an accurae readng of he adabac heang model parameers. The amoun of lberaed hea by he concree can be obaned based on he hea release model because of he nverson of he parameers. Dfferenal evoluon algorhm can be adoped n he nverse analyss o oban he beer resuls. The basc dea of he algorhm s relaed o muaon and crossover operaons on he curren populaon o generae anoher populaon and use he selec operaon based on greedy deas selec he wo populaons by one-o-one, o generae he fnal new populaons. Basc operaons nclude muaon, crossover and selecon. The basc sraegy of deal dfferenal evoluonary algorhm s descrbed as follows: 1) Muaon operaon Dfferenal evoluon mehod of paren dfference vecor s known as one of he mos basc varable composons. Each vecor par ncludes wo dfferen ndvduals x x, r1 r2 n a paren group (generaon ). The dfference vecor s defned as: Dr xr x 1,2 1 r2 (2) In he formula, r 1 and r 2 represen he ndex number of ndvduals n he populaon. When he dfferenal vecor s added o anoher random seleced ndvdual vecor, muaon vecor wll be generaed. For each arge vecor x, muaon operaon s: v 1 xr K * xr xr (3) In he formula, r 1, r 2, r3 1,2,..., NP, r 1, r 2, r 3 are dfferen from he curren arge vecor ndex. K s a scalng facor, conrollng he dfferenal vecor scalng, K 0,2. 2) Crossover operaon Crossover operaon s performed o arge vecor ndvdual and he muaon vecor n u populaon, o generae es ndvdual. To ensure he ndvdual x evoluon, frsly, 1 u s conrbued a leas by one o he crossover facor CR equaon s: 1 u 1 v hrough random selecon. For anoher, accordng s conrbued by 1 v or 1 x.the crossover operaon

4 J. Xu, Z. Shen, S. Yang, X. Xe, Z. Yang j j In he equaon, number of varables; CR s he crossover probably consan. 1 v j, rand CR or j randn 1 u, j 1 xj, rand CR or j randn (4) rand j 0,1 s even-dsrbued random number; j represens he rand j 1,2,..., D s randomly seleced n dmenson varable ndex. 3) Selecon operaon Dfferenal evoluon mehod uses greedy search sraegy o es ndvduals generaed by muaon and crossover operaon compee wh 1 u s beer han 1 x, u wll be seleced as offsprng. Oherwse wll reman he offsprng. Lke mnmzng opmzaon, selecon operaon equaon s: u, f u f x x 1 x, f u f x u 1 x, when he fness of x as (5) Dfferenal evoluon mehod uses an approprae muaon, whch s easy and smple o perform. 2.3 Equvalen negave hea source mehod The emperaure range vares beween he nner and ouer concree due o he hea release n he concree and he changes n he exernal envronmen. The dfference n emperaure faclaes he formaon of emperaure sress. A ceran number of waer ppes s usually nsalled o preven he emperaure dfference and o elmnae he emperaure effecs, whch reduce emperaure sress. Waer ppes have a coolng effec on he neror layou of concree. The waer ppe equvalen algorhm could be used o acheve beer coolng performance for smulang mass concree. Based on he coolng effec from he average sense, equvalen negave hea source mehod bulds equvalen hea conducon equaon of ppe coolng effec hrough he hea snk calculaon mehod. The hermal absorbed by he coolng waer hea, per un me s: 0m m p m p m mp m p e e me e e (6) m p where s dabec hermal rse, m s dabec hermal rse coeffcen, p s ppe cool coeffcen and deermne he coolng effec. p can be defned as followng: p k / D (7) 2 k (8) L / c w wqw (9) where D represens he dameer of coolng ppe; L represens he lengh of coolng ppe, c w represens specfc hea of coolng waer; w represens bulk densy of coolng waer; q w represens coolng waer flow.

5 Fne Elemen Smulaon of Prevenon Thermal Crackng n Mass Concree 3 Sress feld calculaon prncple By he physcal equaon, geomerc and equlbrum equaon can be obaned eher a me n he regon R on he fne elemen governng equaons: [ K ]{ } { P G } { P C } { P T } { P S } { P (10) In he formula: } s R n hree drecons of all nodes n he regon of concree; G { P } s he { perod caused by he exernal load equvalen nodal force ncremen. S I s caused by varable emperaure ncremen equvalen nodal force; { } s 0 equvalen nodal force ncremen caused by shrnkage. { P } s auogenous volume deformaon caused by he equvalen nodal force ncremen. To reduce he workloads for exploaon furher, he above model can be based on ABAQUS plaform for he secondary developmen. The Pyhon language s used o conrol he proceedng analyss (Pawucke, 2009). Forran subrounes are appled for he aforemenoned model. 0 } P 4 Thermal parameers nverson examples If here s a concree column, lengh 200m, dameer 0.845m, adabac boundary, he densy of concree s 2410kg/m 3. Specfc hea s 0.868kJ/ (kg. ). Thermal dffusvy s m 2 / h; nal emperaure s 20 ; hermal conducvy s kJ/ (m. d); The rse of adabac emperaure s 24 (1-exp (-0.09τ)). Noce ha when he concree ouer wall s nsulaon, here s a coolng waer ppe n (Fg. 1. Ppe flow s 0.90 m 3 / h. Waer nle waer emperaure s 4. Through he fne elemen calculaon, he relaonshp can be obaned beween emperaure changes over me. A poson s seleced randomly as measurng pon o oban 50 emperaure values a he dfferen me for he measured value. The dfferenal evoluon algorhm s used o nverse he parameers of he rse of he adabac emperaure, and resuls are shown a he able 1: Inverson parameer Inverson resul Fgure 1 Concree column wh waer Table 1 The resuls of hermodynamc parameers nverson Accurae values Relave error Objecve T 0( ) % a % funcon value Ierave mes Compuaonal mes of emperaure

6 J. Xu, Z. Shen, S. Yang, X. Xe, Z. Yang Judgng from he nverson resuls n he able, dfferenal evoluon algorhm can realze concree hermodynamcs parameers nverson mehod, and error can be obaned n he case of he small number of eraons suffcen accuracy. In he above example, when he number of eraons ncreases n he calculaon, he number of eraons s over 15 mes, and relave error of parameers can be reduced o less han 1%. In fg1, shows ha he nverson calculaon s conssen beween emperaure and he measured value. I s proved ha he mehod of dfferenal evoluon algorhm s an effecve mehod. 5 Sluce Engneerng Calculaons 5.1 Overvew One concree sluce s bul on a sol base wh slab - wall "nvered T-shaped" srucure model. Sze of he wall along he flow drecon: lengh 20m, hegh 10m, hckness 2.00m, boom hckness 2m, model s shown n Fgure 2. Fgure 2 Three-dmenson sluce model Slab pourng began on May 1. Afer weny days, hs was compleed, upper wall, he wall pourng sared, whch has las 12 hours. Temperaure Ta cos[ ( ) / 6.0]. For emperaure feld calculaon, he boom and four sdes of he foundaon s nsulaon, bu oher overhead surfaces are hea dsspaon. For sress feld calculaon, he boom of he foundaon s all consraned. Is surroundng s lnked consrans. The hermodynamc parameers of he foundaon par are aken as he same hose of concree s. The emperaure aken for he concree pourng s he ar emperaure plus 3. There are hea convecon flms beween he ouer surface of concree and ar afer concree pourng. When wo dfferen layers combne ogeher, he node of wo elemens e n he conac surface. The calculaon parameers can be seen n Table 2. Table 2 Base plae and he per wh concree hermodynamcs calculaon parameers Parameer Hea conducvy kj/(m h ) Specfc hea kj/(kg ) Expanson coeffcen 1/ Bulk wegh kn/m 3 Adabac emperaure rse Posson rao Base plae (1 e ) Per (1 e ) Elascy modulus GPa (1 e ) (1 e )

7 Fne Elemen Smulaon of Prevenon Thermal Crackng n Mass Concree 5.2 Analyss seps The frs sep s o mesh he model. Snce he model s farly srucured, s easy o make no all hexahedral meshes. The elemens selec DC3D8 o analyze he hermal feld of he model and C3D8R o analyze he sress feld of he model. Durng emperaure conrol calculaon analyss, he sequenal couplng of he sress emperaure s used and mplemened on GPU plaform o accelerae he soluon speed (Du e al., 2015). Frs, he ransen emperaure feld s analyzed, and hen analyzed emperaure feld s mpored no sress feld o do sequenal couplng. The ransen emperaure feld calculaon uses dfferen mesh sze from he mesh sze of he sac sress feld calculaon. In order o oban he precse emperaure feld, we use very fne mesh sze n emperaure analyss. However, we use coarse mesh n sress feld analyss, as here are many analyss seps whch wll consume much me. In hs case, he oal duraon of he ransen emperaure feld analyss s 40 days, and akes 30 analyss seps n he sress feld o analyze varaon and dsrbuon of he sress feld and emperaure n he per pourng process. In he process of concree pourng, he analyss of concree pourng layers s acheved by cell acvang model change, whle TIE acheved he hea ransfer and force of he conac pon beween pourng layers, and beween he casng layer and he rock. The node poson of he conac surface durng bndng mus be conssen wh faclae o reduce he error caused durng he analyss. In he calculaon process, concree hydraon hea s generaed by he subroune. Deals have already descrbed n prevous pars; he program code can be done. The convecve hea exchange s done by sub-program beween he free surface and he ar FILM. In he sress calculaon, a cusomzed consuve UMAT s used for he sress feld calculaons. 5.3 Temperaure feld analyss resuls Based on he fgure 3, he emperaure of concree ncreased n slab casng afer four days. The hghes emperaure reached 37 degrees. A he begnnng of he per casng was he hghes emperaure of 31 degrees. I showed he slab afer reachng he hghes emperaure could gradually become smaller and smaller. The per on he fourh day of he pourng emperaure rose o he hghes pon agan. Ths was due o he per of he hydraon hea generaed afer casng, hen he emperaure feld ended o be a decrease, as he per pourng concree exohermc became slow and connuous hea exchanged wh he envronmen, he emperaure of he per and could gradually close o amben emperaure.

8 J. Xu, Z. Shen, S. Yang, X. Xe, Z. Yang (a)boom pourng Day 1 (b) Boom pourng Day 4 (d) Per pourng Day 1 (e) Per pourng Day 4 Fgure 3 Temperaure feld calculaon conour 5.4 Sress feld analyss resuls In fgure 4, he area n he mddle of he slab and above he slab appeared ensle sress afer he concree slab has been casng four days, whle area a he boom of he slab was compressve sress.

9 Fne Elemen Smulaon of Prevenon Thermal Crackng n Mass Concree (a) Slab pourng day 4, Maxmum sress dsrbuon (b) Slab pourng day 24, Maxmum sress dsrbuon (c) Maxmum sress dsrbuon (10 days afer per pourng) Fgure 4 Sress feld calculaon conour The per afer casng, he ensle sress area became smaller and smaller. However, he maxmum ensle sress n he area ncreased because he elasc modulus of concree ncreased wh he growh of he age as o rsng ensle sress. 6. Concluson Ths sudy ams o develop he massve concree emperaure feld, sress feld calculaon, back analyss calculaons, and coolng ppe processng furher based on he ABAQUS sofware plaform. A complee analyss scheme s esablshed o solve he hermosa problem. The dfferenal evoluon s also nroduced, whch has a srong capably for convergence and robusness. Ths algorhm kno s negraed no he calculaon of mass concree emperaure o deermne he concree emperaure parameers. From he analyss of one concree column and sluce, hs sysem can successfully analyze mass concree emperaure crackng by employng he presened heory. The oher opmzaon mehod also can be aken such as parcle swarm

10 J. Xu, Z. Shen, S. Yang, X. Xe, Z. Yang opmzaon, shuffled frog-leapng algorhm, genec algorhm o solve concree hermal parameer. In he fuure, he much more complcaed consuve model can be adoped o smulae mass concree consrucon. Acknowledgemens Ths research was funded by he Naonal Naural Scence Foundaon of Chna (Gran No ) and he Open Research Fund of he Fundamenal Scence on Radoacve Geology and Exploraon Technology Laboraory (Gran No. RGET1502) and A Projec Funded by he Prory Academc Program Developmen of Jangsu Hgher Educaon Insuons (Gran No.3014-SYS1401). References Fusch, P., Duko, M., Perć, D., & Owen, D. R. J. (1994). On numercal negraon of he fve-parameer model for concree. Compuers & srucures, 53(4), Sprngenschmd, R. (1998). Prevenon of hermal crackng n concree a early ages (Vol. 15). CRC Press. Clough, R. W., & Wlson, E. L. (1999). Early fne elemen research a Berkeley. In Ffh US Naonal Conference on Compuaonal Mechancs (pp. 1-35). De Schuer, G. (2002). Fne elemen smulaon of hermal crackng n massve hardenng concree elemens usng degree of hydraon based maeral laws. Compuers & Srucures, 80(27), Xe, X., e al. (2017). Passvely self-algned assembly of compac barrel hnges for hghperformance, ou-of-plane mems acuaors. IEEE 30h Inernaonal Conference on Mcro Elecro Mechancal Sysems (MEMS), pp Xe, X., e al. (2014). Scalable, MEMS-enabled, vbraonal acle acuaors for hgh resoluon acle dsplays. Journal of Mcromechancs and Mcroengneerng, 24(12), Yang, C., e al., (2016). Compac, planar, ranslaonal pezoelecrc bmorph acuaor wh Archmedes spral acuang ehers. Journal of Mcromechancs and Mcroengneerng, 26(12), Yang, C., e al., & Lvermore, C. (2017). Resealable, ulra-low leak mcro valve usng lqud surface enson sealng for vacuum applcaons. 19h Inernaonal Conference on Sold-Sae Sensors, Acuaors and Mcrosysems, pp Hael JH, e al. (2003). A numercal model for predcng he hermomechancal condons durng hydraon of early-age concree. Appled Mahemacal Modellng. 27(1):1-26. P.B. Lourenço, J. Pna-Henrques. (2006). Valdaon of analycal and connuum numercal mehods for esmang he compressve srengh of masonry. Compuers & Srucures, 2006:84(29), Inyeop Chu, e al. (2013). Applcaon of a hermal sress devce for he predcon of sresses due o hydraon hea n mass concree srucure. Consrucon and Buldng Maerals, 2013:45(1), Prce KV. (1999). An nroducon o dfferenal evoluon. New deas n opmzaon, 1999.

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