Back Analysis of Self-Compacting Concrete Rheological Parameters Based on H-B Model

Transcription

1 Internatonal Conference on Archtectural, Cvl and Hydraulcs Engneerng (ICACHE 2015) Back Analyss of Self-Compactng Concrete Rheologcal Parameters Based on H-B Model Shua Zeng1, a, Janjun Sh1,b, Wenqang Guo1,c 1 School of Urban Constructon,he Unversty of South Chna,HengYang ,Hunan Provnce,Chna a @qq.com, b sjj6621@163.com, c qq.com Keywords: H-B rheologcal model.fresh self-compactng concrete.back analyss. L-box. V-funnel Abstract. he rheologcal parameters of Fresh SCC were examned through the theory of rheology, the rheologcal model of Fresh SCC was assumed to be H-B rheologcal model, the flowng tme of Fresh SCC n the smulated L-box through Fluent, later compared wth the flowng tme of Fresh SCC n the actual L-box, the target functon was establshed accordng to the least square method, three rheologcal parameters τ0, k and n were optmzed performng the pattern search method, and 6 sets of rheologcal parameters of τ0, k and n acqured from the back analyss underwent the V-funnel verfcaton test, whch demonstrates the feasblty to back-analyze the H-B model rheologcal parameters to some extent. 1.Introducton Self-compactng concrete (SCC) can fll the formwork to form the unform compactng concrete only by gravty wthout the applcaton of concrete vbratng. o date, many domestc and foregn scholars have appled the theory of rheology to examne the rheologcal parameters of fresh SCC. Yang Zhou [1] operated CFD to make the fnte element normal analyss based on Bnghan model, and back-analyzed the rheologcal parameter τ0 and μp of fresh SCC, and demonstrated the feasblty to back-analyzed the rheologcal parameters. Jngq L[2] dd the L-box smulaton based on H-B rheologcal model, three parameters τ0, k, n of the Herschel-Bulkley(H-B) model were expermentally measured, and the relablty of smulatng SCC flowng performance n the formwork usng H-B model was valdated after a comparson of SCC flowng tme n the actual L-box. he latest research dscovers that the concrete wth hgh flowng such as self-compactng concrete s a shear thckenng materal, whch s sutable to the characterzaton of power-law rheologcal models ncludng H-B model[3]. 2. H-B rheologcal model Larrd.F.de[4] et al., found that fresh concrete can be descrbed by H-B rheologcal model. he mathematcal expresson of H-B model s: 0 k( / t)n (1) In Eq.1: τ s the shear stress; τ0 s the yeld stress; k s the vscosty coeffcent; / t s the shear rate; n s the power law ndex relatng to the flud type. Wheren, f n=1, t s the Bngham flud; f n 1, t s the shear thckenng flud, and the vscosty of flud vares wth the shear stress and shear rate. When n 1, t s the shear thnnng flud wth the decreasng vscosty. 3. Back-analyss of rheologcal parameters of fresh SCC he back analyss of fresh SCC rheologcal parameters was made usng the drect method, whch converts the back analyss problem of parameters nto the optmal problem of a target functon, successvely revse the tral value of rheologcal parameters usng the normal analyss and teratve he authors - Publshed by Atlants Press 183

2 least error functon, untl the optmal value s obtaned [5]. he target functon s bult by comparng the flowng tme of fresh SCC n L-box and the flowng tme of SCC n the L-box smulaton, and the optmal value of rheologcal parameters of H-B model was gradually obtaned combnng the pattern search method. 3.1 L-box test and numercal smulaton of fresh SCC L-box s the modfed one, the mesh n 20mm 15mm was used to dvde the sde walls of the L-box, 7 feature ponts at 100mm, 200mm 700mm was marked. In testng the vertcal part was flled n12l fresh SCC, after 1mn of standng, the actve door was rapdly lfted to flow the concrete mx to the horzontal part, whch were done by referrng to User Gude for SCC Desgn and Constructon [6]. Meantme, the flowng tme of SCC flowng to 7 feature ponts was recorded usng the stopwatch. able 1 present the dfferent materals and able 2 present the results of 6 SCC groups n ths test. able 1 Mx desgn of the SCC SCC W(kg) C(kg) FA(kg) S(kg) G(kg) SP(kg) SP(%) W/(C+FA) % % % % % % able 2 Flow tme of characterstc ponts measured by L - box test SCC ρ (kg/m 3 ) he smulaton was made on fresh SCC flowng n L-box, the fnte element software Fluent was operated to smply SCC as the ncompressble vscous flud. he analogue model (Fg.1) was constructed accordng to the actual dmenson of L-box, where the number 1 means SCC, 0 means the ar, and the number between 0 and 1 means the mx of these two materals. Fluent settng for the parameter calculaton: he two phase flow VOF model was used, the frst, second phase was ar and SCC respectvely, and the materal propertes were defned by H-B model. he nlet condton s pressure nlet and outlet condton s the pressure outlet, the reference pressure pont s standard atmospherc pressure, and the relatve pressure s 0. he gravty effect at the y drecton was consdered. 3.2 he constructon and optmzaton of back-analyss target functon In the actual L-box flowng test, the flowng tme at 7 feature ponts were determned. As the tme was very lttle at, but the human error was bgger, so the remanng 6 feature ponts were selected. 100 he target functon was establshed accordng to the least square method: (2) 200 f ( x) ( ) In Eq.2, means the tme of SCC flowng to the feature ponts n the L-box smulaton test, means the tme of SCC flowng to the feature ponts n the actual L-box test. =200mm,300mm 700mm. 184

3 Fg.1 he three-dmensonal analogue mode of L- box hree rheologcal parameters τ 0, k, n to be back-analyzed were ncluded n and, the fnte element normal analyss was made to tral-calculate the target functon value n a stepwse way accordng to the gven rheologcal parameters, untl the flowng tme at 6 feature ponts n smulaton was bascally consstent wth the flowng tme at the actual L-box feature ponts, namely the rheologcal parameters when the optmal value solved n Eq.2 was exactly the value obtaned from the back-analyss. able 3 Flow tme of characterstc ponts measured by L - box test SCC (τ0,a,b) f ( x ) 1 (190,45,1.16) (240,61,1.25) (250,60,1.05) (280,111,1.10) (220,52,1.09) (180,46,1.20) he pattern search method was ntroduced durng the process of seekng the optmal soluton n Eq.2. he pattern search method alternatvely executed two searches: axal search and pattern search, from the gven startng pont. As to the soluton to three parameters problem n H-B model, τ 0, k and n were set as three drectons of the space rectangular coordnate system x, y and z, where e 1 =(1,0,0), e 2 =(0,1,0), e 3 =(0,0,1); the search was done along e 1, e 2 and e 3 respectvely, and the specfc steps were shown n Reference [7]. After several teratve calculatons, 6 groups of test results were ultmately obtaned ( shown n able 3). he comparson between able 3 and able 2 suggests that the flowng tme n smulaton was bascally consstent wth the measured value. For example, t can be shown n the comparson fgure (Fg.2 and Fg.3) when Group 5 SCC flew to 400mm. he test errors can be manly attrbuted to: he measured tme n L-box test was only accurate to 0.1S, whle t was accurate to 0.01S n smulaton. In addton, there was some dfference as to the slp boundary walls between the smulaton and actual test. 185

4 Fg.2 he tme of SCC flow to 400 mm dstance =1.80S Fg.3 he tme of SCC flow to 400 mm dstance =1.88S 3.3 V-funnel verfcaton test and analyss he V-funnel test and the V-funnel numercal smulaton were compared after 6 groups of rheologcal parameters were obtaned from the back analyss. he V-funnel test process was referred to the SCC Appled echnology Procedure [8], fresh SCC corresponds to the SCC used n the L-box test as prevously descrbed, and the fnal tme of SCC flowng through the V-funnel was recorded. hen the rheologcal parameters τ 0, k and n obtaned from the back analyss were used as the known nputs to conduct the V-funnel smulaton test. he test results are gven n the followng able4. able 4 V-funnel test valdaton results SCC tral value Smulaton value Absolute error relatve error () v s v () s (%) % % % % % % able 4 shows that the result of the smulated values s closer than that of the tested values, but all smulated values are smaller than the tested values, n whch Group 1 has the bggest error wth the absolute error of 1.8 seconds and the relatve error of 15.20%, the possble cause s that coarse aggregate has frcton and collson at the outlet durng the actual V-funnel test whch led to more 186

5 tme of fnal flowng, but ths was not consdered n the smulaton. Accordng to the relatve error, the requrements of engneerng precson can be more or less satsfed, whch ndcates that the rheologcal parameters obtaned from the back analyss are relable to some extent. 4. Conclusons he rheologcal parameters of Fresh SCC were examned through the theory of rheology, fresh SCC was assumed to conform to the H-B rheologcal model, accordng to the verfcaton result of rheologcal parameters obtaned from the back analyss, the relatve error s around 10%, so t wll be feasble to seek the optmzaton of rheologcal parameters through the establshment of the target functon usng the flowng tme at dfferent dstances n the L-box test as the feature parameters. In the V-funnel smulaton verfcaton test usng the software Fluent, the rheologcal parameters obtaned from the back analyss were used as the known nputs to measure the fnal flowng tme of SCC through the V-funnel, t s found that the smulated values are always smaller than the tested values after the comparatve analyss, the possble cause s that SCC coarse aggregate has frcton and collson at the outlet durng the actual V-funnel test whch led to more tme of fnal flowng, but ths was not consdered n the smulaton. Acknowledgements hs work was fnancally supported by the macro-mcro mechancal performance of self-compactng concrete composte materal (Foundaton for Returnees of Unversty of South Chna, Program No.: 2007XQD16) References [1] Yang Zhou, Jan-jun sh, et al Back-analyss of the fresh self-compactng concrete rheologcal parameter based on Bngham model [J] Chna Rural Water and Hydropower, 2014, (9) : ,IN Chnese [2] Jngq L, We Xu. flow CFD smulaton of self-compactng concrete based on the Herschel -- Bulkley rheologcal model. [J]. Engneerng mechancs, 2013, 30 (1) : , IN Chnese [3] Dmtr Feys,Ronny Verhoeven,Geert De Schutter.Fresh self compactng concrete,a shear thckennmateral.[j]cement and concrete research,2008,38: [4] Larrard D F, Ferrars C F, Sedran.Fresh concrete: A Herschel Bulkley materal [J].Materals and Structures,1998, 31: [5] Xn-mng zhao et al. Numercal nverson method of geotechncal back analyss [J] Advances n Scence and echnology of Water Resources, 2003, 23 (2) : 55 to 57, IN Chnese [6] User Gude for SCC Desgn and Constructon CCES [S] Bejng: Chna buldng ndustry press, , IN Chnese [7] Xng-yuan Wu. Pattern search method n the applcaton of the optmzaton problem. [J]Software Gude. 2009, 8 (8) : , IN Chnese [8] SCC Appled echnology Procedure.CECS [S]Bejng:Chna plannng press, , IN Chnese 187