Zhenhong Wang, 1 Yi Liu, 1,2 Guoxin Zhang, 1,2 and Shuping Yu 1,3. 1. Introduction

Transcription

1 Mathematcal Problems n Engneerng Volume 2015, Artcle ID , 12 pages Research Artcle Senstvty Analyss of Temperature Control Parameters and Study of the Smultaneous Coolng Zone durng Dam Constructon n Hgh-Alttude Regons Zhenhong Wang, 1 Y Lu, 1,2 Guoxn Zhang, 1,2 and Shupng Yu 1,3 1 Department of Structures and Materals, Chna Insttute of Water Resources and Hydropower Research, Bejng , Chna 2 State Key Laboratory of Smulaton and Regulaton of Water Cycle n Rver Basn, Chna Insttute of Water Resources and Hydropower Research, Bejng , Chna 3 Henan Yellow Rver Reconnassance, Desgn and Research Insttute Bejng Branch, Bejng , Chna Correspondence should be addressed to Zhenhong Wang; fathzhen@126.com Receved 26 August 2014; Revsed 18 December 2014; Accepted 2 January 2015 Academc Edtor: Wezhong Da Copyrght 2015 Zhenhong Wang et al. Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted. There are unprecedented dffcultes n buldng concrete gravty dams n the hgh alttude provnce Tbet wth problems nduced by lack of experence and technologes and unque weather condtons, as well as the adopton of constructon materals that are dsadvantageous to temperature control and crack preventon. Based on the understandngs of the mentoned problems and leveragng the need of buldng gravty dam n Tbet, 3D fnte element method s used to study the temperature control and crack preventon of the dam durng constructon. The calculaton under recommend temperature control measures and standards shows that the heght and number of smultaneous coolng zone have the more obvous nfluencers on concrete stress; therefore, t s suggested to ncrease the heght of smultaneous coolng zone to decrease the stress caused by temperature gradent of adjon layers so as to rase the safety level of the whole project. The research methods and deas used on ths project have sgnfcant values and can be taken as references n smlar projects n hgh alttude regons. 1. Introducton Dams have been successfully bult around the world, especally n low-alttude regons [1, 2]. In hgh-alttude regons, such as Tbet, however, the lack of experences n dam-related technologes and systematc theores ntroduces challenges n buldng dams. A hgh alttude mples a complcated clmate that features dry and thn ar, strong sun radaton, and severe temperature dfference between day and nght [3, 4]. Compared wth buldng dams n low-alttude regons that have warm and humd ar and a small temperature dfference between day and nght, buldng dams n hghalttude regons requres specfc, straghtforward, and talored measures and standards for temperature control and crack preventon. Cracks n large volumes of concrete are always a challenge n the feld of engneerng. Many engneerng cases nvolve cracks caused by temperature at dfferent levels n largevolume concrete structures, such as dams, durng and after constructon. These cracks make structures appear weak, and they severely affect durablty and safety [5 9]. Because temperature-nduced crackng problems contnue to be a major challenge n engneerng, desgners and bulders also contnue to study large-volume concrete projects and develop approprate temperature control measures and standards to decrease temperature stress and avod or reduce cracks. Ths study focuses on the Jexu Dam, a gravty dam beng bult n Tbet. To analyze the senstvtes of condtons and parameters durng the constructon process n the regon, the 3D fnte element method [10 13] s used. The dscusson concludes by presentng rules on the condtons and parameters that affect temperature stress n the dam. Ths study consders heat transfer and the hardenng development process of concrete [14 17], the shrnkage deformaton caused

2 2 Mathematcal Problems n Engneerng by temperature changes n concrete [18, 19], and the ppe coolng measures of concrete [20]. From the fndngs and nformaton obtaned from smlar projects, a set of measures and standards sutable for dam constructon n hgh-alttude regons are proposed to gude the safe constructon of dams. 2. Calculaton Prncples and Methods 2.1. Dfferental Equaton for Heat Conducton. Dfferental equaton [21] (1) apples to the temperature feld of even and sotropc homogeneous sold: 2 T x T y T z α ( θ τ T )=0. (1) τ In the equaton, T stands for temperature ( C), x, y,andz are the three coordnates of a pont (m), α stands for thermal dffusvty (m 2 h 1 ), θ stheadabatctemperaturerseof concrete ( C), and τ stands for maturty (day). The prncple of mnmum gravtatonal energy ndcates that the dfferental equaton for heat conducton (1) can be converted: temperature T(x, y, z, τ) s set as the ntal temperature T 0 (x,y,z) when τ = 0; the heat conducton matrx [H] e, heat capacty matrx [R] e,andtemperatureload array {F} e are acheved when the extremum s gven for each boundary and through spatal dscretzaton and dfference n the tme doman. After ntegraton, the partal dfferental of temperature at each nodal s determned: { I {T} }=[H]{T} + [R] + {F} =0. (2) T τ In the above equaton, H j = H e j, R j = R e j, F = F e. Equaton (2) s a set of lnear dfferental equatons wth τ as the ndependent varable. In the equaton, R s the heat capacty matrx, H s the heat conducton matrx, F s the temperature load column matrx, T s the nodal temperature array, and {T}/ τ s the dervatve array of nodal temperature aganst tme Fnte Element Method of the Stress Feld. The stran ncrement of concrete under complex stress ncludes the elastc stran ncrement, creep stran ncrement, temperature stran ncrement, dry shrnkage stran ncrement, and autogenous volume stran ncrement [21]; thus, {Δε n } = {Δε e n } + {Δεc n }+{ΔεT n }+{Δεs n }+{ε0 n }, (3) where {Δε e n } s the elastc stran ncrement, {Δεc n } s the creep stran ncrement, {Δε T n } s the temperature stran ncrement, {Δε s n } s the dry shrnkage stran ncrement, and {Δε0 n } s the autogenous volume stran ncrement. We obtan a fnte element governng equaton of any tme nterval Δt on the area R from the physcal equaton, the geometrc equaton, and the equlbrum equaton as follows: [K ] {Δδ} ={ΔP G }+{ΔP C }+{ΔP T }+{ΔP S }+{ΔP0 }, (4) where {Δδ } s the dsplacement ncrement of all nodes n three drectons n area R and {ΔP G }, {ΔP C }, {ΔP T }, {ΔP S }, and {ΔP 0 } are the equvalent nodal force ncrement caused by the external load, creep, temperature change, dry shrnkage, and autogenous volume deformaton wthn Δt, respectvely The 3D Fnte Element Method Software SAPTIS. The Structure Analyss Program for Temperature and Induced Stress (SAPTIS) software package facltates the FORTRAN language-programmed, large-scale multfeld smulaton, and nonlnear analyss. The software s used to smulate the calculaton of temperature, stress, seepage, and deformaton, among other factors, n the entre process of foundaton excavaton, pourng process, water storage process, and longterm operaton of concrete dams. The man features of the program nclude the excavaton and pourng smulaton method, the hydraton heat model, the water cooled model, the temperature boundary condtons, the elastc modulus model, the creep model, autogenous volume deformaton, and MgO concrete characterstcs n the entre smulaton process of dams. The program has a rch element lbrary. 3D problems nclude 8 20 varable node hexahedron soparametrc elements, 6 15 varable node pentahedron soparametrc elements, and 8-node hexahedron soparametrc elements, as well as bar elements, jont elements, and contact elements, tonameafew.saptishasavaretyofsolvers.thedrect soluton method or the teratve soluton method can be used to solve large lnear equatons. SAPTIS s characterzed by ts hgh speed and small memory capacty. It can use a computer to conduct smulaton analyss, as well as general structural stress and deformaton analyss of large concrete structures; t can also use a server for parallel computng. The software s successfully appled to more than 50 large and medum concrete dams of the Three Gorges, Ertan, Longtan, Xaowan, Xluodu, Jnpng, Danjangkou, and other dams, as well as for the smulaton analyss of the temperature and stress felds of other structures. Favorable economc benefts are acheved as aresult Adabatc Temperature Rse Model. Consder Exponental Model: θ (τ) =θ 0 (1 e ατb ), Hyperbolc Model: θ (τ) = θ 0τ (α+τ), θ { 0 (1 e aτb ) Combnaton Model: θ= { θ 0 τ { n+τ, where θ(τ) stheadabatctemperaturerseofconcrete( C), θ 0 s the fnal adabatc temperature rse ( C), a and b are the law parameters of the adabatc temperature rse, and n s a constant. (5)

3 Mathematcal Problems n Engneerng Elastc Modulus Model Exponental Model: E (τ) =E 0 +E c (1 e ατβ ), Hyperbolc Model: E (τ) =E 0 + E cτ (τ+α), (6) where Φ represents the ppe coolng effect and Ψ represents the adabatc temperature rse effect. The detals are dscussed n [21]. Theequatonndcatesthattheproblemcanbesmplfed, and the common coolng effect of coolng water ppes can be approxmately calculated wth the exstng fnte element program and computatonal grd. where E 0 s the ntal elastc modulus of concrete (GPa), E c sthefnalelastcmodulusofconcrete(gpa),τ s the age of concrete, and α and β are the varaton coeffcents of the elastc modulus of concrete Creep Model Model 1. Consder C (t, τ) =(A 1 + A 2 τ + A 3 τ 2 )(1 e k 1(t τ) )+(B 1 + B 2 τ + B 3 τ 2 ) Model 2. Consder (1 e k 2(t τ) )+De k 3(t τ) (1 e k 3(t τ) ). C (t, τ) =(A 1 +A 2 τ α 1 )(1 e k 1(t τ) )+(B 1 +B 2 τ α 2 ) (1 e k 2(t τ) )+De k 3t (1 e k 3(t τ) ), where C(t, τ) s the specfc creep, 10 6 /MPa; k 1, k 2,andk 3 are the creep rate parameters; A 1, A 2, A 3, B 1, B 2, B 3,andD are the specfc creep parameters, 10 6 /MPa; t s the tme (day); and τ s the loadng age (day) Autogenous Volume Model. Autogenous volume deformaton s determned by the drect nput of expermental data and the deformaton values between the two expermental ages through splne functon nterpolaton Water Coolng Model. The contact surfaces of concrete wth ar, water, rocks, and other meda transfer heat and have a coolng effect. Wth the ppe coolng effect consdered, the problem s complex, such that t cannot be solved by theoretcal methods; accurately solvng t wth the fnte element method s also dffcult. An approxmate soluton can be obtaned only through consderaton of the coolng water ppes as a negatve heat source and of the functon of the coolng water ppes, on average. If the ntal temperature of concrete s set to T 0, the ntake water temperature s set to T w, the fnal adabatc temperature rse of concrete s set to θ 0, and the tme s set to t; the average temperature of concrete s calculated as follows: (7) (8) T (t) =T w +(T 0 T w )Φ(t) +θ 0 Ψ (t). (9) Therefore, the equvalent thermal conductvty equaton of concrete s as follows: T t =a 2 T+(T 0 T w ) Φ t +θ Ψ 0 t, (10) 3. Overvew of the Gravty Dam 3.1. Project Overvew. Jexu Hydropower Staton s located at the boarder of Sangr County and Jacha County n Shannan Regon of the Tbet Autonomous Regon. The staton s a thrd-stage power plant n the gorge secton from Sangr County to Jacha County along mdstream of Yarlung Tsangpo Rver. It s 7 km away from a planned Dagu Hydropower Plant n the upstream and 18 km away from the Zangmu Hydropower Plant currently beng bult n the downstream. Jexu Hydropower Plant s prmarly desgned for power generaton. In the up dam ste, the catchment area s 157,407 km 2,andtheaverageflowatthedamstes 1,010 m 3 s 1. The standard mpounded level of the dam s at 3,374 m, and the storage capacty s mllon m 3,wthan adjusted storage capacty of 9.85 mllon m 3. Four generators are nstalled wth a total capacty of 560 MW and a frm capacty of 152 MW. The average power generaton volume s 2,755.6 mllon kwh. The Jexu Hydropower Staton rver dam s a concrete gravty dam. From left to rght are a left bank waterretanng dam secton, dverson dam secton, bottom outlet dam secton, overflow dam secton, and rght bank waterretanng dam secton. The dam crest s 340 m long, the crest elevaton s 3,378.0 m, the maxmum dam heght s m, the wdest bottom of the dam s 99.8 m, and the total volume of dam concrete s around 1.64 mllon m 3.The largest dam secton s 32.5 m wde. The project s constructed n 14 dam sectons. The dam has fve flood release orfces wth a dmenson of 14 m 21.5m,onebottomoutletfor flood release wth a dmenson of 5 m 8m,andfourpower generaton water nlets. The dam s a complcated structure, wth ts constructon ongong for a year now; t has a long constructon cycle and nvolves complcated constructon condtons Engneerng Dffcultes (1) Specal geologcal condtons make temperature control challengng. The project s located n Tbet, a hgh-alttude regon. Therefore, t s characterzed by thn ar, dry clmate, strong solar radaton, severe temperature dfference between day and nght, and largemonthlyaveragetemperaturevarance.sucha clmate s dsadvantageous n controllng temperature to prevent cracks on concrete. (2) The constructon materals used n buldng the dam are not helpful for temperature control and crack preventon. The composton of concrete used for the project shows that wthn the same regon and smlar

4 4 Mathematcal Problems n Engneerng Project Jexu Gravty Dam Zangmu Gravty Dam Table 1: Comparson of the key temperature control parameters of Jexu and Zangmu. Thermal expanson coeffcent [ C 1 ] Dam concrete adabatc temperature rse [ C] Autogenetc volume deformaton [10 6 ] 90 d modulus of elastcty [GPa] 90 d tensle strength [MPa] 90 d ultmate tensle apprecaton [10 4 ] structure, the coeffcent of thermal expanson of concrete s C 1, and the adabatc temperature rse s 26.3 C, whch s 1.22 tmes and 3 Chgherthan those of Zangmu, respectvely. However, the modulus of elastcty and tensle strength n both statons are smlar. The materal parameters used for the Jexu project are dsadvantageous for crack preventon, and temperature control n Jexu s also more dffcult than that n Zangmu. Table 1 shows a comparson of the key temperature control parameters of Jexu and Zangmu Calculaton Model and Boundary Condtons Computatonal Grd and Boundary Condtons. Boundary condtons of the temperature feld: the bottom surface and surroundng sdes of the foundaton are adabatc boundares; the upper surface of the foundaton s the thrd boundary that consders temperature and solar radaton; both sdes of the dam are adabatc boundares; the upstream face and thedownstreamfaceofthedambeforempoundmentare the thrd boundares that consder temperature and solar radaton; and the upstream face and the downstream face of the dam after mpoundment are the frst boundares, and ther temperature s the reservor temperature. Boundary condtons of the stress feld: the bottom surface of the foundaton s regarded as a fxed surface; the surroundngsdesofthefoundatonaresupportednthe normal drecton, whereas the other boundary faces are freely deformed faces. Because the ambent ar temperature and water temperature consderably affect the upstream face and thedownstreamfaceofthedamandthetemperatureand stress gradents are large, a relatvely dense grd s set. Fgure 1 shows the smulaton grd, and Fgure2 shows the boundary condtons of the smulaton calculaton model Calculaton Parameter Model. The body of the dam uses four-graded concrete derved from the test data: adabatc temperature rse model of concrete: T(t) = (26.26 t)/(t ), C, elastc modulus model of concrete: E(t) = 32.6 (1 e 0.38t0.28 ),GPa. The autogenous volume deformaton of concrete uses the test dataoftable 2. Fgure 1: Smulaton grd. 4. Senstvty Analyses of the Temperature Control Parameters of Dams n Hgh- Alttude Regons 4.1. Senstvty Analyss of Pourng n Dfferent Seasons. The hgh restrant zone of gravty dams s essental to temperature control,andtsalsothemostchallengngaspecttodealwth. Thsstudymanlyfocusedonthetemperatureandstressn the hgh restrant zone. (1) Table 3 shows that, n pourng the concrete of the hgh restrant zone, the hghest temperature s 26.3 C durng summer, whereas t s 25.5 C and 24.5 C durng autumn and wnter, respectvely. The hghest temperature dfference s large from season to season wth the same temperature control measures. Water ppe coolng nvolves three stages: decrease n the hghest temperature durng the frst stage, decrease n thecontroltemperaturerateandgradentdurngthe mddle stage, and coolng down to the jont groutng temperature durng the second stage. Fgure 3(a) shows that the temperature reasonably dropped (.e., wthout reboundng or decreasng rapdly). (2) The hgh restrant regon has the strongest stress, wth the maxmum stress occurrng durng the second stage when the temperature drops to the target level. In general, the hgh restrant zone of concrete poured durng the hgh-temperature season shows the hghest maxmum temperature, temperature dfference, and maxmum stress. In Tbet s Jexu Staton, the stress of concrete poured durng autumn s hgher than that poured durng summer, whch s aganst the general rule that the hghest stress occurs durng autumn.

5 Mathematcal Problems n Engneerng 5 Ar and solar radaton Upstream water temperature Dam Downstream water temperature Dam Adabatc boundary Foundaton Adabatc boundary Normal constrant Foundaton Fxed constrant Normal constrant (a) Temperature boundary (b) Stress boundary Fgure 2: Boundary condtons of the smulaton model. Temperature ( C) Stress (MPa) /2/ /16/2017 3/1/2018 5/15/2018 7/29/ /12/ /26/2018 3/11/2019 5/25/2019 8/8/ /2/ /16/2017 3/1/2018 5/15/2018 7/29/ /12/ /26/2018 3/11/2019 5/25/2019 8/8/2019 Summer Autumn Wnter Summer Autumn Wnter (a) Temperature (b) Stress Fgure 3: Process curve of concrete temperature and stress at characterstc ponts n the basc restrant zone durng pourng at dfferent seasons. Table 2: Autogenous volume deformaton of concrete. Age (day) dat (10 6 ) Age (day) dat (10 6 ) Age (day) dat (10 6 ) Age(day) dat(10 6 ) Age(day) dat(10 6 ) Note. Negatve values ndcate that the autogenous volume deformaton s of shrnkage type. Startng season Pourng temperature ( C) Frst stage Table 3: Concrete temperature stress as affected by the pourng season. Water temperature ( C) Mddle Stage Second Stage Intervals (day) Maxmum temperature n the hgh restrant zone ( C) Maxmum tensle stress n the hgh restrant zone Elevaton Safety σ x (Mpa) (m) coeffcent Summer Autumn Wnter Note.(1)σ x s the along-rver stress, and (2) k s the safety coeffcent. Strength control s desgned based on 180 days; the tensle strength of thrd-grade concrete s 2.53 Mpa, whereas that of fourth-grade concrete s 2.73 Mpa. The same data are presented n Fgure 3.

6 6 Mathematcal Problems n Engneerng Temperature ( C) Stress (MPa) /25/2018 7/14/2018 9/2/ /22/ /11/2018 1/30/2019 3/21/2019 5/10/2019 5/25/2018 7/14/2018 9/2/ /22/ /11/2018 1/30/2019 3/21/2019 5/10/ m 3.0 m 1.5 m 3.0 m (a) Temperature (b) Stress Fgure 4: Process curve of concrete temperature and stress n the hgh restrant zone wth dfferent pourng thcknesses. Table 4: Effect of pourng thckness on temperature stress. Start of pourng June Thckness (m) Maxmum temperature n the hgh restrant zone ( C) Maxmum tensle stress n the hgh restrant zone σ x (Mpa) Elevaton (m) Safety coeffcent k Table 3 and Fgure 3(b) show that the maxmum alongrver stress of the hgh restrant zone durng summer s 1.45 Mpa, whch s lower than the 1.63 Mpa value durng autumn and s at ts lowest durng wnter. Two reasons account for ths phenomenon: (1) Jexu Dam s located n an area where the ar temperature drop s sgnfcant from October to December. The average ar temperature n October s 10.4 C, whch drops to 0.7 CnDecember.Durngthe begnnng of pourng n autumn, a sgnfcant ar temperature drop occurs, and untl January of the followng year, the drop s 10.1 C; (2) the maxmum concrete temperature of pourng durng summer s hgher than that durng autumn, so the compressve stress reserve s also relatvely large. The maxmum concrete temperature of pourng durng autumn s possbly lower than that of pourng durng summer, but the concrete stress of pourng durng autumn s hgher than that of pourng durng summer Senstvty Analyss of Pourng Thckness. Pourng concrete at the hgh restrant zone causes the thckness to sgnfcantly affect temperature stress. A thck concrete pourng wll have a hgh nternal temperature, foundaton temperature dfference, and maxmum stress. By contrast, a thn concrete pourng wll have a low nternal temperature, temperature dfference, and stress, but t cannot be too thn. To analyze the stress nvolved, ths study focuses on two stuatons n whch the thckness s 1.5 and 3.0 m. (1) Table 4 and Fgure4(a) show that when concrete s poured durng summer at 1.5 m, the maxmum temperature s 26.3 C, and when the thckness s 3 m, the maxmum temperature s 29.2 C, whch s 2.9 C hgher than 26.3 C. Therefore, the ar temperature durng summer n Jexu Dam s far lower than the nternal temperature of concrete. A thck pourng wll be dsadvantageous to the producton of heat, and ths wll cause the maxmum temperature to ncrease. (2) Fgure 4(b) shows that the maxmum concrete stress occursattheendofthesecondstageofcoolng; the temperature drops to the lowest temperature (target temperature). The dfference n maxmum temperature results n the varaton n the foundaton temperature, so a temperature dfference at the jont groutng also occurs. Table 4 shows that the maxmum stress s observed to be too hgh when the concrete poured s 3 m thck. The pourng thckness n the hgh restrant zone s recommended to be 1.5 m, and concrete surface heat preservaton should also be observed, especally when pourng s done durng hgh- and low-temperature seasons Senstvty Analyss of Pourng Intervals. The length of pourng ntervals s a problem every constructor needs to address. Ths research manly focuses on the effect of ntervals on temperature and stress. The study consders stuatons n whch the nterval s 15, 20, and 28 days. (1) Table 5 and Fgure 5(a) ndcate that the maxmum nternal temperature occurs from days 5 to day 7. The correlaton between the maxmum temperature and the nterval length s trval when the pourng nterval s from 15 days to 28 days. However, because of the effect of waterng ppe coolng, the longer s the nterval, the lower s the temperature at the bottom

7 Mathematcal Problems n Engneerng /9/2018 9/7/ /6/2018 3/6/2019 6/4/2019 9/2/ /1/2019 Temperature ( C) Stress (MPa) /9/2018 9/7/ /6/2018 3/6/2019 6/4/2019 9/2/ /1/ day 15 day 20 day 28 day 10 day 15 day 20 day 28 day (a) Temperature (b) Stress Fgure 5: Process curve of concrete temperature and stress n the basc restrant zone at dfferent pourng ntervals. Interval (day) Maxmum temperature n the hgh restrant zone ( C) Table 5: Effect of pourng ntervals on temperature stress. Maxmum tensle stress n the hgh restrant zone Elevaton Safety σ x (Mpa) (m) coeffcent Maxmum tensle stress n the low restrant zone and the free zone Elevaton Safety σ x (Mpa) (m) coeffcent concrete, and the hgher s the bottom concrete strength. As a result, the new concrete has a hgher restrant and stress than the old concrete. (2) Fgure 5(b) showsthatasthentervalandtheelastc modulus ncrease, the maxmum tensle stress of concrete becomes large. In addton, the stress caused by the temperature dfference between day and nght s hgh when the nterval s long and when the modulus of elastcty s hgh. Short-term stress overlad wth long-term stress tends to cause great stress at the surface of the concrete, especally f a long nterval occurs durng wnter and when the ar temperature abruptly drops because of nadequate nsolaton. The nternal and external temperature dfference can cause cracks on the concrete surface. Durng the low-temperature season, the surface nsulaton therefore needs to be excellent, and the pourng nterval should not be too long to avod harmful stress when new concrete s poured on old concrete Senstvty Analyss of the Pourng Temperature. Ths secton examnes how pourng temperature affects temperate stress n hgh-alttude regons, such as Tbet. Table 6 and Fgure 6(a) ndcate that (1) the pourng temperature s 12 Cand14 C n the hgh restrant zone f concrete s poured durng summer. Every 2 Cncreasen the pourng temperature causes the maxmum temperature of concrete to ncrease by about 1.2 C, the maxmum stress to ncrease by about 0.04 Mpa, and the crack resstance safety coeffcent to ncrease by 1.74 and (2) Wth the same temperature control measures, a hgh pourng temperature ncreases the maxmum temperature and stress durng the end of the frst stage of coolng. Fgure 6(b) shows that the ncrease n pourng temperature has hardly any effect on the tme of maxmum stress. Meanwhle, the stress at the end of the frst stage of coolng ncreases but s stll wthn the safe range. 5. Temperature Control Measures and Standards durng Dam Constructon 5.1. Optmzed Opton for Temperature Control and Standards. Fgure 7 and Table 7 present the suggestons for temperature control measures and standards for Jexu Dam. These are based on the fndngs of prevous senstvty studes on constructon condtons and temperature control parameters, combned wth the actual envronment features and specfc materals nvolved, as well as relevant nsghts from other hgh-alttude projects. Usng the results on number 13 steepsloped water-retanng dam, ths study revews the temperature, stress, and safety of the dam under the recommended temperature control measures and standards.

8 8 Mathematcal Problems n Engneerng Temperature ( C) Stress (MPa) /4/2018 8/3/ /2/ /1/2018 1/30/2019 3/31/2019 6/4/2018 8/3/ /2/ /1/2018 1/30/2019 3/31/ C 14 C (a) Temperature 12 C 14 C (b) Stress Fgure 6: Process curve of concrete temperature and stress n the basc restrant zone under dfferent pourng temperature values. Pourng temperature ( C) Maxmum temperature at the hgh restrant zone ( C) Table 6: Effect of pourng temperature on temperature stress. Maxmum temperature at the low restrant zone ( C) Maxmum tensle stress n the hgh restrant zone σ x (Mpa) Elevaton (m) Safety coeffcent Maxmum tensle stress n the low restrant zone σ x (Mpa) Elevaton (m) Safety coeffcent k Note. In the summary of pourng temperature, shows the temperature n the hgh restrant zone, low restrant zone, and the free zone. The length of the bottom of the dam secton along the rver s L=45m. Accordng to specfcatons [2], countng from the bottom of the dam, the elevaton below 0.2L s thehghrestrantzone,theelevatonof0.2l to 0.4L s the low restrant zone, and the elevaton above 0.4L s the no restrant zone. These specfcatons are used for the desgn of the temperature control measures, and ther standards are dfferent. The steep slope secton of the dam s subject to the constrants of the foundaton wthn a relatvely large range. From the perspectve of safety, the bottom of 0.2L s measured from the top of the slope; the elevaton of 9 m above 3,325 m sthehghrestrantzone,theelevatonof3,334mto3,343m s the low restrant zone, and the elevaton above 3,343 m s thenorestrantzone. The temperature control measures and standards of the hgh restrant zone are strct, whereas those of the other zones are less strct, as shown n Fgure 7(a) and Table 7.The 9 m requrement for rrgaton areas ndcates that to reduce the mutual restrant caused by the temperature dfference between the upper and lower rrgaton areas durng water coolng, the three rrgaton areas (3,300 m to 3,327 m) should be smultaneously cooled from the mddle stage of coolng. The water temperature and flow rate are dscussed n Table 7. After separaton from the hgh restrant zone, each rrgaton area s separately cooled Temperature Stress of the Dam. Thssectonfocuseson the temperature and stress of the dam under the recommended temperature control measures and standards. To understand well the scentfc ratonalty of the recommended measures, a comparson s made to show ther advantages. The two sets of measures are smlar, except that case 1 sets an 18 m smultaneous coolng zone or one smultaneous coolng zone under a 3,300 m elevaton, whereas case 2 added a 27 m smultaneous coolng zone above the elevaton of 3300 m on the bass of case 1 to further reduce the mutual restrant of the upper and lower zones. A smultaneous coolng zone s defned as follows: startng from the mddle stage of coolng, the concrete n the zone begns to cool down smultaneously n order to obtan the coordnate temperature drop and consstent change of concrete, as well as to reduce the mutual restrant and stress; the water temperature and flow rate of the ppe n the smultaneous coolng zone are the same. From Table 8 and Fgures 8 to 10, wecanconcludethe followng. (1) The number and heght of the smultaneous coolng zone does not have a sgnfcant effect on the maxmum temperature, whch s Cforbothcases. (2) Settng one smultaneous coolng zone of 18 m under an elevaton of 3,300 m and startng the smultaneous coolng from the mddle stage result n a small temperature dfference between the upper and lower pourng sectons, the deformaton occurs at the same pace. A relatvely small restrant s therefore formed at the base of concrete. The dam secton s on a steep slope and s steep n both axal and along-rver drectons, wth the slope heght at 43 m.

9 Mathematcal Problems n Engneerng 9 None restran zone 6 C P 14 C D: 1.5 m 3.0m T 30 C m m Low restran zone Hgh restran zone m 6 C P 13 C D: 1.5 m 3.0m T 28 C m m m m 6 C P 12 C D: 1.5 m 1.5m T 26 C m 9 m 9 m 9 m 9 m 9 m m m Smultaneous coolng of three zones m m m 9 m 9 m 9 m 9 m 9 m 9 m m P: pourng temperature (monthly average temperature +3 C) D: dstance between water ppes T: the maxmum allowable temperature of concrete m 9 m (a) Arrangement of basc temperature control measures (b) Coolng method Fgure 7: Temperature control measures and coolng methods for the steep slope secton of the dam. Pourng temperature Smultaneous coolng Dstance between water ppes Water ppe coolng Pourng thckness Concrete temperature control measures Table 7: Temperature control measures. Hgh restrant zone Low restrant zone No restrant zone Begnnng stage ofsmultaneouscoolng Heght of the smultaneous coolng Frst stage coolng Mddle stage of coolng Second stage coolng Control ndex 12 C 13 C 14 C Hgh restrant zone 1.5m 1.5m Low restrant zone 1.5m 3.0 m No restrant zone 1.5 m 3.0 m Water temperature Flow Startng age Targeted temperature Water temperature Flow Startng age Targeted temperature Water temperature Flow Startng Targeted temperature Mddle stage 18 m below elevaton 3,300 m 27 m above elevaton 3,300 m 8.0 C 1.5 m 3 h day 19 C-20 C 12 C 0.8 m 3 h 1 30day 45 day 16 C 18 C 6 C 8 C 1.0 m 3 h 1 90 day 10 C Hgh restrant zone 1.5m Low restrant zone and no restrant zone 3.0 m Intervals between layers 10 day Surface nsulaton 5cm vnylnsulaton board

10 10 Mathematcal Problems n Engneerng Temperature ( C) Stress (MPa) /27/ /27/ /26/ /26/2018 1/25/2019 2/24/2019 3/26/2019 4/25/2019 5/25/2019 6/24/2019 7/24/2019 9/27/ /27/ /26/ /26/2018 1/25/2019 2/24/2019 3/26/2019 4/25/2019 5/25/2019 6/24/2019 7/24/2019 Case 1 Case 2 Case 1 Case 2 (a) Temperature (b) Stress Fgure 8: Process curves of the concrete temperature and stress at m elevaton for dfferent cases. Case Case 1 18 Case Table 8: Effect of the amount and heght of the smultaneous coolng zone on temperature stress. Heght of the smultaneous coolng zone (m) Basc restran zone smultaneous coolng measure 18 m below the 3,300 m elevaton Smultaneous coolng durng the mddle and second stages On the bass of case 1, addng 27 m above the 3,300 m elevaton Maxmum temperature at the hgh restrant zone ( C) Note: (1) means that the frst smultaneous coolng zone s 18 m, and the second one s 27 m. Maxmum tensle stress n the hgh restrant zone σ x (Mpa) Elevaton (m) Safety coeffcent k The 18 m coolng zone s stll wthn the 43 m slope zone. Therefore, the mddle secton of the along-rver drecton of the hgh restrant zone stll bears a large stress at 1.65 Mpa. The safety coeffcent s only (3) On the bass of case 1, another smultaneous coolng zone s added above the 3,300 m elevaton level. The 45 m coolng zone wll cover the entre slope, and coolng starts from the mddle stage. The change n heght and organzaton of the coolng zone makes the temperature dfference along the alttude small and further ncreases the heght of smultaneous deformaton. The maxmum stress n the hgh restrant regon sgnfcantly changes to lower than 1.40 Mpa. The safety coeffcent ncreases to 1.82, whch s much better than that of case 1. In concluson, the heght and amount of the coolng zone obvously affect the stress of concrete, especally at dam secton number 13, whch s very steep. To decrease the stress n the hgh restrant zone at the second coolng stage, ncreasng both the amount and the heght of the coolng zone onthesteepslopetocovertheentreheghtofthesteepwll decrease the temperature stress caused by the temperature drop between adjon layers. 6. Conclusons (1)Specalandft-for-pursetemperaturecontrolmeasuresshouldbeusednbuldngconcretegravty dams n hgh-alttude provnces, such as Tbet, where the weather condtons are unque, that s, dry thn ar, strong sun radaton, and severe temperature dfference between day and nght. The lack of choces forconstructonmateralsbecauseofthelocatons dsadvantageous to crack preventon through temperature control. (2)Theunqueweathercondtonsanddsadvantageous temperature control parameters n hgh-alttude areas ental the need to conduct senstvty research on constructon condtons and parameters n order

11 Mathematcal Problems n Engneerng 11 (a) Temperature ( C) MAX TEMPERA (b) Stress (0.01 Mpa) SGMA X MAX Fgure 9: Envelope dagrams of the concrete temperature and stress n the mddle secton of the dam n case 1. (a) Temperature ( C) MAX TEMPERA (b) Stress (0.01 Mpa) SGMA X MAX Fgure 10: Envelope dagrams of the concrete temperature and stress n the mddle secton of the dam n case 2. to determne the mechansm of nfluence nvolved. Researchshowsthatstressshghestwhenthepourng s done durng autumn, 1.5 m s the deal thckness for the hgh restrant zone, long pourng ntervals should be avoded, and the pourng temperature should be strctly controlled. (3)Theheghtandamountofthesmultaneouscoolng zone consderably affect stress. The smultaneous coolng zone can reduce the temperature dfference n the heght drecton, coordnate the deformaton, anddecreasethemutualrestrantoftheupperand lower zones and the temperature stress caused by

12 12 Mathematcal Problems n Engneerng the temperature drop between adjon layers. Wthn the allowed condtons, ncreasng the heght of the coolng zone, especally on a slope, s advsed. (4) The experence n the temperature control of Zangmu, whch s the same concern confronted n Jexu, shows that ntellgent water flow makes the nternal coolng process ratonal and optmzed. Real-tme temperature examnaton ndcates that feedback, calculaton, and flow adjustment, as well as the automatc nterventon of coolng water flow, are realzed to prevent cracks through control of the temperature process, such as avodance of hgh-temperature ncreases and rapd temperature drops. Conflct of Interests The authors declare that there s no conflct of nterests regardng the publcaton of ths paper. Acknowledgments The authors acknowledge the support and fundng provded by the Natonal Key Basc Research Program of Chna (973 Program) (2013CB036406, 2013CB035904), the Key Projects n the Natonal Scence and Technology Pllar Program durng the Twelfth Fve-year Plan Perod (2013BAB06B02), the Specal Scentfc Research Project of the Chna Insttute of Water Resources and Hydropower Research, and the Specal Scentfc Research Project of the State Key Laboratory ofsmulatonandregulatonofwatercyclenrverbasn. References [1] P. Hu, P. Yang, G. Zhang, Z. Ren, and L. Le, Research on temperature control and crack preventon on double curvature archdamnlaxwahydropowerstaton, Hydropower,vol.33, no.11,pp.51 54,2007. [2] SL , Desgn Gudelnes of Concrete Arch Dam,2003. [3] T. Zhang and J. Chen, Study of specal constructon measures n hgh alttude and cold regons, Hunan Water Resources and Hydropower,vol.6,pp.48 51,2010. [4] A. Lu, Concrete constructon n wnter n North Tbet, Jln water resource and hydropower, Extended Heat Reserve,vol.5, pp. 1 3, [5] Z.-H. Wang, Y.-M. Zhu, and S.-P. Yu, Study on temperature control and crack preventon of thn-walled concrete structure, X an Constructon Technology Unversty Journal,vol.39,no.6, pp , [6] D. Yuan, Reasons of cracks n concrete s underground part and preventon methods, Constructon Technologes, no.4,pp.92 93, [7]B.Dng,G.Wang,S.Huangetal., Arevewoncausesof crackng n domestc concrete dams and preventve measures, Water Resources and Hydropower Engneerng, no.4,pp.12 18, [8]N.Sh,J.Ouyang,R.Zhang,andD.Huang, Expermental study on early-age crack of mass concrete under the controlled temperature hstory, Advances n Materals Scence and Engneerng,vol.2014,ArtcleID671795,10pages,2014. [9]Z.Zhang,X.Guo,andR.Du, Analyssofhydratonheatnduced stresses and cracks n massve concrete walls, Journal of Hoha Unversty,vol.30,no.5,pp.12 16,2002. [10] G. De Schutter, Fnte element smulaton of thermal crackng n massve hardenng concrete elements usng degree of hydratonbasedmaterallaws, Computers and Structures,vol.80,no , pp , [11] C. Baley and M. Cross, A fnte volume procedure to solve elastc sold mechancs problems n three dmensons on an unstructured mesh, Internatonal Journal for Numercal Methods n Engneerng,vol.38,no.10,pp ,1995. [12] Y. Ballm, A numercal model and assocated calormeter for predctng temperature profles n mass concrete, Cement and Concrete Compostes,vol.26,no.6,pp ,2004. [13]A.I.H.Malkawl,S.A.Mutasher,andT.J.Qu, Thermalstructural modelng and temperature control of roller compacted concrete gravty dam, Performance of Constructed Facltes,vol.17,no.4,pp ,2003. [14] P. Léger and M. Leclerc, Hydrostatc, temperature, tmedsplacement model for concrete dams, Engneerng Mechancs,vol.133,no.3,pp ,2007. [15] F. Zhu and K. L, Modelng heat and mosture transfer wthn porous textles under hgh temperature gradents, Advanced Materals Research, vol , pp , [16] J. Komonen and V. Penttala, Influence of admxture type and concrete temperature on strength and heat of hydraton of concrete, n Proceedngs of the 10th Internatonal Congress on the Chemstry of Cement,H.Justnes,Ed.,vol.3,pp.1 8,Amarka AB and Congrex Goteborg AB, Gothenburg, Sweden, [17] A. K. Schndler, Concrete hydraton, temperature development, and settng at early-ages [Ph.D. thess], UnverstyofTexasat Austn, Austn, Tex, USA, [18] D. Lelèvre, V. Ncolas, and P. Glouannec, Numercal modelng of heat and mass transfer n porous materals durng dryng and shrnkage, n COMSOL Conference,2012. [19] Z. P. Bazant and S. Baweja, Creep and shrnkage predcton model for analyss and desgn of concrete structures model B 3, Materals and Structures,vol.28,no.6,pp ,1995. [20] Z. Zuo, Y. Hu, Y. Duan, and J. Yang, Smulaton of the temperature feld n mass concrete wth double layers of coolng ppes durng constructon, Tsnghua Unversty, vol. 52,no.2,pp ,2012. [21] B. Zhu, Thermal Stresses and Temperature Control of Mass Concrete, Chna Electrc Power Press, Bejng, Chna, 1998.

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