Numerical Simulation of Early Age Cracking of Reinforced ... - MDPI

applied sciences Article

Numerical Simulation of Early Age Cracking of Reinforced Concrete Bridge Decks with a Full-3D Multiscale and Multi-Chemo-Physical Integrated Analysis Tetsuya Ishida 1, * 1 2 3 4

*

ID

, Kolneath Pen 1 , Yasushi Tanaka 2 , Kosuke Kashimura 3 and Ichiro Iwaki 4

Department of Civil Engineering, The University of Tokyo, Tokyo 113-8656, Japan; [email protected] Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan; [email protected] Research Institute of General Research Laboratory, Yokogawa Bridge Holdings Co., Ltd., Chiba 261-0002, Japan; [email protected] College of Engineering, Nihon University, Fukushima 963-8642, Japan; [email protected] Correspondence: [email protected]

Received: 13 February 2018; Accepted: 2 March 2018; Published: 7 March 2018

Abstract: In November 2011, the Japanese government resolved to build “Revival Roads” in the Tohoku region to accelerate the recovery from the Great East Japan Earthquake of March 2011. Because the Tohoku region experiences such cold and snowy weather in winter, complex degradation from a combination of frost damage, chloride attack from de-icing agents, alkali–silica reaction, cracking and fatigue is anticipated. Thus, to enhance the durability performance of road structures, particularly reinforced concrete (RC) bridge decks, multiple countermeasures are proposed: a low water-to-cement ratio in the mix, mineral admixtures such as ground granulated blast furnace slag and/or fly ash to mitigate the risks of chloride attack and alkali–silica reaction, anticorrosion rebar and 6% entrained air for frost damage. It should be noted here that such high durability specifications may conversely increase the risk of early age cracking caused by temperature and shrinkage due to the large amounts of cement and the use of mineral admixtures. Against this background, this paper presents a numerical simulation of early age deformation and cracking of RC bridge decks with full 3D multiscale and multi-chemo-physical integrated analysis. First, a multiscale constitutive model of solidifying cementitious materials is briefly introduced based on systematic knowledge coupling microscopic thermodynamic phenomena and microscopic structural mechanics. With the aim to assess the early age thermal and shrinkage-induced cracks on real bridge deck, the study began with extensive model validations by applying the multiscale and multi-physical integrated analysis system to small specimens and mock-up RC bridge deck specimens. Then, through the application of the current computational system, factors that affect the generation and propagation of early age thermal and shrinkage-induced cracks are identified via experimental validation and full-scale numerical simulation on real RC slab decks. Keywords: multiscale modelling; concrete bridge deck; crack assessment; early-age cracking; blast-furnace slag concrete

1. Introduction Much of Japan’s infrastructure was constructed during the past half century, and parts of this infrastructure are undergoing severe deterioration due to environmental and loading actions. Road structures in cold and snowy regions are reported to deteriorate more quickly and severely than expected due to a combination of frost damage, chloride attack from de-icing agents, alkali–silica Appl. Sci. 2018, 8, 394; doi:10.3390/app8030394

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reaction (ASR), cracking and fatigue. For such structures, it is necessary to combat deterioration and ensure durability performance in design and to consider the inevitable environmental and loading actions during service. In November 2011, the Japanese government resolved to build “Revival Roads” in the Tohoku region to accelerate recovery from the Great East Japan Earthquake of March 2011. The Tohoku region experiences cold and snowy weather in the winter, so complex degradation involving multiple factors, such as those mentioned above, is anticipated. Thus, to enhance the durability performance of road structures, more particularly reinforced concrete (RC) slab decks, multiple countermeasures are proposed: a low water-to-cement ratio in the mix, mineral admixtures such as blast furnace slag (BFS) and/or fly ash to mitigate the risks of chloride attack and ASR, anticorrosion rebar and 6% entrained air for frost damage [1]. It should be emphasised here that such high durability specifications may contradictorily increase the risk of early age cracking induced by temperature and shrinkage due to the large amount of cement and the use of mineral admixtures. Meanwhile, to achieve the rational design, construction and maintenance of concrete structures, prediction of the performance of structures throughout their lifespan is crucial, from the beginning of the hydration reaction to the end of their service life, with consideration of various material and mix proportions, structural dimensions and curing and environmental conditions. Faria et al. [2] proposed a thermo-mechanical model for computing strain and stresses whereby the effects are coupled. Once there is a thermal gradient, volumetric change would occur. If the volumetric change is not permitted, the thermal stresses would increase. On the contrary, once discontinuity occurs due to concrete cracking, the thermal field would be altered. In this model, the moisture equilibrium and transport is not considered. Furthermore, Jendele et al. [3] proposed thermo-hygro-mechanical simulations of early-age concrete cracking considering stress state, concrete creep, autogenous shrinkage and drying shrinkage to predict the early-age shrinkage and crack width. The hydration model was first fitted to the semi-adiabatic measurements on relatively small specimens, which are then scaled up to a structural level. In terms of computational process, various variables were required as the inputs for simulations such as sorption isotherms, intrinsic and relative permeability, porosity, Young’s modulus, Poisson’s ratio, compressive strength, and other parameters. While the former could not be extended for other durability issues which requires moisture transport such as chloride ingression, carbonation, ASR, calcium leaching and corrosion, the latter requires quite a high amount of material parameters that would be practically complicated. On the other hand, aiming for a unified approach to the evaluation of the behaviour of concrete structures in various conditions, the Concrete Laboratory of the University of Tokyo has been working to develop a multiscale integrated analysis platform, DuCOM-COM3 [4,5]. The platform consists of two systems: a thermodynamic coupled analysis system, DuCOM, which integrates various micro-physical-chemical–based models of cementitious composites, and a nonlinear dynamic RC structure analysis system COM3, which deals with macroscopic mechanical responses and damage to RC structures. With using only simple inputs such as such as mix proportions, structural geometry and boundary conditions in terms of history of environmental exposure of the structure, DuCOM-COM3 attempts to tackle the physio-chemical properties of concrete structures from its young age onward while also incorporate various ion transport phenomena for future performance-based durability design. Against this background, this paper presents a numerical simulation of early age deformation and cracking of RC structures with full 3D multiscale and multi-physical integrated analysis. First, a multiscale constitutive model of solidifying cementitious materials is briefly introduced based on systematic knowledge of microscopic thermodynamic phenomena and microscopic structural mechanics. With the aim to assess the early age thermal and shrinkage-induced cracks on real bridge decks, the study began with extensive model validations by applying the multiscale and multi-physical integrated analysis system to small specimens and mock-up RC bridge deck specimens. Then, through the application of the current computational system, factors that affect the generation and propagation

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of early age thermal and shrinkage-induced cracks are identified via experimental validation and full-scale numerical simulation on real RC slab decks. 2. Overview of Multiscale and Multi-Physical Modelling Figures 1 and 2 gives an overview of the multiscale and multi-physical modelling to simulate time-dependent deformation and cracking of concrete structures. The system consists of thermodynamic multi-chemo-physical modelling with DuCOM and nonlinear structural analysis with COM3. The former includes various thermodynamic models, such as multicomponent hydration, micropore structure formation and moisture equilibrium/transport, whilst the latter is a 3D finite-element analysis that implements constitutive laws of uncracked/cracked and hardening/aging/matured concrete. By inputting the basic data, such as mix proportions, structural geometry and boundary conditions in terms of history of environmental exposure of the structure, over time-space domain, the kinematic chemo-physical and mechanical events of representative elementary volume (REV) from different scales would be individually solved in a certain timestep. All other time-dependent properties of concrete such as elastic modulus, temperature, pore pressure, creep, moisture status, total porosity of interlayer, gel and capillary pores are computed internally based on the micromodels of materials inside the DuCOM system [6]. In the multiscale constitutive model, concrete is idealised as a two-phase composite in which cement paste and elastic aggregate co-exist (Figure 2A) [4]. The aggregate is assumed to be rigid and to show elastic deformation, and the shrinkage caused by aggregates is also considered. The hardened cement paste matrix is considered to be an assembly of fictitious clusters, referring to the solidification theory. As cement hydration proceeds, the number of clusters increases. The overall capacity of a cement matrix is obtained by summing the capacities of all clusters, which show time-dependent deformation relevant to the history. Based on the water status in the micro-pores, the time-dependent deformation, which consists of elastic, viscoelastic, viscoplastic and plastic components, is numerically computed. During the drying process, the water in pores is gradually lost. Consequently, in microscale pores, a water meniscus forms, and some shrinkage stress is generated by capillary tension. In contrast, in nanoscale pores, shrinkage stress is generated by disjoining pressure. These shrinkage stresses are quantified in the multiscale model and integrated as the overall shrinkage stresses, as shown in Figure 2B, which are given to compute the volumetric stress of cement paste carried by both skeleton solid and pore pressure, referring to Biot’s theorem of a two-phase continuum [6,7]. The volumetric change generated by cement hydration and shrinkage is systematically included in the modelling of concrete mechanics, which deals with macroscopic structural responses based on the space-averaged constitutive laws on the fixed four-way cracked concrete model (Figure 2C). It is important to mention that the microfracture cracking criteria are determined based on the local tensile strength depending on the moisture state inside the concrete because drying has both negative and positive effects. Microcracks caused by drying reduce the tensile strength, while negative pore water pressure in a dry state works as pre-stress and enhances local resistance against the tensile load [8]. Thus, in the model, various local tensile strengths were considered according to the moisture status in the micropores and nanopores (Figure 2D).

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Figure Figure 1. 1. Multiscale Multiscaleand andmulti-physical multi-physical modelling modelling to to simulate simulate time-dependent time-dependent concrete concrete performance. performance. Figure 1. Multiscale and multi-physical modelling to simulate time-dependent concrete performance.

Figure deformation and and Figure2.2.Multiscale Multiscaleand andmulti-physical multi-physical modelling modelling to to simulate simulate time-dependent deformation Figure 2. Multiscale and multi-physical modelling to simulate time-dependent deformation and cracking. cracking. cracking.

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3. Numerical Simulation of Early-Age Behaviour of Small Specimens to Actual Rc Deck Slabs 3.1. Target of Analysis The subject of this analysis is Shinkesen Bridge in Rikuzentaka, Iwate prefecture, Tohoku region, Japan. This bridge is amongst the 250 bridges that are scheduled to be constructed to accelerate the infrastructural recovery from the Great East Japan Earthquake. Before the Shinkesen Bridge was constructed, substantial precedents existed for the use of fly ash as the cementitious material in mixture designs for the bridge deck [1]. However, some problems have arisen in terms of a limited supply of fly ash concrete from ready-mixed concrete manufacturing plants due to the insufficiency of separate silos for fly ash and the insufficiency in high-standard fly ash itself due to the minimal number of thermal power plants. These restrictions have been the motivating factor for the development of an alternative method that makes use of BFS to tackle the deterioration issues in the Tohoku region. BFS blended cement has been shown to possess greater frost resistance, chloride binding, a higher tolerance for ASR and a denser micropore structure than ordinary Portland cement (OPC) [9–11], which is practically ideal for the environmental conditions in the Tohoku region. The Shinkesen Bridge was selected as the primary entry for the introduction of BFS concrete for nationwide concrete durability design. With the use of a low water-to-binder ratio and BFS in the mix proportion, early-age cracking might be bound to occur due to low creep and high autogenous shrinkage properties. In addition, it is universally understood that cracking would permit deleterious ions such as chloride and carbonated ions to deteriorate the concrete body unrestrained. Therefore, to quantitatively and qualitatively assure the validity and performance of the mix design, an in-depth study comprising both experiments and multiscale thermodynamic integrated analysis was conducted from a laboratory scale on the order of decimetres up to a structural scale on the order of decametres, followed by assessment and evaluation of the bridge deck via analytical results. 3.2. Experimental Outline and Model Validation via Small-Scale Specimens (Decimetres) As mentioned above, the Shinkesen Bridge deck was implemented with BFS concrete. In accordance with small-scale specimens, OPC concretes were simultaneously used as a reference. To reflect on the properties of micropore structures and evaluate free volumetric change, deformation and cracks due to shrinkage, mass loss and shrinkage tests were conducted on 200 × 200 × 800 mm3 prismatic OPC specimens. Then, using the mixture designs proposed for the Shinkesen Bridge, compression tests were executed on cylindrical specimens with radius of 100 mm and height of 200 mm according to JIS A 1108 specification to determine the concrete with the most appropriate strength for application on the bridge. Because curing conditions adversely influence the properties of concrete with BFS, especially its early strength to resist thermal and shrinkage-induced cracks, shrinkage tests were then performed on 100 × 100 × 400 mm3 prismatic specimens by applying various prolonged seal-curing durations. It is important to mention that, in addition to prolonged curing, expansive additives were used to lessen the cracking tendency. Finally, to study the effects of restraints imposed by reinforcing bars, 400 × 400 × 200 mm3 prismatic specimens were used to trace the strain progress of all proposed mixture designs. Each test was designed for different environments, from a controlled chamber to ambient conditions, incorporating details such as temperature, humidity, solar radiation and rainfall. The details of each experiment and its corresponding validation will be explicitly displayed in the following sections. The numerical models have been well-verified in environmental controlled condition. Yet, the fluctuation in environmental conditions necessitates further model validation because it significantly affects the microscopically thermodynamic phenomena of the whole concrete body and, consequently, the mechanical properties. Furthermore, since our current DuCOM-COM3 computational platform does not possess a sophisticated expansive agent model, the model validation process will also aim to ensure the capability in predicting the behavior under these complex actual considerations.

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3.2.1. Influence of Environmental Conditions: Rainfall, Shade and Indoors Appl. Sci. Sci. 2018, 2018, 8, 8, xx FOR FOR PEER PEER REVIEW Appl. Figure 3a represents aREVIEW one-fourth

of 18 18 of finite-element model of the 200 × 200 × 800 mm3 66prismatic specimens that were used in the experiments concrete shrinkage under direct rainfall, shade and 3.2.1. Influence Influence of Environmental Environmental Conditions:on Rainfall, Shade and Indoors Indoors 3.2.1. of Conditions: Rainfall, Shade and indoor environment. Apart from the indoor case, for which numerical models have been verified, the Figure 3a 3a represents represents aa one-fourth one-fourth finite-element finite-element model model of of the the 200 200 ×× 200 200 ×× 800 800 mm mm33 prismatic prismatic Figure fluctuation in environmental conditions necessitates further model validation because it significantly specimens that that were were used used in in the the experiments experiments on on concrete concrete shrinkage shrinkage under under direct direct rainfall, rainfall, shade shade and and specimens affects the microscopic thermodynamic phenomena of the whole concrete body and, consequently, indoor environment. environment. Apart Apart from from the the indoor indoor case, case, for for which which numerical numerical models models have have been been verified, verified, the the indoor the mechanical The displacement restraints based upon the symmetric fluctuation in inproperties. environmental conditions necessitates furtherwere modelapplied validation because significantly fluctuation environmental conditions necessitates further model validation because itit significantly condition actual placement of the specimens. words, a vertical restraint affectsand the microscopic microscopic thermodynamic phenomenaInof ofother the whole whole concrete bodydisplacement and, consequently, consequently, affects the thermodynamic phenomena the concrete body and, was applied at the bottom surface, whereas longitudinal and transverse displacement restraints the mechanical mechanical properties. properties. The The displacement displacement restraints restraints were were applied applied based based upon upon the the symmetric symmetric were the applied at theand X-symmetric planeof and Y-symmetric plane, respectively. As necessitated by the condition and actual placement placement of thethe specimens. In other other words, vertical displacement displacement restraint condition actual the specimens. In words, aa vertical restraint was applied at the bottom surface, whereas longitudinal and transverse displacement restraints were computational platform, the mix proportion, casting temperature and curing conditions were identical was applied at the bottom surface, whereas longitudinal and transverse displacement restraints were applied at the the X-symmetric X-symmetric plane and the the Y-symmetric Y-symmetric plane, respectively. As necessitated necessitated by the the and at and respectively. As by to theapplied experimental conditions.plane The implemented mixtureplane, designs for the specimens were OPC55 computational platform, the mix proportion, casting temperature and curing conditions were computational mix 3b proportion, casting temperature and curing were data, OPC45 as indicatedplatform, in Table 1.the Figure depicts the environmental condition. Theconditions environmental identical to to the experimental experimental conditions. The The implemented implemented mixture mixture designs designs for for the the specimens specimens were were identical which consist ofthe the temperatureconditions. and relative humidity of rainfall, shade and indoor conditions, were OPC55 and OPC45 as indicated in Table 1. Figure 3b depicts the environmental condition. The OPC55 anddata OPC45 as indicated Table 1. Figure 3b depicts environmental condition. The obtained from loggers at each in corresponding location. Thethe rainfall specimens were exposed to environmental data, which consist of the temperature and relative humidity of rainfall, shade and environmental data, which consist of the temperature and relative humidity of rainfall, shade and directindoor sunshine and rainfall, as shown in Figure 4a, whereas shaded specimens were sheltered from conditions, were were obtained obtained from from data data loggers loggers at at each each corresponding corresponding location. location. The The rainfall rainfall indoor conditions, directspecimens sunshine were and rain (Figure 4b). The indoorand specimens were keptininFigure a storage room without direct exposed to direct sunshine rainfall, as shown 4a, whereas shaded specimens were exposed to direct sunshine and rainfall, as shown in Figure 4a, whereas shaded exposure to thewere ambient environment. Rainfalland is of paramount determining concrete specimens were sheltered from direct direct sunshine sunshine and rain (Figure 4b). 4b).important The indoor indoorin specimens were kept kept specimens sheltered from rain (Figure The specimens were in a storage room without direct exposure to the ambient environment. Rainfall is of paramount shrinkage behaviour. To simply account for the water absorption of concrete via rainfall, the emissivity in a storage room without direct exposure to the ambient environment. Rainfall is of paramount important in determining determining concrete shrinkage behaviour. Toone simply account for the the water absorption coefficient in the surface mass flux isshrinkage assumedbehaviour. to increase hundred times from itsabsorption original value. important in concrete To simply account for water of concrete via rainfall, the emissivity coefficient in the surface mass flux is assumed to increase one [12]. of concrete via rainfall, the emissivity in the surface mass flux be is assumed one However, the actual hydraulic pressurecoefficient on the exposed surface could acquiredtoinincrease the model hundred times from its original value. However, the actual hydraulic pressure on the exposed surface hundreddata timesoffrom its original value. However, the actual hydraulic pressure exposed surface The rainfall Koriyama in Fukushima prefecture was retrieved fromon thethe Japan Meteorological could be be acquired acquired in in the the model model [12]. [12]. The The rainfall rainfall data data of of Koriyama Koriyama in in Fukushima Fukushima prefecture prefecture was was could Agency and applied in the analysis.

retrieved from from the the Japan Japan Meteorological Meteorological Agency Agency and and applied applied in in the the analysis. analysis. retrieved

(a) (a)

(b) (b)

Figure 3. (a) (a) Finite-element(FE) (FE)model model of of one one fourth ofof the specimen; (b) environmental environmental condition. Figure 3. (a) Finite-element onefourth fourthof the specimen; (b) environmental condition. Figure 3. Finite-element (FE) model the specimen; (b) condition. Table 1. Mix Mix proportion proportion of 200 200 × 200 200× 800 mm mm prismatic specimens andand curing condition. 1. of ×× 800 specimens and curing condition. TableTable 1. Mix proportion of 200 × ×200 800 mm3 3prismatic prismatic specimens curing condition. 3

Series Series

Series

Unit Content Content (kg/m (kg/m33)) Unit Seal-Cured 3 Unit Content (kg/m W C Ex Ex SS )G G Seal-Cured W C Air (%) Seal-Cured 4.5 W172 172 C 313 -Ex - 834 834 S 997 997 G 77 days days 4.5 313 4.5 66 172164 7 days 164 313 338 20 20- 791 791834992 992 997 77 days days 338

w/b (%) (%) Air Air (%) (%) w/b

w/b (%)

OPC55 55 OPC55 55 OPC55 55 OPC45 45 OPC45 45

OPC45 45 6 164 338 20 791 992 7 days Note: w/b w/b == water-to-binder water-to-binder ratio; ratio; W W == Water; Water; C C == Cement; Cement; Ex Ex == Expansive Expansive additives; additives; SS == Sand; Sand; G G == Note: Note: w/b = water-to-binder ratio; W = Water; C = Cement; Ex = Expansive additives; S = Sand; G = Gravels. Gravels. Gravels.

(a) (a)

(b) (b)

Figure 4. (a) (a) Specimenswith withdirect direct rainfall rainfall exposure; exposure; (b) shaded specimens. Figure 4. Specimens with direct (b) shaded specimens. Figure 4. (a) Specimens rainfall exposure; (b) shaded specimens.

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Figures 5–7 5–7 portray portray aaa comparison comparison between between the the measured measured values values from from data data loggers loggers and and the the Figures 5–7 portray comparison between the measured values from data loggers and the Figures Figures 5–7 portray a comparison between the measured values from data loggers and the analytical results of the experimented specimens. Figure 5 shows that a change in the mass of the analyticalresults resultsof ofthe theexperimented experimentedspecimens. specimens.Figure Figure555shows showsthat thataaachange changein inthe themass massof ofthe the analytical results of the experimented specimens. Figure shows that change in the mass of the analytical specimens could be simulated well for the shaded and indoor cases. The analytical results for the specimens could be simulated well for the shaded and indoor cases. The analytical results for the specimens could could be be simulated simulated well well for for the the shaded shaded and and indoor indoor cases. cases. The The analytical analytical results results for for the the specimens specimens with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the specimens with with direct direct rainfall rainfall appear appear to to have have been been underestimated. underestimated. Figures Figures 666 and and 777 illustrate illustrate the the specimens with direct rainfall appear to have been underestimated. Figures and illustrate the specimens concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with concretestrain strainin inOPC55 OPC55and andOPC45, OPC45,respectively. respectively.IfIf Ifattention attentionwas wasgiven givento tothe thespecimens specimenswith withdirect direct concrete strain in OPC55 and OPC45, respectively. attention was given to the specimens with direct concrete direct rainfall, similar to the behaviour in mass change, a minimal discrepancy was found in the rainfall, similar to the behaviour in mass change, a minimal discrepancy was found in the trend rainfall, similar similar to to the the behaviour behaviour in in mass mass change, change, aa minimal minimal discrepancy discrepancy was was found found in in the the trend trend rainfall, trend between the measured and analytical strain. As extra water from rainfall was supplied to betweenthe themeasured measuredand andanalytical analyticalstrain. strain.As Asextra extrawater waterfrom fromrainfall rainfallwas wassupplied suppliedto tothe theconcrete concrete between the measured and analytical strain. As extra water from rainfall was supplied to the concrete between the concrete through exposed the strain measured strainthis reflected this phenomenon through through the exposed exposed the surfaces, thesurfaces, measured strain reflected this phenomenon through concrete concrete through the exposed surfaces, the measured reflected phenomenon through concrete through the surfaces, the measured strain reflected this phenomenon through concrete expansion. Hence, the authors have come to understand that the simplified method of expansion.Hence, Hence,the theauthors authorshave havecome cometo tounderstand understandthat thatthe thesimplified simplifiedmethod methodof ofreproducing reproducing expansion. Hence, the authors have come to understand that the simplified method of reproducing expansion. reproducing the rainfall effect should be enhanced to increase the accuracy of numerical prediction, therainfall rainfalleffect effectshould shouldbe beenhanced enhancedto toincrease increasethe theaccuracy accuracyof ofnumerical numericalprediction, prediction,but butthis thiseffect effect the rainfall effect should be enhanced to increase the accuracy of numerical prediction, but this effect the but this effect would be relatively minimal in the case of large-scale concrete structures. In the case would be relatively minimal in the case of large-scale concrete structures. In the case of shaded would be be relatively relatively minimal minimal in in the the case case of of large-scale large-scale concrete concrete structures. structures. In In the the case case of of shaded shaded would of shaded specimens, it is believed that the deviation between the measured and analytical strain in specimens, itit it isis is believed believed that that the the deviation deviation between between the the measured measured and and analytical analytical strain strain in in OPC55 OPC55 specimens, believed that the deviation between the measured and analytical strain in OPC55 specimens, OPC55 likely resulted from the influence of the wind, unlike the indoor specimens. likelyresulted resultedfrom fromthe theinfluence influenceof ofthe thewind, wind,unlike unlikethe theindoor indoorspecimens. specimens. likely resulted from the influence of the wind, unlike the indoor specimens. likely

Figure 5. Mass change of each series (M-Measured & A-Analytical). A-Analytical). Figure5.5. 5.Mass Masschange changeof ofeach eachseries series(M-Measured (M-Measured&& Figure Mass change of each series (M-Measured Figure A-Analytical).

Figure 6. Concrete shrinkage strain of OPC45. Figure Concrete shrinkage strain of OPC45. Figure6.6. 6.Concrete Concreteshrinkage shrinkagestrain strainof ofOPC45. OPC45. Figure

Figure 7. 7. Concrete Concrete shrinkage shrinkage strain strain of of OPC55. OPC55. Figure Concrete shrinkage Figure Figure 7. Concrete shrinkage strain of OPC55.

3.2.2.Compressive Compressive Strength CompressiveStrength 3.2.2. Compressive Strength 3.2.2. Referring to JIS AA 1108 specification, compression tests onaon φ100 200-cylinder specimen with Referringto toJIS JISAA 1108 specification, compression tests a ϕ100 × 200-cylinder specimen Referring to JIS 1108 specification, compression tests on aaφ100 φ100 200-cylinder specimen with Referring 1108 specification, compression tests on ×××200-cylinder specimen with radius of 100 mm and height of 200 mm, were also conducted for various mixture designs (Table 2). with radius of 100 mm and height of 200 mm, were also conducted for various mixture designs radiusof of100 100mm mmand andheight heightof of200 200mm, mm,were werealso alsoconducted conductedfor forvarious variousmixture mixturedesigns designs(Table (Table2). 2). radius The specimens underwent seal-curing conditions for 28 days before exposure to the ambient (Table 2). The specimens underwent seal-curing conditions for 28 days before exposure to the ambient The specimens specimens underwent underwent seal-curing seal-curing conditions conditions for for 28 28 days days before before exposure exposure to to the the ambient ambient The environment in a storeroom (Figure 8). In the DuCOM system, the strength model assumes close environment in In DuCOM system, the model assumes environment in a storeroom (Figure 8). In the DuCOM system, the strength model assumes close environment in a storeroom (Figure 8). In the DuCOM system, the strength model assumes aaaclose relationship with capillary porosity development, whereby the present and initial capillary porosity relationshipwith withcapillary capillaryporosity porositydevelopment, development,whereby wherebythe thepresent presentand andinitial initialcapillary capillaryporosity porosity relationship are considered based on their ratio. BFS concrete has a finer pore size distribution and lower porosity are considered based on their ratio. BFS concrete has a finer pore size distribution and lower porosity are considered based on their ratio. BFS concrete has a finer pore size distribution and lower porosity

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relationship with capillary porosity development, whereby the present and initial capillary porosity are considered based on their ratio. BFS concrete has a finer pore size distribution and lower porosity than OPC concrete, which affects the long-term strength [13]. To revalidate the model, Figure 9 shows the compressive strength of each mix design series. It can be observed that the compressive strength can be satisfactorily predicted. Table 2. Trial mixture designs of potential concrete to be used for Shinkesen Bridge deck.

Appl. Sci. Sci. 2018, 2018, 8, 8, FOR PEER PEER REVIEW Appl. xx FOR REVIEW w/b (%) Series

Air (%)

Unit Proportion (kg/m3 ) W

C

Ex

S

G

Ad

of 18 18 88 of

OPC53 which 314[13]. 802 the than OPC OPC concrete, concrete, which52.9 affects the the 4.5 long-term166 strength [13]. To To- revalidate revalidate the1044 model,3.14 Figure 99 shows shows than affects long-term strength model, Figure OPC44 44 6 164 353 20 653 1112 2.24 the compressive compressive strength strength of of each each mix mix design design series. series. ItIt can can be be observed observed that that the the compressive compressive strength strength the BFS44 44 6 160 344 20 662 1112 2.18 can be be satisfactorily satisfactorily predicted. predicted. can

Figure 8. Environmental condition after 28 28 days days of of seal-curing. seal-curing. Figure Figure 8. 8. Environmental Environmental condition condition after after 28 days of seal-curing.

Figure 9. 9. Compressive Compressive strength of of concrete concrete (M-Measured Figure Compressivestrength (M-Measured and and A-Analytical). A-Analytical). Table 2. 2. Trial Trial mixture designs of of potential potential concrete to to be be used used for for Shinkesen Shinkesen Bridge Bridge deck. deck. Table mixture designs concrete 3.2.3. Influence of Curing Conditions on Concrete

Unit Proportion (kg/m33on )) the curing period to (kg/m The use of a high-performance mix design as Unit such Proportion requires a study Series w/b w/b (%) (%) Air Air (%) (%) Series W being C vulnerable Ex SS to cracking G Adrisk. Thus, referring determine the optimum choice for execution without W C Ex G Ad 3 prismatic plain concrete specimens were prepared with to Figure 10, five OPC53 100 × 100 52.9 × 400 mm4.5 OPC53 52.9 4.5 166 314 802 1044 3.14 166 314 - 802 1044 3.14 five different curing periods (7, to the environment of the OPC44 4414, 28, 56 164days) 353before 20 exposure 653 1112 1112 2.24 OPC44 44 66 and 91 164 353 20 653 2.24 control chamber (aBFS44 constant 2044 The design BFS44 44◦ C and 60% 160 humidity). 344 20 20 662 662 mix 1112 2.18of these specimens 66 relative 160 344 1112 2.18 was BFS44 (Table 2). Figure 11 shows the finite element of the prismatic specimens whereby the 3.2.3. Influence Influence of Curing Curing Conditions onsame Concrete boundary conditions are applied in the manner as that of previous cases. Unlike OPC concrete, 3.2.3. of Conditions on Concrete the use of a low water-to-cement ratio as such in BFS concrete allows autogenous shrinkage to play a The use use of of aa high-performance high-performance mix mix design design as as such such requires requires aa study study on on the the curing curing period period to to The predominant role, on par with that of drying shrinkage, in determining the properties of the concrete. determine the the optimum optimum choice choice for for execution execution without without being being vulnerable vulnerable to to cracking cracking risk. risk. Thus, Thus, determine Thus, to properly capture the autogenous and drying shrinkage of BFS concrete, the driving force of referring to to Figure Figure 10, 10, five five 100 100 ×× 100 100 ×× 400 400 mm mm33 prismatic prismatic plain plain concrete concrete specimens specimens were were prepared prepared referring shrinkage in the model is divided into two entities: capillary tension force and disjoining pressure. with five five different different curing curing periods periods (7, (7, 14, 14, 28, 28, 56 56 and and 91 91 days) days) before before exposure exposure to to the the environment environment of of with The former, which dominates the nanoscale pores, is of paramount significance under low relative the control control chamber chamber (a (a constant constant 20 20 °C °C and and 60% 60% relative relative humidity). humidity). The The mix mix design design of of these these specimens specimens the humidity, but the latter, which governs the microscale pores, contributes significantly with a high was BFS44 BFS44 (Table (Table 2). 2). Figure Figure 11 11 shows shows the the finite finite element element of of the the prismatic prismatic specimens specimens whereby whereby the the was relative humidity [6]. The applicability of the BFS model in actual specimens exposed to various curing boundary conditions conditions are are applied applied in in the the same same manner manner as as that that of of previous previous cases. cases. Unlike Unlike OPC OPC concrete, concrete, boundary durations would also be confirmed through this model validation. the use use of of aa low low water-to-cement water-to-cement ratio ratio as as such such in in BFS BFS concrete concrete allows allows autogenous autogenous shrinkage shrinkage to to play play the predominant role, role, on on par par with with that that of of drying drying shrinkage, shrinkage, in in determining determining the the properties properties of of the the aa predominant concrete. Thus, Thus, to to properly properly capture capture the the autogenous autogenous and and drying drying shrinkage shrinkage of of BFS BFS concrete, concrete, the the driving driving concrete. force of of shrinkage shrinkage in in the the model model is is divided divided into into two two entities: entities: capillary capillary tension tension force force and and disjoining disjoining force pressure. The The former, former, which which dominates dominates the the nanoscale nanoscale pores, pores, is is of of paramount paramount significance significance under under low low pressure.

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3 prismatic specimen. Figure 10.FE FE modelofofone-eighth one-eighth ofthe the 400×× 400 400 × 200 mm Figure 200mm mm33prismatic prismaticspecimen. specimen. Figure10. 10. FEmodel model of one-eighthof of the400 400 × 400 × × 200

Figure 11. 11. Concrete shrinkage strain strain in 100 × mm×3 400 specimens (M-Measured and A-Analytical). (M-Measured and Figure Concrete shrinkage in 100 100× ×400 100 mm3 specimens Figure 11. Concrete shrinkage strain in 100 × 100 × 400 mm3 specimens (M-Measured and A-Analytical). The trend of the analytical results shown in Figure 11 could be acceptable in terms of strain A-Analytical).

prediction despite some discrepancies, especially during the sealing period. Our current expansive The trend of the analytical results shown in Figure 11 could be acceptable in terms of strain The model trend would of the analytical shown expansive in Figure 11 could be acceptable inconsideration terms of strain additive only applyresults instantaneous strain to concrete without of prediction despite some discrepancies, especially during the sealing period. Our current expansive prediction despite discrepancies, especiallycould during the sealing Our current expansive its long-term effect,some whereby complete expansion continue to at period. least a week [14]. Although, to additive model would only apply instantaneous expansive strain to concrete without consideration additivebetter modelaccuracy would only apply instantaneous expansive strain toinconcrete without consideration provide in predicting strain at an early stage for cases which expansive additives are of its long-term effect, whereby complete expansion could continue to at least a week [14]. Although, of its long-term effect,aim whereby completethe expansion continue to at least a weekmodel. [14]. Although, applied, the authors to investigate issue andcould develop a more sophisticated Because to provide better accuracy in predicting strain at an early stage for cases in which expansive additives to better accuracy incracks, predicting at an early stage for cases in which expansive theprovide most prevalent forms of thatstrain is, thermal and shrinkage-induced cracks, are moreadditives likely to are applied, the authors aim to investigate the issue and develop a more sophisticated model. Because are applied, thecuring authors aim tothe investigate issue and develop a morecondition sophisticated model. Because occur after the period, minimal the variation during the sealing could be reasonably the most prevalent forms of cracks, that is, thermal and shrinkage-induced cracks, are more likely to the most prevalent forms of cracks, that is, thermal and shrinkage-induced cracks, are more likely to disregarded. Therefore, it could be concluded that the overall trend and strain value of concrete under occur after the curing period, the minimal variation during the sealing condition could be reasonably occur after the curing period, theacceptably minimal variation seal-curing conditions could be traced. during the sealing condition could be reasonably disregarded. Therefore, it could be concluded that the overall trend and strain value of concrete under disregarded. Therefore, it could be concluded that the overall trend and strain value of concrete under seal-curing conditions could be acceptably traced. 3.2.4. Influence of Reinforcing on Concrete seal-curing conditions could beBars acceptably traced. was understood that byBars observing the strain progress of small RC specimens, the shrinkage 3.2.4.ItInfluence of Reinforcing on Concrete 3.2.4. Influence of Reinforcing Bars on of Concrete behaviour and cracking susceptibility concrete using the mix proportions could be more revealing It was understood that byrestraints observing the strain progress of small RC specimens, the shrinkage to a certain degree due that to the thestrain reinforcing bars. Hence, prismatic RC the specimens of It was understood by observingofthe progress of small RC specimens, shrinkage behaviour and cracking susceptibility of concrete using the mix proportions could be more revealing 3 400 × 400 ×and 200cracking mm with the aforementioned mixture Table 2 werecould used for the experiment. behaviour susceptibility of concrete usingdesigns the mixinproportions be more revealing to a certain degree due to the restraints of the reinforcing bars. Hence, prismatic RC specimens Six reinforcing bars with a diameter of 19 mm were embedded transversely and longitudinally at both to a certain degree due 3to the restraints of the reinforcing bars. Hence, prismatic RC specimens of 400 × 400 × 200 mm3 with the aforementioned mixture designs in Table 2 were used for the the400 top ×and of the specimens. Figuredesigns 12 shows finite-element of of 400bottom × 200 regions mm with theprismatic aforementioned mixture in the Table 2 were usedmodel for the experiment. Six reinforcing bars with a diameter of 19 mm were embedded transversely and 3 one-eighth of Six the 400 × 400 × bars 200 mm specimen, which theembedded reinforcements were inserted experiment. reinforcing withprismatic a diameter of 19 in mm were transversely and longitudinally at both the top and bottom regions of the prismatic specimens. Figure 12 shows the into the elements purple boxes according to the theirprismatic reinforcement ratios.Figure The specimens longitudinally at marked both theby top and bottom regions of specimens. 12 showswere the finite-element model of one-eighth of the 400 × 400 × 200 mm33 prismatic specimen, in which the under seal-curing conditions for 28 days before relocated to a storage room with exposure finite-element model of one-eighth of the 400 they × 400were × 200 mm prismatic specimen, in which the reinforcements were inserted into the elements marked by purple boxes according to their to the ambient environment, as into shown Figure 8. To incorporate the effect of expansive reinforcements were inserted thein elements marked by purple boxes accordingadditives to their reinforcement ratios. The specimens were under seal-curing conditions for 28 days before they were in concrete, weratios. used The a simple modelwere thatunder imposes instantaneous expansive on thethey concrete reinforcement specimens seal-curing conditions for 28 strain days before were relocated to a storage room with exposure to the ambient environment, as shown in Figure 8. To dependingtoon degree of restraints, such as and external boundaries. relocated a the storage room with exposure torebar the ambient environment, as shown in Figure 8. To incorporate the effect of expansive additives in concrete, we used a simple model that imposes incorporate the effect of expansive additives in concrete, we used a simple model that imposes

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instantaneous strain concrete depending degree of restraints, such as rebar instantaneous strain on on thethe concrete depending on on thethe degree of restraints, such as 10 rebar Appl. Sci. 2018, 8,expansive 394expansive of 18 and external boundaries. and external boundaries.

Figure model of one fourth of specimen. Figure 12. FE model of fourth of specimen. Figure 12.12. FEFE model ofone one fourth ofthe thethe specimen.

Figure shows that the analyses proved that the strain progress specimens could Figure 1313 shows that the analyses proved that the strain progress ofof thethe specimens could bebe Figure 13 shows that the analyses proved that the strain progress of the specimens could be predicted satisfactorily. Furthermore, based result, it could be proven that the simple model predicted satisfactorily. based on this result, ititcould be that the model of predicted satisfactorily. Furthermore, based on on thisthis result, could beproven proven that thesimple simple model of an expansive agent could provide a reasonable output without affecting the strain behaviour an expansive agent could provide a reasonable output without affecting the strain behaviour of the of an expansive agent could provide a reasonable output without affecting the strain behaviour of of the concrete in the long run. Also, concrete expands in the initial place, risk of cracking in the concrete in the long run. Also, as concrete expands in the place, the risk of cracking in theinearly the concrete in the long run. Also, as as concrete expands in initial the initial place, thethe risk of cracking the early is heavily reduced because of the expansion effect. Therefore, main concern should period isperiod heavily reduced because of theof expansion effect.effect. Therefore, our main concern should not be early period is heavily reduced because the expansion Therefore, ourour main concern should not be with how well model predicts expansion concrete, with strain with well thewell model predicts the expansion of concrete, but withbut thebut progress of progress strain over time not behow with how thethe model predicts thethe expansion of of concrete, with thethe progress of of strain over time is relevant much more relevant to the initialisation of cracks. Based results of all because itbecause is because muchitmore torelevant the initialisation of cracks. of Based on the results ofthe all of the over time isitmuch more to the initialisation cracks. Based on on the results ofmodel all of of the model it can confirmed that computational models can trace mechanistic validations, itvalidations, can be confirmed that the computational models can models trace thecan mechanistic behaviour of the model validations, it can be be confirmed that thethe computational trace thethe mechanistic behaviour of concrete reasonably well a small scale. concrete reasonably well on a small scale. behaviour of concrete reasonably well on on a small scale.

3 RC specimens (M-Measured and A3 RC 3 mm Figure Concrete shrinkage in400 400 ×200 400 × 200 Figure 13. 13. Concrete shrinkage ××400 ×mm 200 specimens (M-Measured and AFigure 13. Concrete shrinkage strainstrain instrain 400in×400 RCmm specimens (M-Measured and A-Analytical). Analytical). Analytical).

3.3. Application of the Analytical Model on a Mock-Up Slab Specimen Application of the Analytical Model a Mock-Up Slab Specimen 3.3.3.3. Application of the Analytical Model on on a Mock-Up Slab Specimen To represent a restraint condition as close to reality as possible, two I-section girders were placed To represent a restraint condition asplaced close to as possible, two I-section girders placed Toconcrete represent a restraint condition to reality possible, I-section girders at the supports as they wouldasbeclose onreality theas actual steeltwo girders whereas halfwere of were theplaced actual at the concrete supports as they would be placed on the actual steel girders whereas half of the actual at the concrete they would be placed actual steel girders half of the actual specimen weresupports used foras the finite element modelonasthe indicated in Figure 14.whereas The replicated specimen specimen were used for finite element model as indicated inthe Figure 14. The replicated specimen specimen were used for thethe finite element model asfor indicated 14.surface The replicated specimen was cast with ‘BFS44’ mix design and water-cured 42 daysinonFigure top before exposure to was cast with ‘BFS44’ mix design and water-cured for 42 days on the top surface before exposure was cast with ‘BFS44’ mix design and water-cured for 42 days on the top surface before exposure the outside environment. For Figure 14b, the diameters of the reinforcing bars were 19 and 16 mmto into the outside environment. 14b, the diameters of reinforcing bars were and mm the outside environment. ForFor Figure 14b, the diameters of the reinforcing bars were 19 19 and 16 16 mm in in both top and bottom sections as Figure coloured and shown with thethe reinforcement ratio. The environmental both top and bottom sections as coloured and shown with the reinforcement ratio. The environmental both top and bottom sections as coloured and shown with the reinforcement ratio. The environmental data for Rikuzentaka in Iwate prefecture were obtained from the Japan Meteorological Agency and data Rikuzentaka inanalysis Iwate prefecture were obtained from the Japan Meteorological Agency and data forfor Rikuzentaka in Iwate prefecture were from Japan and identically input to the as shown inobtained Figure 15. Tothe trace theMeteorological expansion andAgency contraction identically to the shown Figure 15. trace the expansion contraction identically input thein analysis as as shown in in Figure 15. ToTo trace the expansion and contraction behaviour of input the to deck a analysis quantitative manner, strain gauges were also embedded atand the locations behaviour of the deck in a quantitative manner, strain gauges were also embedded at the locations behaviour of the deck in a quantitative manner, strain gauges were also embedded at the locations shown in Figure 16. These strain gauges perform measurements in transverse, longitudinal and shown in Figure 16. These strain gauges perform measurements in transverse, longitudinal and shown Figure 16.AsThese strainingauges measurementsmodels in transverse, longitudinal and verticalindirections. portrayed Figureperform 16, four finite-element of the mock-up specimen vertical directions. As portrayed in Figure 16, four models the mock-up specimen vertical directions. portrayed Figure 16, four finite-element of of the mock-up specimen were established to As conduct mesh in sensitivity analysis to finite-element minimise themodels calculation efforts with acceptable were established to conduct mesh sensitivity analysis to minimise the calculation efforts with were established to conduct mesh sensitivity analysis to minimise the calculation efforts with accuracy in the following large-scale bridge model. This element discretisation process was necessary acceptable accuracy following large-scale bridge model. This element discretisation process acceptable in in the following large-scale bridge model. This element discretisation process because theaccuracy convergence inthe computation of thermodynamically microscopic aspects in DuCOM had to was necessary because the convergence in computation of thermodynamically microscopic aspects was necessary because the convergence in computation of thermodynamically microscopic aspects be ensured to provide reasonably accurate results for its counterpart, COM3, to analyse the macroscopic in DuCOM had ensured provide reasonably accurate results counterpart, COM3, in DuCOM had to to be be ensured to to provide reasonably accurate results forfor its its counterpart, COM3, to to structural behaviour. analyse macroscopic structural behaviour. analyse thethe macroscopic structural behaviour.

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Figure14. 14.(a) (a)Overview Overviewofofmock-up mock-upslab slabspecimen; specimen;(b) (b)FE FEmodel modelofofhalf halfofofthe themock-up mock-upspecimen. specimen. Figure Figure 14. (a) Overview of mock-up slab specimen; (b) FE model of half of the mock-up specimen.

Figure 15. Environmental conditions. Figure 15. Environmental conditions.

Due to issues with the embedded strain gauges after removal the formwork, the measured issueswith withthe theembedded embeddedstrain straingauges gaugesafter afterremoval removalofof ofthe theformwork, formwork,the themeasured measured Due to issues data from the 42nd and 56th days were lost. Nonetheless, the whole trend of the strain could still be the 42nd and 56th days were lost. data from the 42nd and 56th days were lost. Nonetheless, the whole trend of the strain could still be captured, whereby the rearrangement of the strain gauges might have affected the strain progress progress captured, whereby the rearrangement of the strain gauges might have affected the strain progress and resulted resulted in inaaslightly slightlygreater greatershrinkage shrinkage strain value. Two main conclusions could be drawn strain value. Two main conclusions could be drawn from and resulted in a slightly greater shrinkage strain value. Two main conclusions could be drawn from from the result ofanalysis. this analysis. First, the computational model can capture the strain progress with the result of this First, the computational model can capture the strain progress with only the result of this analysis. First, the computational model can capture the strain progress with only only minimal differences. Good agreement was also achieved between the measured and analytical minimaldifferences. differences.Good Goodagreement agreementwas wasalso alsoachieved achievedbetween betweenthe themeasured measuredand andanalytical analyticalvalues values minimal values for the concrete temperature. Second, the differences between the computed strains of thefinitefour for the concrete temperature. Second, the differences between the computed strains of the four for the concrete temperature. Second, the differences between the computed strains of the four finitefinite-element models with distinctive aspect ratios and element sizes were also negligible. Thus, it can element models with distinctive aspect ratios and element sizes were also negligible. Thus, it can element models with distinctive aspect ratios and element sizes were also negligible. Thus, it can bebe be confirmed that the element with a length of around 300 mm could reasonably be implemented in confirmed that theelement element with length around 300mm mmcould could reasonably implemented the confirmed that the with a alength ofofaround 300 reasonably bebeimplemented ininthe the large-scale analysis. large-scale analysis. large-scale analysis. 3.4. Preliminary Analysis Concrete Deck Slab Shinkesen Bridge Evaluate the Occurrence Cracks 3.4.Preliminary PreliminaryAnalysis Analysisonon onConcrete ConcreteDeck DeckSlab Slabofof ofShinkesen ShinkesenBridge Bridgetoto toEvaluate Evaluatethe theOccurrence Occurrenceofof ofCracks Cracks 3.4. To combat the complex degradation processes from the cold environment, frost damage, chloride Tocombat combatthe thecomplex complexdegradation degradationprocesses processesfrom fromthe thecold coldenvironment, environment,frost frostdamage, damage, To attack from de-icing alkali–silica reaction andreaction fatigue, aand holistic countermeasure approach was chloride attack fromsalt, de-icing salt,alkali–silica alkali–silica fatigue, holisticcountermeasure countermeasure chloride attack from de-icing salt, reaction and fatigue, a aholistic undertaken to enhance the durability performance of the RC deck slab. The multiple protection approachwas wasundertaken undertakentotoenhance enhancethe thedurability durabilityperformance performanceofofthe theRC RCdeck deckslab. slab.The The multiple approach multiple strategy incorporates a low water-to-binder ratio (w/b), the use of mineral admixture, epoxy-coated protectionstrategy strategyincorporates incorporatesa alow lowwater-to-binder water-to-binderratio ratio(w/b), (w/b),the theuse useofofmineral mineraladmixture, admixture, protection reinforcing barsreinforcing and 6% entrained air [1]. Because theair early-age cracks such as shrinkage cracks allow epoxy-coated bars and 6% entrained [1]. Because the early-age cracks such as epoxy-coated reinforcing bars and 6% entrained airconcrete [1]. Because the early-age cracks such more migration of deleterious ions into the body of under such severe conditions, it isasof shrinkage cracks allow more migration of deleterious ions into the body of concrete under such shrinkage cracks allow moreand migration deleterious ions into thebefore body the of concrete under such great significance toit control delay itsofoccurrence [10]. Therefore, Shinkesen Bridge was severe conditions, is of great significance to control and delay its occurrence [10]. Therefore, before severe conditions, it is of assessment great significance to controlfor and delay its occurrence [10]. Therefore, before constructed, a cracking was performed various mixture designs. theShinkesen ShinkesenBridge Bridgewas wasconstructed, constructed, acracking crackingassessment assessmentwas wasperformed performedfor forvarious variousmixture mixture the Figure 17 outlines the layout of theafinite-element model of the Shinkesen Bridge for preliminary designs. designs. analysis of crack propagation. Considering the symmetric condition and actual construction procedure Figure 17outlines outlines thelayout layout ofthe thefinite-element finite-element model ofthe theShinkesen Shinkesen Bridgefor forpreliminary preliminary Figure 17be the of model of Bridge that would adopted, the RC deck slab was modelled in combination with the girders and their analysisofofcrack crackpropagation. propagation.Considering Consideringthe thesymmetric symmetriccondition conditionand andactual actualconstruction construction analysis stiffeners tothat achieve structural resemblances that slab havewas an effect on the restraint condition. To capture procedurethat would beadopted, adopted, theRC RCdeck deck modelled combination withthe the girders procedure would be the slab was modelled inincombination with girders the temperature and moisture gradients inside the RC deck slab properly, and based on the mesh and their stiffeners to achieve structural resemblances that have an effect on the restraint condition. and their stiffeners to achieve structural resemblances that have an effect on the restraint condition. sensitivity analysis conducted the mock-up slab inside specimen, the deck maximum length ofand thebased element capturethe thetemperature temperature andon moisture gradients theRC RC slabproperly, properly, ToTocapture and moisture gradients inside the deck slab and based onon was taken to be 250 mm. To shorten the computational time, and as a conservative measure, the themesh meshsensitivity sensitivityanalysis analysisconducted conductedononthe themock-up mock-upslab slabspecimen, specimen,the themaximum maximumlength lengthofofthe the the ◦ C temperature ambient environment was set to dry conditions with a constant 15 and 70% relative element was taken to be 250 mm. To shorten the computational time, and as a conservative measure, element was taken to be 250 mm. To shorten the computational time, and as a conservative measure, humidity on the concrete surface the calculation, whereas the asphalt layer would exist theambient ambient environment wasset setthroughout dryconditions conditions witha aconstant constant15 15°C°C temperature and70% 70% the environment was totodry with temperature and on the top surface in reality. The environmental conditions were decided based on the average value relativehumidity humidityononthe theconcrete concretesurface surfacethroughout throughoutthe thecalculation, calculation,whereas whereasthe theasphalt asphaltlayer layer relative would exist on the top surface in reality. The environmental conditions were decided based on the would exist on the top surface in reality. The environmental conditions were decided based on the average value in accordance with the local meteorological data. The effects of concrete mixture average value in accordance with the local meteorological data. The effects of concrete mixture

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Sci. 2018, 8, x FOR PEER REVIEW 18 in Appl. accordance with the local meteorological data. The effects of concrete mixture designs 12 onofcrack designs on crack generationwere and propagation investigated in Japan, the analysis. In Japan, the typicalnot generation and propagation investigatedwere in the analysis. In the typical w/b should designs on crack generation and propagation were investigated in the analysis. In Japan, the typical w/b should not exceed 65%. In most cases, a w/b of 55% was endorsed, whereby the upper limit of is exceed 65%. In most cases, a w/b of 55% was endorsed, whereby the upper limit of water content w/b should not exceed 65%. In most cases, a3 w/b of 55% was endorsed, whereby the upper limit3of 3 water contentasis175 recommended 175 limit kg/m ofand limit of theiscement content isasrecommended recommended kg/m and as lower thelower cement content recommended 300 kg/m [15]. water content is recommended as 175 kg/m3 and lower limit of the cement content is recommended 3 [15]. As seen in Table 3, the mixture designs consist of five series: BFS42, OPC42, BFS55, asseen 300 kg/m Asas in Table 3, the mixture designs consist of five series: BFS42, OPC42, BFS55, OPC55 and 300 kg/m3 [15]. As seen in Table 3, the mixture designs consist of five series: BFS42, OPC42, BFS55, OPC55 and BFS42-EX whereby ‘EX’ represents the use of expansive additives. BFS42-EX whereby ‘EX’whereby represents the use of expansive OPC55 and BFS42-EX ‘EX’ represents the use ofadditives. expansive additives.

Figure 16. Concrete shrinkage strain at corresponding gauges and concrete temperatures. *  to  Figure Concreteshrinkage shrinkagestrain strain at at corresponding corresponding gauges * to  1 to 8 Figure 16.16.Concrete gaugesand andconcrete concretetemperatures. temperatures. * represent different locations of strain gages; I, II, III, IV represent the four finite element analytical represent different locations of strain gages; I,III, II,IV III,represent IV represent the finite four finite element analytical represent different locations of strain gages; I, II, the four element analytical models. models. models.

Figure 17. Cont.

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Figure ofaabridge bridgespan. span. Figure17. 17.FE FEmodel model of one-fourth one-fourth of Table3.3.Mixture Mixture designs designs used for Table for parametric parametricstudy. study.

Series

Series

w/b (%)

OPC55 OPC55 BFS5555 BFS55 OPC42 55 OPC42 42 BFS42 BFS42 42 BFS42-EX BFS42-EX 42

w/b (%)

Air (%)

Air (%)

55 55 42 42 42

4.5 4.5 6 6 6

4.5 W 4.5 170 6 170 153 6 153 6 153

Unit Proportion (kg/m33) Unit Proportion (kg/m ) W C Ex S G Ad G 170 C310 -Ex 802 S1044 3.14 170 310 310 - - 802 802 1044 1044 3.14 310 802 153 364 - 653 1112 1044 2.24 364 653 1112 153 364 - 662 1112 2.18 364 662 1112 153 364 364 20 1112 1112 2.18 20 662 662

Ad 3.14 3.14 2.24 2.18 2.18

Figure 18 portrays the computed longitudinal strain after 2 years, which is the strain along the Figure 18 on portrays computed strain years, which the strainfrom along bridge axis, the topthe surface of thelongitudinal RC deck slab. The after strain2 contours wereisextracted thethe bridge axis, theslab top highlighted surface of the RCthe deck slab. The strain were extracted portion portion ofon deck with black rectangle. Duecontours to the restraints from thefrom steelthe girders, of high deck tensile slab highlighted rectangle. Due the restraints the steellength girders, strains werewith seenthe to black be localised around thetoelements with afrom longitudinal of high 60 tensile were seen to bethat localised around the elements a longitudinal lengthobserved of 60 mm, mm, strains which would resemble of cracks. Because these highwith tensile strains are mostly around the resemble 60-mm elements, the transverse width wasare calculated by multiplying thethe which would that of cracks. Becausemaximum these highcrack tensile strains mostly observed around maximum strainthe with the element length ofcrack 60 mm. According to the JSCE standard, thethe limit value 60-mm elements, transverse maximum width was calculated by multiplying maximum of crack width for concrete in60 a mm. severely corrosive environment is 0.0035c, where c refers to width the strain with the element length of According to the JSCE standard, the limit value of crack concrete cover [16]. Therefore, in the case of the Shinkesen Bridge, the allowable crack width would for concrete in a severely corrosive environment is 0.0035c, where c refers to the concrete cover [16]. be equivalent 0.14 of mm. main aspects, on BFS concrete, would be pinpointed from to Therefore, in thetocase theFour Shinkesen Bridge,focusing the allowable crack width would be equivalent themm. parametric study, including the influence the (1) binder (2) w/b, (3)from prolonged curing, 0.14 Four main aspects, focusing on BFS of concrete, wouldtype, be pinpointed the parametric and (4) expansive additives. First, after 7 days of seal curing, a higher tensile strain is observed in the study, including the influence of the (1) binder type, (2) w/b, (3) prolonged curing, and (4) expansive case of BFS55 than with OPC55. Furthermore, at 55% w/b, neither BFS55 nor OPC55 satisfy the JSCE additives. First, after 7 days of seal curing, a higher tensile strain is observed in the case of BFS55 than cracking criteria. If attention is paid to the case of 42% w/b, a reduction in maximum tensile strain with OPC55. Furthermore, at 55% w/b, neither BFS55 nor OPC55 satisfy the JSCE cracking criteria. could be seen in the OPC42 case, whereas higher maximum tensile strain was seen in BFS42 because If attention is paid to the case of 42% w/b, a reduction in maximum tensile strain could be seen in of the synergistic effect of high autogenous shrinkage and self-desiccation from a low w/b. Although the OPC42 case, whereas higher maximum tensile strain was seen in BFS42 because of the synergistic OPC42 seems to satisfy the JSCE cracking criteria, its low resistance against durability issues such as effect of high autogenous shrinkage and self-desiccation from a low w/b. Although OPC42 seems to ASR and chloride ingression mean that it might not be a good candidate for areas with severe satisfy the JSCE cracking criteria, its low consistent resistance with against issues such as ASR chloride environments, such as Tohoku. Then, thedurability universal understanding that and prolonged ingression mean that it might not be a good candidate for areas with severe environments, seal curing would reduce the moisture loss through the concrete’s surface, seal curing BFS42 upsuch to 28 as Tohoku. Then, consistent with the universal understanding that prolonged seal curing would reduce days significantly helped to reduce the maximum tensile strain. Finally, after incorporating expansive theadditives moistureinside loss through the concrete’s surface, seal curing BFS42 up to 28 days significantly helped BFS42, further improvement in reducing the generation of tensile strain was to illustrated. reduce the maximum Finally, after incorporating expansive BFS42, In additiontensile to the strain. lower intensity in the maximum crack width,additives based oninside the strain further improvement in nodal reducing the generation tensile strain was illustrated. addition to the contour, the amount of strain that reached a of longitudinal strain of 1000 μ is alsoIn minimal, which infers that lessincrack propagation would occur than on in the without expansive additives. Hence, lower intensity the maximum crack width, based the case strain contour, the amount of nodal strain asreached a conservative measurestrain in cases in which curing could not be conducted or that a longitudinal of 1000 µ is prolonged also minimal, which infers thatproperly less crack propagation maintained, the in recommendation to expansive use expansive additives in the protection strategy is would occur than the case without additives. Hence, as multiple a conservative measure in cases quite reasonable. in which prolonged curing could not be properly conducted or maintained, the recommendation to

use expansive additives in the multiple protection strategy is quite reasonable.

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Figure 18. 18. Parametric Parametric study study focusing focusing on on four four different differentaspects. aspects.**εεmax max = maximum longitudinal strain; Figure = maximum longitudinal strain; w max = maximum crack width. wmax = maximum crack width.

3.5. Post-Construction Analysis on on Concrete Concrete Deck Deck of of Shinkesen Shinkesen Bridge: Bridge: Verification Verification with with on-Site on-Site Measured 3.5. Post-Construction Analysis Data Measured Data Figure 19 19 represents represents the the entire entire overview overview of of the the 438-m 438-m seven-spanned seven-spanned steel steel girder–supported girder–supported Figure bridge. The casting sequence was carried out according to the numbers shown after considering the the bridge. The casting sequence was carried out according to the numbers shown after considering influence of moment distribution. For long-term monitoring, the strain and temperature gauges were influence of moment distribution. For long-term monitoring, the strain and temperature gauges were embedded on on casting casting lot lot 88 over over the the top top of of Pier Pier 33 support. support. The The top top surface surface of of the the concrete concrete underwent underwent embedded wet-curing for approximately 22 days, following by seal-curing for another 7 days before the RC deck deck wet-curing for approximately 22 days, following by seal-curing for another 7 days before the RC was exposed to the ambient environment. Figure 20 illustrates the finite-element model of one-fourth of the Shinkesen Bridge span, which imposes additional elements to consider over the finite-element model mentioned in Section 3.5. To precisely consider the real conditions of the concrete bridge deck,

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was exposed to the ambient environment. Figure 20 illustrates the finite-element model of one-fourth 15 15of of18 18 of the Shinkesen Bridge span, which imposes additional elements to consider over the finite-element Appl. Sci. 2018, 8, x FOR PEER REVIEW 15 of 18 mentioned in Section 3.5. To precisely the real conditions of the concrete bridge deck, aamodel time between Lots to casting was in time delay delay between Lots 11 and and 88 due due to the theconsider casting sequence sequence was also also included included in the the analysis. analysis. To To a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. account for effect the model, the restraint a time delay between Lots and 8 due joint to thein sequence was also included in the analysis. Toat account for the the effect of of the the1expansion expansion joint incasting the finite-element finite-element model, the longitudinal longitudinal restraint at To account for the effect of the expansion joint in the finite-element model, the longitudinal restraint Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as seen account for the effect of the expansion joint in the finite-element model, the longitudinal restraint at Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as seen at Lot is20. replaced with a rigid body whose sole aim is to from allow slight translational movement, as in Figure The nodes on the rigid body were restrained moving vertically. Insertion Lot 8 is8replaced a rigid body whose sole aim is to allow slight translational movement, as of seen in Figure 20. Thewith nodes on the rigid body were restrained from moving vertically. Insertion of the the seen in Figure 20. The nodes on the rigid body were restrained from moving vertically. Insertion rigid body was performed end of 88 to maintain the conditions in bridge in Figure The nodes on at the rigid body were restrained moving vertically. Insertion theof rigid body20. was performed at the the end of Lot Lot to maintainfrom the symmetric symmetric conditions in the theof bridge the body was performed atwas the of Lot 8 applied to maintain the symmetric conditions the bridge rigidrigid body was performed at the endend of Lot 8 to maintain the symmetric conditions in in the bridge span. The reinforcement ratio cautiously as calculated from the detail span. The reinforcement ratio was cautiously applied as calculated from the structural structural detail span. The reinforcement ratio was cautiously applied as calculated from the structural detail drawings, span. Thewhereby reinforcement ratio was cautiously applied as calculated fromThe theenvironmental structural detail drawings, lot more reinforcing bars top data drawings, whereby lot 88 possesses possesses more reinforcing bars in in the the top section. section. The environmental data whereby lot 8 possesses more reinforcing bars in the top section. The environmental data from drawings, whereby lot 8 possesses more reinforcing bars in the top section. The environmental data from the beginning of Lot 1 casting were also obtained from the Japan Meteorological agency as from the beginning of Lot 1 casting were also obtained from the Japan Meteorological agencythe as beginning of Lot 1 casting were also obtained from the Japan Meteorological agency as portrayed in from the beginning of Lot 1 casting were also obtained from the Japan Meteorological agency as portrayed portrayedin inFigure Figure21. 21. Figure 21. portrayed in Figure 21. Appl. Appl.Sci. Sci.2018, 2018,8,8,xxFOR FORPEER PEERREVIEW REVIEW

L6 L6 L6

L12 L12 L12 P1 P1 P1

L2 L2 L2

L10 L10 L10 P2 P2 P2

L4 L4 L4

L8 L1 L9 L5 L8 L1 L9 L5 L8 STEEL L1 GIRDERS L9 L5 STEEL GIRDERS STEEL GIRDERS P3 P3 P3

P4 P4 P4

L3 L3 L3

L11 L11 L11 P5 P5 P5

L13 L13 L13

L7 L7 L7

P6 P6 P6

Longitudinal-B Longitudinal-B Longitudinal-B Transverse-B Transverse-B Transverse-B

Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure Figure19. 19.Overview Overviewof ofShinkesen ShinkesenBridge Bridgeand andthe thecasting castingsequence sequence(Red (Redcircle circle==Gauge Gaugelocation). location). Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location).

Figure20. 20.FE FEmodel modelof ofone-fourth one-fourthof ofthe thespan spanof ofShinkesen ShinkesenBridge. Bridge. Figure Figure 20. FE model of one-fourth the span Shinkesen Bridge. Figure 20. FE model of one-fourth ofofthe span ofofShinkesen Bridge.

Figure21. 21.Environmental Environmentalcondition conditionof ofShinkesen ShinkesenBridge Bridgeafter afterLot Lot casted up to 250 days. Figure condition of Shinkesen Bridge after Lot casted up 250 days. Figure 21. Environmental condition of Shinkesen Bridge after Lot1111casted castedup up to 250 days. Figure 21. Environmental toto 250 days.

Figure between the analytical strain and the measured strain. The Figure 22 22 shows 22 shows shows aa comparison comparison between between the theanalytical analyticalstrain strainand andthe themeasured measuredstrain. strain.The The definition zero strain loggers was approximately 3 h after the casting on Lot 8 at definition of of initial initial in data loggers was approximately 3 h after the casting on Lot 8 at the initial zero strain in data loggers was approximately 3 h after the casting on Lot 8 atthe the 19th therefore taken from the start of the 19th day for verification day. The The analytical 19th day. The analytical analytical strain strain was was therefore thereforetaken takenfrom fromthe thestart startof ofthe the19th 19thday dayfor forverification verification process. strain progress can be well-traced for both longitudinal and can be process. ItIt can can be be observed observed that that the the strain strainprogress progresscan canbe bewell-traced well-tracedfor forboth bothlongitudinal longitudinaland and

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Figure 22 shows a comparison between the analytical strain and the measured strain. The definition of initial zero strain in data loggers was approximately 3 h after the casting on Lot 8 at the 19th day.8,The analytical strain was therefore taken from the start of the 19th day for verification Appl. Sci. 2018, x FOR PEER REVIEW 16 of 18 process. It can be observed that the strain progress can be well-traced for both longitudinal and transverse directions thethe concrete temperature, in addition to the directionsinside insidethe theconcrete. concrete.Furthermore, Furthermore,forfor concrete temperature, in addition to good agreement in the trend,trend, an underestimation seemsseems to occur the seal-curing period, the good agreement inoverall the overall an underestimation to during occur during the seal-curing whereby the concrete entirely is sealed and cover it is logically that period, whereby the isconcrete entirely sealedwith andformwork. cover withHence, formwork. Hence,reasonable it is logically the measured value greater than the analytical because the simulation considers thesimulation surface of reasonable that theismeasured value is greaterresults than the analytical results because the the concrete to surface virtuallyoftouch the ambient environment. In the addition, if attention is givenIntoaddition, the girders’ considers the the concrete to virtually touch ambient environment. if temperature, the computational almost matches the data from theexactly temperature gauge. attention is given to the girders’ platform temperature, theexactly computational platform almost matches the However, minimal deviation temperature is of littledeviation concern as long as the longitudinal strain, data from the temperature gauge.inHowever, the minimal in temperature is of little concern which for the infamous deck for cracking observed in most geographical as longaccounts as the longitudinal strain, transverse which accounts the infamous transverse deck crackingconditions, observed is considered. in most geographical conditions, is considered.

Figure Figure 22. 22. Concrete Concreteshrinkage shrinkage strain strain at at corresponding corresponding gauges gauges and and temperature temperature of Shinkesen Bridge.

4. Conclusions To provide a durable concrete infrastructure in severe environmental conditions, a comprehensive experimental and analytical study was conducted on a bridge in the Tohoku region, Shinkesen Bridge. This study focused mainly on the bridge’s early-age performance (i.e., thermal and shrinkage-induced cracks), and extension to long-term durability will be addressed in a future study.

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4. Conclusions To provide a durable concrete infrastructure in severe environmental conditions, a comprehensive experimental and analytical study was conducted on a bridge in the Tohoku region, Shinkesen Bridge. This study focused mainly on the bridge’s early-age performance (i.e., thermal and shrinkage-induced cracks), and extension to long-term durability will be addressed in a future study. First and foremost, on a small scale (decimetres), validation of the multiscale integrated computational system was satisfactory and agreed well with the experimental results. Verification with a medium-scale experimental mock-up slab specimen was then carried out to further confirm the capability of the numerical model, which also presented consistency with the experimental results. In addition, to reduce the calculation effort for large-scale analysis, an element discretisation process was performed in the mock-up slab specimen to determine the appropriate element size. Preliminary parametric studies on different mixture designs suggested the validity of the proposed mix design for Shinkesen Bridge. Finally, after bridge construction was complete, the computational model was again verified with acceptable agreement with data from strain gauges embedded in the concrete deck slab. The conclusions achieved are summarised as follows. 1.

2.

3.

The multiscale thermodynamic integrated analysis was verified and validated from the laboratory scale on the order of decimetres up to the structural scale on the order of decametres, which adequately confirms its ability to assess the behaviour of actual structures. By conducting the preliminary analyses before bridge construction, the superiority and inferiority of each mix proportion could be displayed to a great extent, which helped the engineers to be more decisive and confident when designing their mix proportions. Through the success of the study, the multi-scale thermodynamic computational platform would be implemented for long-term performance study by tracing the behavior of concrete through the course of time to propose maintenance plan abiding with preventive maintenance strategy currently endorsed in Japanese civil engineering situation.

Acknowledgments: This study was financially supported by the Council for Science, Technology and Innovation, “Cross-ministerial Strategic Innovation Promotion Program (SIP), Infrastructure Maintenance, Renovation and Management” through a grant by Japan Science and Technology Agency (JST). Author Contributions: Tetsuya Ishida and Yasushi Tanaka conceived and designed the analytical and experimental scheme; Tetsuya Ishida and Yasushi Tanaka supervised over the analytical process, Kosuke Kashimura and Ichiro Iwaki performed the experiments; Kolneath Pen analyzed the data; Tetsuya Ishida and Kolneath Pen wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7.

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