Numerical Simulation of Early Age Cracking of Reinforced Concrete Bridge Decks with a Full-3D Multiscale and Multi-Chemo-Physical Integrated Analysis

Tetsuya Ishida; Kolneath Pen; Yasushi Tanaka; Kosuke Kashimura; Ichiro Iwaki

doi:10.3390/app8030394

Numerical Simulation of Early Age Cracking of Reinforced Concrete Bridge Decks with a Full-3D Multiscale and Multi-Chemo-Physical Integrated Analysis

Ishida, Tetsuya;Pen, Kolneath;Tanaka, Yasushi;Kashimura, Kosuke;Iwaki, Ichiro 2018-03-07 00:00:00 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 1 , 1 2 3 4 ID Tetsuya Ishida * , Kolneath Pen , Yasushi Tanaka , Kosuke Kashimura and Ichiro Iwaki Department of Civil Engineering, The University of Tokyo, Tokyo 113-8656, Japan; kolneath@concrete.t.u-tokyo.ac.jp Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan; yasuxi@iis.u-tokyo.ac.jp Research Institute of General Research Laboratory, Yokogawa Bridge Holdings Co., Ltd., Chiba 261-0002, Japan; k.kashimura@ybhd.co.jp College of Engineering, Nihon University, Fukushima 963-8642, Japan; iwaki.ichirou@nihon-u.ac.jp * Correspondence: tetsuya.ishida@civil.t.u-tokyo.ac.jp 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 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 394 2 of 18 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 Appl. Sci. 2018, 8, 394 3 of 18 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). Appl. Sci. 2018, 8, 394 4 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 18 Figure 1. Multiscale and multi-physical modelling to simulate time-dependent concrete performance. Figure 1. Multiscale and multi-physical modelling to simulate time-dependent concrete performance. Figure 1. Multiscale and multi-physical modelling to simulate time-dependent concrete performance. Figure 2. Multiscale and multi-physical modelling to simulate time-dependent deformation and Figure 2. Multiscale and multi-physical modelling to simulate time-dependent deformation and Figure 2. Multiscale and multi-physical modelling to simulate time-dependent deformation and cracking. crack crack ing ing . . Appl. Sci. 2018, 8, 394 5 of 18 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 mm 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 mm 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 mm 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. Appl. Sci. 2018, 8, 394 6 of 18 3.2.1. Inﬂuence of Environmental Conditions: Rainfall, Shade and Indoors Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 18 Figure 3a represents a one-fourth ﬁnite-element model of the 200 200 800 mm prismatic specimens that were used in the experiments on concrete shrinkage under direct rainfall, shade and 3.2.1. Influence of Environmental Conditions: Rainfall, Shade and Indoors 3.2.1. Influence of Environmental Conditions: Rainfall, Shade and Indoors indoor environment. Apart from the indoor case, for which numerical models have been veriﬁed, the Figure 3a represents a one-fourth finite-element model of the 200 × 200 × 800 mm 3 prismatic Figure 3a represents a one-fourth finite-element model of the 200 × 200 × 800 mm prismatic ﬂuctuation in environmental conditions necessitates further model validation because it signiﬁcantly specimens that were used in the experiments on concrete shrinkage under direct rainfall, shade and specimens that were used in the experiments on concrete shrinkage under direct rainfall, shade and affects the microscopic thermodynamic phenomena of the whole concrete body and, consequently, indoor environment. Apart from the indoor case, for which numerical models have been verified, the indoor environment. Apart from the indoor case, for which numerical models have been verified, the the mechanical properties. The displacement restraints were applied based upon the symmetric fluctuation in environmental conditions necessitates further model validation because it significantly fluctuation in environmental conditions necessitates further model validation because it significantly condition and actual placement of the specimens. In other words, a vertical displacement restraint affects the microscopic thermodynamic phenomena of the whole concrete body and, consequently, affects the microscopic thermodynamic phenomena of the whole concrete body and, consequently, was applied at the bottom surface, whereas longitudinal and transverse displacement restraints were the mechanical properties. The displacement restraints were applied based upon the symmetric the mechanical properties. The displacement restraints were applied based upon the symmetric applied condition at thean X-symmetric d actual placement of the specimens. In plane and the Y-symmetric other words, a vertic plane, respectively al d.isplacement re As necessitated strain by t the condition and actual placement of the specimens. In other words, a vertical displacement 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 X-symmetric plane and the Y-symmetric plane, respectively. As necessitated by the to the ap experimental plied at the X-conditions. symmetric pThe lane and implemented the Y-symmixtur metric p e ldesigns ane, respectively. A for the specimens s necessit wer ated e OPC55 by the and computational platform, the mix proportion, casting temperature and curing conditions were computational platform, the mix proportion, casting temperature and curing conditions were OPC45 as indicated in Table 1. Figure 3b depicts the environmental condition. The environmental data, identical to the experimental conditions. The implemented mixture designs for the specimens were identical to the experimental conditions. The implemented mixture designs for the specimens were which consist of the temperature 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 and OPC45 as indicated in Table 1. Figure 3b depicts the environmental condition. The obtained from data loggers at each corresponding location. The 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 direct sunshine and rainfall, as shown in Figure 4a, whereas shaded specimens were sheltered from indoor conditions, were obtained from data loggers at each corresponding location. The rainfall indoor conditions, were obtained from data loggers at each corresponding location. The rainfall direct sunshine and rain (Figure 4b). The indoor specimens were kept in a storage room without direct specimens were exposed to direct sunshine and rainfall, as shown in Figure 4a, whereas shaded specimens were exposed to direct sunshine and rainfall, as shown in Figure 4a, whereas shaded exposure to the ambient environment. Rainfall is of paramount important in determining concrete specimens were sheltered from direct sunshine and rain (Figure 4b). The indoor specimens were kept specimens were sheltered from direct sunshine and rain (Figure 4b). The indoor specimens were kept 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 concrete shrinkage behaviour. To simply account for the water absorption coefﬁcient in the surface mass ﬂux is assumed to increase one hundred times from its original value. important in determining concrete shrinkage behaviour. To simply account for the water absorption of concrete via rainfall, the emissivity coefficient in the surface mass flux is assumed to increase one of concrete via rainfall, the emissivity coefficient in the surface mass flux is assumed to increase one However, the actual hydraulic pressure on the exposed surface could be acquired in the model [12]. hundred times from its original value. However, the actual hydraulic pressure on the exposed surface hundred times from its original value. However, the actual hydraulic pressure on the exposed surface The rainfall data of Koriyama in Fukushima prefecture was retrieved from the Japan Meteorological could be acquired in the model [12]. The rainfall data of Koriyama in Fukushima prefecture was could be acquired in the model [12]. The rainfall data of Koriyama in Fukushima prefecture was Agency and applied in the analysis. retrieved from the Japan Meteorological Agency and applied in the analysis. retrieved from the Japan Meteorological Agency and applied in the analysis. (a) (b) (a) (b) Figure Figure 3. 3. (a) (Finite-element a) Finite-element (F (FE) E) mode modell of of on one e fourth of the fourth of the specimen; ( specimen; b) e (b n)vironmental c environmental ondition. condition. Figure 3. (a) Finite-element (FE) model of one fourth of the specimen; (b) environmental condition. Table 1. Mix proportion of 200 × 200 × 800 mm 3 prismatic specimens and curing condition. Table 1. Mix proportion of 200 × 200 × 800 mm prismatic specimens and curing condition. Table 1. Mix proportion of 200 200 800 mm prismatic specimens and curing condition. Unit Content (kg/m 3 ) Unit Content (kg/m ) Series w/b (%) Air (%) Seal-Cured Series w/b (%) Air (%) Seal-Cured Unit Content (kg/m ) WC Ex S G WC Ex S G w/b (%) Air (%) Series Seal-Cured W C Ex S G OPC55 55 4.5 172 313 - 834 997 7 days OPC55 55 4.5 172 313 - 834 997 7 days OPC55 55 4.5 172 313 - 834 997 7 days OPC45 45 6 164 338 20 791 992 7 days OPC45 45 6 164 338 20 791 992 7 days OPC45 45 6 164 338 20 791 992 7 days Note: w/b = water-to-binder ratio; W = Water; C = Cement; Ex = Expansive additives; S = Sand; G = Note: w/b = water-to-binder ratio; W = Water; C = Cement; Ex = Expansive additives; S = Sand; G = Note: w/b = water-to-binder ratio; W = Water; C = Cement; Ex = Expansive additives; S = Sand; G = Gravels. Gravels. Gravels. (a) (b) (a) (b) Figure 4. (a) Specimens with direct rainfall exposure; (b) shaded specimens. Figure Figure 4. 4. (a ( ) a Specimens ) Specimens w with ith d dir irect rainfal ect rainfall l ex exposur posure; ( e; b( )b sha ) shaded ded specimens. specimens. Appl. Sci. 2018, 8, 394 7 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18 Figures 5–7 portray a comparison between the measured values from data loggers and the Figures 5–7 portray a comparison between the measured values from data loggers and the Figures 5–7 portray a comparison between the measured values from data loggers and the 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 analytical results of the experimented specimens. Figure 5 shows that a change in the mass of the analytical results of the experimented specimens. Figure 5 shows that a change in the mass of the analytical results of the experimented specimens. Figure 5 shows that a change in the mass of the 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 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 with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the specimens with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the specimens with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the specimens with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with direct concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with direct concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with direct 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 to the behaviour in mass change, a minimal discrepancy was found in the trend rainfall, similar to the behaviour in mass change, a minimal discrepancy was found in the trend trend between the measured and analytical strain. As extra water from rainfall was supplied to between the measured and analytical strain. As extra water from rainfall was supplied to the concrete between the measured and analytical strain. As extra water from rainfall was supplied to the concrete between the measured and analytical strain. As extra water from rainfall was supplied to the concrete the concrete through the exposed surfaces, the measured strain reﬂected this phenomenon through through the exposed surfaces, the measured strain reflected this phenomenon through concrete through the exposed surfaces, the measured strain reflected this phenomenon through concrete through the exposed surfaces, the measured strain reflected this phenomenon through concrete concrete expansion. Hence, the authors have come to understand that the simpliﬁed method of expansion. Hence, the authors have come to understand that the simplified method of reproducing expansion. Hence, the authors have come to understand that the simplified method of reproducing expansion. Hence, the authors have come to understand that the simplified method of reproducing reproducing the rainfall effect should be enhanced to increase the accuracy of numerical prediction, the rainfall effect should be enhanced to increase the accuracy of numerical prediction, but this effect the rainfall effect should be enhanced to increase the accuracy of numerical prediction, but this effect the rainfall effect should be enhanced to increase the accuracy of numerical prediction, but this effect 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 relatively minimal in the case of large-scale concrete structures. In the case of shaded would be relatively minimal in the case of large-scale concrete structures. In the case of shaded of shaded specimens, it is believed that the deviation between the measured and analytical strain in specimens, it is believed that the deviation between the measured and analytical strain in OPC55 specimens, it is believed that the deviation between the measured and analytical strain in OPC55 specimens, it is believed that the deviation between the measured and analytical strain in OPC55 OPC55 likely resulted from the inﬂuence of the wind, unlike the indoor specimens. likely resulted from the influence of the wind, unlike the indoor specimens. likely resulted from the influence of the wind, unlike the indoor specimens. likely resulted from the influence of the wind, unlike the indoor specimens. Figure 5. Mass change of each series (M-Measured & A-Analytical). Figure 5. Mass change of each series (M-Measured & A-Analytical). Figure 5. Mass change of each series (M-Measured & A-Analytical). Figure 5. Mass change of each series (M-Measured & A-Analytical). Figure 6. Concrete shrinkage strain of OPC45. Figure 6. Concrete shrinkage strain of OPC45. Figure 6. Concrete shrinkage strain of OPC45. Figure 6. Concrete shrinkage strain of OPC45. Figure 7. Concrete shrinkage strain of OPC55. Figure 7. Concrete shrinkage strain of OPC55. Figure 7. Concrete shrinkage strain of OPC55. Figure 7. Concrete shrinkage strain of OPC55. 3. 3.2.2. 2.2. C Compr ompre essive ssive St Str rengt ength h 3.2.2. Compressive Strength 3.2.2. Compressive Strength Referrin Referring g to to JIS A JIS A 1108 1108 spe speciﬁcation, cification, cocompr mpression ession testests ts on on a φa 100' × 100 200-c200-cylinder ylinder specim specimen en with Referring to JIS A 1108 specification, compression tests on a φ100 × 200-cylinder specimen with Referring to JIS A 1108 specification, compression tests on a φ100 × 200-cylinder specimen with rad with ius r of adius 100of mm 100 and h mmeand ight of height 200 m of m200 , were mm, also wer coe nducted also conducted for variou for s mixtur various e designs (T mixture designs able 2). radius of 100 mm and height of 200 mm, were also conducted for various mixture designs (Table 2). radius of 100 mm and height of 200 mm, were also conducted for various mixture designs (Table 2). The specim (Table 2). The enspecimens s underwen underwent t seal-cur seal-curing ing condition conditions s for 28 days for 28 days before beforexposure to e exposure to the theambient ambient The specimens underwent seal-curing conditions for 28 days before exposure to the ambient The specimens underwent seal-curing conditions for 28 days before exposure to the ambient environment in a environment in a store storer roo oom m (F (Figur igure 8). In e 8). In the the Du DuCOM COM system, th system, the e strength m strength model odel assume assumes s a clo a close se environment in a storeroom (Figure 8). In the DuCOM system, the strength model assumes a close environment in a storeroom (Figure 8). In the DuCOM system, the strength model assumes a close relationship with capillary porosity development, whereby the present and initial capillary porosity relationship with capillary porosity development, whereby the present and initial capillary porosity 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 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 Appl. Sci. 2018, 8, 394 8 of 18 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. Unit Proportion (kg/m ) Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 18 Appl. Sci. 2018, 8, x FOR PEER w/b REVIEW (%) Air (%) 8 of 18 Series W C Ex S G Ad than OPC con OPC53 crete, which 52.9 affects the lon 4.5 g-term st 166 rengt 314 h [13]. To reva - li802 date the m 1044 odel, F 3.14 igure 9 shows than OPC concrete, which affects the long-term strength [13]. To revalidate the model, Figure 9 shows OPC44 44 6 164 353 20 653 1112 2.24 the compressive strength of each mix d the compressive strength of each mix de es siign se gn serie ries s. . It can be observe It can be observed d that the compressive that the compressive strength strength BFS44 44 6 160 344 20 662 1112 2.18 can be satisfactorily predicted. can be satisfactorily predicted. Figure 8. Environmental condition after 28 days of seal-curing. Figure 8. Environmental condition after 28 days of seal-curing. Figure 8. Environmental condition after 28 days of seal-curing. Figure 9. Compressive strength of concrete (M-Measured and A-Analytical). Figure 9. Figure 9. Com Compr pressive essive streng strength th of con of concr crete ( ete (M-Measur M-Measured a ed and nd A-Analy A-Analytical). tical). Table 2. Trial mixture designs of potential concrete to be used for Shinkesen Bridge deck. 3.2.3. Inﬂuence Table 2. of Trial Curing mixtu Conditions re designs of on potential Concrete concrete to be used for Shinkesen Bridge deck. Unit Proportion (kg/m ) The use of a high-performance mix design as Unit Pr such requir opores tion (kg/m a study on ) the curing period to Series w/b (%) Air (%) Series w/b (%) Air (%) determine the optimum choice for execution withoutWC being vulner Ex ableS to cracking G Ad risk. Thus, referring WC Ex S G Ad to Figure 10, ﬁveOPC5 100 3 100 52.9 400 mm4.5 prismatic 166 plain 314 - 8 concrete02 specimens 1044 3.1 wer4 e prepared with OPC53 52.9 4.5 166 314 - 802 1044 3.14 ﬁve different curing periods (7, 14, 28, 56 and 91 days) before exposure to the environment of the OPC4 OPC44 4 4444 6 6 1164 64 3353 2 53 200 6 653 53 11112 112 22..2244 control chamber (aBFS4 constant 4 2044C and 60%6 relative 160 humidity). 344 20 6 The62 mix1112 design 2.18 of these specimens BFS44 44 6 160 344 20 662 1112 2.18 was BFS44 (Table 2). Figure 11 shows the ﬁnite element of the prismatic specimens whereby the 3. boundary 3.2. 2.3. In 3. Infl fluen uen conditions c ce of C e of Cu urin rin are g g applied C Co ondit nditions o ions o in the n nsame C Co oncret ncret manner e e as that of previous cases. Unlike OPC concrete, the use of a low water-to-cement ratio as such in BFS concrete allows autogenous shrinkage to play a The use of a high-performance mix design as such requires a study on the curing period to The use of a high-performance mix design as such requires a study on the curing period to predominant role, on par with that of drying shrinkage, in determining the properties of the concrete. determine th determine the optimum c e optimum chhoice for oice for exe execcution witho ution withouut being vulnerable t being vulnerable to cr to crack ackiing r ng riisk sk. . Thus, Thus, Thus, to properly capture the autogenous and drying shrinkage of BFS concrete, the driving force of referring to Figure 10, five 100 × 100 × 400 mm prismatic plain concrete specimens were prepared referring to Figure 10, five 100 × 100 × 400 mm prismatic plain concrete specimens were prepared shrinkage in the model is divided into two entities: capillary tension force and disjoining pressure. wit with h five five d diiffffe erent rent curin curing g p pe eriods (7 riods (7, 14 , 14, , 2 28 8, 56 and , 56 and 91 d 91 da ays) befor ys) before e exposure to exposure to the environ the environm ment of ent of The former, which dominates the nanoscale pores, is of paramount signiﬁcance under low relative the control chamber (a constant 20 °C and 60% relative humidity). The mix design of these specimens the control chamber (a constant 20 °C and 60% relative humidity). The mix design of these specimens humidity, but the latter, which governs the microscale pores, contributes signiﬁcantly with a high was BFS was BFS444 ( 4 (T Tab able 2 le 2)). Fig . Figu ure 1 re 111 show showss tth he e ffiinit nitee e elleem ment of the ent of the prismat prismatiic spe c speccimens whe imens wherreby the eby the relative humidity [6]. The applicability of the BFS model in actual specimens exposed to various curing boundary conditions are applied in the same manner as that of previous cases. Unlike OPC concrete, boundary conditions are applied in the same manner as that of previous cases. Unlike OPC concrete, durations would also be conﬁrmed through this model validation. the the use of use of a a low low wa water- ter-to-cement to-cement ra rati tio a o ass such such iin n BFS BFS concrete concrete al allows autogenous lows autogenous shri shrinkage to pl nkage to play ay a predominant role, on par with that of drying shrinkage, in determining the properties of the a predominant role, on par with that of drying shrinkage, in determining the properties of the concrete. Thus, to properly concrete. Thus, to properly ca capture the pture the autogenous autogenous an and dry d dryiing sh ng shrinkage rinkage of of BFS BFS concrete, the concrete, the drivin driving g force of shrinkage in the model is divided into two entities: capillary tension force and disjoining force of shrinkage in the model is divided into two entities: capillary tension force and disjoining pressu pressure. The re. The former former, wh , whic ich domin h domina atte es t s th he nano e nanosca scalle e pores, pores, is is of p of pa arra amount mount s siig gn nifi ificance cance und unde er lo r low w relative humidity, but the latter, which governs the microscale pores, contributes significantly with a relative humidity, but the latter, which governs the microscale pores, contributes significantly with a high high rel rela attiive ve humid humidiitty y [6 [6]. ]. The app The applic licabi abilit lity y of of t th he e BF BFS S mode model l in in act actu ua all specimen specimens expo s exposed sed t to o vario variou us s curing durations would also be confirmed through this model validation. curing durations would also be confirmed through this model validation. Appl. Sci. 2018, 8, 394 9 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 18 Figure 10. FE model of one-eighth of the 400 × 400 × 200 mm prismatic specimen. Figure 10. FE model of one-eighth of the 400 400 200 mm prismatic specimen. Figure 10. FE model of one-eighth of the 400 × 400 × 200 mm prismatic specimen. Figure 11. Concrete shrinkage strain in 100 100 400 mm specimens (M-Measured and A-Analytical). Figure 11. Concrete shrinkage strain in 100 × 100 × 400 mm specimens (M-Measured and Figure 11. Concrete shrinkage strain in 100 × 100 × 400 mm 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 additive The t model rend o would f the an only alyt apply ical res instantaneous ults shown in expansiv Figure e 1 strain 1 could to be concr ac ete cept without able in t consider erms of a st tion rai of n prediction despite some discrepancies, especially during the sealing period. Our current expansive prediction despite some discrepancies, especially during the sealing period. Our current expansive its long-term effect, whereby complete expansion could continue to at least a week [14]. Although, to additive model would only apply instantaneous expansive strain to concrete without consideration pr adovide ditive better modeaccuracy l would only in pr a edicti pply i ng ns strain tantane at ou ans early expastage nsive for strai cases n to concrete wi in which expansive thout consi additives deratiar on e of its long-term effect, whereby complete expansion could continue to at least a week [14]. Although, of its long-term effect, whereby complete expansion could continue to at least a week [14]. Although, applied, the authors aim to investigate the issue and develop a more sophisticated model. Because to provide better accuracy in predicting strain at an early stage for cases in which expansive additives t the o provide bet most prevalent ter accur forms acyof incracks, predictthat ing sis, train thermal at an e and arly st shrinkage-induced age for cases in which e cracks, xpansive are more ad likely ditives to are applied, the authors aim to investigate the issue and develop a more sophisticated model. Because are applied, the authors aim to investigate the issue and develop a more sophisticated model. Because occur after the curing period, the minimal variation during the sealing condition could be reasonably the most prevalent forms of cracks, that is, thermal and shrinkage-induced cracks, are more likely to the most preva disregarded. Ther lent efor forms of cra e, it could c be ks, tha concluded t is, therma that the l anoverall d shrintr kage-induced cr end and strain ack value s, are more of concrete likely to under occur after the curing period, the minimal variation during the sealing condition could be reasonably occur after the curing period, the minimal variation during the sealing condition could be reasonably seal-curing conditions could be acceptably traced. 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 Bars on Concrete seal-curing conditions could be acceptably traced. It was understood that by observing the strain progress of small RC specimens, the shrinkage 3.2.4. Influence of Reinforcing Bars on Concrete 3.2.4. Influence of Reinforcing Bars on Concrete behaviour and cracking susceptibility of concrete using the mix proportions could be more revealing It was understood that by observing the strain progress of small RC specimens, the shrinkage to a certain degree due to the restraints of the reinforcing bars. Hence, prismatic RC specimens of It was understood that by observing the strain progress of small RC specimens, the shrinkage behaviour and cracking susceptibility of concrete using the mix proportions could be more revealing 400 400 200 mm with the aforementioned mixture designs in Table 2 were used for the experiment. behaviour and cracking susceptibility of concrete using the mix proportions could 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 to the restraints of the reinforcing bars. Hence, prismatic RC specimens of 400 × 400 × 200 mm with the aforementioned mixture designs in Table 2 were used for the the top and bottom regions of the prismatic specimens. Figure 12 shows the ﬁnite-element model of of 400 × 400 × 200 mm with the aforementioned mixture designs in Table 2 were used for the experiment. Six reinforcing bars with a diameter of 19 mm were embedded transversely and one-eighth of the 400 400 200 mm prismatic specimen, in which the reinforcements were inserted experiment. Six reinforcing bars with a diameter of 19 mm were embedded transversely and longitudinally at both the top and bottom regions of the prismatic specimens. Figure 12 shows the into the elements marked by purple boxes according to their reinforcement ratios. The specimens were longitudinally at both the top and bottom regions of the prismatic specimens. Figure 12 shows the finite-element model of one-eighth of the 400 × 400 × 200 mm prismatic specimen, in which the under seal-curing conditions for 28 days before they were relocated to a storage room with exposure finite-element model of one-eighth of the 400 × 400 × 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 shown in Figure 8. To incorporate the effect of expansive additives reinforcements were inserted into the elements marked by purple boxes according to their reinforcement ratios. The specimens were under seal-curing conditions for 28 days before they were in concrete, we used a simple model that imposes instantaneous expansive strain on the concrete reinforcement ratios. The specimens were under seal-curing conditions for 28 days before they were relocated to a storage room with exposure to the ambient environment, as shown in Figure 8. To depending on the degree of restraints, such as rebar and external boundaries. relocated to a storage room with exposure to 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 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 18 instantaneous expansive strain on the concrete depending on the degree of restraints, such as rebar instantaneous expansive strain on the concrete depending on the degree of restraints, such as rebar Appl. Sci. 2018, 8, 394 10 of 18 and external boundaries. and external boundaries. Figure 12. FE model of one fourth of the specimen. Figure 12. FE model of one fourth of the specimen. Figure 12. FE model of one fourth of the specimen. Figur Figu ere 1313 shows shows t that hat the thanalyses e analyses p proved roved t that hat the the strain strain pr progre ogressss of the spe of the specimen cimens co s could uld be be Figure 13 shows that the analyses proved that the strain progress of the specimens could be predicted prpredicted edicted satisfactorily. Furthermore, b satisfactorily satisfactorily. Furthermore, b . Furthermore, based ased on ased on on this this this rre esult, sult, it result, it it could could could be be proven th pr be proven th oven thatat the the at the simple simple simple model model model of anof expansive an expansive agent could provide agent could provide a reasonable a reasonoutput able output wi withoutthout affecting affecti the ng the strainstra behaviour in behaviour of of the of an expansive agent could provide a reasonable output without affecting the strain behaviour of the concrete in the long run. Also, as co concr the concrete in the long run. Also, as co ete in the long run. Also, as concrete ncrete expan ncrete expan expands in ds in the ds in t initial h t e in he in it place, iait l p ial l p a the cle, t arisk ce, t he h of rie sk cracking risk of c of c racrkin in ackin the g in t gearly in t he he period early per is heavily iod is heav reduced ily red because uced bec of the ause expansion of the expa effect. nsion e Ther ffect efor . Therefore e, our main , ou concern r main conce should rn not shou beld early period is heavily reduced because of the expansion effect. Therefore, our main concern should not be w with not be w how ith h well ith h ow well the the ow well the model pr model predic edicts model predic the expansion ts the ts the expansio expansio of concr n of concret ete, n of concret but with e, b e the u , b t wi u pr t wi ogr th the progress of th the progress of ess of strain over stra time stra in in because over tiit me bec is much ausmor e it is e muc relevant h more re to theleva initialisation nt to the init of cracks. ialisation o Based f cron acks the . B ra esults sed on of th all e res of the ultsmodel of all of over time because it is much more relevant to the initialisation of cracks. Based on the results of all of the model v validations, the model v ait lidat can alidat ions, beions, conﬁrmed it cit c an be confirme an be confirme that the computational d that d that the co the co mputational models mputational can models c trace models c the a mechani n tr an tr ace the mech ace the mech stic behaviour anistic anistic of concr behavio ete reasonably ur of concret well e re on asa onab small ly wel scale. l on a small scale. behaviour of concrete reasonably well on a small scale. 3 3 3 Figure 13. Concrete shrinkage strain in 400 × 400 × 200 mm RC specimens (M-Measured and A- Figure 13. Concrete shrinkage strain in 400 × 400 × 200 mm RC specimens (M-Measured and A- Figure 13. Concrete shrinkage strain in 400 400 200 mm RC specimens (M-Measured and A-Analytical). Analytical). Analytical). 3.3. Application of the Analytical Model on a Mock-Up Slab Specimen 3.3. 3.A 3. ppl Appl icati ico ati n of on of the tAnal he Anal ytic yt ali cModel on al Model on a Mock a Mock -Up -Up Slab Spe Slab Spe cimen cimen To represent a restraint condition as close to reality as possible, two I-section girders were placed To represent a restraint condition as close to reality as possible, two I-section girders were placed To represent a restraint condition as close to reality as possible, two I-section girders were placed at the concrete supports as they would be placed on the actual steel girders whereas half of the actual at the concrete supports as they would be placed on the actual steel girders whereas half of the actual at the concrete supports as they would be placed on the actual steel girders whereas half of the actual specimen were used for the ﬁnite element model as indicated in Figure 14. The replicated specimen specimen were used for the finite element model as indicated in Figure 14. The replicated specimen specimen were used for the finite element model as indicated in Figure 14. The replicated specimen was cast with ‘BFS44’ mix design and water-cured for 42 days on the top surface before exposure to was cast with ‘BFS44’ mix design and water-cured for 42 days on the top surface before exposure to was cast with ‘BFS44’ mix design and water-cured for 42 days on the top surface before exposure to the outside environment. For Figure 14b, the diameters of the reinforcing bars were 19 and 16 mm in the outside environment. For Figure 14b, the diameters of the reinforcing bars were 19 and 16 mm in the outside environment. For Figure 14b, the diameters of the reinforcing bars were 19 and 16 mm in 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 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 for Rikuzentaka in Iwate prefecture were obtained from the Japan Meteorological Agency and data for Rikuzentaka in Iwate prefecture were obtained from the Japan Meteorological Agency and identically input to the analysis as shown in Figure 15. To trace the expansion and contraction identically input to the analysis as shown in Figure 15. To trace the expansion and contraction identically input to the analysis as shown in Figure 15. To trace the expansion and contraction behaviour of the deck in a quantitative manner, strain gauges were also embedded at the locations behavio behavio ur u of the r of the deck deck in a quantitative manner, st in a quantitative manner, st rain gauges we rain gauges we re also embed re also embed ded at the loc ded at the loc ations ations 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 in Figure 16. These strain gauges perform measurements in transverse, longitudinal and vertical directions. As portrayed in Figure 16, four ﬁnite-element models of the mock-up specimen vert vert icaica l dli d rec irec tions. tions. As As port port raye raye d in d Fi ingu Fire gure 16,16 fo, fo ur ur finfin ite-el ite-el ement ement m m odels odels of o th f t e h mock-up e mock-up spe spe cimen cimen were established to conduct mesh sensitivity analysis to minimise the 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 accept accept able able ac ac curac curac y in y in th t e fol he fol lowin lowin g lg l arge- arge- scasca le br le id brge model. Th idge model. Th is e is e lement d lement d iscretisation p iscretisation p rocess rocess because the convergence in 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 D in D uCOM h uCOM h ad t ad t o be en o be en sured t sured t o prov o prov ide re ide re ason ason ably ably accur accur atea res te res ultu s lt for s for its cou its cou nten rpart terpart , CO , CO M3, M3, to t o structural behaviour. analyse the macroscopic structural behaviour. analyse the macroscopic structural behaviour. Appl. Sci. 2018, 8, 394 11 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 18 (a) (b) (a) (b) Figure 14. (a) Overview of mock-up slab specimen; (b) FE model of half of the mock-up specimen. Figure 14. (a) Overview of mock-up slab specimen; (b) FE model of half of the mock-up specimen. Figure 14. (a) Overview of mock-up slab specimen; (b) FE model of half of the mock-up specimen. Figure Figure 15. 15. Envi Envir ronmental conditions onmental conditions.. Figure 15. Environmental conditions. Due to issues with the embedded strain gauges after removal of the formwork, the measured Due to issues with the embedded strain gauges after removal of the formwork, the measured Due to issues with the embedded strain gauges after removal of the formwork, the measured data from the 42nd and 56th days were lost. Nonetheless, the whole trend of the strain could still be data from the 42nd and 56th days were lost. Nonetheless, the whole trend of the strain could still be 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 captured, whereby the rearrangement of the strain gauges might have affected the strain progress captured, whereby the rearrangement of the strain gauges might have affected the strain progress and resulted in a slightly greater shrinkage strain value. Two main conclusions could be drawn and resulted in a slightly greater shrinkage 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 of this analysis. First, the computational model can capture the strain progress with the result of this analysis. 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 minimal differences. Good agreement was also achieved between the measured and analytical values minimal differences. Good agreement was also achieved between the measured and analytical values values 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 finite- for the concrete temperature. Second, the differences between the computed strains of the four finite- ﬁnite-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 be element models with distinctive aspect ratios and element sizes were also negligible. Thus, it can be be conﬁrmed that the element with a length of around 300 mm could reasonably be implemented in confirmed that the element with a length of around 300 mm could reasonably be implemented in the confirmed that the element with a length of around 300 mm could reasonably be implemented in the the large-scale analysis. large-scale analysis. large-scale analysis. 3.4. Preliminary Analysis on Concrete Deck Slab of Shinkesen Bridge to Evaluate the Occurrence of Cracks 3.4. Preliminary Analysis on Concrete Deck Slab of Shinkesen Bridge to Evaluate the Occurrence of Cracks 3.4. Preliminary Analysis on Concrete Deck Slab of Shinkesen Bridge to Evaluate the Occurrence of Cracks To combat the complex degradation processes from the cold environment, frost damage, chloride To combat the complex degradation processes from the cold environment, frost damage, To combat the complex degradation processes from the cold environment, frost damage, attack from de-icing salt, alkali–silica reaction and fatigue, a holistic countermeasure approach was chloride attack from de-icing salt, alkali–silica reaction and fatigue, a holistic countermeasure chloride attack from de-icing salt, alkali–silica reaction and fatigue, a holistic countermeasure undertaken to enhance the durability performance of the RC deck slab. The multiple protection approach was undertaken to enhance the durability performance of the RC deck slab. The multiple approach was undertaken to enhance the durability performance of the RC deck slab. The multiple strategy incorporates a low water-to-binder ratio (w/b), the use of mineral admixture, epoxy-coated protection strategy incorporates a low water-to-binder ratio (w/b), the use of mineral admixture, protection strategy incorporates a low water-to-binder ratio (w/b), the use of mineral admixture, reinforcing bars and 6% entrained air [1]. Because the early-age cracks such as shrinkage cracks allow epoxy-coated reinforcing bars and 6% entrained air [1]. Because the early-age cracks such as epoxy-coated reinforcing bars and 6% entrained air [1]. Because the early-age cracks such as more migration of deleterious ions into the body of concrete under such severe conditions, it is of shrinkage cracks allow more migration of deleterious ions into the body of concrete under such shrinkage cracks allow more migration of deleterious ions into the body of concrete under such great signiﬁcance to control and delay its occurrence [10]. Therefore, before the Shinkesen Bridge was severe conditions, it is of great significance to control and delay its occurrence [10]. Therefore, before severe conditions, it is of great significance to control and delay its occurrence [10]. Therefore, before constructed, a cracking assessment was performed for various mixture designs. the Shinkesen Bridge was constructed, a cracking assessment was performed for various mixture the Shinkesen Bridge was constructed, a cracking assessment was performed for various mixture Figure 17 outlines the layout of the ﬁnite-element model of the Shinkesen Bridge for preliminary designs. designs. analysis of crack propagation. Considering the symmetric condition and actual construction procedure Figure 17 outlines the layout of the finite-element model of the Shinkesen Bridge for preliminary Figure 17 outlines the layout of the finite-element model of the Shinkesen Bridge for preliminary that would be adopted, the RC deck slab was modelled in combination with the girders and their analysis of crack propagation. Considering the symmetric condition and actual construction analysis of crack propagation. Considering the symmetric condition and actual construction stiffeners to achieve structural resemblances that have an effect on the restraint condition. To capture procedure that would be adopted, the RC deck slab was modelled in combination with the girders procedure that would be adopted, the RC deck slab was modelled in combination with the 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 on the mock-up slab specimen, the maximum length of the element To capture the temperature and moisture gradients inside the RC deck slab properly, and based on To capture the temperature and moisture gradients inside the RC deck slab properly, and based on was taken to be 250 mm. To shorten the computational time, and as a conservative measure, the the mesh sensitivity analysis conducted on the mock-up slab specimen, the maximum length of the the mesh sensitivity analysis conducted on the mock-up slab specimen, the maximum length of the ambient environment was set to dry conditions with a constant 15 C temperature 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 throughout the calculation, whereas the asphalt layer would exist the ambient environment was set to dry conditions with a constant 15 °C temperature and 70% the ambient environment was set to dry conditions with a constant 15 °C temperature and 70% on the top surface in reality. The environmental conditions were decided based on the average value relative humidity on the concrete surface throughout the calculation, whereas the asphalt layer relative humidity on the concrete surface throughout the calculation, whereas the asphalt layer 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 Appl. Sci. 2018, 8, 394 12 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 18 in accordance with the local meteorological data. The effects of concrete mixture designs on crack generation designs on and crack propagat generaion tionwer ande p investigated ropagation win ere the invest analysis. igated In in Japan, the analy the sis typical . In Japa w/b n, thshould e typicanot l 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 exceed 65%. In most cases, a w/b of 55% was endorsed, whereby the upper limit of water content is w/b should not exceed 65%. In most cases, a w/b of 55% was endorsed, whereby the upper limit of 3 3 3 water content is recommended as 175 kg/m and lower limit of the cement content is recommended recommended as 175 kg/m and lower limit of the cement content is recommended as 300 kg/m [15]. water content is recommended as 175 kg/m and lower limit of the cement content is recommended as 300 kg/m [15]. As seen in Table 3, the mixture designs consist of five series: BFS42, OPC42, BFS55, As seen in Table 3, the mixture designs consist of ﬁve series: BFS42, OPC42, BFS55, OPC55 and as 300 kg/m [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’ represents the use of expansive additives. OPC55 and BFS42-EX whereby ‘EX’ represents the use of expansive additives. Figure 16. Concrete shrinkage strain at corresponding gauges and concrete temperatures. *  to  Figure 16. Concrete shrinkage strain at corresponding gauges and concrete temperatures. *  to  Figure 16. Concrete shrinkage strain at corresponding gauges and concrete temperatures. * 1 to 8 represent different locations of strain gages; I, II, III, IV represent the four finite element analytical represent different locations of strain gages; I, II, III, IV represent the four finite element analytical represent different locations of strain gages; I, II, III, IV represent the four finite element analytical models. models. models. Figure 17. Cont. Appl. Sci. 2018, 8, 394 13 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 18 Figure 17. FE model of one-fourth of a bridge span. Figure 17. FE model of one-fourth of a bridge span. TTable 3. able 3. Mixtur Mixture e d designs esigns us used ed for parametric for parametric st study udy. . Unit Proportion (kg/m ) Series w/b (%) Air (%) Unit Proportion (kg/m ) WC Ex S G Ad w/b (%) Air (%) Series W C Ex S G Ad OPC55 55 4.5 170 310 - 802 1044 3.14 OPC55 55 4.5 170 310 - 802 1044 3.14 BFS55 55 4.5 170 310 - 802 1044 3.14 BFS55 55 4.5 170 310 - 802 1044 3.14 OPC42 42 6 153 364 - 653 1112 2.24 OPC42 42 6 153 364 - 653 1112 2.24 BFS42 42 6 153 364 - 662 1112 2.18 BFS42 42 6 153 364 - 662 1112 2.18 BFS42-EX 42 6 153 364 20 662 1112 2.18 BFS42-EX 42 6 153 364 20 662 1112 2.18 Figure 18 portrays the computed longitudinal strain after 2 years, which is the strain along the Figure 18 portrays the computed longitudinal strain after 2 years, which is the strain along the bridge axis, on the top surface of the RC deck slab. The strain contours were extracted from the bridge axis, on the top surface of the RC deck slab. The strain contours were extracted from the portion portion of deck slab highlighted with the black rectangle. Due to the restraints from the steel girders, of deck slab highlighted with the black rectangle. Due to the restraints from the steel girders, high high tensile strains were seen to be localised around the elements with a longitudinal length of 60 tensile mm, which strains would r were seen esem toble t be h localised at of cracks around . Becau the se these high t elements with ensile str a longitudinal ains are mostly o length b of served 60 mm, which aroun would d the 60-mm element resemble that of s, the tran cracks. Because sverse max these imum high crack tensile widt strains h was c ara elc mostly ulated by mu observed ltiply aring t ound he the maximum strain with the element length of 60 mm. According to the JSCE standard, the limit value 60-mm elements, the transverse maximum crack width was calculated by multiplying the maximum of crack width for concrete in a severely corrosive environment is 0.0035c, where c refers to the strain with the element length of 60 mm. According to the JSCE standard, the limit value of crack width 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 to 0.14 mm. Four main aspects, focusing on BFS concrete, would be pinpointed from Therefore, in the case of the Shinkesen Bridge, the allowable crack width would be equivalent to the parametric study, including the influence of the (1) binder type, (2) w/b, (3) prolonged curing, 0.14 mm. Four main aspects, focusing on BFS concrete, would be pinpointed from 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 resistance against durability issues such as ASR and chloride environments, such as Tohoku. Then, consistent with the universal understanding that prolonged ingression mean that it might not be a good candidate for areas with severe environments, such as seal curing would reduce the moisture loss through the concrete’s surface, seal curing BFS42 up to 28 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 the moisture loss through the concrete’s surface, seal curing BFS42 up to 28 days signiﬁcantly helped additives inside BFS42, further improvement in reducing the generation of tensile strain was to reduce the maximum tensile strain. Finally, after incorporating expansive additives inside BFS42, illustrated. In addition to the lower intensity in the maximum crack width, based on the strain further improvement in reducing the generation of tensile strain was illustrated. In addition to the contour, the amount of nodal strain that reached a longitudinal strain of 1000 μ is also minimal, which infers that less crack propagation would occur than in the case without expansive additives. Hence, lower intensity in the maximum crack width, based on the strain contour, the amount of nodal strain as a conservative measure in cases in which prolonged curing could not be properly conducted or that reached a longitudinal strain of 1000 is also minimal, which infers that less crack propagation maintained, the recommendation to use expansive additives in the multiple protection strategy is would occur than in the case without expansive additives. Hence, as 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. Appl. Sci. 2018, 8, 394 14 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 18 Figure 18. Parametric study focusing on four different aspects. * εmax = maximum longitudinal strain; Figure 18. Parametric study focusing on four different aspects. * " = maximum longitudinal strain; max wmax = maximum crack width. w = maximum crack width. max 3.5. Post-Construction Analysis on Concrete Deck of Shinkesen Bridge: Verification with on-Site Measured 3.5. Post-Construction Analysis on Concrete Deck of Shinkesen Bridge: Veriﬁcation with on-Site Data Measured Data Figure 19 represents the entire overview of the 438-m seven-spanned steel girder–supported Figure 19 represents the entire overview of the 438-m seven-spanned steel girder–supported bridge. The casting sequence was carried out according to the numbers shown after considering the bridge. The casting sequence was carried out according to the numbers shown after considering the 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 casting lot 8 over the top of Pier 3 support. The top surface of the concrete underwent embedded on casting lot 8 over the top of Pier 3 support. The top surface of the concrete underwent wet-curing for approximately 22 days, following by seal-curing for another 7 days before the RC deck wet-curing for approximately 22 days, following by seal-curing for another 7 days before the RC deck 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, Appl. Sci. 2018, 8, 394 15 of 18 was exposed to the ambient environment. Figure 20 illustrates the ﬁnite-element model of one-fourth Appl. Sci. 2018, 8, x FOR PEER REVIEW 15 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 15 of 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 model mentioned in Section 3.5. To precisely consider the real conditions of the concrete bridge deck, a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. To a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. To a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. account for the effect of the expansion joint in the finite-element model, the longitudinal restraint at a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. To account for the effect of the expansion joint in the finite-element model, the longitudinal restraint at To account for the effect of the expansion joint in the ﬁnite-element model, the longitudinal restraint Lot account 8 is rep forl t ac hed wit e effect h of a r tih ge exp id boa dy whos nsion joe sole int in taim he f i in s t ito e-el allow sl ementight model, transl the atlong ionait l udin movem al re ent str , as see aint at n Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as seen at Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as in Figure 20. The nodes on the rigid body were restrained from moving vertically. Insertion of the Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as seen in Figure 20. The nodes on the rigid body were restrained from moving vertically. Insertion of the seen in Figure 20. The nodes on the rigid body were restrained from moving vertically. Insertion of rigid body w in Figure 20. a The node s performed s on at the end o the rigid body we f Lot 8 to maintain the re restrained from sy moving vert mmetric conditions ically. Insein the rtion of bridg the e rigid body was performed at the end of Lot 8 to maintain the symmetric conditions in the bridge the rigid body was performed at the end of Lot 8 to maintain the symmetric conditions in the bridge span. rigid body w The reinforcement as performed rat at the end o io was cafut Lot 8 to maintain the iously applied as casy lcu mmetric conditions lated from the struct in the ura bridg l detea il span. The reinforcement ratio was cautiously applied as calculated from the structural detail span. The reinforcement ratio was cautiously applied as calculated from the structural detail drawings, span. The reinforcement ratio was cautiously applied as calculated from the structural detail drawings, whereby lot 8 possesses more reinforcing bars in the top section. The environmental data drawings, whereby lot 8 possesses more reinforcing bars in the top section. The environmental data whereby lot 8 possesses more reinforcing bars in the top section. The environmental data from the from the beginning of drawings, whereby lot 8 po Lot 1 c ssesasstin es mo g were also ob re reinforcingta bars ined from the Jap in the top section. The an Meteo en rological vironment agency as al data from the beginning of Lot 1 casting were also obtained from the Japan Meteorological agency 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 in Figure 21. portrayed in Figure 21. Figure 21. portrayed in Figure 21. L4 L3 L13 L6 L12 L2 L10 L8 L1 L9 L5 L11 L7 L4 L3 L13 L6 L12 L2 L10 L8 L1 L9 L5 L11 L7 L6 L12 L2 L10 L4 L8 STEEL GIRDE L1 L9 RS L5 L11 L3 L13 L7 STEEL GIRDERS STEEL GIRDERS P1 P2 P3 P4 P5 P6 P1 P2 P3 P4 P5 P6 P2 P1 P3 P4 P5 P6 Longitudinal-B Longitudinal-B Longitudinal-B Transverse-B Transverse-B Transvers e-B Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure 20. FE model of one-fourth of the span of Shinkesen Bridge. Figure 20. FE model of one-fourth of the span of Shinkesen Bridge. Figure 20. FE model of one-fourth of the span of Shinkesen Bridge. Figure 20. FE model of one-fourth of the span of Shinkesen Bridge. Figure 21. Environmental condition of Shinkesen Bridge after Lot 1 casted up to 250 days. Figure 21. Environmental condition of Shinkesen Bridge after Lot 1 casted up to 250 days. Figure 21. Environmental condition of Shinkesen Bridge after Lot 1 casted up to 250 days. Figure 21. Environmental condition of Shinkesen Bridge after Lot 1 casted up to 250 days. Figure 22 shows a comparison between the analytical strain and the measured strain. The Figure 22 shows a comparison between the analytical strain and the measured strain. The 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 defin definit ition o ion off iin nit itia ial l zero zero st strra ain in in in dat dat aa lo lo ggers ggers wa wa s s ap ap proximat proximat elel y y 3 h a 3 h a ftf etr t er t he c he c ast ast ing on ing on Lot Lot 8 at 8 at th t e he 19th day. The analytical strain was therefore taken from the start of the 19th day for verification 19th day. The analytical strain was therefore taken from the start of the 19th day for verification 19th day. The analytical strain was therefore taken from the start of the 19th day for verification process. It can be observed that the strain progress can be well-traced for both longitudinal and process. It can be observed that the strain progress can be well-traced for both longitudinal and process. It can be observed that the strain progress can be well-traced for both longitudinal and Appl. Sci. 2018, 8, 394 16 of 18 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. The analytical strain was therefore taken from the start of the 19th day for veriﬁcation Appl. Sci. 2018, 8, 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 inside the concrete. Furthermore, for the concrete temperature, in addition to the transverse directions inside the concrete. Furthermore, for the concrete temperature, in addition to good agreement in the overall trend, an underestimation seems to occur during the seal-curing period, the good agreement in the overall trend, an underestimation seems to occur during the seal-curing wher period, whe eby the r concr eby the concrete is entir ete is entirely sealed and ely se cover aled with and cover wi formwork.th formwork. Hence, it is logically Hence,r i easonable t is logica that lly the measured value is greater than the analytical results because the simulation considers the surface of reasonable that the measured value is greater than the analytical results because the simulation consi the concr ders the surf ete to virtually ace of touch the concrete to vi the ambient envir rtual onment. ly touch the a In addition, mbient envi if attention ronment. In a is given to the ddigir tion, i ders’ f temperature, the computational platform almost exactly matches the data from the temperature gauge. attention is given to the girders’ temperature, the computational platform almost exactly matches the data from However, the temperature the minimal deviation gauge. Howe in temperatur ver, the m e isini ofmal little deviation concern in temper as long asature is o the longitudinal f little costrain, ncern which accounts for the infamous transverse deck cracking observed in most geographical conditions, as long as the longitudinal strain, which accounts for the infamous transverse deck cracking observed in most is consider geogr ed.aphical conditions, is considered. Figure 22. Concrete shrinkage strain at corresponding gauges and temperature of Shinkesen Bridge. Figure 22. Concrete shrinkage strain at corresponding gauges and 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. First and foremost, on a small scale (decimetres), validation of the multiscale integrated Appl. Sci. 2018, 8, 394 17 of 18 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. 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. 2. 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. 3. 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. Tanaka, Y.; Ishida, T.; Iwaki, I.; Sato, K. Multiple protection design for durable concrete bridge deck in cold regions. JSCE 2017, 5, 68–77. [CrossRef] 2. Faria, R.; Azenha, M.; Figueiras, J.A. Modelling of concrete at early ages: Application to an externally restrained slab. Cem. Concr. Compos. 2006, 28, 572–585. [CrossRef] 3. Jendele, L.; Smilauer, V.; Cervenka, J. Multiscale hydro-thermo-mechanical model for early-age and mature concrete structures. Adv. Eng. Softw. 2014, 72, 134–146. [CrossRef] 4. Maekawa, K.; Ishida, T.; Kishi, T. Multi-Scale Modeling of Structural Concrete, 1st ed.; Taylor & Francis: New York, NY, USA, 2009; ISBN 978-0-415-46554-0. 5. Maekawa, K.; Okamura, H.; Pimanmas, A. Non-Linear Mechanics of Reinforced Concrete; Spon Press: London, UK, 2003; ISBN 978-0-415-27126-4. 6. Maekawa, K.; Ishida, T.; Kishi, T. Multi-scale Modeling of Concrete Performance—Integrated Material and Structural Mechanics. J. Adv. Concr. Technol. 2003, 1, 91–126. [CrossRef] 7. Luan, Y.; Ishida, T. Enhanced shrinkage model based on early age hydration and moisture status in pore structure. J. Adv. Concr. Technol. 2013, 11, 360–373. [CrossRef] Appl. Sci. 2018, 8, 394 18 of 18 8. Biot, M.A. General Theory of three-dimensional consolidation. J. Appl. Phys. 1941, 12, 155–164. [CrossRef] 9. Gebreyouhannes, E.; Yoneda, T.; Ishida, T.; Maekawa, K. Multi-scale based simulation of shear critical reinforced concrete beams subjected to drying. J. Adv. Concr. Technol. 2014, 12, 363–377. [CrossRef] 10. Hussain, S.E. Effect of microsilica and blast furnace slag on pore solution composition and alkali-silica reaction. Cem. Concr. Compos. 1991, 13, 219–225. [CrossRef] 11. Dhir, R.K.; El-Mohr, M.A.K.; Dyer, T.D. Chloride binding in GGBS concrete. Cem. Concr. Res. 1996, 26, 1767–1773. [CrossRef] 12. Mehta, P.K.; Monteiro, P.J.M. Concrete: Microstructure, Properties, and Materials, 3rd ed.; McGraw-Hill: New York, NY, USA, 2006; ISBN 978-0-07-158919-2. 13. Iqbal, P.O.; Ishida, T. Modeling of chloride transport coupled with enhanced moisture conductivity in concrete exposed to marine environment. Cem. Concr. Res. 2009, 39, 329–339. [CrossRef] 14. Ishida, T.; Luan, Y.; Sagawa, T.; Nawa, T. Modeling of early age behavior of blast furnace slag concrete based on micro-physical properties. Cem. Concr. Res. 2009, 41, 1357–1367. [CrossRef] 15. Collepardi, M.; Borsoi, A.; Collepardi, S.; Olagot, J.J.O.; Troli, R. Effects of shrinkage reducing admixture in shrinkage compensating concrete under non-wet curing conditions. Cem. Concr. Res. 2005, 27, 704–708. [CrossRef] 16. JSCE. Standard Speciﬁcation for Concrete Structures—2007; JSCE: Tokyo, Japan, 2010; ISBN 978-4-8106-0752-9. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Sciences Multidisciplinary Digital Publishing Institute http://www.deepdyve.com/lp/multidisciplinary-digital-publishing-institute/numerical-simulation-of-early-age-cracking-of-reinforced-concrete-yj0rcmt00m

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Publisher: Multidisciplinary Digital Publishing Institute
Copyright: © 1996-2019 MDPI (Basel, Switzerland) unless otherwise stated
ISSN: 2076-3417
DOI: 10.3390/app8030394
Publisher site: See Article on Publisher Site

Abstract

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 1 , 1 2 3 4 ID Tetsuya Ishida * , Kolneath Pen , Yasushi Tanaka , Kosuke Kashimura and Ichiro Iwaki Department of Civil Engineering, The University of Tokyo, Tokyo 113-8656, Japan; kolneath@concrete.t.u-tokyo.ac.jp Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan; yasuxi@iis.u-tokyo.ac.jp Research Institute of General Research Laboratory, Yokogawa Bridge Holdings Co., Ltd., Chiba 261-0002, Japan; k.kashimura@ybhd.co.jp College of Engineering, Nihon University, Fukushima 963-8642, Japan; iwaki.ichirou@nihon-u.ac.jp * Correspondence: tetsuya.ishida@civil.t.u-tokyo.ac.jp 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 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 394 2 of 18 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 Appl. Sci. 2018, 8, 394 3 of 18 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). Appl. Sci. 2018, 8, 394 4 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 18 Figure 1. Multiscale and multi-physical modelling to simulate time-dependent concrete performance. Figure 1. Multiscale and multi-physical modelling to simulate time-dependent concrete performance. Figure 1. Multiscale and multi-physical modelling to simulate time-dependent concrete performance. Figure 2. Multiscale and multi-physical modelling to simulate time-dependent deformation and Figure 2. Multiscale and multi-physical modelling to simulate time-dependent deformation and Figure 2. Multiscale and multi-physical modelling to simulate time-dependent deformation and cracking. crack crack ing ing . . Appl. Sci. 2018, 8, 394 5 of 18 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 mm 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 mm 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 mm 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. Appl. Sci. 2018, 8, 394 6 of 18 3.2.1. Inﬂuence of Environmental Conditions: Rainfall, Shade and Indoors Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 18 Figure 3a represents a one-fourth ﬁnite-element model of the 200 200 800 mm prismatic specimens that were used in the experiments on concrete shrinkage under direct rainfall, shade and 3.2.1. Influence of Environmental Conditions: Rainfall, Shade and Indoors 3.2.1. Influence of Environmental Conditions: Rainfall, Shade and Indoors indoor environment. Apart from the indoor case, for which numerical models have been veriﬁed, the Figure 3a represents a one-fourth finite-element model of the 200 × 200 × 800 mm 3 prismatic Figure 3a represents a one-fourth finite-element model of the 200 × 200 × 800 mm prismatic ﬂuctuation in environmental conditions necessitates further model validation because it signiﬁcantly specimens that were used in the experiments on concrete shrinkage under direct rainfall, shade and specimens that were used in the experiments on concrete shrinkage under direct rainfall, shade and affects the microscopic thermodynamic phenomena of the whole concrete body and, consequently, indoor environment. Apart from the indoor case, for which numerical models have been verified, the indoor environment. Apart from the indoor case, for which numerical models have been verified, the the mechanical properties. The displacement restraints were applied based upon the symmetric fluctuation in environmental conditions necessitates further model validation because it significantly fluctuation in environmental conditions necessitates further model validation because it significantly condition and actual placement of the specimens. In other words, a vertical displacement restraint affects the microscopic thermodynamic phenomena of the whole concrete body and, consequently, affects the microscopic thermodynamic phenomena of the whole concrete body and, consequently, was applied at the bottom surface, whereas longitudinal and transverse displacement restraints were the mechanical properties. The displacement restraints were applied based upon the symmetric the mechanical properties. The displacement restraints were applied based upon the symmetric applied condition at thean X-symmetric d actual placement of the specimens. In plane and the Y-symmetric other words, a vertic plane, respectively al d.isplacement re As necessitated strain by t the condition and actual placement of the specimens. In other words, a vertical displacement 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 X-symmetric plane and the Y-symmetric plane, respectively. As necessitated by the to the ap experimental plied at the X-conditions. symmetric pThe lane and implemented the Y-symmixtur metric p e ldesigns ane, respectively. A for the specimens s necessit wer ated e OPC55 by the and computational platform, the mix proportion, casting temperature and curing conditions were computational platform, the mix proportion, casting temperature and curing conditions were OPC45 as indicated in Table 1. Figure 3b depicts the environmental condition. The environmental data, identical to the experimental conditions. The implemented mixture designs for the specimens were identical to the experimental conditions. The implemented mixture designs for the specimens were which consist of the temperature 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 and OPC45 as indicated in Table 1. Figure 3b depicts the environmental condition. The obtained from data loggers at each corresponding location. The 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 direct sunshine and rainfall, as shown in Figure 4a, whereas shaded specimens were sheltered from indoor conditions, were obtained from data loggers at each corresponding location. The rainfall indoor conditions, were obtained from data loggers at each corresponding location. The rainfall direct sunshine and rain (Figure 4b). The indoor specimens were kept in a storage room without direct specimens were exposed to direct sunshine and rainfall, as shown in Figure 4a, whereas shaded specimens were exposed to direct sunshine and rainfall, as shown in Figure 4a, whereas shaded exposure to the ambient environment. Rainfall is of paramount important in determining concrete specimens were sheltered from direct sunshine and rain (Figure 4b). The indoor specimens were kept specimens were sheltered from direct sunshine and rain (Figure 4b). The indoor specimens were kept 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 concrete shrinkage behaviour. To simply account for the water absorption coefﬁcient in the surface mass ﬂux is assumed to increase one hundred times from its original value. important in determining concrete shrinkage behaviour. To simply account for the water absorption of concrete via rainfall, the emissivity coefficient in the surface mass flux is assumed to increase one of concrete via rainfall, the emissivity coefficient in the surface mass flux is assumed to increase one However, the actual hydraulic pressure on the exposed surface could be acquired in the model [12]. hundred times from its original value. However, the actual hydraulic pressure on the exposed surface hundred times from its original value. However, the actual hydraulic pressure on the exposed surface The rainfall data of Koriyama in Fukushima prefecture was retrieved from the Japan Meteorological could be acquired in the model [12]. The rainfall data of Koriyama in Fukushima prefecture was could be acquired in the model [12]. The rainfall data of Koriyama in Fukushima prefecture was Agency and applied in the analysis. retrieved from the Japan Meteorological Agency and applied in the analysis. retrieved from the Japan Meteorological Agency and applied in the analysis. (a) (b) (a) (b) Figure Figure 3. 3. (a) (Finite-element a) Finite-element (F (FE) E) mode modell of of on one e fourth of the fourth of the specimen; ( specimen; b) e (b n)vironmental c environmental ondition. condition. Figure 3. (a) Finite-element (FE) model of one fourth of the specimen; (b) environmental condition. Table 1. Mix proportion of 200 × 200 × 800 mm 3 prismatic specimens and curing condition. Table 1. Mix proportion of 200 × 200 × 800 mm prismatic specimens and curing condition. Table 1. Mix proportion of 200 200 800 mm prismatic specimens and curing condition. Unit Content (kg/m 3 ) Unit Content (kg/m ) Series w/b (%) Air (%) Seal-Cured Series w/b (%) Air (%) Seal-Cured Unit Content (kg/m ) WC Ex S G WC Ex S G w/b (%) Air (%) Series Seal-Cured W C Ex S G OPC55 55 4.5 172 313 - 834 997 7 days OPC55 55 4.5 172 313 - 834 997 7 days OPC55 55 4.5 172 313 - 834 997 7 days OPC45 45 6 164 338 20 791 992 7 days OPC45 45 6 164 338 20 791 992 7 days OPC45 45 6 164 338 20 791 992 7 days Note: w/b = water-to-binder ratio; W = Water; C = Cement; Ex = Expansive additives; S = Sand; G = Note: w/b = water-to-binder ratio; W = Water; C = Cement; Ex = Expansive additives; S = Sand; G = Note: w/b = water-to-binder ratio; W = Water; C = Cement; Ex = Expansive additives; S = Sand; G = Gravels. Gravels. Gravels. (a) (b) (a) (b) Figure 4. (a) Specimens with direct rainfall exposure; (b) shaded specimens. Figure Figure 4. 4. (a ( ) a Specimens ) Specimens w with ith d dir irect rainfal ect rainfall l ex exposur posure; ( e; b( )b sha ) shaded ded specimens. specimens. Appl. Sci. 2018, 8, 394 7 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18 Figures 5–7 portray a comparison between the measured values from data loggers and the Figures 5–7 portray a comparison between the measured values from data loggers and the Figures 5–7 portray a comparison between the measured values from data loggers and the 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 analytical results of the experimented specimens. Figure 5 shows that a change in the mass of the analytical results of the experimented specimens. Figure 5 shows that a change in the mass of the analytical results of the experimented specimens. Figure 5 shows that a change in the mass of the 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 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 with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the specimens with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the specimens with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the specimens with direct rainfall appear to have been underestimated. Figures 6 and 7 illustrate the concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with direct concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with direct concrete strain in OPC55 and OPC45, respectively. If attention was given to the specimens with direct 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 to the behaviour in mass change, a minimal discrepancy was found in the trend rainfall, similar to the behaviour in mass change, a minimal discrepancy was found in the trend trend between the measured and analytical strain. As extra water from rainfall was supplied to between the measured and analytical strain. As extra water from rainfall was supplied to the concrete between the measured and analytical strain. As extra water from rainfall was supplied to the concrete between the measured and analytical strain. As extra water from rainfall was supplied to the concrete the concrete through the exposed surfaces, the measured strain reﬂected this phenomenon through through the exposed surfaces, the measured strain reflected this phenomenon through concrete through the exposed surfaces, the measured strain reflected this phenomenon through concrete through the exposed surfaces, the measured strain reflected this phenomenon through concrete concrete expansion. Hence, the authors have come to understand that the simpliﬁed method of expansion. Hence, the authors have come to understand that the simplified method of reproducing expansion. Hence, the authors have come to understand that the simplified method of reproducing expansion. Hence, the authors have come to understand that the simplified method of reproducing reproducing the rainfall effect should be enhanced to increase the accuracy of numerical prediction, the rainfall effect should be enhanced to increase the accuracy of numerical prediction, but this effect the rainfall effect should be enhanced to increase the accuracy of numerical prediction, but this effect the rainfall effect should be enhanced to increase the accuracy of numerical prediction, but this effect 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 relatively minimal in the case of large-scale concrete structures. In the case of shaded would be relatively minimal in the case of large-scale concrete structures. In the case of shaded of shaded specimens, it is believed that the deviation between the measured and analytical strain in specimens, it is believed that the deviation between the measured and analytical strain in OPC55 specimens, it is believed that the deviation between the measured and analytical strain in OPC55 specimens, it is believed that the deviation between the measured and analytical strain in OPC55 OPC55 likely resulted from the inﬂuence of the wind, unlike the indoor specimens. likely resulted from the influence of the wind, unlike the indoor specimens. likely resulted from the influence of the wind, unlike the indoor specimens. likely resulted from the influence of the wind, unlike the indoor specimens. Figure 5. Mass change of each series (M-Measured & A-Analytical). Figure 5. Mass change of each series (M-Measured & A-Analytical). Figure 5. Mass change of each series (M-Measured & A-Analytical). Figure 5. Mass change of each series (M-Measured & A-Analytical). Figure 6. Concrete shrinkage strain of OPC45. Figure 6. Concrete shrinkage strain of OPC45. Figure 6. Concrete shrinkage strain of OPC45. Figure 6. Concrete shrinkage strain of OPC45. Figure 7. Concrete shrinkage strain of OPC55. Figure 7. Concrete shrinkage strain of OPC55. Figure 7. Concrete shrinkage strain of OPC55. Figure 7. Concrete shrinkage strain of OPC55. 3. 3.2.2. 2.2. C Compr ompre essive ssive St Str rengt ength h 3.2.2. Compressive Strength 3.2.2. Compressive Strength Referrin Referring g to to JIS A JIS A 1108 1108 spe speciﬁcation, cification, cocompr mpression ession testests ts on on a φa 100' × 100 200-c200-cylinder ylinder specim specimen en with Referring to JIS A 1108 specification, compression tests on a φ100 × 200-cylinder specimen with Referring to JIS A 1108 specification, compression tests on a φ100 × 200-cylinder specimen with rad with ius r of adius 100of mm 100 and h mmeand ight of height 200 m of m200 , were mm, also wer coe nducted also conducted for variou for s mixtur various e designs (T mixture designs able 2). radius of 100 mm and height of 200 mm, were also conducted for various mixture designs (Table 2). radius of 100 mm and height of 200 mm, were also conducted for various mixture designs (Table 2). The specim (Table 2). The enspecimens s underwen underwent t seal-cur seal-curing ing condition conditions s for 28 days for 28 days before beforexposure to e exposure to the theambient ambient The specimens underwent seal-curing conditions for 28 days before exposure to the ambient The specimens underwent seal-curing conditions for 28 days before exposure to the ambient environment in a environment in a store storer roo oom m (F (Figur igure 8). In e 8). In the the Du DuCOM COM system, th system, the e strength m strength model odel assume assumes s a clo a close se environment in a storeroom (Figure 8). In the DuCOM system, the strength model assumes a close environment in a storeroom (Figure 8). In the DuCOM system, the strength model assumes a close relationship with capillary porosity development, whereby the present and initial capillary porosity relationship with capillary porosity development, whereby the present and initial capillary porosity 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 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 Appl. Sci. 2018, 8, 394 8 of 18 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. Unit Proportion (kg/m ) Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 18 Appl. Sci. 2018, 8, x FOR PEER w/b REVIEW (%) Air (%) 8 of 18 Series W C Ex S G Ad than OPC con OPC53 crete, which 52.9 affects the lon 4.5 g-term st 166 rengt 314 h [13]. To reva - li802 date the m 1044 odel, F 3.14 igure 9 shows than OPC concrete, which affects the long-term strength [13]. To revalidate the model, Figure 9 shows OPC44 44 6 164 353 20 653 1112 2.24 the compressive strength of each mix d the compressive strength of each mix de es siign se gn serie ries s. . It can be observe It can be observed d that the compressive that the compressive strength strength BFS44 44 6 160 344 20 662 1112 2.18 can be satisfactorily predicted. can be satisfactorily predicted. Figure 8. Environmental condition after 28 days of seal-curing. Figure 8. Environmental condition after 28 days of seal-curing. Figure 8. Environmental condition after 28 days of seal-curing. Figure 9. Compressive strength of concrete (M-Measured and A-Analytical). Figure 9. Figure 9. Com Compr pressive essive streng strength th of con of concr crete ( ete (M-Measur M-Measured a ed and nd A-Analy A-Analytical). tical). Table 2. Trial mixture designs of potential concrete to be used for Shinkesen Bridge deck. 3.2.3. Inﬂuence Table 2. of Trial Curing mixtu Conditions re designs of on potential Concrete concrete to be used for Shinkesen Bridge deck. Unit Proportion (kg/m ) The use of a high-performance mix design as Unit Pr such requir opores tion (kg/m a study on ) the curing period to Series w/b (%) Air (%) Series w/b (%) Air (%) determine the optimum choice for execution withoutWC being vulner Ex ableS to cracking G Ad risk. Thus, referring WC Ex S G Ad to Figure 10, ﬁveOPC5 100 3 100 52.9 400 mm4.5 prismatic 166 plain 314 - 8 concrete02 specimens 1044 3.1 wer4 e prepared with OPC53 52.9 4.5 166 314 - 802 1044 3.14 ﬁve different curing periods (7, 14, 28, 56 and 91 days) before exposure to the environment of the OPC4 OPC44 4 4444 6 6 1164 64 3353 2 53 200 6 653 53 11112 112 22..2244 control chamber (aBFS4 constant 4 2044C and 60%6 relative 160 humidity). 344 20 6 The62 mix1112 design 2.18 of these specimens BFS44 44 6 160 344 20 662 1112 2.18 was BFS44 (Table 2). Figure 11 shows the ﬁnite element of the prismatic specimens whereby the 3. boundary 3.2. 2.3. In 3. Infl fluen uen conditions c ce of C e of Cu urin rin are g g applied C Co ondit nditions o ions o in the n nsame C Co oncret ncret manner e e as that of previous cases. Unlike OPC concrete, the use of a low water-to-cement ratio as such in BFS concrete allows autogenous shrinkage to play a The use of a high-performance mix design as such requires a study on the curing period to The use of a high-performance mix design as such requires a study on the curing period to predominant role, on par with that of drying shrinkage, in determining the properties of the concrete. determine th determine the optimum c e optimum chhoice for oice for exe execcution witho ution withouut being vulnerable t being vulnerable to cr to crack ackiing r ng riisk sk. . Thus, Thus, Thus, to properly capture the autogenous and drying shrinkage of BFS concrete, the driving force of referring to Figure 10, five 100 × 100 × 400 mm prismatic plain concrete specimens were prepared referring to Figure 10, five 100 × 100 × 400 mm prismatic plain concrete specimens were prepared shrinkage in the model is divided into two entities: capillary tension force and disjoining pressure. wit with h five five d diiffffe erent rent curin curing g p pe eriods (7 riods (7, 14 , 14, , 2 28 8, 56 and , 56 and 91 d 91 da ays) befor ys) before e exposure to exposure to the environ the environm ment of ent of The former, which dominates the nanoscale pores, is of paramount signiﬁcance under low relative the control chamber (a constant 20 °C and 60% relative humidity). The mix design of these specimens the control chamber (a constant 20 °C and 60% relative humidity). The mix design of these specimens humidity, but the latter, which governs the microscale pores, contributes signiﬁcantly with a high was BFS was BFS444 ( 4 (T Tab able 2 le 2)). Fig . Figu ure 1 re 111 show showss tth he e ffiinit nitee e elleem ment of the ent of the prismat prismatiic spe c speccimens whe imens wherreby the eby the relative humidity [6]. The applicability of the BFS model in actual specimens exposed to various curing boundary conditions are applied in the same manner as that of previous cases. Unlike OPC concrete, boundary conditions are applied in the same manner as that of previous cases. Unlike OPC concrete, durations would also be conﬁrmed through this model validation. the the use of use of a a low low wa water- ter-to-cement to-cement ra rati tio a o ass such such iin n BFS BFS concrete concrete al allows autogenous lows autogenous shri shrinkage to pl nkage to play ay a predominant role, on par with that of drying shrinkage, in determining the properties of the a predominant role, on par with that of drying shrinkage, in determining the properties of the concrete. Thus, to properly concrete. Thus, to properly ca capture the pture the autogenous autogenous an and dry d dryiing sh ng shrinkage rinkage of of BFS BFS concrete, the concrete, the drivin driving g force of shrinkage in the model is divided into two entities: capillary tension force and disjoining force of shrinkage in the model is divided into two entities: capillary tension force and disjoining pressu pressure. The re. The former former, wh , whic ich domin h domina atte es t s th he nano e nanosca scalle e pores, pores, is is of p of pa arra amount mount s siig gn nifi ificance cance und unde er lo r low w relative humidity, but the latter, which governs the microscale pores, contributes significantly with a relative humidity, but the latter, which governs the microscale pores, contributes significantly with a high high rel rela attiive ve humid humidiitty y [6 [6]. ]. The app The applic licabi abilit lity y of of t th he e BF BFS S mode model l in in act actu ua all specimen specimens expo s exposed sed t to o vario variou us s curing durations would also be confirmed through this model validation. curing durations would also be confirmed through this model validation. Appl. Sci. 2018, 8, 394 9 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 18 Figure 10. FE model of one-eighth of the 400 × 400 × 200 mm prismatic specimen. Figure 10. FE model of one-eighth of the 400 400 200 mm prismatic specimen. Figure 10. FE model of one-eighth of the 400 × 400 × 200 mm prismatic specimen. Figure 11. Concrete shrinkage strain in 100 100 400 mm specimens (M-Measured and A-Analytical). Figure 11. Concrete shrinkage strain in 100 × 100 × 400 mm specimens (M-Measured and Figure 11. Concrete shrinkage strain in 100 × 100 × 400 mm 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 additive The t model rend o would f the an only alyt apply ical res instantaneous ults shown in expansiv Figure e 1 strain 1 could to be concr ac ete cept without able in t consider erms of a st tion rai of n prediction despite some discrepancies, especially during the sealing period. Our current expansive prediction despite some discrepancies, especially during the sealing period. Our current expansive its long-term effect, whereby complete expansion could continue to at least a week [14]. Although, to additive model would only apply instantaneous expansive strain to concrete without consideration pr adovide ditive better modeaccuracy l would only in pr a edicti pply i ng ns strain tantane at ou ans early expastage nsive for strai cases n to concrete wi in which expansive thout consi additives deratiar on e of its long-term effect, whereby complete expansion could continue to at least a week [14]. Although, of its long-term effect, whereby complete expansion could continue to at least a week [14]. Although, applied, the authors aim to investigate the issue and develop a more sophisticated model. Because to provide better accuracy in predicting strain at an early stage for cases in which expansive additives t the o provide bet most prevalent ter accur forms acyof incracks, predictthat ing sis, train thermal at an e and arly st shrinkage-induced age for cases in which e cracks, xpansive are more ad likely ditives to are applied, the authors aim to investigate the issue and develop a more sophisticated model. Because are applied, the authors aim to investigate the issue and develop a more sophisticated model. Because occur after the curing period, the minimal variation during the sealing condition could be reasonably the most prevalent forms of cracks, that is, thermal and shrinkage-induced cracks, are more likely to the most preva disregarded. Ther lent efor forms of cra e, it could c be ks, tha concluded t is, therma that the l anoverall d shrintr kage-induced cr end and strain ack value s, are more of concrete likely to under occur after the curing period, the minimal variation during the sealing condition could be reasonably occur after the curing period, the minimal variation during the sealing condition could be reasonably seal-curing conditions could be acceptably traced. 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 Bars on Concrete seal-curing conditions could be acceptably traced. It was understood that by observing the strain progress of small RC specimens, the shrinkage 3.2.4. Influence of Reinforcing Bars on Concrete 3.2.4. Influence of Reinforcing Bars on Concrete behaviour and cracking susceptibility of concrete using the mix proportions could be more revealing It was understood that by observing the strain progress of small RC specimens, the shrinkage to a certain degree due to the restraints of the reinforcing bars. Hence, prismatic RC specimens of It was understood that by observing the strain progress of small RC specimens, the shrinkage behaviour and cracking susceptibility of concrete using the mix proportions could be more revealing 400 400 200 mm with the aforementioned mixture designs in Table 2 were used for the experiment. behaviour and cracking susceptibility of concrete using the mix proportions could 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 to the restraints of the reinforcing bars. Hence, prismatic RC specimens of 400 × 400 × 200 mm with the aforementioned mixture designs in Table 2 were used for the the top and bottom regions of the prismatic specimens. Figure 12 shows the ﬁnite-element model of of 400 × 400 × 200 mm with the aforementioned mixture designs in Table 2 were used for the experiment. Six reinforcing bars with a diameter of 19 mm were embedded transversely and one-eighth of the 400 400 200 mm prismatic specimen, in which the reinforcements were inserted experiment. Six reinforcing bars with a diameter of 19 mm were embedded transversely and longitudinally at both the top and bottom regions of the prismatic specimens. Figure 12 shows the into the elements marked by purple boxes according to their reinforcement ratios. The specimens were longitudinally at both the top and bottom regions of the prismatic specimens. Figure 12 shows the finite-element model of one-eighth of the 400 × 400 × 200 mm prismatic specimen, in which the under seal-curing conditions for 28 days before they were relocated to a storage room with exposure finite-element model of one-eighth of the 400 × 400 × 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 shown in Figure 8. To incorporate the effect of expansive additives reinforcements were inserted into the elements marked by purple boxes according to their reinforcement ratios. The specimens were under seal-curing conditions for 28 days before they were in concrete, we used a simple model that imposes instantaneous expansive strain on the concrete reinforcement ratios. The specimens were under seal-curing conditions for 28 days before they were relocated to a storage room with exposure to the ambient environment, as shown in Figure 8. To depending on the degree of restraints, such as rebar and external boundaries. relocated to a storage room with exposure to 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 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 18 instantaneous expansive strain on the concrete depending on the degree of restraints, such as rebar instantaneous expansive strain on the concrete depending on the degree of restraints, such as rebar Appl. Sci. 2018, 8, 394 10 of 18 and external boundaries. and external boundaries. Figure 12. FE model of one fourth of the specimen. Figure 12. FE model of one fourth of the specimen. Figure 12. FE model of one fourth of the specimen. Figur Figu ere 1313 shows shows t that hat the thanalyses e analyses p proved roved t that hat the the strain strain pr progre ogressss of the spe of the specimen cimens co s could uld be be Figure 13 shows that the analyses proved that the strain progress of the specimens could be predicted prpredicted edicted satisfactorily. Furthermore, b satisfactorily satisfactorily. Furthermore, b . Furthermore, based ased on ased on on this this this rre esult, sult, it result, it it could could could be be proven th pr be proven th oven thatat the the at the simple simple simple model model model of anof expansive an expansive agent could provide agent could provide a reasonable a reasonoutput able output wi withoutthout affecting affecti the ng the strainstra behaviour in behaviour of of the of an expansive agent could provide a reasonable output without affecting the strain behaviour of the concrete in the long run. Also, as co concr the concrete in the long run. Also, as co ete in the long run. Also, as concrete ncrete expan ncrete expan expands in ds in the ds in t initial h t e in he in it place, iait l p ial l p a the cle, t arisk ce, t he h of rie sk cracking risk of c of c racrkin in ackin the g in t gearly in t he he period early per is heavily iod is heav reduced ily red because uced bec of the ause expansion of the expa effect. nsion e Ther ffect efor . Therefore e, our main , ou concern r main conce should rn not shou beld early period is heavily reduced because of the expansion effect. Therefore, our main concern should not be w with not be w how ith h well ith h ow well the the ow well the model pr model predic edicts model predic the expansion ts the ts the expansio expansio of concr n of concret ete, n of concret but with e, b e the u , b t wi u pr t wi ogr th the progress of th the progress of ess of strain over stra time stra in in because over tiit me bec is much ausmor e it is e muc relevant h more re to theleva initialisation nt to the init of cracks. ialisation o Based f cron acks the . B ra esults sed on of th all e res of the ultsmodel of all of over time because it is much more relevant to the initialisation of cracks. Based on the results of all of the model v validations, the model v ait lidat can alidat ions, beions, conﬁrmed it cit c an be confirme an be confirme that the computational d that d that the co the co mputational models mputational can models c trace models c the a mechani n tr an tr ace the mech ace the mech stic behaviour anistic anistic of concr behavio ete reasonably ur of concret well e re on asa onab small ly wel scale. l on a small scale. behaviour of concrete reasonably well on a small scale. 3 3 3 Figure 13. Concrete shrinkage strain in 400 × 400 × 200 mm RC specimens (M-Measured and A- Figure 13. Concrete shrinkage strain in 400 × 400 × 200 mm RC specimens (M-Measured and A- Figure 13. Concrete shrinkage strain in 400 400 200 mm RC specimens (M-Measured and A-Analytical). Analytical). Analytical). 3.3. Application of the Analytical Model on a Mock-Up Slab Specimen 3.3. 3.A 3. ppl Appl icati ico ati n of on of the tAnal he Anal ytic yt ali cModel on al Model on a Mock a Mock -Up -Up Slab Spe Slab Spe cimen cimen To represent a restraint condition as close to reality as possible, two I-section girders were placed To represent a restraint condition as close to reality as possible, two I-section girders were placed To represent a restraint condition as close to reality as possible, two I-section girders were placed at the concrete supports as they would be placed on the actual steel girders whereas half of the actual at the concrete supports as they would be placed on the actual steel girders whereas half of the actual at the concrete supports as they would be placed on the actual steel girders whereas half of the actual specimen were used for the ﬁnite element model as indicated in Figure 14. The replicated specimen specimen were used for the finite element model as indicated in Figure 14. The replicated specimen specimen were used for the finite element model as indicated in Figure 14. The replicated specimen was cast with ‘BFS44’ mix design and water-cured for 42 days on the top surface before exposure to was cast with ‘BFS44’ mix design and water-cured for 42 days on the top surface before exposure to was cast with ‘BFS44’ mix design and water-cured for 42 days on the top surface before exposure to the outside environment. For Figure 14b, the diameters of the reinforcing bars were 19 and 16 mm in the outside environment. For Figure 14b, the diameters of the reinforcing bars were 19 and 16 mm in the outside environment. For Figure 14b, the diameters of the reinforcing bars were 19 and 16 mm in 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 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 for Rikuzentaka in Iwate prefecture were obtained from the Japan Meteorological Agency and data for Rikuzentaka in Iwate prefecture were obtained from the Japan Meteorological Agency and identically input to the analysis as shown in Figure 15. To trace the expansion and contraction identically input to the analysis as shown in Figure 15. To trace the expansion and contraction identically input to the analysis as shown in Figure 15. To trace the expansion and contraction behaviour of the deck in a quantitative manner, strain gauges were also embedded at the locations behavio behavio ur u of the r of the deck deck in a quantitative manner, st in a quantitative manner, st rain gauges we rain gauges we re also embed re also embed ded at the loc ded at the loc ations ations 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 in Figure 16. These strain gauges perform measurements in transverse, longitudinal and vertical directions. As portrayed in Figure 16, four ﬁnite-element models of the mock-up specimen vert vert icaica l dli d rec irec tions. tions. As As port port raye raye d in d Fi ingu Fire gure 16,16 fo, fo ur ur finfin ite-el ite-el ement ement m m odels odels of o th f t e h mock-up e mock-up spe spe cimen cimen were established to conduct mesh sensitivity analysis to minimise the 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 accept accept able able ac ac curac curac y in y in th t e fol he fol lowin lowin g lg l arge- arge- scasca le br le id brge model. Th idge model. Th is e is e lement d lement d iscretisation p iscretisation p rocess rocess because the convergence in 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 D in D uCOM h uCOM h ad t ad t o be en o be en sured t sured t o prov o prov ide re ide re ason ason ably ably accur accur atea res te res ultu s lt for s for its cou its cou nten rpart terpart , CO , CO M3, M3, to t o structural behaviour. analyse the macroscopic structural behaviour. analyse the macroscopic structural behaviour. Appl. Sci. 2018, 8, 394 11 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 18 (a) (b) (a) (b) Figure 14. (a) Overview of mock-up slab specimen; (b) FE model of half of the mock-up specimen. Figure 14. (a) Overview of mock-up slab specimen; (b) FE model of half of the mock-up specimen. Figure 14. (a) Overview of mock-up slab specimen; (b) FE model of half of the mock-up specimen. Figure Figure 15. 15. Envi Envir ronmental conditions onmental conditions.. Figure 15. Environmental conditions. Due to issues with the embedded strain gauges after removal of the formwork, the measured Due to issues with the embedded strain gauges after removal of the formwork, the measured Due to issues with the embedded strain gauges after removal of the formwork, the measured data from the 42nd and 56th days were lost. Nonetheless, the whole trend of the strain could still be data from the 42nd and 56th days were lost. Nonetheless, the whole trend of the strain could still be 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 captured, whereby the rearrangement of the strain gauges might have affected the strain progress captured, whereby the rearrangement of the strain gauges might have affected the strain progress and resulted in a slightly greater shrinkage strain value. Two main conclusions could be drawn and resulted in a slightly greater shrinkage 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 of this analysis. First, the computational model can capture the strain progress with the result of this analysis. 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 minimal differences. Good agreement was also achieved between the measured and analytical values minimal differences. Good agreement was also achieved between the measured and analytical values values 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 finite- for the concrete temperature. Second, the differences between the computed strains of the four finite- ﬁnite-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 be element models with distinctive aspect ratios and element sizes were also negligible. Thus, it can be be conﬁrmed that the element with a length of around 300 mm could reasonably be implemented in confirmed that the element with a length of around 300 mm could reasonably be implemented in the confirmed that the element with a length of around 300 mm could reasonably be implemented in the the large-scale analysis. large-scale analysis. large-scale analysis. 3.4. Preliminary Analysis on Concrete Deck Slab of Shinkesen Bridge to Evaluate the Occurrence of Cracks 3.4. Preliminary Analysis on Concrete Deck Slab of Shinkesen Bridge to Evaluate the Occurrence of Cracks 3.4. Preliminary Analysis on Concrete Deck Slab of Shinkesen Bridge to Evaluate the Occurrence of Cracks To combat the complex degradation processes from the cold environment, frost damage, chloride To combat the complex degradation processes from the cold environment, frost damage, To combat the complex degradation processes from the cold environment, frost damage, attack from de-icing salt, alkali–silica reaction and fatigue, a holistic countermeasure approach was chloride attack from de-icing salt, alkali–silica reaction and fatigue, a holistic countermeasure chloride attack from de-icing salt, alkali–silica reaction and fatigue, a holistic countermeasure undertaken to enhance the durability performance of the RC deck slab. The multiple protection approach was undertaken to enhance the durability performance of the RC deck slab. The multiple approach was undertaken to enhance the durability performance of the RC deck slab. The multiple strategy incorporates a low water-to-binder ratio (w/b), the use of mineral admixture, epoxy-coated protection strategy incorporates a low water-to-binder ratio (w/b), the use of mineral admixture, protection strategy incorporates a low water-to-binder ratio (w/b), the use of mineral admixture, reinforcing bars and 6% entrained air [1]. Because the early-age cracks such as shrinkage cracks allow epoxy-coated reinforcing bars and 6% entrained air [1]. Because the early-age cracks such as epoxy-coated reinforcing bars and 6% entrained air [1]. Because the early-age cracks such as more migration of deleterious ions into the body of concrete under such severe conditions, it is of shrinkage cracks allow more migration of deleterious ions into the body of concrete under such shrinkage cracks allow more migration of deleterious ions into the body of concrete under such great signiﬁcance to control and delay its occurrence [10]. Therefore, before the Shinkesen Bridge was severe conditions, it is of great significance to control and delay its occurrence [10]. Therefore, before severe conditions, it is of great significance to control and delay its occurrence [10]. Therefore, before constructed, a cracking assessment was performed for various mixture designs. the Shinkesen Bridge was constructed, a cracking assessment was performed for various mixture the Shinkesen Bridge was constructed, a cracking assessment was performed for various mixture Figure 17 outlines the layout of the ﬁnite-element model of the Shinkesen Bridge for preliminary designs. designs. analysis of crack propagation. Considering the symmetric condition and actual construction procedure Figure 17 outlines the layout of the finite-element model of the Shinkesen Bridge for preliminary Figure 17 outlines the layout of the finite-element model of the Shinkesen Bridge for preliminary that would be adopted, the RC deck slab was modelled in combination with the girders and their analysis of crack propagation. Considering the symmetric condition and actual construction analysis of crack propagation. Considering the symmetric condition and actual construction stiffeners to achieve structural resemblances that have an effect on the restraint condition. To capture procedure that would be adopted, the RC deck slab was modelled in combination with the girders procedure that would be adopted, the RC deck slab was modelled in combination with the 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 on the mock-up slab specimen, the maximum length of the element To capture the temperature and moisture gradients inside the RC deck slab properly, and based on To capture the temperature and moisture gradients inside the RC deck slab properly, and based on was taken to be 250 mm. To shorten the computational time, and as a conservative measure, the the mesh sensitivity analysis conducted on the mock-up slab specimen, the maximum length of the the mesh sensitivity analysis conducted on the mock-up slab specimen, the maximum length of the ambient environment was set to dry conditions with a constant 15 C temperature 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 throughout the calculation, whereas the asphalt layer would exist the ambient environment was set to dry conditions with a constant 15 °C temperature and 70% the ambient environment was set to dry conditions with a constant 15 °C temperature and 70% on the top surface in reality. The environmental conditions were decided based on the average value relative humidity on the concrete surface throughout the calculation, whereas the asphalt layer relative humidity on the concrete surface throughout the calculation, whereas the asphalt layer 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 Appl. Sci. 2018, 8, 394 12 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 12 of 18 in accordance with the local meteorological data. The effects of concrete mixture designs on crack generation designs on and crack propagat generaion tionwer ande p investigated ropagation win ere the invest analysis. igated In in Japan, the analy the sis typical . In Japa w/b n, thshould e typicanot l 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 exceed 65%. In most cases, a w/b of 55% was endorsed, whereby the upper limit of water content is w/b should not exceed 65%. In most cases, a w/b of 55% was endorsed, whereby the upper limit of 3 3 3 water content is recommended as 175 kg/m and lower limit of the cement content is recommended recommended as 175 kg/m and lower limit of the cement content is recommended as 300 kg/m [15]. water content is recommended as 175 kg/m and lower limit of the cement content is recommended as 300 kg/m [15]. As seen in Table 3, the mixture designs consist of five series: BFS42, OPC42, BFS55, As seen in Table 3, the mixture designs consist of ﬁve series: BFS42, OPC42, BFS55, OPC55 and as 300 kg/m [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’ represents the use of expansive additives. OPC55 and BFS42-EX whereby ‘EX’ represents the use of expansive additives. Figure 16. Concrete shrinkage strain at corresponding gauges and concrete temperatures. *  to  Figure 16. Concrete shrinkage strain at corresponding gauges and concrete temperatures. *  to  Figure 16. Concrete shrinkage strain at corresponding gauges and concrete temperatures. * 1 to 8 represent different locations of strain gages; I, II, III, IV represent the four finite element analytical represent different locations of strain gages; I, II, III, IV represent the four finite element analytical represent different locations of strain gages; I, II, III, IV represent the four finite element analytical models. models. models. Figure 17. Cont. Appl. Sci. 2018, 8, 394 13 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 18 Figure 17. FE model of one-fourth of a bridge span. Figure 17. FE model of one-fourth of a bridge span. TTable 3. able 3. Mixtur Mixture e d designs esigns us used ed for parametric for parametric st study udy. . Unit Proportion (kg/m ) Series w/b (%) Air (%) Unit Proportion (kg/m ) WC Ex S G Ad w/b (%) Air (%) Series W C Ex S G Ad OPC55 55 4.5 170 310 - 802 1044 3.14 OPC55 55 4.5 170 310 - 802 1044 3.14 BFS55 55 4.5 170 310 - 802 1044 3.14 BFS55 55 4.5 170 310 - 802 1044 3.14 OPC42 42 6 153 364 - 653 1112 2.24 OPC42 42 6 153 364 - 653 1112 2.24 BFS42 42 6 153 364 - 662 1112 2.18 BFS42 42 6 153 364 - 662 1112 2.18 BFS42-EX 42 6 153 364 20 662 1112 2.18 BFS42-EX 42 6 153 364 20 662 1112 2.18 Figure 18 portrays the computed longitudinal strain after 2 years, which is the strain along the Figure 18 portrays the computed longitudinal strain after 2 years, which is the strain along the bridge axis, on the top surface of the RC deck slab. The strain contours were extracted from the bridge axis, on the top surface of the RC deck slab. The strain contours were extracted from the portion portion of deck slab highlighted with the black rectangle. Due to the restraints from the steel girders, of deck slab highlighted with the black rectangle. Due to the restraints from the steel girders, high high tensile strains were seen to be localised around the elements with a longitudinal length of 60 tensile mm, which strains would r were seen esem toble t be h localised at of cracks around . Becau the se these high t elements with ensile str a longitudinal ains are mostly o length b of served 60 mm, which aroun would d the 60-mm element resemble that of s, the tran cracks. Because sverse max these imum high crack tensile widt strains h was c ara elc mostly ulated by mu observed ltiply aring t ound he the maximum strain with the element length of 60 mm. According to the JSCE standard, the limit value 60-mm elements, the transverse maximum crack width was calculated by multiplying the maximum of crack width for concrete in a severely corrosive environment is 0.0035c, where c refers to the strain with the element length of 60 mm. According to the JSCE standard, the limit value of crack width 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 to 0.14 mm. Four main aspects, focusing on BFS concrete, would be pinpointed from Therefore, in the case of the Shinkesen Bridge, the allowable crack width would be equivalent to the parametric study, including the influence of the (1) binder type, (2) w/b, (3) prolonged curing, 0.14 mm. Four main aspects, focusing on BFS concrete, would be pinpointed from 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 resistance against durability issues such as ASR and chloride environments, such as Tohoku. Then, consistent with the universal understanding that prolonged ingression mean that it might not be a good candidate for areas with severe environments, such as seal curing would reduce the moisture loss through the concrete’s surface, seal curing BFS42 up to 28 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 the moisture loss through the concrete’s surface, seal curing BFS42 up to 28 days signiﬁcantly helped additives inside BFS42, further improvement in reducing the generation of tensile strain was to reduce the maximum tensile strain. Finally, after incorporating expansive additives inside BFS42, illustrated. In addition to the lower intensity in the maximum crack width, based on the strain further improvement in reducing the generation of tensile strain was illustrated. In addition to the contour, the amount of nodal strain that reached a longitudinal strain of 1000 μ is also minimal, which infers that less crack propagation would occur than in the case without expansive additives. Hence, lower intensity in the maximum crack width, based on the strain contour, the amount of nodal strain as a conservative measure in cases in which prolonged curing could not be properly conducted or that reached a longitudinal strain of 1000 is also minimal, which infers that less crack propagation maintained, the recommendation to use expansive additives in the multiple protection strategy is would occur than in the case without expansive additives. Hence, as 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. Appl. Sci. 2018, 8, 394 14 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 18 Figure 18. Parametric study focusing on four different aspects. * εmax = maximum longitudinal strain; Figure 18. Parametric study focusing on four different aspects. * " = maximum longitudinal strain; max wmax = maximum crack width. w = maximum crack width. max 3.5. Post-Construction Analysis on Concrete Deck of Shinkesen Bridge: Verification with on-Site Measured 3.5. Post-Construction Analysis on Concrete Deck of Shinkesen Bridge: Veriﬁcation with on-Site Data Measured Data Figure 19 represents the entire overview of the 438-m seven-spanned steel girder–supported Figure 19 represents the entire overview of the 438-m seven-spanned steel girder–supported bridge. The casting sequence was carried out according to the numbers shown after considering the bridge. The casting sequence was carried out according to the numbers shown after considering the 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 casting lot 8 over the top of Pier 3 support. The top surface of the concrete underwent embedded on casting lot 8 over the top of Pier 3 support. The top surface of the concrete underwent wet-curing for approximately 22 days, following by seal-curing for another 7 days before the RC deck wet-curing for approximately 22 days, following by seal-curing for another 7 days before the RC deck 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, Appl. Sci. 2018, 8, 394 15 of 18 was exposed to the ambient environment. Figure 20 illustrates the ﬁnite-element model of one-fourth Appl. Sci. 2018, 8, x FOR PEER REVIEW 15 of 18 Appl. Sci. 2018, 8, x FOR PEER REVIEW 15 of 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 model mentioned in Section 3.5. To precisely consider the real conditions of the concrete bridge deck, a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. To a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. To a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. account for the effect of the expansion joint in the finite-element model, the longitudinal restraint at a time delay between Lots 1 and 8 due to the casting sequence was also included in the analysis. To account for the effect of the expansion joint in the finite-element model, the longitudinal restraint at To account for the effect of the expansion joint in the ﬁnite-element model, the longitudinal restraint Lot account 8 is rep forl t ac hed wit e effect h of a r tih ge exp id boa dy whos nsion joe sole int in taim he f i in s t ito e-el allow sl ementight model, transl the atlong ionait l udin movem al re ent str , as see aint at n Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as seen at Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as in Figure 20. The nodes on the rigid body were restrained from moving vertically. Insertion of the Lot 8 is replaced with a rigid body whose sole aim is to allow slight translational movement, as seen in Figure 20. The nodes on the rigid body were restrained from moving vertically. Insertion of the seen in Figure 20. The nodes on the rigid body were restrained from moving vertically. Insertion of rigid body w in Figure 20. a The node s performed s on at the end o the rigid body we f Lot 8 to maintain the re restrained from sy moving vert mmetric conditions ically. Insein the rtion of bridg the e rigid body was performed at the end of Lot 8 to maintain the symmetric conditions in the bridge the rigid body was performed at the end of Lot 8 to maintain the symmetric conditions in the bridge span. rigid body w The reinforcement as performed rat at the end o io was cafut Lot 8 to maintain the iously applied as casy lcu mmetric conditions lated from the struct in the ura bridg l detea il span. The reinforcement ratio was cautiously applied as calculated from the structural detail span. The reinforcement ratio was cautiously applied as calculated from the structural detail drawings, span. The reinforcement ratio was cautiously applied as calculated from the structural detail drawings, whereby lot 8 possesses more reinforcing bars in the top section. The environmental data drawings, whereby lot 8 possesses more reinforcing bars in the top section. The environmental data whereby lot 8 possesses more reinforcing bars in the top section. The environmental data from the from the beginning of drawings, whereby lot 8 po Lot 1 c ssesasstin es mo g were also ob re reinforcingta bars ined from the Jap in the top section. The an Meteo en rological vironment agency as al data from the beginning of Lot 1 casting were also obtained from the Japan Meteorological agency 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 in Figure 21. portrayed in Figure 21. Figure 21. portrayed in Figure 21. L4 L3 L13 L6 L12 L2 L10 L8 L1 L9 L5 L11 L7 L4 L3 L13 L6 L12 L2 L10 L8 L1 L9 L5 L11 L7 L6 L12 L2 L10 L4 L8 STEEL GIRDE L1 L9 RS L5 L11 L3 L13 L7 STEEL GIRDERS STEEL GIRDERS P1 P2 P3 P4 P5 P6 P1 P2 P3 P4 P5 P6 P2 P1 P3 P4 P5 P6 Longitudinal-B Longitudinal-B Longitudinal-B Transverse-B Transverse-B Transvers e-B Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure 19. Overview of Shinkesen Bridge and the casting sequence (Red circle = Gauge location). Figure 20. FE model of one-fourth of the span of Shinkesen Bridge. Figure 20. FE model of one-fourth of the span of Shinkesen Bridge. Figure 20. FE model of one-fourth of the span of Shinkesen Bridge. Figure 20. FE model of one-fourth of the span of Shinkesen Bridge. Figure 21. Environmental condition of Shinkesen Bridge after Lot 1 casted up to 250 days. Figure 21. Environmental condition of Shinkesen Bridge after Lot 1 casted up to 250 days. Figure 21. Environmental condition of Shinkesen Bridge after Lot 1 casted up to 250 days. Figure 21. Environmental condition of Shinkesen Bridge after Lot 1 casted up to 250 days. Figure 22 shows a comparison between the analytical strain and the measured strain. The Figure 22 shows a comparison between the analytical strain and the measured strain. The 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 defin definit ition o ion off iin nit itia ial l zero zero st strra ain in in in dat dat aa lo lo ggers ggers wa wa s s ap ap proximat proximat elel y y 3 h a 3 h a ftf etr t er t he c he c ast ast ing on ing on Lot Lot 8 at 8 at th t e he 19th day. The analytical strain was therefore taken from the start of the 19th day for verification 19th day. The analytical strain was therefore taken from the start of the 19th day for verification 19th day. The analytical strain was therefore taken from the start of the 19th day for verification process. It can be observed that the strain progress can be well-traced for both longitudinal and process. It can be observed that the strain progress can be well-traced for both longitudinal and process. It can be observed that the strain progress can be well-traced for both longitudinal and Appl. Sci. 2018, 8, 394 16 of 18 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. The analytical strain was therefore taken from the start of the 19th day for veriﬁcation Appl. Sci. 2018, 8, 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 inside the concrete. Furthermore, for the concrete temperature, in addition to the transverse directions inside the concrete. Furthermore, for the concrete temperature, in addition to good agreement in the overall trend, an underestimation seems to occur during the seal-curing period, the good agreement in the overall trend, an underestimation seems to occur during the seal-curing wher period, whe eby the r concr eby the concrete is entir ete is entirely sealed and ely se cover aled with and cover wi formwork.th formwork. Hence, it is logically Hence,r i easonable t is logica that lly the measured value is greater than the analytical results because the simulation considers the surface of reasonable that the measured value is greater than the analytical results because the simulation consi the concr ders the surf ete to virtually ace of touch the concrete to vi the ambient envir rtual onment. ly touch the a In addition, mbient envi if attention ronment. In a is given to the ddigir tion, i ders’ f temperature, the computational platform almost exactly matches the data from the temperature gauge. attention is given to the girders’ temperature, the computational platform almost exactly matches the data from However, the temperature the minimal deviation gauge. Howe in temperatur ver, the m e isini ofmal little deviation concern in temper as long asature is o the longitudinal f little costrain, ncern which accounts for the infamous transverse deck cracking observed in most geographical conditions, as long as the longitudinal strain, which accounts for the infamous transverse deck cracking observed in most is consider geogr ed.aphical conditions, is considered. Figure 22. Concrete shrinkage strain at corresponding gauges and temperature of Shinkesen Bridge. Figure 22. Concrete shrinkage strain at corresponding gauges and 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. First and foremost, on a small scale (decimetres), validation of the multiscale integrated Appl. Sci. 2018, 8, 394 17 of 18 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. 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. 2. 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. 3. 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. Tanaka, Y.; Ishida, T.; Iwaki, I.; Sato, K. Multiple protection design for durable concrete bridge deck in cold regions. JSCE 2017, 5, 68–77. [CrossRef] 2. Faria, R.; Azenha, M.; Figueiras, J.A. Modelling of concrete at early ages: Application to an externally restrained slab. Cem. Concr. Compos. 2006, 28, 572–585. [CrossRef] 3. Jendele, L.; Smilauer, V.; Cervenka, J. Multiscale hydro-thermo-mechanical model for early-age and mature concrete structures. Adv. Eng. Softw. 2014, 72, 134–146. [CrossRef] 4. Maekawa, K.; Ishida, T.; Kishi, T. Multi-Scale Modeling of Structural Concrete, 1st ed.; Taylor & Francis: New York, NY, USA, 2009; ISBN 978-0-415-46554-0. 5. Maekawa, K.; Okamura, H.; Pimanmas, A. Non-Linear Mechanics of Reinforced Concrete; Spon Press: London, UK, 2003; ISBN 978-0-415-27126-4. 6. Maekawa, K.; Ishida, T.; Kishi, T. Multi-scale Modeling of Concrete Performance—Integrated Material and Structural Mechanics. J. Adv. Concr. Technol. 2003, 1, 91–126. [CrossRef] 7. Luan, Y.; Ishida, T. Enhanced shrinkage model based on early age hydration and moisture status in pore structure. J. Adv. Concr. Technol. 2013, 11, 360–373. [CrossRef] Appl. Sci. 2018, 8, 394 18 of 18 8. Biot, M.A. General Theory of three-dimensional consolidation. J. Appl. Phys. 1941, 12, 155–164. [CrossRef] 9. Gebreyouhannes, E.; Yoneda, T.; Ishida, T.; Maekawa, K. Multi-scale based simulation of shear critical reinforced concrete beams subjected to drying. J. Adv. Concr. Technol. 2014, 12, 363–377. [CrossRef] 10. Hussain, S.E. Effect of microsilica and blast furnace slag on pore solution composition and alkali-silica reaction. Cem. Concr. Compos. 1991, 13, 219–225. [CrossRef] 11. Dhir, R.K.; El-Mohr, M.A.K.; Dyer, T.D. Chloride binding in GGBS concrete. Cem. Concr. Res. 1996, 26, 1767–1773. [CrossRef] 12. Mehta, P.K.; Monteiro, P.J.M. Concrete: Microstructure, Properties, and Materials, 3rd ed.; McGraw-Hill: New York, NY, USA, 2006; ISBN 978-0-07-158919-2. 13. Iqbal, P.O.; Ishida, T. Modeling of chloride transport coupled with enhanced moisture conductivity in concrete exposed to marine environment. Cem. Concr. Res. 2009, 39, 329–339. [CrossRef] 14. Ishida, T.; Luan, Y.; Sagawa, T.; Nawa, T. Modeling of early age behavior of blast furnace slag concrete based on micro-physical properties. Cem. Concr. Res. 2009, 41, 1357–1367. [CrossRef] 15. Collepardi, M.; Borsoi, A.; Collepardi, S.; Olagot, J.J.O.; Troli, R. Effects of shrinkage reducing admixture in shrinkage compensating concrete under non-wet curing conditions. Cem. Concr. Res. 2005, 27, 704–708. [CrossRef] 16. JSCE. Standard Speciﬁcation for Concrete Structures—2007; JSCE: Tokyo, Japan, 2010; ISBN 978-4-8106-0752-9. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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Numerical Simulation of Early Age Cracking of Reinforced Concrete Bridge Decks with a Full-3D Multiscale and Multi-Chemo-Physical Integrated Analysis

Numerical Simulation of Early Age Cracking of Reinforced Concrete Bridge Decks with a Full-3D Multiscale and Multi-Chemo-Physical Integrated Analysis

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Numerical Simulation of Early Age Cracking of Reinforced Concrete Bridge Decks with a Full-3D Multiscale and Multi-Chemo-Physical Integrated Analysis

Numerical Simulation of Early Age Cracking of Reinforced Concrete Bridge Decks with a Full-3D Multiscale and Multi-Chemo-Physical Integrated Analysis

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