## 3 Numerical Simulation of Early-Age Behaviour of Small Specimens to Actual Rc Deck Slabs
### 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 attack from de-icing salt, alkali-silica reaction and fatigue, a holistic countermeasure approach was undertaken to enhance the durability performance of the RC deck slab. The multiple protection strategy incorporates a low water-to-binder ratio (w/b), the use of mineral admixture, epoxy-coated reinforcing bars and 6% entrained air [1]. Because the early-age cracks such as shrinkage cracks allow more migration of deleterious ions into the body of concrete under such severe conditions, it is of great significance to control and delay its occurrence [10]. Therefore, before the Shinkesen Bridge was constructed, a cracking assessment was performed for various mixture designs. Figure 17 outlines the layout of the finite-element model of the Shinkesen Bridge for preliminary analysis of crack propagation. Considering the symmetric condition and actual construction procedure that would be adopted, the RC deck slab was modelled in combination with the girders and their stiffeners to achieve structural resemblances that have an effect on the restraint condition. To capture the temperature and moisture gradients inside the RC deck slab properly, and based on the mesh sensitivity analysis conducted on the mock-up slab specimen, the maximum length of the element was taken to be 250 mm. To shorten the computational time, and as a conservative measure, the ambient environment was set to dry conditions with a constant 15 \({}^{\circ}\)C temperature and 70% 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 average value  
Figure 14: (**a**) Overview of mock-up slab specimen; (**b**) FE model of half of the mock-up specimen. Figure 15: Environmental conditions. in accordance with the local meteorological data. The effects of concrete mixture 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 water content is recommended as 175 kg/m\({}^{3}\) and lower limit of the cement content is recommended as 300 kg/m\({}^{3}\)[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. Figure 16: Concrete shrinkage strain at corresponding gauges and concrete temperatures. * 1 to 8 represent different locations of strain gases; I, II, III, IV represent the four finite element analytical models. Figure 17: _Cont_. 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 portion of deck slab highlighted with the black rectangle. Due to the restraints from the steel girders, high tensile strains were seen to be localised around the elements with a longitudinal length of 60 mm, which would resemble that of cracks. Because these high tensile strains are mostly observed around the 60-mm elements, the transverse maximum crack width was calculated by multiplying the maximum strain with the element length of 60 mm. According to the JSCE standard, the limit value of crack width for concrete in a severely corrosive environment is 0.0035c, where c refers to the concrete cover [16]. Therefore, in the case of the Shinkesen Bridge, the allowable crack width would be equivalent to 0.14 mm. Four main aspects, focusing on BFS concrete, would be pinpointed from the parametric study, including the influence of the (1) binder type, (2) w/b, (3) prolonged curing, and (4) expansive additives. First, after 7 days of seal curing, a higher tensile strain is observed in the case of BFS55 than with OPC55.