## 2 Methodology
### Numerical Procedure  
The potential for base plate cracking greatly depends on the magnitude of tensile stress induced by shrinkage and thermal contraction since humidity and temperature changes may produce identical stresses in a plate structure of hardening concrete. A numerical procedure was devised to calculate shrinkage and thermal stresses. It included a temperature model considering hydration heat of cement and heat transfer between concrete and the surrounding environment, a moisture model that could capture the relative humidity development of early-age concrete, and a mechanical model to compute strains and stresses. Concrete creep effect was pronounced at an early age, and it was properly considered in the mechanical model. For heat transfer in concrete, the governing equation is described as follows:  
\[\rho c\dot{T}=\
abla\cdot(k_{T}\cdot\
abla T)+\dot{Q} \tag{1}\]  
where \(\rho\) is the mass density of concrete (kg/m\({}^{3}\)); \(c\) is the specific heat capacity of concrete (J/kg\({}^{\circ}\)C); \(T\) is the temperature of concrete (\({}^{\circ}\)C); \(k_{T}\) is the thermal conductivity of concrete; (W/m\({}^{\circ}\)C) and \(\dot{Q}\) is the rate of hydration heat generation (W/m\({}^{3.\circ}\)C). The rate of hydration heat is expressed by an Arrhenius law of the following form [23]:  
\[\dot{Q}=a\ f(\alpha)\ \ e^{-\frac{E_{a}}{kT}} \tag{2}\]  
where is the maximum value of the heat generation rate (J/s); \(E_{a}\) is the activation energy (J/mol); \(R\) is the universal gas constant (8.314 J/mol K\({}^{-1}\)); and \(f\) (\(\alpha\)) describes the evolution of the normalized heat generation rate as a function of the hydration degree \(\alpha\). Figure 4: The main flows of in-site CRTS III base plate construction and curing. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline _uv/b_ & **Cement** & **Fly Ash** & **Water** & **Coarse** & **Sand** & **Air Entraining** & **Super** \\
**Ratio** & (kg/m\({}^{3}\)) & (kg/m\({}^{3}\)) & (kg/m\({}^{3}\)) & (kg/m\({}^{3}\)) & (kg/m\({}^{3}\)) & Agent (kg/m\({}^{3}\)) & **Super** \\ \hline
0.34 & 309 & 132 & 150 & 1046 & 756 & 2.2 & 4.85 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mixture proportion of base plate concrete. For moisture diffusion in concrete, the governing equation is as follows:  
\[\dot{H}=\
abla\cdot[D(H)\cdot\
abla H]-\dot{H}_{\text{s}} \tag{3}\]  
where \(H\) is the RH of concrete, \(H_{\text{s}}\) is the rate of RH drop due to self-desiccation, and \(D\)(\(H\)) is the moisture diffusivity (m\({}^{2}\)/s). According to [24], \(D\)(\(H\)) can be approximated by the following:  
\[D(H)=D_{1}\bigg{(}\alpha_{0}+\frac{1-\alpha_{0}}{1+(1-h/1-h_{c})^{r}}\bigg{)} \tag{4}\]  
where \(D_{1}\) and \(h_{c}\) are rare empirical parameters. The default values recommended by the fib Model Code [25] were used in this study. With simulated results of temperature and relative humidity field, thermal and hygrometric (i.e., shrinkage or swelling) strains can be calculated by the following relations:  
\[\dot{\epsilon}^{\text{T}}(t)=\alpha_{T}\dot{T}(t),\ \ \dot{\epsilon}^{sh}(t)=k_{sh} \dot{H}(t) \tag{5}\]  
where \(\alpha_{T}\) is the coefficient of thermal expansion, and \(k_{sh}\) is the shrinkage coefficient of the concrete that \(\alpha_{T}\) depends on \(T\) and \(k_{sh}\) depends on \(H\) but only weakly. As simplification, they can be assumed to be constant [26]. For step-by-step finite element analysis of stress, an incremental form of the constitutive equation used for coding needs to be deduced. The stress-dependent strains due to elasticity and concrete creep can be characterized by a compliance function obtained from creep tests. Since early-age concrete creep greatly dependents on the evolution of internal humidity and temperature and, hence, further depends on weather conditions and on the adopted curing regime, properly considering the effects of temperature and humidity on creep strain is required. To this end, the microprestress solidification (MPS) theory-based creep model was adapted.