## 3 Finite Element Simulation of the CRCP Segment
### Thermo-Mechanical Properties  
Young hardening of concrete with total strain crack model in accordance with the Euro-code 2 EN 1992-1-1 model available in Diana FE program is used to simulate the early-age crack development in the CRCP segment under external varying temperature field [23]. The concrete class C40/50 is normally used in the construction of CRCP's in Belgium [12]. The thermal-mechanical parameters used in the FE analysis are demonstrated in Table 3. The specific heat parameter refers to the capacity of concrete to store heat. The value of specific heat capacity of concrete is taken as 2.87 \(\times\) 106 J/m\({}^{3}\)\({}^{\circ}\)C based on previous studies [23; 30; 31; 32].  
The thermal conductivity of concrete determines the amount of heat transfer through conduction. Therefore, it is considered as an important factor in modeling the temperature  
Figure 3: Geometry configuration of the CRCP segment.  
\begin{table}
\begin{tabular}{c c} \hline \hline Concrete class & C40/50 \\ Aggregate type & Limestone \\ Coefficient of thermal expansion of concrete (1/\({}^{\circ}\)C) & 10.0 \(\times\) 10\({}^{-6}\) \\ Concrete thermal conductivity (W/m \({}^{\circ}\)C) & 2.7 \\ Concrete volumetric heat specific capacity (J/m\({}^{3}\)\({}^{\circ}\)C) & 2.87 \(\times\) 10\({}^{6}\) \\ Convection-radiation coefficient between concrete and air (W/m\({}^{2}\)\({}^{\circ}\)C) & 7.55 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Thermo-mechanical parameters used in the FE model.  
gradients in early age concrete [33]. The constant value of thermal conductivity is assumed to be 2.7 W/m\({}^{\circ}\)C [12; 26; 30]. Owing to the difficulties in accurately determining the early-age thermal properties of concrete, constant values have been used in the present study. The coefficient of thermal expansion (CTE) is a key parameter that provides a measure of volumetric changes in a material at varying temperatures. The CTE of concrete is affected significantly by the aggregate, which makes up 70% to 85% of the total solid volume of the concrete. It depends on the type of aggregate and its mineralogical composition, because of the large differences in the thermal properties of various types of aggregates [34; 35]. Experimental investigations have revealed that the CTE of concrete remains constant after the final setting [12; 32; 33]. Therefore, a constant value of CTE as illustrated in Table 3 is used in the present study.  
The type of cement has a dominant influence on the early-age cracking of concrete. The blast furnace slag cement (CEM III) is very often used for the construction of CRCPs in Belgium because of its low heat release, low permeability, and good durability [36]. The heat of hydration model valid for blast furnace slag cement is used to define the heat development in terms of adiabatic heat curve [37]. The development of mechanical properties (tensile strength, compressive strength, and elastic modulus) with respect to time are formulated as a function of the degree of reaction in accordance with the Eurocode 2 EN 1992-1-1 model code [23]. Input parameters for Euro-code 2 EN 1992-1-1 creep and shrinkage model are illustrated in Table 4.  
Reinforcing steel bars are modeled as embedded reinforcement with a young modulus of 200 GPa and yield strength of 500 MPa. The constitutive behavior of reinforcement is defined as elastoplastic with no hardening. Young modulus of and yield strength of steel. In embedded reinforcement, the perfect-bonding contact with zero bond-slip is considered between the reinforcing bars and concrete for the smooth convergence of the FE analysis [38; 39; 40].