# Numerical Analysis of a Moderate Fire inside a Segment of a Subway Station
## 3 Transient Simulation of Non-Stationary Heat Conduction  
Heat conduction within the tested structure was simulated by means of three-dimensional non-stationary Finite Element simulations using the commercial software Abaqus FEA 2016. The Finite Element mesh (Figure 10) was the result of a convergence study. It was a satisfactory trade-off between simulation accuracy and computational effort [49]. The mesh consisted of 139,040 linear hexahedral brick finite elements, with eight nodes and one temperature degree of freedom per node. These elements are referred to as \"DC3D8\" by Abaqus [42]. The characteristic size of the finite elements amounted to 3 cm. Notably, there are studies [23; 50] showing that the steel bars have an insignificant influence on the heat conduction problem. For this reason, the thermal properties of concrete were assigned to all finite elements for the simulation of the non-stationary heat conduction problem. This analysis was only made for the analysis of heat conduction. For the subsequent thermomechanical analysis, the specific properties of concrete and steel were assigned to the corresponding elements.  
The thermal properties of the concrete of the tested structure were unknown. As a remedy, the values of the specific heat capacity and the thermal conductivity were estimated in accordance with building codes [43; 44; 51; 52] and scientific studies [53; 54; 55]; see Table 4. These values refer to room temperature. Notably, the experimental measurements suggest that the temperature of the structure remained below 100 \({}^{\circ}\)C during the first 30 min of the fire test (see Figure 8) and, thus, that the  
Figure 10: Three-dimensional Finite Element mesh of the analyzed structure and the Cartesian coordinate system used.  
Figure 9: Measured evolutions of total strains of steel rebar: (**a**) top slab, at the midspan of the left cell, and (**b**) center of the right wall.  
evaporable water of the concrete was not released [53; 56]. This served as a motivation to assume, in the spirit of a reductionist approach, that the thermal properties of concrete at room temperature are a reasonable approximation throughout the entire analysis, although the thermal conductivity of concrete decreases to some 90% of its room-temperature value, provided that the material is heated up to 100 \({}^{\circ}\)C; see the building codes [43; 44; 52] and the scientific studies [1; 53; 55; 57; 58].  
As regards the boundary conditions, the simulations were based on histories of temperature fields that were prescribed at the inner and outer surfaces of the simulated structure. This approach was appealing as it rendered a computational fluid dynamics simulation of heat transfer from the hot air to the simulated structure dispensable. Such simulations are rather challenging, because of thermal instabilities occurring inside the highly turbulent air flow [34; 59; 60]. Herein, the temperature at the outer surface of the simulated structure was set equal to the initial temperature, \(T_{ini}=10\)\({}^{\circ}\)C, throughout the entire simulation. This agrees with the experimental measurements. As for the time-dependent temperature field prescribed at the heated inner surface, two different strategies were implemented within the framework of a sensitivity analysis: (i) spatially-uniform heating of the entire inner surface of the structure and (ii) piecewise spatially-uniform heating of three sub-regions of the inner surface.