2.1.2. Model Establishment of Double-Deck Bridge

FDS is used to establish a double-deck bridge section. The shape and dimensions of the bridge refer to the Shiziyang bridge in Guangzhou, China. In order to simplify the model, the bridge model in this paper does not consider the influence of the girder on the temperature field. A 3D view of the model of the bridge is shown in Figure 1. In the bridge model, the longitudinal direction of the bridge is in the *x*-direction with a 48 m length, the transverse direction is in the *y*-direction with a 42 m length, and the vertical direction is in the *z*-direction with varying length. *Fire* **2022**, *5*, x FOR PEER REVIEW 4 of 14

**Figure 1.** Three-dimensional (3D) view of the bridge.

**Figure 1.** Three-dimensional (3D) view of the bridge. **Table 1.** Parameters of materials used in the bridge model. The main material of the bridge is steel. The thermal parameters of the steel include thermal conductivity and specific heat. These parameters have been studied by many scholars and can be expressed as follows [11,12]:

$$\lambda(\theta) = \begin{cases} -0.022\theta + 48, & 0 \le \theta \le 900 \, ^\circ \text{C} \\\ 282, \theta > 900 \, ^\circ \text{C} \end{cases} \tag{6}$$

$$\mathcal{L}^{(\alpha)} \quad \text{and} \quad \alpha \ll \alpha^{-5} \omega^2, \quad \alpha \ll \alpha^{-5} \alpha \ll \alpha \pi \tag{7}$$

$$\begin{array}{l} \text{\(\uparrow\)} \quad \text{\(\uparrow\)} \quad \text{2\(\&\ \theta\)} \text{\(\uparrow\)} \text{\(\uparrow\)} \\\\ \text{\(\theta\)} = 38.1 \times 10^{-8} \theta^2 + 20.1 \times 10^{-5} \theta + 0.473 \end{array} \tag{7}$$

Figure 1), and its size is 12 m × 3 m × 3 m. Since the study of bridge fire mainly focuses on

an extreme fire source scale [13,14], the fire power is set as the heat release rate of the

tanker during fire. Inagason [15] suggested the heat release rate for a tank fire be set at 200

MW. According to the results of the French regulations [16], the growth stage of a 200 MW

fire source is 600 s, and the stable stage is 4200 s, so the simulation time is 4800 s in this

work. The type of simulated fire source is a t2-growth fire. The growth factor is calculated

at the time specified by French regulations. It is appropriate to set the mesh size as 1/4– 1/16 of the flame characteristic diameter (*D*\*) [17]. Employing the formula

0 0 (/ ) *D Q CTg <sup>p</sup>* [18], the flame characteristic diameter in this paper is calculated

as 7.77 m, and thus, the appropriate mesh size is 0.49 m–1.94 m. Considering both simu-

lation time and accuracy, 1 m is selected as the mesh size. The relevant parameters are

**Settings Parameters**

Ambient temperature 20 °C

Ventilation velocity 2 m/s

Bridge material steel

Simulation time 4200 s

ceiling thermocouple is arranged 2 m apart, tiling the whole top deck of the bridge.

Fire type t2 unsteady state

Mesh size 1 m × 1 m × 1 m

The arrangement of thermocouples inside the utility tunnel is shown in Figure 2. The

In order to ensure that the maximum excess temperature of the hot smoke layer be-

low the ceiling can be measured, the thermocouples are arranged 0.05 m below the ceiling

[19]. There are six thermocouples evenly arranged at the same intervals above the fire

source on the inner surface of the truss (yellow points in Figure 2), and the thermocouples

are arranged 0.05 m away from the surface of the truss. In addition, the 2D slice (blue

Ambient pressure 101,300 Pa

Humidity 40%

**(kJ/kg K)**

Bridge Steel 47.56 7850 0.48 where *λ* is the thermal conductivity function of the steel, *C* is the specific heat function of the steel, *θ* is the temperature.

> *2.2. Parameter Setting* In this study, the thermal physical properties of steel at 20 ◦C are taken without considering the change of the material's thermal physical properties with temperature. The relevant parameters of the bridge and its properties are shown in Table 1.

**Table 2.** Parameter settings of simulation.

2.2.1. Model Parameters

ρ\* 1/2 2/5

shown in Table 2.

=


**Table 1.** Parameters of materials used in the bridge model.
