## 3 Fire Test Results and Discussion  
Figure 7 presents images of the specimens after the fire tests. Spalling occurred on the heated surfaces of the different specimens. The first significant spalling was observed through the digital camera during the first 8-15 min of the fire tests. The spalling lasted approximately 12-22 min, and mainly occurred at furnace temperatures of 645-856 \({}^{\circ}\)C. The spalling of Specimens S60, S120, and S120C was more severe than that of S60C because the moisture content of those three samples (see Table 1) was higher. A higher moisture content is known to promote spalling [22]. After the specimens had cooled to room temperature, extensive map cracks were found in the un-spalled regions of the heated surfaces, and the color of the concrete surface had turned light yellow (see Figure 8a). In addition, a few vertical cracks spaced about 200 mm apart were observed on both the front and back of the different specimens (see Figure 8b). They can be attributed to the following reasons: (1) The excessive expansion of the concrete at elevated temperatures; and (2) the incompatible expansions and contractions of the concrete and steel reinforcements during heating and cooling [23]. Owing to the structural characteristics of a tunnel lining, the vertical cracks within the circumferential joints between the segments would be difficult to discover and repair. Evidently, sufficient attention must be devoted to these vertical cracks, which would eventually aggravate the deterioration of the tunnel lining after a fire. Figure 7: Concrete spalling after fire exposure (MESD: maximum explosive spalling depth in mm; SAR: ratio of the spalled area to the area of the specimen’s softri). (**a**) Specim S60 (MESD = 48.5, SAR = 45.7%); (**b**) specimen S60C (MESD = 29.1, SAR = 5.5%); (**c**) specimen S120 (MESD = 56.2, SAR = 38.8%); (**d**) specimen S120C (MESD = 25.6, SAR = 17.2%). Figure 1b,c show that the positions of the thermocouples along the segment thickness at Section 1-1 and Section 2-2 were different. ABAQUS software was therefore used to develop numerically a temperature distribution at Section 2-2, so the temperature distributions at the two sections could be compared. The meshes of section 2-2 are presented in Figure 9. The segment's concrete was meshed with eight-node solid heat transfer elements (DC3D8). The thermal properties of the concrete, including the density, specific heat capacity and heat conductivity were assumed based on the Eurocode 2 standard [24]. The density of the concrete at room temperature was set to 2350 kg/m\({}^{3}\). The specific heat \(c_{\text{c}}\) (J/kg\(\cdot\)\({}^{\circ}\)C) for a moisture content of \(u=0\) in the concrete was calculated using Equation (2). The effect of water evaporation on the temperature in the concrete was considered by adjusting the specific heat of the concrete: The maximum (\(c_{\text{p, peak}}\)) of the specific heat was at 100-115 \({}^{\circ}\)C followed by a linear decrease in the specific heat between 115 and 200 \({}^{\circ}\)C (see Figure 10). \(c_{\text{p, peak}}\) was taken as 1470 and 2020 J/kg\(\cdot\)\({}^{\circ}\)C for concretes with moisture contents of \(u=1.5\%\) and \(3\%\), respectively. The moisture content \(u\) was set to 2.6%, the \(c_{\text{p, peak}}\) was set to 1873 J/kg\(\cdot\)\({}^{\circ}\)C in that calculation. The upper and lower limits of the thermal conductivity \(\lambda_{\text{c}}\) of the concrete were determined using Equation (3). The value of \(\alpha\) was set to 0.5. The convective heat transfer coefficients were 25 W/m\({}^{2}\)-K for the heated surfaces and 9 W/m\({}^{2}\)-K for the others. The resultant heat emissivity on the surface of the concrete was set to 0.5. \[\left\{