## 3 Results and Discussion
### Stress-Strain Analysis of NC and LC after High Temperature Exposure  
Figure 8 shows the stress(\(\sigma\))-strain(\(\varepsilon\)) curves of NC and LC after high temperature exposure. At all levels, the stress-strain curves in the temperature range below 300 \({}^{\circ}\)C showed slopes similar to that before heating (20 \({}^{\circ}\)C) [29; 30]. While the strain of NC ranged from 0.0028 to 0.004 and that of LC from 0.0033 to 0.0042, brittle failure was observed in the temperature range below 300 \({}^{\circ}\)C. Considering that the failure strain of ordinary concrete ranges from 0.0025 to 0.004, the concrete heated up to 300 \({}^{\circ}\)C appears to have exhibited a tendency similar to that of concrete before heating. Above 500 \({}^{\circ}\)C, the slope of the stress-strain curve tended to decrease at all levels. At 700 \({}^{\circ}\)C, ductile failure occurred with a strain of approximately 0.01. NC showed a failure strain at a relatively higher stress compared to LC at the same target temperature, indicating that the stress at the aggregate-paste interface improved with crushed granite aggregate, which has a relatively high roughness [31]. Figure 7: Residual modulus of elasticity of normal concrete (NC) and lightweight concrete (LC) after high temperature exposure. Figure 9 shows the peak strain of NC and LC after high temperature exposure. The strain showed a tendency to increase at all levels as the temperature increased, but a value (approximately 0.004) similar to that before heating (20 \({}^{\circ}\)C) was observed. In the  
Figure 8: Stress(\(\sigma\))-strain(\(\iota\)) curves of normal concrete (NC) and lightweight concrete (LC) after high temperature exposure: (**a**) NC41; (**b**) LC41; (**c**) NC33; (**d**) LC33; (**e**) NC28; (**f**) LC28. temperature range below 300 \({}^{\circ}\)C, LC41 and LC33 showed a higher peak strain than NC41 and NC33, whereas NC28 exhibited a higher peak strain than LC28. Above 500 \({}^{\circ}\)C, the peak strain sharply increased [32], ranging from 0.0058 to 0.0063 at 500 \({}^{\circ}\)C and from 0.0094 to 0.012 at 700 \({}^{\circ}\)C. At 700 \({}^{\circ}\)C, NC exhibited a higher peak strain than LC at all levels, indicating the significant influence of crushed granite aggregate with a relatively higher stiffness than that of coal-ash aggregate, which is more porous and of low density (see Table 1) [31]. Figure 10 shows the correlation between the ultrasonic pulse velocity and residual modulus of elasticity of NC and LC after high temperature exposure according to the W/B ratio. A high correlation was observed in a linear graph, indicating that the tendencies of the ultrasonic pulse velocity and residual modulus of elasticity to linearly decrease with increasing temperature had a significant influence. Figure 10a shows the correlations of NC and LC at a W/B ratio of 0.41. The correlation coefficient (R\({}^{2}\)) was found to be 0.94 for NC41 and 0.98 for LC41. When  
Figure 10c shows the correlations of NC and LC at a W/B ratio of 0.28. The correlation coefficient (R\({}^{2}\)) was 0.97 for NC28 and 0.94 for LC28. The graph of NC28 was approximately 30% higher in the 2.0-2.5 km/s range and 8% higher in the 2.5-3.0 km/s range than that of LC28. However, the graph of LC28 became higher in the higher range. The difference between NC28 and LC28 was approximately 4% in the 3.2-3.5 km/s range and 9% in the range above 3.5 km/s. In the very low ultrasonic pulse velocity range, the inside of the concrete may exhibit a similar state and stiffness because of the severe damage to the cement matrix. However, in the relatively higher range, it is deemed necessary to consider the aggregate type because it seems to be the dominant factor to influence the state of the paste-aggregate interface. Table 6 summarizes the correlation between the ultrasonic pulse velocity and residual modulus of elasticity.