During post-fire seismic performance simulation, the damage to the mechanical properties due to temperature should be considered. Thus, the damage material model to be used in the simulation should be determined.
Scoria aggregate as a kind of high-quality light aggregate has better thermal resistance than natural aggregate so that the trend in the mechanical properties of SAC when subjected to fire is clearly different from that of NAC. The decisive factor in bringing out this difference in the FEM is the thermomechanical damage model of the concrete. In order to determine the mechanical damage model of SAC after fire, we designed and carried out tests to investigate the mechanical properties of SAC after high temperatures and recorded and analyzed the results.
4.1.1. Test Program
A total of 55 specimens of SAC was prepared as 100 mm × 100 mm × 100 mm cubic specimens and 100 mm × 100 mm × 300 mm prismatic specimens. The test instrumentation follows reference [
35,
36,
37,
38,
39]. Of these, 30 cubic specimens were used for compressive and splitting tensile strength tests and 25 prismatic specimens were used for constitutive relationship tests. The specimens were divided into five groups according to various temperatures: 20 °C, 200 °C, 400 °C, 600 °C, and 800 °C, respectively. Another 55 test blocks of the same specification of NAC were prepared as the control group.
The uniaxial compressive stress-strain relationship of SAC after exposure to high temperatures, and the peak strain, modulus of elasticity, ultimate strain, and splitting tensile strength of SAC after different temperatures, were obtained by extracting the test results. Based on the regression analysis, the variations of cubic compressive strength, splitting tensile strength, peak strain, ultimate strain, and modulus of elasticity of SAC with temperature were obtained.
4.1.2. Material Simulation through Experimental Tests Results Regression
- (1)
Compressive and splitting tensile strengths
The compressive and splitting tensile strengths of the specimens of SAC and NAC after various temperatures were conducted. The effects of temperatures on the strength of SAC are shown in
Table 1.
Figure 2 shows the strength reduction of NAC and SAC after different temperatures.
As the water in the calcium hydroxide inside the test block desorbed at about 450 °C and calcium oxide was generated, the hydration products decreased significantly, the cracks inside the concrete increased rapidly, and the strength loss increased, so the strength of the test block decreased significantly. From
Table 1 and
Figure 2, the trend of strength reduction of SAC was similar to that of NAC, but the strength reduction of SAC after all temperatures was 4.4% less than that of NAC on average, which indicated that the degree of influence of high temperature on the strength of SAC was smaller compared to that of NAC. After 600 °C, the cubic compressive strength and splitting tensile strength of SAC decreased by 55.8% and 63.2%, respectively.
Curve fitting of the data in
Table 1 yielded the cubic compressive strength of SAC after high temperature and the splitting tensile strength of SAC after high temperature, as in
Table 2.
The axial tensile strength of SAC can be calculated according to calculation method of Hu with the following equation [
40],
where
fLtk is the axial tensile strength of concrete and
fLpt is the splitting tensile strength of concrete.
- (2)
Peak Strain
Table 3 shows the peak strains of NAC and SAC after different temperatures. From
Table 3, the peak strains of both NAC and SAC decreased with temperature between 20 °C and 200 °C. When the temperature exceeded 200 °C, the peak strains of both increased with temperature. After 400 °C, the increase in peak strain with increasing temperature was significantly higher for NAC than for SAC, due to the excellent refractoriness of the scoria aggregate that allowed the SAC to produce fewer cracks and thus smaller peak strains after being subjected to the same high temperatures as NAC.
Curve fitting of the test data in
Table 3 yielded the variation law of peak strain versus temperatures for SAC, as in
Table 2.
- (3)
Ultimate strain
The strain at the falling section of the stress-strain curve corresponding to 0.5 times the peak stress value was taken as the ultimate strain, and
Table 4 shows the ultimate strain and relative ultimate strain of concrete after elevated temperatures. From
Table 4, it can be obtained that the ultimate strains of both NAC and SAC decreased with increasing temperature in the range of 20 °C to 200 °C. Conversely, the ultimate strains of both increased with increasing temperature after the temperature exceeded 200 °C. After the same temperature, the ultimate strain of SAC decreased by 42% on average compared to that of NAC. After the temperature exceeded 400 °C, the ultimate strain of SAC decreased by 26% on average compared to that of NAC.
Curve fitting of the test data in
Table 4 yielded the variation law of ultimate strain versus temperature for SAC, as in
Table 2.
- (4)
Elastic modulus
The secant elastic modulus at 40% of the peak stress of the stress-strain curve was taken as the elastic modulus, and
Table 5 shows the residual elastic modulus of the test blocks after elevated temperatures. From
Table 5, it can be obtained that the residual modulus of elasticity of SAC was on average 5.1 times larger than that of NAC after the same temperature, especially after the temperature reached 400 °C; the former was on average eight times larger than the latter because, on the one hand, the cylinder compressive strength of scoria aggregate was higher and the stiffness was larger; on the other hand, scoria aggregate had better fire resistance. As the temperature increased, the residual modulus of elasticity of both NAC and SAC showed a decreasing trend; after 400 °C, the rate of decrease of SAC began to increase significantly, and the residual modulus of elasticity of SAC after 600 °C and 800 °C was 13% and 3% of that at ambient temperature, respectively.
Curve fitting of the experimental data in
Table 5 yielded the variation law of the residual modulus of elasticity versus temperature for SAC, as in
Table 2.
- (5)
Stress-strain curve
Figure 3a shows in detail the uniaxial compressive stress-strain curves of SAC after different temperatures obtained from the test.
Figure 3b shows the stress-strain curves of SAC after different temperatures obtained by regression fitting. As shown in
Figure 3a, after the temperature reached 200 °C, the area of the stress-strain curve gradually decreased with the increase of temperature, the peak strain kept moving to the right side of the curve, the peak strain gradually increased, and the elastic modulus sharply decreased.
- (6)
Constitutive equation
The constitutive relations for steel concrete in the Chinese code for Design of Concrete Structures was selected for the regression fitting of the constitutive equation of SAC after fire, as shown in Equations (2)–(5) [
41]. The whole stress-strain curve in the code is divided into ascending and descending portions. The parameters
n and α in Equations (2) and (5) are independent parameters to control the shapes of the ascending and descending portions, respectively. Among them, the parameter
n is determined by the modulus of elasticity, peak strain, and peak stress of concrete, as shown in Equation (5). Additionally, the value of α is related to the deformation characteristics of concrete and its changes; for example, when the value of α increases, the plasticity deformation capacity of concrete decreases.
where
fc, r is the peak stress of concrete, MPa;
εc,r is the peak strain corresponding to the peak stress of concrete.
Based on the experimental data, the parameters
n and α of the ascending and descending portions of the stress-strain curves of SAC after different temperatures were fitted by regression analysis, and the conclusions are shown in
Table 6. Combined with
Figure 2b and
Table 6, it can be obtained that the ascending portions parameter
n did not change much after different temperatures, while the descending portions parameter α was very large at ambient temperature and after 200 °C, and decreased significantly with the increase of temperature, which indicated that the brittleness of SAC was larger and the ductility was poorer after lower temperatures, making the descending portions very steep.