## 3 Results and Interpretations
### Dynamic Elastic Modulus  
Figure 8 shows the influence of the real-time temperature on the dynamic elastic modulus of the limestone specimen. The static elastic modulus of limestone specimen at room temperature (25 \({}^{\circ}\)C) is only 65 GPa. As the temperature increases, the elastic modulus of the specimen presents a nonlinear variation with a negative exponent. As the temperature increases from 25 to 800 \({}^{\circ}\)C, the dynamic elastic modulus of the limestone specimen under the strain rate of 40-60 s\({}^{-1}\) declines from 193.8 to 31.8 GPa, decreasing by 83.6% at a decrease rate of 0.26 GPa/\({}^{\circ}\)C. As the temperature increases from 200 to 800 \({}^{\circ}\)C, the dynamic elastic modulus of the limestone specimen under the strain rate range of 60-80 s\({}^{-1}\) decreases from 184.4 to 33.4 GPa, reducing by 81.9% at a rate of 0.26 GPa/\({}^{\circ}\)C. As the temperature increases from 300 to 800 \({}^{\circ}\)C, the dynamic elastic modulus of the limestone specimen under the strain rate of 80-100 s\({}^{-1}\) decreases from 210.8 to 72.8 GPa, decreasing by 65.5% at a decrease rate of 0.24 GPa/\({}^{\circ}\)C. The fitting curve in Figure 8 illustrates the variation of the dynamic elastic modulus of the specimen under different strain rates with the temperature. It is evident that the elastic modulus exhibits a similar decreasing trend as the temperature within the strain rate ranges of 60-80 s\({}^{-1}\) and 80-100 s\({}^{-1}\).  
Figure 9 shows the influence of strain rate on the dynamic elastic modulus of the limestone specimen. The dynamic elastic modulus exhibits a nearly nonlinear increase with the strain rate, and the Boltzmann function is employed to analyze the results within the temperature range of 25 to 800 \({}^{\circ}\)C, as depicted in Figure 9. At the real temperature of 25 \({}^{\circ}\)C, the dynamic elastic modulus of the specimen is 73.5 GPa under a strain rate of 31.0 s\({}^{-1}\), while it increases to 142.9 GPa under a strain rate of 48.10 s\({}^{-1}\), exhibiting a significant enhancement of 94.4%. For the real-time temperature of 800 \({}^{\circ}\)C, the dynamic elastic modulus is 31.84 GPa at the strain rate of 46.74 s\({}^{-1}\), which subsequently increases to 92.09 GPa under the strain rate of 95.8 s\({}^{-1}\), demonstrating an impressive increase of up to 189.2%. In comparison with those under a temperature of 25 \({}^{\circ}\)C, the deformation resistance of the specimen is weakened.  
Figure 10 presents the coupling effects of the strain rate and temperature on the dynamic elastic modulus of the limestone specimen. It can be observed that the temperature weakens the dynamic elastic modulus of the limestone specimen. With the increase in temperature, its dynamic elastic modulus decreases. The quantitative relationship can be described as follows:  
Figure 8: Variation in the dynamic elastic modulus \(E_{\text{d}}\) with the temperature \(T\).  
\[E_{\rm d}=9.7\times 10^{-5}T^{2}+3.7\times 10^{-2}\dot{\epsilon}^{2}-4.1\times 10^{- 3}T\dot{\epsilon}-2.8\times 10^{-2}T-1.1\dot{\epsilon}+120.4,\ R^{2}=0.720 \tag{6}\]  
Figure 10: Variation in the dynamic elastic modulus \(E_{\rm d}\) with the temperature \(T\) and strain rate \(\dot{\epsilon}\).  
Figure 9: Variation in the dynamic elastic modulus \(E_{\rm d}\) with the strain rate \(\dot{\epsilon}\).