## 3 Results and Interpretations
### Dynamic Compressive Strength  
Figure 4 presents the influence of real-time temperature on the dynamic compressive strength of the limestone specimen. When the dynamic strain rate is 40-60 s\({}^{-1}\), 60-80 s\({}^{-1}\), and 80-100 s\({}^{-1}\), the dynamic compressive strength of the specimen exhibits a linear decrease as the temperature increases. Within the range of 40-60 s\({}^{-1}\), the dynamic compressive strength of the specimen is approximately 190.5 MPa at a temperature of 25 \({}^{\circ}\)C and 72.6 MPa at a temperature of 800 \({}^{\circ}\)C, exhibiting a reduction of 61.9%. This finding is consistent with the results obtained by [PERSON] et al. [49] when the heated specimen underwent natural cooling to room temperature. The difference lies in that the specimen in our study at real-time high temperature is also affected by thermal shock at the same time. In addition, the strength exhibits a negative correlation with temperature across different strain rates, with descent rates of \(-\)0.15 MPa/\({}^{\circ}\)C, \(-\)0.15 MPa/\({}^{\circ}\)C, and \(-\)0.13 MPa/\({}^{\circ}\)C under the strain rates of 40-60 s\({}^{-1}\), 60-80 s\({}^{-1}\), and 80-100 s\({}^{-1}\), respectively. Figure 5 illustrates the influence of strain rate on the dynamic compressive strength of the limestone specimen. The strength of the limestone specimen increases linearly with the strain rate within a real-time temperature range of 25-800 \({}^{\circ}\)C, which is different from the findings obtained by [PERSON] et al. [50]. At the real-time temperature of 25 \({}^{\circ}\)C, the dynamic compressive strength of the limestone specimen is 112.6 MPa under the strain rate of 31.0 s\({}^{-1}\). However, when the strain rate is increased to 48.1 s\({}^{-1}\), the dynamic compressive strength significantly rises to 208.8 MPa, indicating an impressive increase of 85.4%. When the real-time temperature reaches 800 \({}^{\circ}\)C, the dynamic compressive strength of the limestone specimen is 72.6 MPa under a strain rate of 46.7 s\({}^{-1}\), while at a higher strain rate of 95.8 s\({}^{-1}\), the strength increases to 148.2 MPa, representing a significant improvement of 104.1%. Figure 3: Dynamic stress–strain curves of the limestone specimen under the coupling effect of the real-time temperature and impact loading. Figure 4: Variation in the dynamic compressive strength \(\sigma_{\rm d}\) with the temperature \(T\). Figure 5: Variation in the dynamic compressive stress \(\sigma_{\rm d}\) with the strain rate \(\dot{\epsilon}\). The temperature sensitivity coefficient \(\eta\) is defined in Equation (3) to characterize the effect of temperature on the dynamic compressive strength of the limestone specimen under different strain rates in Figure 6.  
\[\eta=\eta(T)=\frac{d\sigma_{\text{d}}}{d\hat{e}} \tag{3}\]  
When the real-time temperatures are set as 25, 100, 200, 300, 400, 500, 600, 700, and 800 \({}^{\circ}\)C, the temperature sensitivity coefficients \(\eta\) are 5.4, 3.6, 1.6, 1.7, 1.2, 1.4, 1.5, 0.8, and 1.5 MPa/s, respectively. Moreover, the coefficient \(\eta\) presents a non-linear decrease and tends to a stable value as the temperature increases, as illustrated in Figure 6. Through fitting calculation, the expression of \(\eta\) about temperature \(T\) is obtained, as presented in Equation (4). \[\eta=5.36e^{(-T/103.02)}+1.26 \tag{4}\]  
Figure 7 presents the coupling effect of the temperature and strain rate on the dynamic compressive strength of the specimen. It is evident that elevated temperatures have a detrimental impact on the dynamic properties of the specimen, leading to a decrease in its dynamic compressive strength. However, an increase in strain rate results in an enhancement of its dynamic compressive strength.