# Physical and Mechanical Properties and Damage Mechanism of Sandstone at High Temperatures
## 4 Study on Acoustic Emission Characteristics
### Variation Law of Stress Threshold  
In the study of determining the crack initiation threshold stress \(\sigma_{CI}\) and damage threshold stress \(\sigma_{CD}\) using acoustic emission technology, scholars have given different methods. [PERSON] [30] pointed out that the stress at the appearance of the first tensile crack in a rock sample is the crack initiation stress. It has been shown that the crack initiation stress and damage stress threshold can be effectively determined by using the mutation points of the acoustic emission cumulative ringer counting curve, in which the stress at the first mutation point can be taken as the crack initiation stress, and the stress at the sharp increase in the slope of the cumulative ringer counting curve can be taken as the crack damage stress threshold [31]. As can be seen from Figure 14a, with the increase in temperature, the crack initiation and damage threshold both show the trend of rising first and then decreasing, which is consistent with the characteristics of the change in peak stress with temperature. When  
Figure 12: The change rule of the ringing counts at different temperatures: (**a**) maximum ringing count; (**b**) accumulative ringing count. Figure 13: The change rule of the ringing counts at different heating rates: (**a**) maximum ringing count; (**b**) accumulative ringing count. the temperature increases from room temperature to 500 \({}^{\circ}\)C, the crack initiation threshold increases from 39.72 MPa to 70.67 MPa, with an increase of 69.36%, and the damage threshold increases from 50.57 MPa to 91.41 MPa, with an increase of 80.75%, and the crack initiation and damage thresholds reach the maximum at 500 \({}^{\circ}\)C. After 600 \({}^{\circ}\)C, the crack initiation and damage thresholds began to decrease continuously; the crack initiation threshold at 1200 \({}^{\circ}\)C was 28.09 MPa, and the damage threshold was 33.68 MPa, which were 60.25% and 63.15% lower than that of 500 \({}^{\circ}\)C. The above analysis shows that the temperature has an essential effect on the crack initiation and damage thresholds and has a high correlation with the strength of sandstone. According to Figure 14b, the crack initiation threshold is about 58-76% of the peak stress, and the damage threshold is about 86-96% of the peak stress at room temperature up to 1200 \({}^{\circ}\)C, and the ratio shows a certain trend of change depending on the temperature. Before 500 \({}^{\circ}\)C, the percentage of crack initiation threshold and the percentage of damage threshold changed less but generally showed an increasing trend, the percentage of crack initiation threshold and the percentage of damage threshold increased from 70.46% and 93.31% to 75.23% and 96.61%, which indicated that the brittleness of the sandstone was enhanced to a certain extent in this temperature range, and the crack initiation threshold and damage threshold were closer to the peak stress. At 600 \({}^{\circ}\)C, the percentage of crack initiation threshold and damage threshold decreased to 67.38% and 90.44%, respectively, indicating that the physical and chemical properties of the rock in the temperature range of 500-600 \({}^{\circ}\)C have been greatly altered to produce certain damage. As the temperature continues to drop to 1200 \({}^{\circ}\)C, the percentage of crack initiation thresholds and damage thresholds show a decreasing trend, and the percentages of crack initiation thresholds and damage thresholds at 1200 \({}^{\circ}\)C are 59.26% and 89.54%, respectively, which indicates that the thermal damage will make the rock cracking damage at a lower stress level. The heating rate also influences the crack initiation threshold and damage threshold and their percentage. From Figure 15a, the crack initiation threshold and damage threshold are 30.96 MPa and 45.52 MPa at 5 \({}^{\circ}\)C/min and 25.66 MPa and 36.68 MPa at 30 \({}^{\circ}\)C/min, which show a decreasing trend with the heating rate, and this trend is also very much correlated with the change in the peak stress by the heating rate.