## 4 Damage Characterization of Sandstone Under Different Soaking Times and Temperatures
### Energy Evolution Patterns of Sandstones with Different Immersion Times and Temperatures  
The variations in total strain energy, elastic potential energy, and dissipated energy under different soaking times and temperatures are illustrated in Figures 6-8, respectively.  
As illustrated in Figures 6-8, under different soaking times and temperatures, the energy evolution behavior of sandstone follows a similar pattern. Both total energy and elastic potential energy increase parabolically before the peak stress, while dissipated energy tends to develop linearly and slowly before the peak stress. This indicates that prior to the peak stress, the energy input into the rock is primarily stored in the form of elastic potential energy, with minimal increase in dissipated energy. After reaching the peak stress, the total energy continues to increase, but at a significantly reduced rate, while the elastic potential energy decreases rapidly. Dissipated energy gradually increases before reaching the peak stress, with a small rate of change, but after reaching the peak stress, dissipated energy increases sharply.  
In order to more intuitively illustrate the influence of different temperatures and soaking times on the energy variation in sandstone, the total energy, elastic potential energy at peak stress, dissipated energy at peak stress, energy absorption rate, elastic potential  
Figure 8: Evolution of energy in sandstone under different temperatures after 3 h of water immersion.  
Figure 6: Evolution of energy in sandstone under different temperatures after 0.5 h of water immersion.  
Figure 7: Evolution of energy in sandstone under different temperatures after 1 h of water immersion.  
energy absorption rate at peak stress, and dissipated energy release rate at peak stress are summarized in Figure 9.  
According to Figure 9, under the same soaking time, as the temperature increases, the variation patterns of total energy, peak elastic energy, total energy absorption rate, and elastic energy absorption rate are similar, all showing a trend of first decreasing and then increasing, with the lowest values occurring at 55 \({}^{\circ}\)C. This phenomenon occurs because at 55 \({}^{\circ}\)C, the sandstone reaches its maximum water content, which diminishes its energy absorption capacity of the sandstone, resulting in the lowest total energy absorption. As soaking time increases, the plastic deformation ability of the sandstone improves, enabling it to continue absorbing energy in the post-peak stage. At 3 h of soaking, the softening effect within the sandstone increases due to temperature, and the force further promotes the exfoliation of mineral particles and the development of microcracks, this processes the degree of rock failure and increasing the damage, thereby reducing the sandstone's energy absorption capacity, with the lowest values of total energy absorption. The variation patterns of peak elastic energy, total energy absorption rate, and elastic energy absorption rate follow a similar trend. In contrast, the variation patterns of dissipated energy and dissipated energy release rate exhibit an opposite trend compared to the aforementioned patterns, showing an initial increase followed by a decrease. Under different soaking conditions, the peak dissipated energy and dissipated energy release rate are maximal at 55 \({}^{\circ}\)C. Additionally, as the soaking time increases, both the peak dissipated energy and dissipated energy release rate also rise. This phenomenon occurs because dissipated energy is directly related to crack development, which requires a substantial amount of energy. The results indicate that increased water content effectively facilitates the development of internal microcracks in sandstone, consistent with the trends observed in the acoustic emission signals of sandstone in Section 3.