## 5 Model Validation and Variation in Damage Variable
### Model Validation
To investigate the variations of damage variables \(D_{12}\) under the coupled action of water temperature and peak stress, and \(D_{3}\) under the action of peak stress (where \(D_{3}\) is the difference between the total damage variable \(D_{12}\) under the action of water temperature and peak load and the elastic modulus damage variable \(D_{1}\) under the action of water temperature) for argillaceous siltstone soaked at different water temperatures, a graph of the relationships between elastic modulus damage variable \(D_{1}\), damage variable \(D_{12}\), and damage variable \(D_{3}\) with water temperature was plotted, as shown in Figure 11. In the early stage of soaking (1-3 days), changes in water temperature have little effect on damage variable \(D_{1}\), which generally shows an initial increase followed by a decrease with increasing water temperature. This change becomes more pronounced with prolonged soaking. For damage variable \(D_{12}\), the trend is generally consistent with that of \(D_{1}\); however, the magnitude of change is inversely proportional as soaking time increases. In the early soaking stage (1-3 days), water temperature significantly affects \(D_{12}\), but this effect diminishes with longer soaking times. This phenomenon can be attributed to the significant changes in the internal structure of argillaceous siltstone with prolonged soaking and varying water temperatures. Under loading, the internal pores of the argillaceous siltstone are compressed, leading to increased densification. However, the degree of softening caused by different water temperatures varies, particularly in the early soaking stage (1-3 days), resulting in the observed effects. The damage variable \(D_{3}\) indicates the degree of deterioration of argillaceous siltstone after soaking; a smaller \(D_{3}\) value signifies greater damage. As illustrated in Figure 11, the \(D_{3}\) value decreases progressively with increased soaking time, indicating that the damage to argillaceous siltstone intensifies as soaking time extends. During the soaking process at different water temperatures, chemical reactions between the minerals in argillaceous siltstone and water lead to changes in cations (such as Na\({}^{+}\) and Ca\({}^{2+}\)). These reactions involve the hydrolysis of minerals with water. Additionally, during hydration, the minerals in argillaceous siltstone absorb water, swell, and adsorby various ions. The release and migration of these ions reduce the rock's cohesion and shear strength, leading to a decline in the overall mechanical properties of the soft rock, which makes it more prone to softening and even disintegration. To gain a deeper understanding of the mechanisms of water-rock microchemical interactions influenced  
Figure 10: The variation patterns of the constitutive model parameters \(m\) and \(\lambda\). (**a**) The variation pattern of parameter \(m\). (**b**) The variation pattern of parameter \(\lambda\). by water temperature, it is essential to investigate the changes in cation concentrations in argillaceous siltstone during soaking at different water temperatures.