## 1 Introduction
[PERSON] et al., utilizing damage mechanics theory, constructed a rock damage model under temperature-load coupling, showing that the damage in salt rock escalates with higher temperatures but lessens under higher confining pressure [7]. [PERSON] introduced a thermal damage variable, damage modification coefficients, microfracture compaction coefficients, damage cracking stress, and strain parameters to construct a rock statistical damage constitutive model, based on the Hoek-Brown (H-B) strength criterion with temperature effects [8]. [PERSON] et al. applied Weibull parameters to create a rock damage statistical constitutive model based on the Drucker-Prager criterion, defining  
Figure 1: Engineering disaster map. (**a**) Mine collapse. (**b**) Mountain landslide. damage variable [9]. [PERSON] et al., utilizing effective stress theory and a segmented function based on the Weibull distribution, developed constitutive models for rock under uniaxial and triaxial compression at high temperatures, achieving close alignment between theoretical outcomes and laboratory curves [10]. Many researchers have delved into the water-rock interaction mechanisms during immersion, primarily focusing on microchemical actions at the water-rock interface. The rock softens as ions in solution interact with the rock's surface, a phenomenon termed ion adsorption [11]. At the microscopic scale, ion adsorption at the water-rock interface primarily manifests in the retention of ions by clay minerals. According to the surface complexation adsorption theory, the surface of soft rock can be considered a polyacid, where hydroxyl groups can release protons and become basic, while cations are viewed as acids, making them prone to surface complexation adsorption at the water-rock interface [12]. Due to the negative charge on the surface of clay minerals, cations are adsorbed at the water-rock interface through Coulombic forces, forming a surface double-layer structure. At the microscopic level, cations enter the hexagonal pores on the siloxane surface and form covalent bonds with the oxygen in Si-O tetrahedra. Through this ion adsorption process, cations from the aqueous solution accumulate at the water-rock interface, awaiting ion exchange with the clay minerals in the rock. Researchers such as [PERSON] et al. observed that cations in soaking solutions initially adsorb onto rock surfaces, causing an initial drop in concentration, and then form water-soluble compounds that dissolve, increasing the cation concentration again, followed by another adsorption phase, with Na\({}^{+}\) changes being particularly notable [13; 14]. [PERSON] et al. analyzed the additional electrical properties and ion adsorption at the soft rock-water interface based on bilayer, ion migration, and nonlinear dynamics theories, but did not quantify interfacial charge and ion adsorption [15; 16; 17; 18; 19]. [PERSON] et al. investigated the composition, surface charge, and ion exchange of soft rock clay minerals at the water-rock interface using PHREEQ simulations, incorporating mass and charge conservation [20; 21; 22; 23; 24]. This study provides valuable insights into the interfacial processes of soft rock. Despite extensive research into the rock mechanics and water-rock interface chemical interactions during immersion, studies on solution variation primarily consider pH and immersion duration, with limited exploration of water temperature's effects on the chemical behavior and rock mechanics at the water-rock interface. This study addressed this gap by examining the uniaxial mechanical characteristics of argillaceous siltstone under different water temperatures, deriving a damage constitutive model using the Weibull statistical distribution and strain equivalence principles.