## 1 Introduction  
China possesses a wealth of rock cultural heritage sites that hold notable historical, political, and cultural value, with a large number of heritage sites spread widely throughout the country [1]. According to the State Council's announcement in December 2021, the most recent count of China's rock cultural heritage sites returned a total of 24,422, with sandstone and limestone heritage sites making up over 80% of this total [2]. Among these heritage sites, grotto temples represent a category that is not only the most complete and content-rich but also the most fragile, occupying a prominent position in the field of rock cultural heritage sites in China [3]. Immovable cultural heritage sites, being exposed to the elements, undergo long-term influences from natural forces and human activities, with sulfate weathering being the most common and notable form of deterioration [4; 5]. While rocks naturally contain small amounts of sulfates, the majority of sulfate comes from direct adsorption of SOx gases by the rock mass; these gases form salt solutions when they encounter water [6; 7]. Scholars have conducted extensive research on the mechanisms of salt weathering, the migration of crystalline substances, and their destructive effects, yielding valuable results. In their study on the damage mechanisms of limestone caused by sulfates, [PERSON] et al. [8] discovered that salt migration primarily occurs within the larger pores in the top 3 mm of the rock surface. [PERSON] et al. [9] conducted field surveys and monitored the Longyou Grottoes and confirmed that soluble salts, particularly sulfates, are one of the main factors leading to the weathering of these grottoes. They found a close correlation between the mineral composition, the primary structure of the rocks, and the rate of deterioration. [PERSON] et al. [10] identified a relationship between rock pore characteristics and the destructive effects of salt crystallization, demonstrating a proportional relationship. [PERSON] et al. [11] investigated the development of crystals in various salt solutions within porous and non-porous media and concluded that crystal growth only occurs in larger pores. They also identified functional relationships between rock mechanical and structural parameters, including strength, elastic modulus, pore quantity, and distribution. Scholars commonly assess the degree of rock weathering using single or multiple indicators. [PERSON] et al. [12] evaluated the weathering of tombstones based on changes in the magnitude of their hardness, observing an initial rapid decline followed by a slower decaying trend. [PERSON] et al. [13] measured the strength difference before and after salt damage to assess rock damage and proposed a decay function to simulate the process of strength deterioration in salt-weathered sandstone. [PERSON] et al. [14] considered indicators such as mass, wave velocity, and microstructure to assess rock weathering. [PERSON] et al. [15] suggested that salt crystallization disrupts rock particle bonding and established logarithmic models for pore growth and exponential models for strength attenuation based on experimental results. [PERSON] et al. [16] utilized AHP, F-AHP, and AHP-TOPSIS methods to analyze the intrinsic correlations between weathering indicators of rock heritage sites and determine their structural safety and stability. [PERSON] et al. [17] employed a grey correlation analysis to explore the effects of different types of rock-weakening diseases on the preservation status of individual buildings, calculating the degree of disease for each and providing a quantitative classification using a weighted approach. However, research on salt weathering damage processes and mechanisms is more common for sandstone heritage sites than for limestone heritage sites, which remain relatively understudied. Rock heritage sites exposed to the natural environment inevitably face the universal issue of sulfate weathering, which is influenced by factors such as climate, topography, and lithology [18; 19].