Weathering characterization and evaluation of sandstone relics in Helan Pass via the fuzzy-AHP

Evaluating the weathering degree of open-air stone relics is a challenge for their protection. Currently, there is a lack of classification standards for cultural relic weathering, and the gradient relationship between adjacent degrees leads to subjective judgments. To minimize such subjectivity, a three-layer fuzzy comprehensive evaluation model is proposed, including weathering characterization and occurrence environment. The analytic hierarchy process (AHP) determines each stage factor weights, the fuzzy sets method establishes the membership functions, and influencing factors are ranked. By using the example of Helan Pass sandstone relics, the weathering degree is quantitatively classified into 5 levels, i.e., 0 ≤ WD < 0.2 (very low), 0.2 ≤ WD < 0.4 (low), 0.4 ≤ WD < 0.6 (medium), 0.6 ≤ WD < 0.8 (high), and 0.8 ≤ WD ≤ 1 (very high). Moreover, the combined proportion of medium and high weathering degrees reaches 75%, indicating severe threats to the relics. The intuitive results provide data and theoretical guidance for protecting Helan Pass relics, and the method also has potential applications in weathering assessments for other heritage sites.