The degradation of earthen sites due to natural and human factors has become a pressing issue, necessitating urgent protection measures. In this context, accurate assessment of the vulnerability of earthen sites is essential for the development of effective conservation strategies. In this study, a comprehensive evaluation framework that incorporates multiple indicators is proposed. In particular, the entropy weight- (Technique for Order Preference by Similarity to an Ideal Solution) TOPSIS method is employed for quantitative vulnerability assessment and combined with K-means clustering to define vulnerability levels for earthen sites. To validate the proposed approach, the vulnerability of 29 sections of the Ming Great Wall is evaluated. Eventually, the 29 earthen sites are categorized into three levels: high, medium, and low, according to their degree of vulnerability. The results of gray correlation analysis and entropy weight-TOPSIS method are compared using the ontology missing amount in the original data as the validation standard. The results show that the Pearson correlation coefficient value of the entropy weight-TOPSIS method with the ontology missing amount was 0.859, while the Pearson correlation coefficient value of the gray correlation analysis method with the ontology missing amount was 0.691, so that the results of the entropy weight-TOPSIS method can more accurately reflect the actual vulnerability of earthen sites.

The Yungang Grottoes, with over 1500 years of history, have been subjected to air pollution since the last century. Field investigations have indicated that acid gases, particularly sulfur dioxide (SO₂), have accumulated on the surface of the sculptures and caused various types of decay that reduce their artistic value. To shed new light on the gas–stone interaction process, artificially accelerated weathering was performed on local sandstone in the laboratory. In a specially developed test device, fresh specimens were exposed to gaseous SO₂ under different relative humidity and temperature conditions. The physical, mineralogical, and chemical changes of Yungang sandstone were evaluated conjointly using destructive and non-destructive methods. The results show that after weathering, the luminosity of all specimens changed, with a slight alteration in hue toward yellow. The weight increased to various degrees during the aging cycles, which depended on both the accumulation of matter and the detachment of particles. Higher relative humidity and cyclic temperature fluctuations favored the dissolution of carbonates and the hydrolysis of feldspar in sandstone. The concentration of ions, especially dissolved Ca²⁺ and SO₄²⁻, increased considerably over time in the near-surface region of the specimens. A trace of newly formed gypsum was detected in some specimens at the end of the test. Knowing the synergistic impact of different climatic variables will make it possible to identify the mechanisms of the deterioration of sandstone in complex environments.

As a critical parameter, thermal conductivity directly determines the heat transfer and temperature variation within rocks, which can lead to mechanical damage and chemical corrosion. Consequently, understanding the thermal conductivity of stone heritage is vital for assessing their deterioration mechanisms and developing effective conservation strategies. This study obtained sandstone samples from the Yungang Grottoes and subjected them to freeze–thaw cycle experiments to generate weathered sandstone samples. Subsequently, the thermal conductivity of these samples was measured under both dry and water-saturated state using the transient plane source method. To analyze the relationship between air–water saturation, porosity, and thermal conductivity, a saturation influence coefficient was introduced. Thereafter, the effectiveness and applicability of 13 commonly used thermal conductivity mixing law prediction models were evaluated based on experimental data. The results suggested that the influence of water saturation on the thermal conductivity of rocks varies with porosity, and water saturation significantly enhances the thermal conductivity of weathered sandstone. Among the 13 common models, the Geometric mean model was found to be more accurate than other models, with superior performance in both dry (MAE, RMSE, MAPE are 0.148, 0.214, 5.59% respectively) and water-saturated (MAE, RMSE, MAPE are 0.244, 0.170, 8.4% respectively) state. The Albert model demonstrates a good fit in the dry state, whereas the Walsh model (with maximum effect), Ribaud model, and Huang model also exhibit good fitting efficacy in the water-saturated state. This study provides a solid foundation for better predicting the thermal conductivity of weathered stone heritage and developing effective preventive conservation strategies.

In this paper, a mechanical model of a transformer–bushing with an inerter isolation system (IIS) is established. An IIS is composed of an inerter element, a damping element, and a spring element connected in parallel between the same two terminals. Vibration control equations and frequency response functions are also established. The influence of parameters on IIS, including inerter–mass ratio, damping ratio, and frequency ratio, was studied. In the extremum condition that represents the most efficient parameter set of inerter–mass ratio and damping ratio for relative displacement response ratio, an optimal design method was developed by exploiting a performance demand. Finally, the seismic response of the transformer–bushing with IIS was carried out to verify the isolation performance of IIS. The research shows that the equivalent mass coefficient and damping coefficient of IIS can be amplified by an inerter element and the inerter–mass ratio and damping ratio are reduced simultaneously under the conditions of meeting the performance demand after parameter optimization. Meanwhile, the parameter optimization design method proved to be effective for meeting the target demand of the relative displacement response of the bushing and tank, while base shear force and isolation displacement were reduced simultaneously. Based on the results from a response history analysis under ground motion records, IISs can significantly suppress the resonance response of a structure and the continuous vibration response in the stable state. The peak displacement can be reduced by 50% compared with a traditional isolation system.