Historic sites are important components of every city's cultural history because they preserve rich historical knowledge and distinctive values passed down from previous generations to the present. Due to the progress of urbanization and modernization, many historic sites face pressure from damage and transformation. In this paper, a method for assessing cultural heritage damage was developed to measure the extent of spatial damage in historic sites. Using sample data obtained in Xiyang, Qixian, and Xiaoyi, all historic cities in Shanxi Province, Mainland China, and combined weights were estimated using the Delphi technique and the CRITIC weight method. Following this, the Spatial Damage Degree Model (SDDM) based on K-means cluster analysis and K-nearest neighbor (KNN) classification was developed. The findings show that the model efficiently solves the problem of assessing spatial damage levels in historic sites. Through multiple linear regression analysis, it was shown that the damage to historic sites was predominantly caused by three factors: natural erosion, construction damage, and planning and policy. SDDM was used to calculate the spatial damage levels of historic sites, allowing conservators to fully comprehend the features and concerns related to historic sites. As a result, more scientific and rational preservation approaches may be developed, improving the efficiency of historic site restoration and conservation and encouraging the sustainable development of urban and rural heritage.

Green-space resources, in the context of urbanisation, cannot meet the actual needs of residents well, and the study of the balance of green-space resource allocation from the relationship between supply and demand is an urgent problem to be solved. This study quantitatively evaluates the green-space supply level from four dimensions by constructing a framework for assessment in the community life circle. It also evaluates the matching of green space supply and demand, resource distribution fairness, and distribution equilibrium under group differentiation through the supply–demand coupling matrix, Gini coefficient, and the Kruskal–Wallis H non-parametric rank-sum test, respectively. This study shows that (1) a significant spatial imbalance exists in green-space resource allocation in community life circles in different dimensions. (2) The comprehensive green-space supply level in the community life circle matched the total demand of residents to a low degree. (3) There was significant inequality in green-space resource allocation within the community life circle (the Gini coefficient of each evaluation perspective was > 0.4). Based on the study results, we were able to identify community life circles with spatial mismatches, different supply and demand, and other green-space resource allocation problems, which is of great significance to urban green-space research and planning practice under the "green justice" framework.