How do characteristic elements of public spaces affect spatial vitality? An analysis of influence effects and response thresholds from the Hangzhou section of the Beijing-Hangzhou Grand Canal

Spatial vitality is theoretically grounded in classic urban planning and human settlement theories, including Jane Jacobs’ Urban Diversity, Jan Gehl’s Social Space, and Kevin Lynch’s Image of the City . It is explicitly defined as a public space’s capacity to attract sustained recreational engagement and foster diverse social interaction, and it serves as a core metric for evaluating urban public space quality and human settlements development amid global stock-based urban renewal. This study addresses a well-documented critical gap: while macro- and meso-scale urban vitality research is oversaturated, prevailing analytical models are predominantly limited to linear correlation analysis. These models lack quantitative threshold-based causal inference for nonlinear vitality-generating mechanisms in micro-scale waterfront contexts. This study takes 56 micro-scale waterfront public spaces along the UNESCO World Heritage Hangzhou Section of the Beijing-Hangzhou Grand Canal as its research samples. It develops a “built environment-functional activity-spatial vitality” analytical framework, first identifies core vitality drivers via correlation analysis, and finally quantifies nonlinear response thresholds for national Grade I vitality standards through Ordinary Least Squares (OLS) and Spatial Lag Model (SLM)-corrected regression that controls for spatial spillover effects. Results reveal locational centrality, public transport station accessibility, water surface ratio, cultural and sports facility density, and functional integration degree as core vitality drivers. These drivers present heterogeneous thresholds across ecological conservation, commercial-business, and residential living functional typologies, a difference that is interpreted as driven by divergent user demands and context-specific vitality generation pathways. This study advances prevailing linear correlation-focused models by establishing typology-specific, quantifiable thresholds for vitality enhancement. It explicates the core “built environment optimization-functional activity catalysis-sustained vitality generation” mechanism, and further provides empirically grounded, threshold-informed planning guidance and a replicable analytical framework for micro-scale urban public space vitality research.