From Facility Agglomeration to Service Accessibility: A Spatial Mismatch Analysis of Elderly Care and Residential Spaces in the 15-Minute Life Circle for Sustainable Aging—A Case Study of Zhifu District, Yantai

The 15-minute life circle has become a critical planning paradigm for developing age-friendly cities; however, its implementation in small and medium-sized cities (SMSCs) is often constrained by topographical heterogeneity and the oversimplified use of facility density as a proxy for service efficiency. This study challenges the conventional assumption that a higher facility density automatically leads to better service outcomes and proposes a dynamic “space–demand–policy” analytical framework to identify the mechanisms underlying spatial mismatch. Using Zhifu District, Yantai, a rapidly aging urban area with complex topography, as a case study, we integrated kernel density estimation (KDE), slope-adjusted network analysis, a modified Gaussian-based two-step floating catchment area (2SFCA) method, and standard deviational ellipse (SDE) analysis. Our results reveal three key findings. First, a “high-density, low-efficiency” paradox is prevalent: older urban cores contain clusters of facilities but have supply–demand ratios below 0.5 because of limited service diversity and slope-induced reductions in accessibility, with the effective service radius decreasing to 750 m. Second, newly developed areas achieve service coverage rates below 50% when terrain constraints are considered, highlighting the limitations of static planning radii. Third, a 90% overlap between the directional distributions of residential areas and elderly care facilities, as indicated by their SDE major axes, supports the spatial feasibility of community-embedded aging-in-place models; however, physical proximity alone does not guarantee effective service delivery. By adapting generic spatial algorithms to create a terrain-sensitive planning tool, this study provides a transferable framework for evidence-based and targeted elderly care planning in SMSCs facing similar demographic and geographic constraints. The proposed framework contributes to the global sustainability agenda and advances SDG 11 (Sustainable Cities and Communities) and SDG 3 (Good Health and Well-being) by promoting more equitable resource allocation and supporting the development of age-friendly, walkable, and sustainable communities in topographically complex urban areas.