Risk-spatial-utility interaction mechanism in Karst small Towns’ disaster-adaptive landscapes: based on pressure-state-response and coupling coordination model analysis

Karst small towns inherently exhibit disaster-prone environments characterized by pronounced natural-hazard risk, constrained spatial configurations, and low functional utility. Disaster-Adaptive Landscapes (DAL) consist of green, blue, and open spaces and linear corridors that mitigate hazards and support evacuation. In karst small towns, ecologically fragile environments and weak baseline services impose three constraints on DAL: high Risk pressure, tight Spatial capacity, and low Utility. The Risk–Spatial–Utility network (RSU) integrates these dimensions to measure their mismatch, thereby pinpointing priority areas for targeted strengthening of DAL adaptive capacity to natural hazards. Based on statistical data from 21 typical karst small towns in China (2016–2021), this study uses game theory to integrate subjective and objective indicator weights, and then applies coupling coordination and obstacle degree models to identify RSU interaction mechanisms and key drivers. ArcGIS Pro and Stata support spatial processing and statistical analysis. Key findings include: (1). From 2016 to 2021, RSU subsystem scores generally increased. In the Risk subsystem, a higher score reflects stronger socio-ecological and socio-technical coping capacity rather than greater hazard pressure. Together with gains in Spatial and Utility, this trend indicates improved infrastructure support and adaptive capacity. (2). The nonlinear interaction among risk, spatial, and utility highlights the dominant role of spatial and utility in coordinated regulation. Here, spatial resource allocation serves as the key lever, whereas risk-only strategies are less effective. (3). Key drivers of RSU interactions include Infrastructure utility (IU), Density of drainage pipes (DDP), and Distance from river (DFR). IU is the primary bottleneck destabilizing the RSU, while DDP and DFR jointly impose dual pressures. Urbanization indicators (Gross Domestic Product (GDP), Urbanization rate (UR), Proportion of impervious area (PIA)) exacerbate geological vulnerabilities. These insights enable policymakers to calibrate critical factors for optimizing RSU equilibrium, thereby enhancing DAL resilience in karst small towns.