Discontinuities, Limits and Barriers: Quantifying the Intensity of Urban Spatial Ruptures

Urban fragmentation has emerged as a central issue in the study of socio-spatial dynamics in contemporary cities, reflecting processes of inequality, segregation, and spatial discontinuities. This article introduces a new methodological approach to measure fragmentation by focusing on discontinuities at limits rather than on the content of statistical units alone. The method applies robust standardization of selected socioeconomic variables—higher education, foreign-born population, and low-income population—at the census tract scale in the city of Lleida, Spain. Rupture intensity is measured through a Rupture Intensity Index, which integrates standardized differences across 217 limits. Principal component analysis identifies the most influential variables, while cluster analysis characterizes the multidimensional nature of limits. Results show that fragmentation in Lleida does not follow a simple center–periphery model but a tessellated pattern of fracture lines and gradient zones. Intense fractures emerge at borders between advantaged and disadvantaged neighborhoods, whereas gradients mark gradual transitions. The study demonstrates that limits are critical sites for observing and quantifying urban fragmentation and proposes a transferable methodology for comparative research and urban policy design in diverse urban contexts. This approach provides a replicable tool for urban analysis and the design of cohesion-oriented policies.