• A new framework to verified quantitatively the UECCs theory. • UECCs types of BTHUA and 13 cities were simulated and judged. • Evolution states of UECCs were summarized as nine types based on ratio of geometric area. • Urban scale and function, industry transformation, technology progress can affect UECCs. • Implications can be proposed to mitigate the conflicts of UE for different types of cities. The coupling evolution characteristics of urbanization and eco-environment (UE) can be summarized as five types in theory: linear, index curve, logarithmic curve, double index curve, S-shaped curve. According to the ratio of geometric area, the evolution states of the urbanization and eco-environment coupling coil (UECC) can be summarized as nine types: zero, primary, low-level, lower-medium-level, medium-level, upper-medium-level, high-level, highest-level, excessive urbanization. They reflect different evolution laws corresponding to different types of urban development stages, characteristics, patterns. The study quantitatively simulated and verified the coupling coil theory of UECCs, constructed comprehensive identification index systems and models for coupling coils. Results are as follows: from 2000 to 2019, the coupling relationships of UE in Beijing-Tianjin-Hebei urban agglomeration and metropolis, Beijing, Tianjin, Shijiazhuang, accord with S-shaped curve UECC; eco-cities, Zhangjiakou, Chengde, Qinhuangdao, accord with index curve UECC; Baoding, Langfang accord with logarithmic curve UECC; Handan, Xingtai, Cangzhou, Hengshui, Tangshan accord with double index curve UECC; linear UECC never exist in real life. Changes in urban scale and function, transformation of industrial structure, technological progress can be the key driving factors to boost the coupling state of UECCs from a low level to a medium level, and gradually to a high level. Some implications can be proposed to mitigate the conflicts between urbanization and eco-environment for different types of cities.
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