Dimensionless Analysis of the Spatial–Temporal Coupling Characteristics of the Surrounding Rock Temperature Field in High Geothermal Roadway Realized by Gauss–Newton Iteration Method

Understanding the time–space coupling characteristics of the surrounding rock temperature field in high geothermal roadways is essential for controlling heat damage in mines. However, current research primarily focuses on individually analyzing the temperature changes in the surrounding rock of roadways, either over time or space. Therefore, the Gauss–Newton iteration method is employed to model the coupling relationship between temperature, time, and space. The results demonstrate that the dual coupling function describing the temperature field of the surrounding rock in both time and space provides a more comprehensive characterization of the temperature variations. Over time, as ventilation duration increases, the fitting degree of the characteristic curve steadily rises, and the characteristic curve descends overall. In the spatial dimension, the fitting degree of the characteristic curve gradually decreases with the rise of the dimensionless radius, and the characteristic curve ascends overall. Additionally, as thermal conductivity increases, the fitting degree of the characteristic curve steadily rises.