Approximate analytical solution and sensitive study for air temperature in high geothermal insulated tunnels

Abstract

As tunnel engineering advances toward deeper, larger, and longer projects, the prevalence of high geothermal tunnels has significantly increased. Optimizing thermal insulation layers based on accurate and efficient air temperature distribution is crucial for mitigating thermal hazards. However, analytical solutions have received less attention when considering coupled air and rock temperature equations. This study developed an analytical model to predict air temperature in tunnels, accounting for both axial and radial heat conduction in the insulation layer and surrounding rock. An approximate analytical solution to the coupled air and rock temperature equations was derived, yielding expressions for their temperature distributions. The results indicated that the predicted temperature distributions closely aligned with reference data, with a maximum deviation of 5 %. These expressions enabled the quantification of air temperature variation along the tunnel and facilitated rapid determination of sensitive analysis for parameters influencing air temperature. For example, in the secondary heat hazard area of the Zhenglong coal mine, the sensitivity-critical value for insulation layer thickness and inlet air velocity were approximately 10 cm and 2 m/s. Subsequently, variance analysis using SPSS ranked the critical factors influencing air temperature: inlet air velocity > original rock temperature > insulation layer thermal conductivity > insulation layer thickness. These findings can inform the design of thermal insulation and ventilation strategies in high-geothermal tunnels.