Heat balance model for long-term prediction of the average temperature in a subway tunnel and surrounding soil

For a long-term forecast of the average air temperature in a metro tunnel and surrounding soil, heat balance conditions are modeled in a system that includes two parallel tunnels, a near-tunnels underground space, the earth's surface and atmospheric air with seasonal temperature variation. It is assumed that the air in the tunnels is well mixed, and the thermal effect of ventilation is taken into account by replacing the air in the tunnels with atmospheric air. The system of heat balance equations is solved numerically by the finite element method. A numerical analysis of the influence of the model parameters on the average temperature in the tunnels and surrounding soil is carried out. The dimensions of the soil region with an elevated temperature, located between the tunnels, are estimated. The model is validated using available literature data from Moscow, Guangzhou and Glasgow subway systems.