Analytical Solution to Axial and Radial Temperature of Tunnel in Cold Region

Abstract:

Based on superpositon principle and the orthogonal expansions of Bessel eigenfuncion,the analytical solution to radial temperature of circle tunnel in cold region was obtained subject to time and distance dependent boundary changes of the third kind.The analytical solutions of the annual mean temperature and temperature amplitude were obtained by energy banlance method and experiential method with a consideration of heat conduction/convection between the tunnel ground and the air flow in the tunnel.The annual mean temperature presented an exponential growth with the increasing distance from entry of tunnel,the annual temperature amplitude a negative exponential growth.Applicablity and accuracy of the equation were examined by comparing the calculated results with the mesaured results.It is found that the calculated values agree well with those measured in the field.In determining the temperature distribution outside the tunnel,wind speed and thermal properties parameters of surrounding rock,the axial and radial temperature can be calculated with the analytical solution.The necessary length of anti-icicle treatment from tunnel entrance area can also be determined.The analytical solution proves to be useful for engineers and technicians.

Key words:tunnel in cold regions; non-homogeneous; convection; axial and radial temperature; anayltical solution