Analytical method for calculating variation and transition state duration of subsurface soil temperature under thermal disturbance conditions

In the present study, we proposed an analytical method for the heat conduction problem in the finite domain with arbitrary initial conditions under periodic boundary conditions by using the Laplace transform, and developed a method for calculating the time required for a subsurface soil to attain steady periodic temperature under arbitrary initial conditions. The evolution process and the transition state duration of the subsurface soil temperature under the periodic boundary condition and a constant initial value were analyzed by applying these two methods. The effects of soil thermal diffusivity, subsurface depth, ground surface temperature fluctuation amplitude, and initial temperature on the time required for the subsurface soil temperature to attain a steady state were systematically investigated. We then quantified the transition state duration in three typical thermal disturbance scenarios: increasing ground surface temperature, extensive ground-filling construction, and increasing subsurface temperature. To facilitate straightforward reference, several tables considering multiple factors were compiled for calculating the transient state durations under the three typical scenarios. The results obtained in this paper can be directly applied to the prediction of subsurface soil temperature and provide a reference for the evaluation of shallow geothermal energy resources.