Three-dimensional nonlinear analysis of coupled problem of heat transfer in the surrounding rock and heat convection between the air and the surrounding rock in the Fenghuo mountain tunnel

Abstract

According to the basic theories of heat transfer, geocryology and fluid mechanics, based on the supposition that the air in the tunnel be laminar flow air, taking the coupled problem of heat transfer of the surrounding rock and heat convection between the air and the surrounding rock into account, and taking the coupled effect of temperature and moisture fields of the surrounding rock into account, a three-dimensional calculational model is presented. The finite element formulation is obtained by Galerkin's method, and the solution approach is provided in detail. The finite element program is written according to the three-dimensional calculational model, the finite element formulation and the solution approach. The general situation of Fenghuo mountain tunnel in Qinghai–Tibet railway is introduced. The three-dimensional calculational model is applied to Fenghuo mountain tunnel in Qinghai–Tibet railway. The results show that the developed model, the finite element scheme, the solution approach and the finite element program is reliable, and that the seasonal thawing will not happen in the surrounding rock on condition that the insulation layer with a thickness of 5 cm and heat conductivity λ equal to 0.03 W/(m °C) is paved between the inner and outer linings of Fenghuo mountain tunnel. Using the developed model, the thawing–freezing situation of the rock surrounding the tunnels can be analyzed and predicated under the condition of not knowing the air temperature in the tunnel. Hence considerable cost for field monitoring of the air temperature in the tunnel would be saved. The calculational model and the finite element scheme can directly be used to analyze the projects of the hydraulic tunnels, the ventilated embankments, the aqueducts and the underground pipelines in cold regions, and artificially frozen pipes in non-cold regions, etc.