HE Chun-xiong, WU Zi-wang, ZHU Lin-nan
Based on the analyses of fundamental meteorological and hydrogeological conditions at the site of the Dabanshan Tunnel in the Qilian Mountains, a combined convection-conduction model was constructed for turbulent air flow in the tunnel and temperature field in the surrounding rock. Then, with the in situ conditions of air temperature, atmosphere pressure, wind force, as well as the hydro-thermal conditions, the relationship between the temperature on the surface of the tunnel wall and the air temperature at the entry and exit of the tunnel has been obtained, the freeze-thaw conditions in the surrounding rock wall of the tunnel is predicted, and the simulated result is compared with that obtained in the case of laminar air flow in the tunnel. Many tunnels, constructed in the cold regions of the Tibetan Plateau, are at an elevation above 4000 m and nearby the ridge of mountain. Since there is cold air flowing in the cold regions almost all the time and there is no wind protective screen, the wind-velocity in situ of the tunnels is more than 5 m/s, and because of the difference of atmospheric pressure, air temperature between the entry and exit of the tunnel, the air flow in the tunnel would be turbulent. In order to deal with the complex random unsteady nature of the turbulent air flow, the Reynolds time-average equations were used, that is, based on the classical Navier-Stokes equations, introduced the pulsate kinetic energy equation (K-equation) and dissipativity equation (ε-equation), then, by the Boussinesq assumption, the algebraic relationship of the turbulent kinematic viscosity vt, pulsate kinetic energy K and dissipativity ε are obtained. Combining these equations about the turbulent air flow in tunnel with the convective and conductive equations about the air temperature in the tunnel and about the temperature field with phase-change in surrounding rock wall, the whole mathematical model with a system of equations was constructed. In order to predict the freeze-thaw conditions for the Dabanshan Tunnel, the parameters about the turbulent air flow in the model are chosen by the routine methods in air fluid dynamics, and the thermal parameters and initial and boundary conditions in the model are defined as follows. The air density ρ=0.774 kg/m3, the thermal capacity of air Cp=1.8744 kJ/kg·K, heat conductivity λ=2.0×10-2 W/m·K and the dynamic viscosity μ=9.218×10-6 kg/m·s, the thermal diffusivity α=1.3788×10-5 m2/s and the kinematic viscosity v=1.19×10-5 m2/s. In the surrounding rock wall, the dry volumetric weight γd=2400 kg/m3, the content of water and unfrozen water in rock are 3% and 1%, respectively, and the thermal conductivity λu=1.9 W/m·K, λf=2.0 W/m·K, heat capacity Cv=0.8 kJ/kg·K, and Cf=(0.8+2.1(V-Vu)+4.182Vu/1+V)×rd, Cu=((0.8+4.182V)/1+V)×γd. The wind speed at the entry and exit is approximated as V(t)=[0.028×(t-7)2+2.5](m/s), where t is the t-th month in a year. The initial wind speed in the tunnel are set to be U(0,x,r)=Ua(1-(r/R)2), V(0,x,r)=0 The effective air pressure p=0 at the entry of wind and p=(1+βL/2R)×U2/2at the exit,where β is the coefficient of resistence along the tunnel wall, and ∂p/∂r|r=R=0. The kinetic energy K=0.01×(U2+V2)/2and the dissipativity ε=Cv3/4K3/2/0.4(R-r) at the entry, and K and ε are calculated by the local one direction method at the exit, and K=0, ε=0 on the surface of surrounding rock wall.
