Solutions to phase change problem due to internal thermal erosion of frozen soil

To solve the thermal erosion problem of frozen soil due to gradual expansion of the seepage pores during the process of freezing engineering catastrophe,a corresponding mathematical model of phase change heat transfer based on the convective heat transfer boundary condition ( the third type boundary condition) in the cylindrical coordinate system was established under certain assumptions. The heat balance integral method (HBIM) was adopted to solve the nondimensionalized partial differential equation and the problem was also numerically solved for verification via a fi- nite-difference procedure facilitated by coordinate transformations after the equation was dispersed using power law scheme. For the solution of the erosion phase change position,the calculation results of the two methods were in good agreement. The maximum deviation between the two methods was less than 1% in the calculated time range. The results show that Stephen number St,Biot number Bi,and sub-cooling coefficient φ are the main factors influencing the moving velocity of phase change position. The dimensionless phase change position almost linearly increases with time under the condition of different parameter combinations. When the St and Bi are doubled,the velocity of phase change position is doubled under the condition that other parameters are constant. While the velocity of phase change position is only reduced by 5% when φ is doubled. It is indicated that in engineering practice,reducing the average tempera- ture of frozen soil can slow down the rate of phase change,but it is of limited effectiveness. On the contrary,the meas- ures such as lowering the temperature of water flow or slowing the flow rate of water flow can effectively slow down the phase change rate. When the results are adopted to predict the actual freezing engineering disasters,it is necessary to consider the difference of soil properties and the influence of groundwater temperature and convective heat transfer co- efficient changing with the pore size. The phase change erosion rate obtained by the method can be regarded as the up- per limit of the erosion speed in engineering practice.