The Study On Coupled Hydro-thermal-mechanical Frost Heave Models For Freezing Soils Based On Porous Media Theory

The frost heave in soils is a complicated hydro-thermal-mechanical coupling process.Thus,it is of great theoretical significance to study the mechanism of hydro-thermal-mechanical coupling action and understand the mechanism of frost heave with the object of predicting and controlling frost heave.Based on the porous media theory,this paper starts from the equilibrium equation and thermodynamic law and then analyze the mechanism of hydro-thermal-mechanical action in freezing soil by using of the continuous medium method.The frost heave models for different freezing soils are established and verified numerically.The main research contents include:(1)the soil is equivalent to a continuous medium,and the average soil skeleton stress of unsaturated unfrozen soil is first derived.The relationship between effective stress and stress of each phase in equivalent medium is established.Based on the derived effective stress,the effective stress principle of soil and the choice of independent variables in modeling are discussed.Using the same method as that of unfrozen soils,the average soil skeleton stresses of saturated and unsaturated freezing soils are derived,which provides theoretical support for freezing soil modeling based on continuum method.(2)The universal balance equations of medium in continuous space and space with discontinuities are derived.The balance equation of each phase in saturated freezing soils is thus established.Making advantage of the second law of thermodynamics,the dissipative inequality is deduced and the constitutive relations describing the water-heat-stress frost heave characteristics of saturated freezing soil are established.The free energy function and entropy function of saturated freezing soils are then determined,and the specific energy conservation equation and constitutive equation are obtained.The saturated freezing soil is divided into active region and passive zone,and closed partial differential equations of active zone,passive zone and discontinuity(warm end of the warmest ice lens)are established respectively.A three-dimensional water-heat-stress coupled separated ice lens frost heave model of saturated freezing soil with frozen fringes is established.The three-dimensional frost heave model is simplified to one-dimensional frost heaving model,and the numerical simulation results are compared with the one-dimensional frost heaving test results to verify the effectiveness of this model.(3)The unsaturated freezing soil is divided into four phases: solid matrix,pore water,ice and vapor.The balance equations of each phase are established respectively.Based on the second law of thermodynamics,the constitutive relations of unsaturated freezing soil are obtained.The free energy function and entropy function of each phase are given,and the conservation equation and constitutive relation describing the frost heaving characteristics of unsaturated soil are obtained.The unsaturated freezing soil is divided into active and passive regions,and a three-dimensional water-heat-vapor-stress coupled separated ice lens frost heave model of unsaturated freezing soil with frozen fringe is established.The three-dimensional frost heaving model is simplified,and the one-dimensional frost heaving model of unsaturated freezing soil is numerically realized and verified by experiments.(4)The frost fringe does not occur in some freezing soils.Based on the diffusion interface in phase field theory,the freezing soil with and without frozen fringe is described in a unified way.According to the different contributions of film water,capillary water and vapor in freezing soil,the freezing soil is regarded as a multiphase and multicomponent mixture composed of solid matrix,film water,capillary water and vapor phase based on phase field theory.The thermodynamic framework of freezing soil is derived,and the driving force of water migration related to the phase transition degree and gradient of film water is obtained.Neglecting the salt component in soil,a thermodynamics-based mathematical model is presented for freezing soils and the free energy function of each phase is determined,the specific constitutive equations are thus obtained.These constitutive equations can describe the characteristics of freezing soil,Based on the established mathematical model,the supercooling of film water and capillary water in freezing soil is analyzed.The water migration equations of film water,capillary water and vapor are derived.The COMSOL software is used to analyze the simplified mathematical model,and the frost heave model can describe the frozen soil with or without frozen fringe.