Theoretical Study On Multi-process Coupling Phenomena Of Saturated Soil Based On Volume Averaging Technique

With the development of modern geoengineering and geotechnique,such as the construction of repositories for high level radioactive waste,the disposal of municipal solid waste and the technique of microbially induced carbonate precipitation,etc,the multi-process coupled phenomena of soil has been concerned and researched more and more by engineers and scholars.The coupld phenomena of multi processes of soil refers to the macroscopically thermodynamic behaviors of soil arising from the occurrences and evolutions of the deformation of soil skeleton,the seepage of bulk fluid(pore fluid)and the transport of solute and heat,etc.,as well as the interactions between these thermodynamic processes.The macroscopically thermodynamic behaviors of soil are determined by the thermodynamic behaviors of the soil skeleton,the bulk fluid and its constituents,and by the interactions between the soil skeleton and the bulk fluid,as well as by the interactions between the constituents of the soil skeleton and the bulk fluid.How to systematically pass the thermodynamic behaviors of soil and the interactions between different thermodynamic processes from one scale to others(microscale,mesoscale,macroscale)and establish a trans-scale,multi-process coupled model has become an urgent but difficult problem.Most of the existed multi-process coupling theory are based on intuition,experience,or macroscopic recognition,thus are lack of a consistent and unified scientifically theoretical basis.This study aims at the theoretical research of the multiprocess coupled phenomena of saturated soil by use of volume averaging technique and thermodynamics.The main achievements of this study are listed as follows:(1)Based on the work conjugate principle,the work-conjugate velocity for a phase or constituent of saturated soil is defined.The work-conjugate velocity guarantees that the input power into a phase or constituen right equals to the product of its macroscopic stress and the work-conjugate velocity,thus the work-conjugate velocity is the solely macroscopic velocity that describes the real motion of a phase or constituent in the macroscopic field.(2)Based on the work conjugate principle,a new spatial averaging theorem is established.Compared with the traditional spatial averaging theorem,the work conjugate principle-based spatial averaging theorem is capable of accurately transforming the velocity-related flux density(the convective flux of mass,momentum,energy and entropy,as well as the stress power)from one scale to others(microscale,mesocale and macroscale).(3)Based on the work-conjugate velocity and the work conjugate principle-based spatial averaging theorem,the macroscopic balance equations of mass,momentum,energy and entropy for saturated soil are derived from the microscopic and/or mesoscopic ones by use of the volume averaging technique.In the derivation,the discrete configuration of soil skeleton is captured resulting in the concept of Terzaghi’s effective stress is reproduced in its macroscopic momentum balance equation and the frictional mechanism of energy dissipation in its macroscopic energy balance equation theoretically.The work-conjugate velocity and the work conjugate principle-based spatial averaging theorem give rise to the coexistence of two kinds of velocities: the workconjugate velocity and the mass averaged velocity,which guarantees that the volume averaging technique is capable of capturing the elastic and plastic deformation of clay skeleton in a consistent and unified manner,as well as the average motion and dispersive motion of bulk fluid and its constituents in a consistent and unified manner.That is to say,the plastic strain of soil skeleton and the dispersive fluxes of the bulk fluid and its constituents are not necessary to be introduced as additional assumptions.(4)Based on the macroscopic entropy balance equation of satrated soil and the second law of thermodynamics,the restrictions of the inequality of the total entropy of saturated soil on its constitutive eqautions are derived,namely the nonequilibrium results and the equilibrium results.The difference between this study and the existed studies is that,on the one hand,the effective stess of soil skeleton is balanced by its intrinsic stress and the thermodynamic pressure of bulk fluid at nonequilibrium state,and the effective stess of soil skeleton is balanced by its back stress and the thermodynamic pressure of bulk fluid at equilibrium state on the other.(5)Based on the Ziegler’s principle of thermodynamic orthogonality,the framework of constitutive theory for saturated soil is formulated,which is applicable to both linear and nonlinear irreversible processes.Each constitutive equation of the constitutive theory specifies the relationship between a thermodynamic variable describing the corresponding irreversible process and its main driving force.By analyzing each constitutive equation,the main driving force and the influence factors for the occurrence and evolution of a single thermodynamic process,as well as the coupled mechanisms between different thermodynamic processes are specified.(6)The classical forms of the functions of the free energy density and the dissipative rate density for a single continuum under a single physical,chemical or mechanical field are analyzed,then a uniformly functional form for the free energy densities and the dissipative rate densities of different continua is proposed.The dispersion-type free energy density function and the dispersion-type dissipative rate density function for the soil skeleton,as well as for the bulk fluid,are constructed,which achieves the uniform description of the functional forms for the free energy densities and the dissipative rate densities of different phases of saturated clay.(7)The approximate expressions for the free energy densities of adsorbed fluid,clay prticles and bulk fluid,as well as that for the totally dissipative rate density of saturated clay are formulated by method of Taylor seires expansion.Based on the established framework of constitutive theory,the constutive equations that describe the linear processes of saturated clay nearby by the equilibrium state are derived,then the linear coupled model of saturated clay for modeling the coupled phenomena of multi processes is obtained.Finally,the linear coupled model is applied to predict and analyze the transport process of solute in a deforming clay liner.