Investigation On The Dynamic Response Of The Coupled Thermo-Hydro-Mechanical Problems For Saturated Porous Foundation

Research of the coupled multi-fields is an indispensable aspect of geotechnical engineering,engineering geology,and many other engineering fields.These problems are related to the extensive intersection of engineering thermophysics and many other disciplines.In the case of coupled multi-fields,the determination of the seepage of soil pore water,heat transfer,as well as the migration and diffusion of component materials or pollutants has been an urgent problem in geotechnical engineering at home and abroad.The solutions to these coupled multi-physics problems can provide a theoretical basis and analytical methods for many engineering fields.This study begins with an examination of Biot's dynamic poroelastic theory and then introduces the thermal conduction law that is modified by the classical Fourier thermal conduction law and Darcy's law to investigate the dynamic response of saturated porous soil using analytical methods.The rheological property of the soil mass is considered and the distribution of the physical variables of an isotropic saturated porous viscoelastic foundation under an external load is analyzed.We consider the anisotropy of the soil mass to determine the influence of changes in the soil physical properties on various physical variables in the anisotropic saturated porous elastic foundation,and the difference between the anisotropic saturated porous elastic foundation and the isotropic saturated porous elastic foundation in the study of the coupled thermo-hydro-mechanical dynamic problem is compared.The main achievements are summarized as follows:(1)Based on Biot's dynamic poroelastic theory,the generalized Darcy's law,and the generalized thermoelastic theory have been introduced,the coupled thermo-hydro-mechanical dynamic model in a saturated porous elastic foundation has been established.The coupled thermo-hydro-mechanical dynamic model can be used to describe the effect of the coupled stress field,temperature field,and seepage field.In order to solve coupled dynamic problems of saturated porous foundations,the normal-mode analysis method is used.This study can provides an effective calculation model and method for the study of the coupled problem of saturated porous foundations.(2)For the coupled thermo-hydro-mechanical problem with macroscopic spatial scale and micro temporal scale,the established coupled thermo-hydro-mechanical dynamic model is used in conjunction with the boundary conditions of the half-space subgrade to obtain the analytical expression of all non-dimensional physical variables by using the normal mode analysis method.is used in conjunction with the boundary conditions of the half-space subgrade to obtain the analytical expression of all non-dimensional physical variables by using the normal mode analysis method.In addition,we obtain the coupled thermo-mechanical dynamic model by degrading the coupled thermo-hydro-mechanical dynamic model and discuss the differences between the different foundation models subjected to external loads;the applicable conditions of different foundations are considered.The problem of the coupled thermo-hydro-mechanical dynamic model can also be transformed into a degraded to static problem to verify the accuracy of the normal mode analysis method for solving the saturated poroelastic half-space subgrade.We use the Flex PDF software to solve the dynamic problem and to verify the foundation model.The results of an example indicate that changes in the values of the pore water,load frequency,and thermal relaxation time have a significant impact on all considered physical variables.The influence of pore water on various physical variables is very obvious.When the upper surface of the foundation is subjected to a force source,the physical variable of the most obvious increase except the excess pore water pressure is temperature,it increases by more than 30%;when the upper surface of the foundation is subjected to a heat source,the physical variable of the most obvious increase except the excess pore water pressure is vertical stress,it increases by more than 45%.(3)Based on the coupled thermo-hydro-mechanical dynamic model,the Kelvin-Voigt viscoelastic model is incorporated because it considers the viscoelastic relaxation times;in this manner,the coupled thermo-hydro-mechanical dynamic model for a saturated porous viscoelastic medium is established.The distribution of the various physical variables as a result of changes in the load frequency,viscoelastic relaxation times,permeability coefficient,time of effect,and porosity is analyzed with two different boundary conditions.Two methods are used to verify the proposed method,namely,the coupled thermo-hydro-mechanical dynamic model for a saturated porous viscoelastic medium and the analytical solutions(degradation into a static problem and Flex PDF software).The results of the calculation example demonstrate that the influence of the viscoelastic relaxation times factor ?0 and ?1,permeability coefficient and porosity on the non-dimensional variables is related to the external load.In addition,except for the non-dimension temperature at which the upper surface of the foundation is subjected to the heat source,the physical variables in the saturated porous viscoelastic foundation have obvious hysteresis after being subjected to external loads.(4)Natural soils usually exhibit some anisotropic characteristics due to different deposition conditions and stress states.According to the theory of fractional calculus with the Riemann-Liouville fractional integral operator,the coupled thermo-hydro-mechanical dynamic model for the anisotropic saturated porous elastic foundation is established.The normal mode analysis method is used to obtain the analytical solution of the physical variables when the upper surface of the foundation is subjected to a harmonic load.The effects of different load frequencies,fractional order coefficients,anisotropic heat transfer coefficient parameters,and anisotropic permeability coefficient parameters on the non-dimensional variables are analyzed.When the fractional order coefficient equals one and the anisotropy parameters of the same physical meaning are all taken as the same value,the dynamic model of this anisotropic foundation can be reduced to a foundation model consistent with the coupled thermo-hydro-mechanical dynamic model,thus verifying the accuracy of the foundation model.The results show that a change in the fractional coefficient has only a significant effect on the non-dimensional temperature when the upper surface of the foundation is subjected to a mechanical load.However,when the upper surface of the foundation is subjected to a thermal load,a change in the fractional coefficient has a significant effect on all physical variables.With the increase in the anisotropic heat transfer coefficient parameter,the values of all physical variables gradually increase except for the non-dimensional excess pore water pressure when the upper surface of the foundation is subjected to a mechanical load.A change in the fractional coefficient has a significant effect on the physical variables with a change in the anisotropic heat transfer coefficient parameter.A change in the anisotropic permeability coefficient parameters has a significant effect on all physical variables except for the non-dimensional temperature when the upper surface of the foundation is subjected to a thermal load.The variation of anisotropic permeability coefficient parameters also has obvious influence on the disturbance depth of some physical variables.When the upper surface of the foundation is subjected to a force source,the excess pore water pressure curve basically decays to zero at the depth of z=4.5 and the vertical stress curve basically decays to zero at the depth of z=2.5 when the anisotropic permeability coefficient parameters is ?1=1.With the increase of the anisotropic permeability coefficient parameters,the disturbance depth of the excess pore water pressure curve increases to the depth of z=6 and the disturbance depth of the vertical stress curve increases to the depth of z=5 when the anisotropic permeability coefficient parameters is ?1=2.The research results of this paper do not only provide a theoretical basis for the design of foundations and the study of failure mechanisms but also provide references for understanding the problems of seepage and heat transfer in foundations.