Model of nonlinear coupled thermo-hydro-elastodynamics response for a saturated poroelastic medium

Abstract

Based on the Biot's wave equation and theory of thermodynamic, Darcy law of fluid and the modified Fourier law of heat conduction, a nonlinear fully coupled thermo-hydro-elastodynamic response model (THMD) for saturated porous medium is derived. The compressibility of the medium, the influence of fluid flux on the heat flux, and the influence of change of temperature on the fluid flux are considered in this model. With some simplification, the coupled nonlinear thermo-hydro-elastodynamic response model can be reduced to the thermo-elastodynamic (TMD) model based on the traditional Fourier law and, further more, to the Biot's wave equation without considering the heat phase. At last, the problem of one dimensional cylindrical cavity subjected to a time-dependent thermal/mechanical shock is analyzed by using the Laplace technique, the numerical results are used to discuss the influence of Biot's modulus M and coefficient of thermo-osmosis on displacement and to compare with the results of thermo-elastodynamic response to ascertain the validity of this model. nonlinear, thermo-hydro-elastodynamic, dynamic response, laplace transform

Relaxation Effects of a Saturated Porous Media Using the Two-Dimensional Generalized Thermoelastic Theory

“…The non-dimensional thickness of the layer medium is H = 2, and the non-dimensional width of the thermal/mechanical source is a = 1. The basic physical parameters for the thermal poroelastic medium that is used in the calculation are cited directly from the references Liu et al (2009Liu et al ( , 2010a and are listed in Table 1. Considering the complex coupling mechanical/thermal source in the calculation, the results are obtained when the cavity is subjected to a strip mechanical case or a strip thermal case at the inner boundary, respectively.…”

“…Assuming the soil to be a linear-elastic isotropic-saturated porous medium, the constitutive relation of the poroelastic medium can be presented in terms of the effective stress and temperature change θ (θ = T − T 0 , T is the current temperature and T 0 is the initial temperature) when the effect of deformation on the balance of mass and heat is considered (Liu et al 2009(Liu et al , 2010a.…”

“…A formulation for the same problem was presented by Wang and Dong (2003) also, in which the energy balance equation is re-derived based on the concept of free enthalpy. A fully coupled non-linear model of thermo-hydro-elastodynamic response (THED) for the saturated poroelastic medium was derived by Liu et al (2009) on the basis of the theory of thermodynamic of Biot's, Darcy's law of the fluid, in which the modified heat conduction law of Fourier's was considered. Furthermore, the thermo-elastodynamic response of a spherical cavity and the mode of a spherical cavity's thermo-elastodynamic response in a saturated poroelastic medium were analyzed and the influence of the thermo-osmosis was discussed by Liu et al (2010a,b).…”

Normal Mode Analysis to a Poroelastic Half-Space Problem under Generalized Thermoelasticity

“…Lu et al (2010) investigated a porous elastic medium subjected to a normal force and a thermal source in the context of generalized thermoelastic theory with one relaxation time. Liu et al (2009;2010a) developed a method to overcome one-dimensional problems for an isotropic saturated poroelastic medium including a cylindrical cavity and spherical cavity subjected to a time-dependent thermal/mechanical shock in the context of thermodynamics theory. That same year, Liu et al (2010b) solved a thermo-hydroelastodynamic problem in a two-phase porous thermoelastic medium.…”

Reflection and Refraction of P Wave at the Interface Between Thermoelastic and Porous Thermoelastic Medium

“…Although many scholars (Zhou et al 1998;Abousleiman and Ekbote 2005;Youssef 2007) have contributed solutions to some problems dealing with porous thermoelastic media, the thermoelastodynamic response and wave propagation in a fluidsaturated porous medium have not cause enough attention. Accordingly, Liu et al (2009Liu et al ( , 2010a) developed a thermoelastodynamic model for a fluid-saturated porous medium based on the combination of the modified Biot's theory and the generalized thermoelasticity theory in which the influence factors such as compression of solid phase and liquid phase, effect of motion of fluid on heat flux and effect of the change of temperature on fluid speed were considered.…”