A coupled model for water flow, airflow and heat flow in deformable porous media

Abstract

A fully coupled numerical model to simulate the complex behaviour of soil deformation, water flow, airflow, and heat flow in porous media is developed. The following thermal effects are taken into account: heat transfer through conduction and convection, flow, as well as viscosity and density variation of the fluids due to temperature gradients. The governing equations in terms of soil displacements, water and air pressures, and temperature are coupled non-linear partial differential equations and are solved by the finite element method. Two examples are presented to demonstrate the model performances

A study on how to couple thermo-hydro-mechanical behaviour of unsaturated soils: Physical equations, numerical implementation and examples

“…The previously described balance equations (49), (61), (71) and (73) are discretised using the finite element method [3,4,7,8,28,41,[65][66][67][68][69][70], transforming them into an equivalent system of first-order ordinary differential equations: …”

“…Experience gained in different scientific disciplines [3,[5][6][7][8] suggests that the finite element method is one of the best methods to numerically solve such a coupled system of equations. This study presents in details the coupled physical formulation, finite element discretisation and implementation of the thermo-hydromechanical equations governing the behaviour of porous geomaterials.…”

A finite element analysis of multiphase immiscible flow in deforming porous media for subsurface systems

“…Also, the code of multiphase immiscible¯ow is validated in partially saturated conditions based on a previous study by Schre¯er et al 13 Using the same boundary conditions as in Figure 1(a), a soil column was subjected to an external surface load of 1 . 0 kPa with the soil permeability K 0 .…”

Stability Analysis of Road Embankment Slope Subjected to Rainfall Considering Runoff-Unsaturated Seepage and Unsaturated Fluid–Solid Coupling

“…is the change of the effective stresses, whose [36,37]; H is the functional form of the constitutive law. The Coulomb-Mohr Strength Model was adopted in this paper; is the parameter of stress-paths.…”

“…The particles of the soil are assumed to be incompressible, and the characteristics of fluid-solid interaction can be stated as follows: (1) the effective stress increment is Terzaghi effective stress, and the pore pressure is replaced by fluid pressure increment of average saturated weight; (2) the volumetric strain is produced by effective stress according to Terzaghi Theory; (3) the volumetric strain affects the changing of fluid pressure; (4) Bishop effective stress [36,37] is applied to check the plastic yielding of the constitutive model. Based on Biot consolidation theory, unsaturated soil fluid-solid coupling model must satisfy the fluid equilibrium equation, momentum equilibrium equation, compatibility equation, as well as other requirements such as conduction, capillarity, fluid and mechanical constitutive equation laws, respectively.…”