Coupled heat and water transfer in heterogeneous and deformable soils: Numerical model using mixed finite element method

We present a generic model framework for coupled heat and water transfer (CHWT) in deformable (non-rigid) soils with spatial variations of soil properties. The model backbone is a mixed finite element method (FEM), which solves the Philip and de Vries (1957) CHWT model and achieves conservation of mass and energy on both local and global scales. Spatial variations occur in soil hydraulic and thermal properties due to transient water content and temperature distributions. Based on the mixed FEM scheme, a gradient measure and a clustering model (“k-means”) are proposed to trace the regions with large spatial variations of soil properties, and an adaptive mesh refinement technique is developed to improve the spatial resolution and simulation accuracy. Deformation perturbates local soil topography and alters transient soil water and temperature regimes in the deformed regions. A quasi-static deformation model is presented, and the deformation effects are incorporated into the mixed FEM scheme. When external load exists, soil deformation is simulated with an updated Lagrangian formulation, and the local water content and temperature variations due to soil volume changes are also updated in the CHWT model. Numerical examples, including thermally induced soil water transfer and water infiltration, illustrate the model ability to provide plausible CHWT results, especially the refined solutions near the wetting fronts and the water content and temperature distributions when the soil is deformable. In conclusion, the proposed model framework provides an effective pipeline to incorporate and process the spatial variations of soil properties and soil deformation in CHWT simulations.