Continuum thermodynamic modelling of porous medium with application to ground freezing

Juha Hartikainen

Research output: ThesisDoctoral ThesisMonograph


A thermodynamically consistent approach to model porous medium as a multicomponent mixture of immiscible and miscible phases with applications to ground freezing is presented. The approach is based on the theory of mixtures and the basic principles of continuum mechanics and macroscopic thermodynamics. It includes the balance equations of mass, momentum, angular momentum and energy, and the constitutive relations, which are derived by using the entropy inequality and non-smooth thermodynamic potentials of state and dissipation. It is shown that the approach provides a method to model microscopic processes such as molecular interactions on the macroscopic level by using macroscopic quantities. The approach also shows that constraints on the constitutive quantities have important consequences which it is able to describe as constitutive relations such as a general definition for the constituent temperatures.The approach is used to formulate a model for freezing and thawing of saline water saturated ground. The model includes a description for heat and mass transfer in freezing and thawing ground, phase change of groundwater being affected by groundwater pressure, salt concentration and molecular interactions between water and ground matter, and exclusion of salt during freezing. The density driven groundwater flow in unfrozen and partially frozen ground, and deformations of ground are also included. The quality of the model is investigated by numerical simulations on experimental tests. Noteworthy results of the formulation include the Stokes-Einstein relation for the molecular diffusion coefficient of dissolved salts and an accurate description for the phase change of water. The model is used to investigate the development of permafrost and perennially frozen ground at Forsmark in Sweden on time-scales of 45,000 and 115,000 years by using site-specific information on physical properties of ground. Time histories of ground level air temperatures, shoreline migration, soil and vegetation cover, as well as heat generation from the spent fuel at a depth of 450–470 metres are also considered. The results have been used in the safety assessment of nuclear waste disposal to formulate radionuclide release scenarios as well as to provide input data to groundwater flow modelling.
Translated title of the contributionHuokoisen materiaalin kontinuumi-termodynaaminen mallintaminen ja soveltaminen maan jäätymiseen
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Paavola, Juha, Supervising Professor
Print ISBNs978-952-60-8137-3
Electronic ISBNs978-952-60-8138-0
Publication statusPublished - 2018
MoE publication typeG4 Doctoral dissertation (monograph)


  • porous media
  • continuum thermodynamics
  • non-smooth mechanics
  • ground freezing


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