Bernd Markert

Abstract:

Studying the freezing process in water-saturated soils is of great interest in many engineering fields. During the freezing of fine-grained soils, volume expansion known as frost heave is usually observed. Such phenomenon can cause detrimental deformation and damage to highways, building foundations and pipelines in cold regions subjected to seasonal freezing or during mining and tunneling where artificial freezing is adopted. The frost heave is attributed to the formation and growth of ice lenses associated with water migration to the freezing front. Based on several experimental works and previous studies, it is found that the ice lens formation is related to cracking of the soil in the frozen fringe [1]. Therefore, according to the stress criterion, the soil skeleton separates and a new ice lens forms when the pore pressure exceeds the sum of the overburden stress and the separation strength of the freezing soil. Moreover, suction occurs when the pore water solidifies into ice, facilitating water migration from the unfrozen zone to feed the growth of the ice lens [2].
Here we propose a thermo-hydro-mechanical model consisting of a porous solid matrix and a pore-fluid phase representing solid ice and liquid water based on a coupled phase-field-porous media approach. The model accounts for the phase change, water migration, ice lens formation and soil deformation due to the freezing process. We use the macroscopic theory of porous media (TPM) for the description of the deformable, heterogeneous porous solid [3] with the phase changing fluid constituent described by a unified formulation employing a phase-field model (PFM) [4]. The diffusive interface treatment of the freezing front can be easily implemented numerically as no explicit front tracking and application boundary conditions at the interface is required. The ice lens formation is modeled based on the rigid ice model adopting the stress criterion. In this context, a fracture related PFM is used to describe the crack formation preceding the ice lens initiation [5]. Additionally, the Clapeyron equation is employed to calculate the suction pressure at the water–ice interface. Finally, numerical examples are presented to demonstrate the ability of the proposed model in describing the freezing process in fluid-saturated porous media.

[1] T.F. Azmatch, D. C. Sego, L. U. Arenson, K. W. Biggar, Cold Reg. Sci. Technol. 82 (2012) 8-13.
[2] F. Ming, Y. Zhang, D.q. Li, Geosci. J. 20 (2016) 667–679.
[3] B. Markert, Arch. Comput. Methods Eng. 15 (2008) 371–446.
[4] A.H Sweidan, Y. Heider, B. Markert, Contin. Mech. Thermodyn. (2019) 1-22.
[5] Y. Heider, S. Reiche, S., P. Siebert, B. Markert, Eng. Fract. Mech. 202 (2018) 116–134.