Numerical modelling of distinct ice lenses in frost heave

S.A Ghoreishian Amiri,G Grimstad,H Gao,S Kjelstrup

doi:10.1088/1755-1315/710/1/012039

S.A Ghoreishian Amiri, G Grimstad + Show 2 more

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https://doi.org/10.1088/1755-1315/710/1/012039

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Abstract

Frost heave happens when three conditions coincide: the temperature is below the normal freezing point of bulk water, the sub-cooled water is connected to a water reservoir, and the mechanical conditions of the soil allows the ice lens to grow. Upon further penetration of the freezing front, the relative permeability of the soil around the growing ice lens may dramatically decrease, and the ice lens stops growing. Then, if the three requirements for initiating a new ice lens coincide again, another ice lens will appear and start to grow. In this paper, a new thermo-hydro-mechanical (THM) model has been developed to capture the formation and growth of multiple ice lenses in a freezing ground. Non-equilibrium thermodynamic theory was used to derive the coupled transport equations of heat and mass. Fracture mechanics has been employed to handle the mechanical requirements for the position and growth of ice lens. The governing partial differential equations have been solved using the extended finite element method (X-FEM). In this method, the ice lens is treated as a kind of discontinuity inside the corresponding elements.

Highlights

Frost heave is defined as the upwards movement of the ground surface due to formation of ice within fine-grained soils
Frost heave happens when three conditions coincide: the temperature is below the normal freezing point of bulk water, the sub-cooled water is connected to a water reservoir, and the mechanical conditions of the soil allows the ice lens to grow
The ice lens is treated as a kind of discontinuity inside the corresponding elements

Summary

Introduction

Frost heave is defined as the upwards movement of the ground surface due to formation of ice within fine-grained soils. A similar idea was theoretically derived by [9, 10] using the theory of non-equilibrium thermodynamic A coupled THM model for simulating frost heave phenomenon is presented In this model, the force equilibrium is incorporated with heat and mass balance equations, and a simple stress criterion for initiating new ice lensing is adopted. 2. Conceptual model According to Førland and Kjelstrup Ratkje [9] and Derjaguin and Churaev [10], the transport equations of heat and mass for frost heave yielded by non-equilibrium thermodynamic have the following form: qw kr K Pw Substituting Eq (2) into Eq (9) results in the final form of the heat transfer equation: UwCwqw .T

Force equilibrium The force equilibrium of the system can be written as:

Conclusion