Recently, a constitutive model has been developed to describe the mechanical behaviour of frozen soil as a function of temperature, all the way to the unfrozen state, and vice versa [1]. The model has been implemented as a user-defined soil model (UDSM) in the geotechnical finite element code PLAXIS 2D and applied in practical thermo-hydro-mechanical boundary value problems. One of the problems with the use of a model for frozen / unfrozen soil is that it involves several parameters of which quite a few are not very common to geotechnical engineers. Hence, one of the goals of this study is to provide more information on the meaning and the determination of the model parameters. As an example of the use of the constitutive model and its implementation, one application is presented: it is a chilled pipeline causing a drop in the ground temperature leading to frost heave. Its results show that the model can simulate frost heave in a qualitative manner, and that the robustness of the numerical implementation is still sensitive to the choice of boundary conditions, temperature gradients, and time.

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Knowing that extensive field tests and laboratory tests are time-consuming and expensive, this paper describes a practical approach to obtain crucial properties of frozen soil such as the soil freezing characteristic curve (SFCC), the freezing/melting point of a soil-water system and its hydraulic conductivity by means of limited input data. Different models and empirical equations are combined to provide a closed formulation which can be used in computer simulations to account for moisture migration in partially frozen soils. Input data such as grain size distribution and dry bulk density suffice to obtain the aforementioned properties. Further consideration of the pressure dependence of the freezing/melting temperature of water/ice even allows accounting for the phase change point depression and thus the phenomena of pressure melting.
The model is appropriate not just to represent qualitatively the SFCC of different soil types, but also to provide conformity between the model prediction and measured data of many soil types having a log-normal grain size distribution. This user-friendly approach is used as default setting of a newly implemented user-defined soil model for frozen and unfrozen soil in the geotechnical finite element code PLAXIS 2D.
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Recently, a constitutive model has been developed describing the mechanical behaviour of frozen soil as a function of temperature, all the way to the unfrozen state, and vice versa (Ghoreishian et al., 2016). The model has been implemented as a user-defined soil model in the geotechnical finite element code PLAXIS 2D and applied in practical thermo-hydro-mechanical boundary value problems. One of the problems with the use of a model for frozen / unfrozen soil is that it involves several parameters of which quite a few are not very common to geotechnical engineers. Hence, one of the goals of our study is to provide more information on the meaning and the determination of the model parameters. As an example of the use of the constitutive model, two hypothetical cases are presented. The first one is a chilled pipeline causing a drop in the ground temperature leading to frost heave. The second one is a raft foundation on frozen ground subjected to a thawing period. @en