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This paper reviews eight geoacoustic models applied to frozen soils: crystal growth models (grain cementing, grain coating, matrix supporting, and pore filling), the weighted equation (WE) model, Zimmerman and King's model (KT), the Biot-Gassmann theory modified by Lee (BGTL), and a two-end member model. We verify the capacity of these models to estimate unfrozen water content (UWC) based on "reference" UWC results and joint P and S wave velocities for different soil types. The satisfactory UWC estimates of saline unconsolidated sand and overconsolidated clay based on V p data prove that the KT, BGTL, and two-end member models are capable of modeling "smooth" transitions in the ice crystal growth mode, while they may provide less accurate UWC values when abrupt change of crystallization mode occurs. None of the tested soil types show a single crystallization mode throughout the freezing process, as assumed by individual crystal growth models. V s-based UWC estimates are less accurate due to significant but difficult-to-estimate influence of effective stress and soil initial cementation. All models, except pore filling and matrix supporting, can match V s versus V p measurement results for sands and silts but gradually provide inconsistent estimates with increasing clay content. We conclude that model validation by independent UWC measurements is necessary and that consistency between UWC values estimated from V s and V p is insufficient to ensure proper model validation.

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A systematical testing program on frozen Onsøy clay under isotropic loading and undrained shearing at different temperatures (− 3 ~ − 10 °C), strain rates (0.2~5%/h) and initial Terzaghi effective stress (20~400 kPa) was conducted with the focus on pore pressure development. It is meant to increase the understanding and facilitate the development of an ‘effective stress’-based model for multi-physical analysis for frozen soils. This study adopted the pore pressure measurement method suggested by Arenson and Springman (Can Geotech J 42 (2):412–430, 2005. https://doi.org/10.1139/t04-111) and developed a new testing procedure for frozen soils, including a ‘slow’ freezing method for sample preparation and post-freezing consolidation for securing hydraulic pressure equilibrium. The B-value of frozen soils is less than 1 and significantly dependent on temperature and loading history. The dilative tendency or pore pressure development in an undrained shearing condition is found to be dependent on both unfrozen water content and mean stress, which is consistent with unfrozen soils. Besides, the experimental results reported in the literature regarding uniaxial tests show that the shear strength does not share the same temperature- and salinity-dependency for different frozen soil types. The rate dependency of frozen soils is characterized between rate dependency of pure ice and that of the unfrozen soil and is therefore highly determined by the content of ice and the viscous behavior of ice (through temperature dependency). This paper also explains the pore pressure response in freezing and thawing is dependent on volumetric evolution of soil skeleton.