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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.

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The Skempton pore pressure coefficient, B, is defined as the variation in pore pressure with the unit change in confining pressure under undrained conditions. The B-parameter is an essential parameter to consider the coupled effects of solid-fluid compressibility and skeleton compressibility in the porous system. It is a key factor in exploring a possible definition of effective stress in frozen soil. However, limited experimental and theoretical research is available in the literature to give insight to the problem. Therefore a series of B tests on frozen clay was conducted in this study. Results from these tests along with tests on Ottawa sand, available in the literature, are analyzed considering the effect of the ice crystallization mode on the skeleton stiffness. The measured B values were lower than expected compared with B-value using models which consider single grain bulk stiffness. However, when the difference in bulk stiffness of ice and of soil grains is considered, even an increase in pore volume, for an increase in fluid pressure, at constant Terzaghi effective stress is possible. The “pore stiffness”, different from the solid phase stiffness, can take a negative value and can be used to explain the low measured B values.

The previous laboratory study of joint electrical resistivity and acoustic velocity measurements is reviewed for both consolidated and unconsolidated permafrost in this paper. The relation of logarithm of resistivity log(R) and P-wave velocity Vp is a concave function. An increase of temperature, fine content and salinity results in a decrease of both acoustic velocity and electrical resistivity. Electrical resistivity is sensitive to salinity, while acoustic velocity changes substantially near thawing temperature.The joint measurement results could be used to estimate unfrozen water saturation (UWS) based on Archie's law, weighted equation (WE) or Kuster-Toksoz equations (KT). However, the estimated UWS from different methods is not always consistent. The difference can be up to 20%. It might be due to the fact that UWS is not the only parameter influencing the electrical and acoustic properties. In order to obtain consistent UWS, a joint model that combines the electrical effective medium theory (EMT) and the acoustic selfconsistent approximation (SCA) is proposed. In this method, UWS and aspect ratio which describes particles shape are found simultaneously from the joint SCA-EMT model. Most of the results from the proposed method are between that of Archie's law and WE method, which indicates that the electrical method might overestimate UWS and acoustic method might underestimate it.