Analytical model to predict unfrozen water content based on the probability of ice formation in soils

Abstract

The variation in unfrozen water content with temperature substantially affects coupled heat and water transport in frozen soil, causing frost heave and thaw settlement owing to the ice and water phase change and influencing soil stability in cold regions. Thus, analyzing the mechanism of water freezing and building a predictive model for the unfrozen water content of soils is paramount. In this study, an analytical model based on equivalent contact angle was developed to predict the unfrozen water content. The relationship between the equivalent contact angle and temperature was obtained based on the assumption that the heterogeneous nucleation rate nonlinearly decreased with temperature. The proposed analytical model was validated using existing unfrozen water content data at various temperatures for a silty clay soil material from the Qinghai–Tibet Plateau, and compared to several existing numerical models which predict unfrozen water content in soil materials. The results revealed a close relationship between the unfrozen water content and equivalent contact angle, and the equivalent contact angle increased as the temperature decreased. Meanwhile, the pore water in the soil first froze when the contact angle was smaller. Moreover, the values predicted by the analytical model for the unfrozen water content agreed well with the experimental results, especially under low‐temperature conditions and during the early stage of water freezing.

Freezing‐Thawing Hysteretic Behavior of Soils

“…The impact of freezing rate and soil volume on the probability of ice formation is much smaller compared to the contact angle (Z. Sun & Scherer, 2010;Wan et al, 2020Wan et al, , 2022, and thus, ΔT sc is primarily determined by the contact angle (θ). Fletcher (1958) and Mullin (2001) suggested that nucleation becomes considerable when J reaches 1 (1/(cm 3 •s)), corresponding to the case of ΔT = ΔT sc ,…”

“…Kulkarni et al (2012) indicated that the contact angle of mineral particles generally falls between 18°and 24°. Wan et al (2022) suggested that the contact angle during nucleation is related to pore size, with sand having larger pores exhibiting a smaller contact angle compared to clay, resulting in higher nucleation efficiency. Based on the above studies, it is recommended to consider contact angle ranges for different soil types as follows: 14°-22°f or sand, 18°-26°for silt, and 20°-28°for clay.…”

“…The impact of freezing rate and soil volume on the probability of ice formation is much smaller compared to the contact angle (Z. Sun & Scherer, 2010; Wan et al., 2020, 2022), and thus, Δ T sc is primarily determined by the contact angle ( θ ). Fletcher (1958) and Mullin (2001) suggested that nucleation becomes considerable when J reaches 1 (1/(cm 3 ·s)), corresponding to the case of Δ T = Δ T sc , $$${\Delta }{T}_{\text{sc}}=\frac{{N}_{A}{{\Omega }}_{s}}{{L}_{\text{wi}}}{\left[\frac{16\pi T{{\sigma }_{\mathit{il}}}^{3}}{3k\,\mathrm{ln}(K)}\right]}^{1/2}f{(\theta )}^{1/2}$$$ …”

Mechanism of Unfrozen Water Content Evolution during Melting of Cryogenic Frozen Coal Body Based on 2D NMR

“…Based on the above reasons, the study of the water content and ice-water conversion process of lowtemperature frozen coal pores during the melting process of the coal body is crucial for the development and optimization of low-temperature anhydrous permeability enhancement technology for coal seams. This is of great significance for realizing efficient CBM extraction and safe coal mining [20,21].…”