Discussion of the applicability of the generalized Clausius–Clapeyron equation and the frozen fringe process

Ma, Wei; Zhang, Lianhai; Yang, Chenghu

doi:10.1016/j.earscirev.2015.01.003

Cited by 67 publications

(28 citation statements)

References 47 publications

(66 reference statements)

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“…To determine the freezing temperature of the pore solution and the liquid water content, we calculate the effect of the solutes on the water potential as a function of temperature. Ma et al () give the generalized Clausius‐Clapeyron equation as

((), \frac{1}{ρ_{w}} - \frac{1}{ρ_{i}}) u = L_{f} \frac{T - T_{f}^{0}}{T_{f}^{0}},

where u is pressure (Pa), ρ w and ρ i are the densities of liquid water and ice (kg/m 3 ), L f is the latent heat of fusion for water (J/kg), and T and

T_{f}^{0}

are the temperature and the freezing temperature of free water (K). This assumes the equilibrium case where u = u w = u i , with u w and u i being the gauge pressures of water and ice.…”

Section: Methodsmentioning

confidence: 99%

Submarine Permafrost Map in the Arctic Modeled Using 1‐D Transient Heat Flux (SuPerMAP)

et al. 2019

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Offshore permafrost plays a role in the global climate system, but observations of permafrost thickness, state, and composition are limited to specific regions. The current global permafrost map shows potential offshore permafrost distribution based on bathymetry and global sea level rise. As a first‐order estimate, we employ a heat transfer model to calculate the subsurface temperature field. Our model uses dynamic upper boundary conditions that synthesize Earth System Model air temperature, ice mass distribution and thickness, and global sea level reconstruction and applies globally distributed geothermal heat flux as a lower boundary condition. Sea level reconstruction accounts for differences between marine and terrestrial sedimentation history. Sediment composition and pore water salinity are integrated in the model. Model runs for 450 ka for cross‐shelf transects were used to initialize the model for circumarctic modeling for the past 50 ka. Preindustrial submarine permafrost (i.e., cryotic sediment), modeled at 12.5‐km spatial resolution, lies beneath almost 2.5 ×106km2 of the Arctic shelf. Our simple modeling approach results in estimates of distribution of cryotic sediment that are similar to the current global map and recent seismically delineated permafrost distributions for the Beaufort and Kara seas, suggesting that sea level is a first‐order determinant for submarine permafrost distribution. Ice content and sediment thermal conductivity are also important for determining rates of permafrost thickness change. The model provides a consistent circumarctic approach to map submarine permafrost and to estimate the dynamics of permafrost in the past.

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((), \frac{1}{ρ_{w}} - \frac{1}{ρ_{i}}) u = L_{f} \frac{T - T_{f}^{0}}{T_{f}^{0}},

where u is pressure (Pa), ρ w and ρ i are the densities of liquid water and ice (kg/m 3 ), L f is the latent heat of fusion for water (J/kg), and T and

T_{f}^{0}

are the temperature and the freezing temperature of free water (K). This assumes the equilibrium case where u = u w = u i , with u w and u i being the gauge pressures of water and ice.…”

Section: Methodsmentioning

confidence: 99%

Submarine Permafrost Map in the Arctic Modeled Using 1‐D Transient Heat Flux (SuPerMAP)

et al. 2019

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“…This is the same as the air–water interface in a capillary tube (Miller, 1980). Ma et al (2015b) pointed out that the Clapeyron equation is valid for phase equilibrium state where pressure and temperature remain constant with respect to time. Sufficiently slow freezing or thawing rate is required to ensure an equilibrium condition.…”

Section: Discussionmentioning

confidence: 99%

Comparison of Soil‐Freezing and Soil‐Water Characteristic Curves of Two Canadian Soils

Ren

Vanapalli

2019

Vadose Zone Journal

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Core Ideas The similarity between SFCC and SWCC, and hysteresis of SFCC are reviewed. The SFCC and SWCC of two fine‐grained soils are measured and analyzed. No quantitative similarity is found between the measured SFCC and SWCC. Several concerns regarding the similarity between SFCC and SWCC are discussed. The drying–wetting and freezing–thawing cycles significantly influence the soil pore water in the vadose zone in permafrost and seasonally frozen regions. The soil‐freezing characteristic curve (SFCC) describes the relationship between unfrozen water content and subzero temperature in a soil at frozen condition. Several studies suggest that the SFCC of a frozen saturated soil is similar to soil‐water characteristic curve (SWCC), which describes the relationship between water content and suction for a soil under unfrozen unsaturated condition. In the present study, the similarity between SFCC and SWCC, and possible reasons for the hysteresis of SFCC are succinctly reviewed. The SFCC and SWCC of two Canadian soils were measured and critically interpreted to understand the fundamental behavior of SFCC in comparison with the SWCC. The observed hysteresis of SFCC for the two soils was mainly associated with the supercooling of pore water. The measured SFCC and SWCC of the two soils show quantitative dissimilarity rather than similarity. This may be attributed to the experimental limitations and possible fundamental differences between drying–wetting and freezing–thawing processes. In addition, several concerns regarding the similarity between SFCC and SWCC are discussed. The present study highlights that rigorous investigations are required for better understanding the SFCC to facilitate its use for cold‐region engineering practice applications.

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“…This equation is an attempt to explain the mechanism of frost heave from a physical viewpoint. Ma et al (2015) discussed the applicability of the GCCE and then proposed two models based on GCCE: static model and dynamic model. From the 1970s, because of the oil and gas exploration rush in the Arctic, several largescale and long-term experiments aimed at investigating the effect of frost heave on buried pipelines were performed (Huang et al, 2004;Northwest Alaskan Pipeline Company, I, 1980;Slusarchuk et al, 1978).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional frost heave evaluation based on practical Takashi's equation

Zheng

Kanie

Niu

et al. 2015

Cold Regions Science and Technology

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Discussion of the applicability of the generalized Clausius–Clapeyron equation and the frozen fringe process

Cited by 67 publications

References 47 publications

Submarine Permafrost Map in the Arctic Modeled Using 1‐D Transient Heat Flux (SuPerMAP)

Submarine Permafrost Map in the Arctic Modeled Using 1‐D Transient Heat Flux (SuPerMAP)

Comparison of Soil‐Freezing and Soil‐Water Characteristic Curves of Two Canadian Soils

Three-dimensional frost heave evaluation based on practical Takashi's equation

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