A simplified numerical solution of the Miller model of secondary frost heave

Fowler, A. C.; Noon, C. G.

doi:10.1016/0165-232x(93)90010-6

Cited by 18 publications

(17 citation statements)

References 6 publications

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“…Moreover, he demonstrated that a permeation boundary layer existed below the lowest ice lens across which the entire pressure drop in the water phase essentially occurs. Fowler and Noon [1993] have shown that the solution to this simplified model, which can be solved analytically, gives results in excellent agreement with a numerical solution to the full Miller model. Krantz and Adams [1996] proved that this simplified model agrees well with one‐dimensional frost heave measurements in laboratory core experiments.…”

Section: Methodsmentioning

confidence: 55%

Differential frost heave model for patterned ground formation: Corroboration with observations along a North American arctic transect

Peterson¹,

Krantz²

2008

J. Geophys. Res.

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[1] Frost boils in the Arctic are a manifestation of patterned ground in the form of nonsorted circles. Active frost boils involve convection of water through the soil that can bring basic salts from depth to the surface. As such, active frost boils can mitigate acidification and thereby strongly influence the type of vegetation supported by Arctic soils. The presence or absence of active frost boils is thought to play a pivotal role in establishing the sharp demarcation between moist nonacidic tundra (MNT) and moist acidic tundra (MAT) in the Arctic. The focus of this paper is to corroborate the predictions of a mathematical model that relates observable patterned ground features to ecosystem parameters with observations at the field sites along the North American Arctic Transect (NAAT) established by the Biocomplexity of Patterned-Ground Ecosystems Project. Model predictions indicate that recurrent one-dimensional frost heave can become unstable and evolve into multidimensional differential frost heave (DFH). A laboratory frost heave simulation produced a 28-cm pattern in an active layer of 10 cm, which agrees with linear stability theory predictions. A finite element solution predicts threedimensional patterns with approximately 3-m spacing develop in a 1.0-m active layer with a surface n factor of 0.35, which agrees well with field observations from the NAAT. The lack of significant frost boil activity in the MAT is a result of suppression of DFH owing to denser surface vegetation characterized by low n factors. Prominent active frost boils are observed in the MNT at higher latitudes with more sparse vegetation characterized by higher n factors that promote DFH. However, at the northernmost field sites frost boils cannot be generated even though the n factors are relatively high owing to very rapid freezing conditions that mitigate DFH.

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Section: Methodsmentioning

confidence: 55%

Differential frost heave model for patterned ground formation: Corroboration with observations along a North American arctic transect

Peterson¹,

Krantz²

2008

J. Geophys. Res.

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“…Except under asymptotic conditions, these models must be solved numerically. One-dimensional, numerical solutions to the model by Miller (1977Miller ( ,1978 have been presented by O' Neill andMiller (1982, 1985), Black and Miller (1985), Fowler and Noon (1993), Black (1995) and Krantz and Adams (1996). In several instances, numerical results agree favorably with laboratory results such as those of Konrad (1989).…”

Section: Prior Studiesmentioning

confidence: 72%

A mechanism for differential frost heave and its implications for patterned-ground formation

Peterson¹,

Krantz

2003

J. Glaciol.

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The genesis of some types of patterned ground, including hummocks, frost boils and sorted stone circles, has been attributed to differential frost heave (DFH). However, a theoretical model that adequately describes DFH has yet to be developed and validated. In this paper, we present a mathematical model for the initiation of DFH, and discuss how variations in physical (i.e. soil/vegetation properties) and environmental (i.e. ground/air temperatures) properties affect its occurrence and length scale. Using the Fowler and Krantz multidimensional frost-heave equations, a linear stability analysis anda quasi-steady-state real-time analysis are performed. Results indicate that the following conditions positively affect the spontaneous initiation of DFH: silty soil, small Young’s modulus, small non-uniform surface heat transfer or cold uniform surface temperatures, and small freezing depths. The initiating mechanism for DFH is multidimensional heat transfer within the freezing soil. Numerical integration of the linear growth rates indicates that expression of surface patterns can become evident on the 10–100 year time-scale.

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“…When appropriately tuned for particular soil types, such models can reproduce the major features observed during heave. The predictive capabilities of this approach have been greatly extended by the development of asymptotic methods to aid in the solution of the model equations ͑Fowler, 1989; Fowler and Noon, 1993;Fowler and Krantz, 1994͒. It is only recently, however, that a more fundamental understanding of the factors that determine how the overburden is supported has emerged.…”

Section: Frost Heavementioning

confidence: 99%

The physics of premelted ice and its geophysical consequences

2006

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The surface of ice exhibits the swath of phase-transition phenomena common to all materials and as such it acts as an ideal test bed of both theory and experiment. It is readily available, transparent, optically birefringent, and probing it in the laboratory does not require cryogenics or ultrahigh vacuum apparatus. Systematic study reveals the range of critical phenomena, equilibrium and nonequilibrium phase-transitions, and, most relevant to this review, premelting, that are traditionally studied in more simply bound solids. While this makes investigation of ice as a material appealing from the perspective of the physicist, its ubiquity and importance in the natural environment also make ice compelling to a broad range of disciplines in the Earth and planetary sciences. In this review we describe the physics of the premelting of ice and its relationship with the behavior of other materials more familiar to the condensed-matter community. A number of the many tendrils of the basic phenomena as they play out on land, in the oceans, and throughout the atmosphere and biosphere are developed.

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A simplified numerical solution of the Miller model of secondary frost heave

Cited by 18 publications

References 6 publications

Differential frost heave model for patterned ground formation: Corroboration with observations along a North American arctic transect

Differential frost heave model for patterned ground formation: Corroboration with observations along a North American arctic transect

A mechanism for differential frost heave and its implications for patterned-ground formation

The physics of premelted ice and its geophysical consequences

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