Permafrost – earth materials (soil or rock and included moisture, gases and organic material) that remain at or below 0 °C for at least two consecutive years – plays an important role in the global carbon cycle, natural hazards, and infrastructure performance . The thickness of the active layer overlying permafrost, which thaws and freezes seasonally, is most affected by air temperatures and precipitation . As the global climate changes, associated increases in air temperature and changing precipitation characteristics are likely to induce increased thickness and temperature variability in the active layer. This has substantial implications in terms of infrastructure performance and ground stability , as well as global carbon release , forced migration , and release of potential pathogens during thawing .

Thus, understanding how air temperature and precipitation changes influence both the rate and depth at which permafrost may thaw is important for estimating climate change impacts. The active layer typically ranges from a few centimeters to several meters, but can be more than 10 m thick , which complicates physical modeling of this phenomenon since laboratory tests only provide element-level measurements of the freezing, thawing, and refreezing processes and it often is not possible to create experiments at field scale. Many field studies have investigated warming-induced impacts on permafrost (for example, ) with tested depths ranging from 5 cm up to 2 m, and planform dimensions up to several meters. Recent work by included field experiments at the decameter scale where an approximately 11×13×1.5 m soil volume was tested over a period of 63 d. These field tests demonstrate both the potential for further field testing over larger areas and depths to investigate the impacts of future climate scenarios on permafrost regions and civil infrastructure while also highlighting the challenges in conducting field-scale experimentation, especially at greater depths.

Understanding how temperature fluctuations propagate through the soil column, and how these changes impact various aspects of permafrost response would benefit from methods that are able to link field-scale observations to element-level laboratory tests. Here, hypergravity testing in a geotechnical centrifuge is a promising approach that enables testing of a permafrost layer at prototype scale that captures the full thickness of the active layer – testing can be designed such that the centrifuge model scales to an equivalent prototype that describes the scale of interest in the field. While hypergravity testing has found broad applications within geotechnical engineering , it has also previously been applied to permafrost applications. For example, tests have explored soft sediment deformation during thawing , solufluction during freeze-thaw cycling , ice wedge casting , and periglacial slope stability as a function of soil properties . More recent tests have investigated contaminant transport as a function of permafrost degradation , thawing in saturated clay around subway tunnels , and steel piles in frozen and thawing soils . These tests leverage scaling characteristics based on an enhanced gravity field in the centrifuge such that small-scale models can be used to replicate the conditions at field scale. However, when conducting this class of testing, it is important to ensure that boundary conditions do not affect the process of interest in such a way that laboratory conditions do not replicate the prototype configuration of interest. In the case of permafrost testing in the centrifuge, careful consideration must be given to temperature and heat flux boundary conditions, both in terms of what might be representative conditions for the process at hand, and how the experimental configuration may introduce undesirable heat fluxes into the system that cause deviation from the desired model configuration. As such, it is important to measure temperature in the experiments in such a way that the boundary conditions can be verified and confirmed to provide the necessary temperature and heat flux boundary conditions.

To this end, we are developing the capability to investigate permafrost freeze-thaw in a hypergravity environment with a specific focus on insulation requirements to maintain appropriate boundary conditions that maintain a top-down thawing profile where heat exchange only occurs through the top surface of the soil. This will enable system-level experiments that can tie model predictions of permafrost behavior to field-scale observations of permafrost temperature cycling due to temperature fluctuations at the soil surface. Here, we present preliminary results showing requirements and developed techniques in terms of sample preparation, insulation, and feasible experiment run times for maintaining desired boundary conditions in a 1-m radius geotechnical centrifuge. Our experiments focus on how heat flux, sample preparation, and insulation affect thawing rates and spatial evolution of temperatures of frozen soil.

We include a brief discussion on scaling in a hypergravity setting to illustrate how soil stress and heat diffusion scale in an enhanced gravity field, or g-field. Further details and many examples of different applications can be found in the literature. The basic premise used here is that we test a 1/N scale model of a prototype in a g-field enhanced by the same factor, N, to maintain identical scaling of stresses, as shown below. The factor N is referenced to the earth's gravitational field, such that the scaled model in the centrifuge will experience a gravitational force N times normal gravity. In the following discussion, scale factors for a quantity will be denoted by the symbol for the quantity with an asterisk. For example, if L is the symbol for length, then the ratio of the length in the model to the length in the prototype would be denoted as L*.

When investigating stress-dependent behavior of soil in hypergravity models, it is necessary to ensure that the stresses in the model scale identically to the prototype case to ensure the stress-strain response observed in the scaled model is representative of the desired prototype. Thus, the scaling factor for the stress should be one, or σ*=1. Identical materials are used in the model and prototype so that identical mechanical properties are maintained . In doing so, the scaling factor for density will be ρ*=1. The required scaling factor for gravity can then be calculated as: 1σm=ρmgmhm2σp=ρpgphp3σ*=σmσp=ρ*g*h* The subscripts m and p represent the model and prototype respectively, and h is the depth at which the stress is being calculated. Rearranging and noting that h scales the same as any other length, the scaling factor for gravity is established as: 4g*=σ*ρ*L*5g*=1L* Thus, for a model where lengths have been reduced by a factor N, the gravitational acceleration must be increased by the same factor, g*=N, to achieve the desired scaling of stresses. When considering heat diffusion through the soil, conductive heat transfer is described by the heat equation: 6∂u∂t=α∇2u where u is the temperature and α represents the thermal conductivity of the medium through which heat is diffusing. Temperature will not depend on gravitational acceleration and we assume that the thermal conductivity of the soil does not change based on g-level since it is a material property. Thus, based on the scaling factors necessary for maintaining identical scaling of stresses, the time rate of scaling of conductive heat transfer will scale to be t*=1/N2 since the length scaling factor is squared in the Laplacian on the right-hand side of Eq. (). In other words, heat transfer will occur N2 times faster in the model than in the prototype. This scaling has been experimentally verified by . When considering phase change as described by the Stefan Condition through energy conservation across the interface, we consider the following differential equation: 7ρL∂x∂t=-kL∂u∂x+kS∂u∂x where the density (ρ), latent heat (L), and thermal conductivities of the liquid and solid (kL and kS, respectively) are material properties and thus do not depend on gravity. There is no gravitational term in this equation and thus the enhanced gravity in the centrifuge will not impact thawing/freezing. However, length quantities in the model are scaled down by a factor of N. Considering the left side of the equation, it will have a 1/N factor while the right side of the equation will have a N factor. Solving for time, we find that time rate of scaling for phase change will scale to be t*=1/N2. Thus, heat conduction and phase change will have the same time rate scaling.

Tests were performed at the UC Davis Center for Geotechnical Modeling using the 1-m radius beam centrifuge. For this set of experiments, cohesionless sandy soils were prepared at two different relative densities to assess the influence of void space on the rate at which thawing occurs in the samples. Furthermore, we tested specimens both in an insulated and uninsulated container to evaluate insulation requirements to create a one-dimensional thawing front and temperature profile throughout the majority of the centrifuge container. The model soil depth was 20 cm and tests were conducted at 25 times the earth's gravitational acceleration, or 25g. Thus, in prototype scale the soil depth scales to 5 m. The general configuration for the experiments is shown in Fig.  and, below, we provide details on different aspects of the experimental setup and measurements taken.

Here, we present key results and a summary of observations; however, all data is available in the published data set .

Hypergravity testing in a geotechnical centrifuge provides a means by which to conduct system-level experiments that tie element level phenomena to field scale observations. To investigate the application of this approach in modeling the active layer in permafrost regions, we developed and tested capabilities for conducting hypergravity testing on thawing rates of frozen soil in a 1 m radius geotechnical centrifuge. Specifically, we show that a one-dimensional thawing profile that approximates how soil thaws during higher air temperatures at the soil surface can be achieved without active cooling by adequately insulating the sides and bottom of the centrifuge container. When insulating the container, careful consideration must be given to potential heat entry points, as heat flows readily through the aluminum container and can lead to undesirable thawing patterns. This was illustrated through comparison of the measured temperature time histories with predicted temperature time histories based on the analytical solution to the Stefan Condition. The entry of undesirable heat through small exposures of more conductive material allow heat to be quickly transferred to the other portions of the sample, which can lead to deviations from the one-dimensional thawing profile.

Further, we conducted experiments with two different soil sample preparations – one relatively dense and one relatively loose sample – that show the influence of soil fabric on the rate at which it thaws. For the two specimens prepared with the same silica sand, the influence of the soil density and associated void space was shown to influence the rate at which heat can flow through the sample. Thus, it should be expected that heat flux will be highly dependent on soil fabric and type, both of which will vary spatially in the field. Our results here consider only a very limited set and further research is necessary to establish how heterogeneity influences spatial variability in soil thawing rates. An important consideration for this aspect would be to consider the influence that sample freezing may have on the desired soil fabric. In this work, we ensured that the prepared fabric was minimally disturbed by freezing the sample from the bottom up. Since the sandy material is free-draining, this allowed water to migrate to the top of the sample as ice formed below it without substantial expansion within the soil pore space.

The capabilities and procedures discussed here illustrate the basic requirements to maintain temperature boundary conditions for conducting hypergravity testing of frozen soil, and the spatial and temporal scales that may be considered using this approach. Considering these preliminary results, there are opportunities for substantial expansion on how this approach can be applied. In our work, we did not implement an active cooling system and thawing rates could not be controlled by maintaining a specific temperature at the top soil boundary. However, current research is focused on creating testing capabilities that provide active cooling such that temperature conditions of the centrifuge container and soil samples can be directly controlled, enabling testing of thawing and freezing cycles.