Introduction & Research question
Increasingly rising temperatures induce an increased thawing of permafrost in cold regions. Thawing per- mafrost has a range of consequences for the planet, each constituting a research branch of different scientific disciplines. Permafrost research within the field of civil engineering is mostly concerned about the static instability of the ground caused by permafrost thaw, which induces risks of failure to infrastructure con- structions as well as buildings in cold regions.
When investigating when and how much the ground will thaw at a specific location, engineers do geo- thermal modelling based e.g. on finite elements based calculations to predict future ground temperature conditions and thus stability. Geothermal modelling is thus of high importance when designing construction solutions in the Arctic. As it is the case in any type of modelling, its accuracy is determined by the quality of the input data. A range of physical parameters that influence the temperature evolution of the soil should be measured directly from permafrost cores extracted from the area of interest to obtain the best possible accuracy for a specific project. Salinity depresses the freezing point and allows the ground to thaw at temper- atures below zero degrees. This is especially a concern in the relatively warm permafrost, where the ground might thaw earlier than expected. The grain size is another important property to consider, as fine grained soil such as clay and silt have quite large unfrozen water contents, even at temperatures well below freezing point due to the greater meniscus forces. Even though the methods of determining these properties are well established, they are explained in the thesis as part of the process of how the important data is obtained. The aim of this research project was to determine a reliable laboratory method to directly measure the thermal properties of the permafrost soil grains as well the parameters, called a and b, describing the exponential increase in water content in the soil as the temperature in the permafrost increases towards freezing point. These parameters are required to perform site-specific geothermal modelling as they describe the ice-water ratio in the soil. As the heat capacity and thermal conductivity of water changes according to its physical state, the thermal properties of the bulk soil change with its composition, so knowing these material specific parameters are necessary to make an accurate site-specific model. Determining the thermal properties of the bulk soil in permafrost is possible through in-situ measurements, and through measurements with other equipment, such as a Hydra Probe (HP), the moisture content at a specific temperature step can be determ- ined too. However, the HP only measures the moisture content indirectly, as it actually measures i dielectric permittivity, and some degree of human judgement is included when translating from dielectric permittivity to moisture content. Furthermore, by measuring in-situ, it is not possible to do a controlled change in tem- perature, and the moisture content curve can thus not be determined in the field. The method presented in this thesis seeks to calculate the thermal properties of the soil grains - and thus bulk soil - and the a and b parameters from direct measurements in a temperature controlled environment.
Theory
In this project drilled permafrost cores from the area in and around the town of Ilulissat located in the bottom of the Disco Bay in West Greenland, were used. The specific cores investigated in this project were extracted recent years’ field campaigns, but similar cores were extracted from the same area during this year’s field work with my participation. Due to the long transportation time and the project’s time limitations, those exact cores were not used in this project, but the approach and field investigations were similar to those of previous years and thus provided insight to the procedures of field investigations.
As some investigations require intact permafrost cores, and some do not, it is important to carefully con- duct the necessary experiments in the correct order, as the thawing of the soil specimens is an irreversible process. Strictly nondestructive investigations were conducted in a temperature controlled room at -10°C at the permafrost core storage facilities at DTU in Lyngby prior to the controlled thawing of the specimens. Three permafrost cores were chosen based on their ice content and expected salinity and equipped with two different sensors. A Hydra Probe sensor (HP) was inserted from the top of the permafrost core and used to determine the unfrozen water content by measuring the dielectric permittivity. A Specific Heat sensor (SH) was inserted from the bottom and measured the time dependant temperature profile originating from an emitted heat pulse.
The temperature curve resulting from the heat pulses can be described theoretically by the thermal prop- erties of the soil matrix, which is assumed to consist of homogeneous grains of the same material, air, water and ice. As a simplification the permafrost cores were assumed to be cylinders on infinite length in both dir- ections, and change in thermal properties of water and ice with temperature was assumed to be insignificant. This simplified geometry allows the assumption of a one-dimensional heat flow through the side of the cores cylinder. The cores were gradually thawed by step-wise increasing the temperature. Each temperature step was held sufficiently long for the cores to obtain stable initial temperatures before the heat pulses were emit- ted. This gave a set of data points at several frozen and unfrozen temperatures, for which the temperature evolution curve will look differently according to the composition of the soil at each temperature step. As the thermal properties of water, ice and air is already known, the thermal properties of the grains, the only component with unknown properties, can be solved from the empirical relations shown in Equations (1) to (4) in unfrozen as well as frozen state.
Where λ is the thermal conductivity and C is the heat capacity. The indices t and f denote thawed and frozen bulk conditions respectively, while s, w and i denote soil grains, water and ice. n is the porosity, which is the ratio of volume of empty space in the material relative to the volume of the grains. This void volume is what is available for the water, ice or air to occupy.
ANALYSIS AND CONCLUSION
Destructive investigations of the permafrost cores were conducted after the thawing of the specimens had ended. These included determining the salinity and thereby freezing point depression, grain size distribution as well as organic content which is used to classify the soil type, and grain density and thereby porosity.
Along with these parameters, table values on the thermal properties of the other bulk constituents were used to calculate the thermal properties of the grains by soling an inverse problem. Solving an inverse problem means that the effects are measured and used to determine the cause. As the temperature evolution curve can be described theoretically by the composition and the properties of the constituents (shown in Equations (1) to (4)), the thermal properties of the soil grains as well as the parameters determining the exponential function describing the moisture content curve can be found through iteration. By changing the value of the parameters I am solving for in small increments, the theoretical curves should step-wise obtain a better match on the measured temperature evolution curves. When a good fit is obtained, the found properties are the solution to the problem. The found thermal properties were compared to table values on typical geolo- gical minerals from the area in order to assess whether to obtained parameters are within an expected range. The found parameters describing unfrozen water content were compared to those obtained from the indirect measurements of the Hydra Probe.
To validate this approach, a reference experiment was conducted on glass beads of grain sizes corres- ponding to silt and sand, and the values obtained through the inversions were compared to the thermal properties provided by the manufacturer. One experiment was conducted in dry state, and one in fully saturated state. The simplest system thus contained only glass grains and air, and the complexity of this thermodynamic system was then increased as water was introduced. In unfrozen saturated state, only water and grains were present, but as temperatures dropped below freezing point, and water and ice were present simultaneously in the same system, the complexity of the system was further increased. At all levels of complexity, the known thermal properties should be obtained to validate the method, and by increasing the complexity in this structures step-wise manner, any troubles occurring during he process are easier defined and solved.
Analysis and conclusion
With the data obtained from the controlled thawing of the permafrost cores, it was not possible to find realistic values for the thermal properties of the soil grains. The difference between the thermal properties in frozen and unfrozen state was too large, and comparing the values to table values on relevant minerals revealed that the obtained results were out of a realistic range. No obvious source of error was found in the applied theory nor the calculations, which led the suspicion that some disagreement between theory at experimental setup persisted. This was further implied by the glass beads experiments, where it was found that it was not possible to obtain the thermal properties provided by the manufacturer. Especially in dry conditions, the obtained thermal conductivity was far too low. The reason for this discrepancy was further investigated by conducting a sensitivity study where the solution’s sensitivity to a change in input parameter was investigated. This study showed that it was impossible to obtain the table values from the manufacturer with the present data set.
Two sources of errors were identified. One was that the specimen holder base was made of aluminium, which acted a thermal bridge. As it was placed only 1.5 cm from the SH sensor, it disturbed the measure- ments, and the assumption of an infinitely long cylinder did not hold. The very low thermal conductivity in dry state could be explained by the large Biot’s coefficient for spherical glass beads, see Figure 1, which means that the contact area available for heat conduction between the grains was very small, and as the air in the voids acted as an insulator, the thermal conductivity of the grains were underestimated.
To further investigate the sources of error, including the assumption of an infinitely long cylinder, a new experiment was prepared. Secondary experiments on the glass beads’ heat capacity and thermal conductivity were conducted at the laboratory at DTU in order to hint whether the table values from the manufacturer could be trusted or not. The obtained values from these experiments showed lower values on thermal con- ductivity as well as heat capacity. The low value on thermal conductivity might still be explained by Biot’s coefficient of glass beads, and it is thus not trusted, but the value obtained on heat capacity was trusted as the method of determining it is proven and widely trusted, and the result matched literature values better than the value from the manufacturer. This value was thus used for comparison to the inversion results.
To investigate the influence of the base conductivity, a new cylinder base was made of the less conductive POM material and used in a second temperature controlled experiment on glass beads. Parallel to this, an SH sensor was completely embedded in glass beads placed in a bucket, which allowed a much larger distance to the ends of the cylinder which should agree much more with the applied theory. The experiment was run with these two new setups in dry as well as saturated state. From this experiment the thermal conductivity of the dry glass beads was still far too low, but in dry state it matched the values from the manufacturer quite well. The heat capacities obtained from the two setups agreed very well with each other in dry state and in saturated unfrozen state and they even matched the heat capacity measurement conducted at DTU very well. However, in frozen state, only the data obtained from the bucket setup led to a similar heat capacity, but the inversion fit was too poor to conclude anything. The Temperature spikes were consistently higher in the bucket setup than in the POM base setup, which is unexpected as it is the same material. The most likely explanation is a problem with one of the sensors. It might not emit the expected heat impulse. However, had a thermal bridge still persisted, lower thermal properties on the glass beads had been found in the POM setup than in the bucket setups, but as this was not the case, the assumption of an infinitely long cylinder seems to be valid when replacing the aluminium base with a POM base with a lower thermal conductivity.
From this project it has not been proven that the thermal properties can be found from permafrost cores using the presented approach. Even though it seems to be possible to obtain a good inversion fit in dry state as well as in saturated unfrozen state, the inversion curves do not match in frozen state. In the experiment on permafrost cores, this is very likely due to the thermal bridge composed by the aluminium specimen holder base, but in the glass beads experiment, it might be explained by the empirical equations (1) to (4) that only consider the porosity and not the geometry of the grains. The formulas work very well in natural soils with a range of different grain sizes and shapes, but this study indicates that they do not work very well in a system with perfectly spherical glass beads of the same size. It is most clearly seen in the dry glass beads experiment where the obtained thermal conductivities were far too low, but it might also explain the poor fit in frozen state.
Relatively good geothermal models already exist, but they are all limited by the available data. A model will only be as good the the input, and obtaining good measurements and defining a valid experimental and theoretical approach is thus of high importance in order to utilise the full potential of this engineering tool. This study has found that more research is needed to finalise this method and prove its potential.
Discussion
Climate changes entail significant changes to the environment in the Arctic. Adapting to the future is a major challenge, and making the right decisions rely on the information at hand. Using geothermal modelling in cold regions is very important as it provides important information vital for deciding on the optimal design for any construction project in cold regions. In Greenland this is important in the permafrost regions north of the Arctic Circle, especially in the relatively warm southern permafrost areas, where the ground is expected to thaw in the very near future, and where urban expansion plans and infrastructure projects might collide with challenging ground conditions and impending ground settlements caused by permafrost thaw. Without applying geothermal modelling it is not known how long the permafrost will remain stable and when it loses its bearing capacity. This is important e.g. when constructing roads and airports in the permafrost zone, which is the case in Ilulissat, where the construction of the airport is already well on the way, and the con- nection road is planned, as well as in Qeqqata Kommunia where the longest road in Greenland is planned to run from Kangerlussuaq to Sisimiut crossing several thaw susceptible marine sedimentary deposits on the way. Using geothermal modelling will provide extra information on the sub-surface stability and thereby contribute to choosing the optimal construction design. It has the potential to lower the construction costs as excessive blasting can be avoided, and it gives a better estimate of the expected life time and related maintenance costs of the project.
Not only is geothermal modelling relevant for infrastructure projects, it is also relevant in the field of environmental engineering. As permafrost thaws, groundwater will start flowing and change the hydrology of the terrain. In Ilulissat the water supply zone is located in a highly saline marine sedimentary deposit, which poses the threat that salt from the soil might leach into the supply lakes as the permafrost currently concealing the salt thaws. This would make the water unsuitable for use in the town’s fish factory as well as for drinking and thereby not only constitute an obstacle to the town’s expansion plans but also threaten the supply of water to the current population. In short, thawing permafrost is important when planning con- struction projects, but it also endangers industries and communities relying on essential resources provided by the environment, such as safe water supply.
Scientific investigations on permafrost thaw from a civil engineering perspective is thus of high import- ance to the urban development as well as the welfare of the citizens of the regions in Greenland underlain by permafrost North of the Arctic Circle. Infrastructure expansions as the projects mentioned above not only have a positive impact on the industry, they also affect the mutual understanding between the communities and countries, as an increase in trade, tourism and travel often give a better understanding between cultures. These projects with direct relevance for this project compose a great example on cases where the joint effort of the different parts of Rigsfællesskabet can ensure a sustainable development, in this case in permafrost areas in Greenland, for the common good of all three countries.