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Advantages, disadvantages and comments on considered empirical models (Różański, 2018)_
Empirical models | |||
---|---|---|---|
Model | Advantages | Disadvantages | Comments |
Kersten (1949) | Simple formula; for every type of soil | Equations do not take into account the quartz content which has the largest contribution in overall value of λ | Thermal conductivity in dry state cannot be determined |
Johansen (1975) | Can be used for frozen soils; relatively high quality of prediction; for every type of soil | Possible inaccuracy for dry soil (±20%) | Empirical relations valid for Sr>0.05 (coarse-grained soil) and Sr>0.01 (fine-grained soil) |
Donazzi et al. (1979) | Simple formula; for every type of soil | Weak prediction for soils with low water content | The shape of the λ − Sr curve does not fully comply with the test results and with most other models presented in literature |
Côté and Konrad (2005b) | For every type of soil; includes the type of soil and the shape of grains | The course of the Ke − Sr curve is not entirely consistent with common knowledge for fine-grained soils with low water content | Modification of the Johansen method (1975) with respect to the Kersten number and dry soil conductivity |
Lu et al. (2007) | For every type of soil; very good reflection of thermal conductivity for fine-grained soils with very low water content; the type of soil is taken into account | Unknown influence of the type of soil on the conductivity in the dry state | Modification of the Johansen method with respect to the Kersten number and dry soil conductivity |
Chen (2008) | Simple formula; good quality of prediction | Limited applicability | Only for sands with a high quartz content |
Lu et al. (2014) | Simple formula; for every type of soil; includes the effect of the dry density on thermal conductivity | For the analysed soils, the model clearly overestimated the values of λ in the entire range of water content | Dry soil conductivity should be computed using empirical relation proposed in Lu et al. (2007); possible weaker prediction for soils with high content of sand separate |
He at al. (2017) | Simple formula; for every type of soil; good quality of prediction | Lack of correlation formulas for determining model parameters | Modification of the Johansen method with respect to the Kersten number |
Different approaches used for evaluation of the Kersten number Ke and the conductivity of dry and saturated soil_
Model | Kersten number | Thermal conductivity of | |
---|---|---|---|
dry soil | saturated soil | ||
Johansen (1975) | Coarse-grained soil:Ke ≅ 0.7 log Sr + 1.0 | ||
Côté and Konrad (2005a; 2005b) | λdry = χ10−ηn | - | |
Lu et al. (2007) | λdry = 0.51 − 0.56n | - | |
He at al. (2017) | - | - |
Advantages, disadvantages and comments on the considered theoretical models (Różański, 2018)_
Theoretical models | |||
---|---|---|---|
Model | Advantages | Disadvantages | Comments |
Wiener (1912) | Determination of the range of possible thermal conductivity values of porous media (soils); simple formula | Rough estimate | For coarse soils, due to the contrast between the thermal conductivity of the components, these bounds are very wide |
Mickley (1951) | For every type of soil | Weak prediction for dry soils or with low water content | Should not be applied to the soils with relatively high porosity |
Gemant (1952) | For every type of soil | Complicated formula; need to use nomograms | Not applicable to dry soils; possible overestimation of thermal conductivity results if Gemant formula is not used to determine the thermal conductivity of the soil skeleton λs |
de Vries (1963) | For every type of soil; can be used for partially or fully frozen soils | Need to assume values of shape factors ga; weak prediction for dry soils; weak reflection of real λ − Sr characteristic | For good predictions, one should incorporate in Eq. (22) heterogeneity of solid phase and at least five minerals should be taken into account (Tarnawski & Wagner, 1992, 1993); do not use if the volume fraction of water is less than 0.03 (coarse-grained soil) or 0.05–0.10 (fine-grained soil) |
Gori (1983) | For every type of soil; can be used for different temperatures | Very complex formula; Certain parameters should be determined on the basis of laboratory tests’ results | Possible underestimation of thermal conductivity for dry soils |
Tong et al. (2009) | Includes the impact of many factors on the thermal conductivity of the porous media | Complex formula; a series of laboratory tests have to be performed | Lack of formulas from which model parameters can be computed |
Haigh (2012) | High accuracy of prediction | Complex formula; Underestimation of results by a constant factor, about 1.58 | Only for sandy soils with a porosity higher than 0.333 |