Towards an improved prediction of soil-freezing characteristic curve based on extreme gradient boosting model

Abstract

As an essential property of frozen soils, change of unfrozen water content (UWC) with temperature, namely soil-freezing characteristic curve (SFCC), plays significant roles in numerous physical, hydraulic and mechanical processes in cold regions, including the heat and water transfer within soils and at the land–atmosphere interface, frost heave and thaw settlement, as well as the simulation of coupled thermo-hydro-mechanical interactions. Although various models have been proposed to estimate SFCC, their applicability remains limited due to their derivation from specific soil types, soil treatments, and test devices. Accordingly, this study proposes a novel data-driven model to predict the SFCC using an extreme Gradient Boosting (XGBoost) model. A systematic database for SFCC of frozen soils compiled from extensive experimental investigations via various testing methods was utilized to train the XGBoost model. The predicted soil freezing characteristic curves (SFCC, UWC as a function of temperature) from the well-trained XGBoost model were compared with original experimental data and three conventional models. The results demonstrate the superior performance of the proposed XGBoost model over the traditional models in predicting SFCC. This study provides valuable insights for future investigations regarding the SFCC of frozen soils.

Keywords

Soil freezing characteristic curve (SFCC) / Soil temperature / Unfrozen water content / XGBoost model / Machine Learning / Feature importance

CRediT authorship contribution statement

Kai-Qi Li: Formal analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing – original draft, Writing – review & editing, Conceptualization. Hai-Long He: Conceptualization, Funding acquisition, Project administration, Visualization, Writing – original draft, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was financially supported by the National Natural Science Foundation of China (Grant No. 42177291) and Innovation Capability Support Program of Shaanxi Province (2023-JC-JQ-25 and 2021KJXX-11).

References

Akagawa, S., Iwahana, G., Watanabe, K., Chuvilin, E.M., Istomin, V.A., 2012. Improvement of pulse NMR technology for determination of unfrozen water content in frozen soils. In: Proceedings of the Tenth International Conference on Permafrost, Salekhard, Russia.

H. Anbergen, W. Rühaak, J. Frank, I. Sass. Numerical simulation of a freeze–thaw testing procedure for borehole heat exchanger grouts. Can. Geotech. J., 52 (8) (2015), pp. 1087-1100

D.M. Anderson, A.R. Tice. Predicting unfrozen water contents in frozen soils from surface area measurements. Highw. Res. Rec., 393 (2) (1972), pp. 12-18

R. Bai, Y. Lai, M. Zhang, F. Yu. Theory and application of a novel soil freezing characteristic curve. Appl. Therm. Eng., 129 (2018), pp. 1106-1114

K.J. Bergen, P.A. Johnson, M.V. de Hoop, G.C. Beroza. Machine learning for data-driven discovery in solid Earth geoscience. Science, 363 (6433) (2019), Article eaau0323

J. Bi, G. Wang, Z. Wu, H. Wen, Y. Zhang, G. Lin, T. Sun. Investigation on unfrozen water content models of freezing soils. Front. Earth Sci., 10 (2023), Article 1039330

M. Bittelli, M. Flury, G.S. Campbell. A thermodielectric analyzer to measure the freezing and moisture characteristic of porous media. Water Resour. Res., 39 (2) (2003), Article 1041

P.B. Black, A.R. Tice. Comparison of soil freezing curve and soil water curve data for Windsor sandy loam. Water Resour. Res., 25 (10) (1989), pp. 2205-2210

G.J. Bouyoucos. A new classification of soil moisture. Soil Sci., 11 (1) (1921), pp. 33-48

Buehrer, T.F., Rose, M.S., 1943. Studies in soil structure V. Bound water in normal and puddled soils. College of Agriculture, University of Arizona (Tucson, AZ).

J.W. Cahn, J.G. Dash, H. Fu. Theory of ice premelting in monosized powders. J. Cryst. Growth, 123 (1–2) (1992), pp. 101-108

D.F. Cao, H.H. Zhu, B. Wu, J.C. Wang, S.K. Shukla. Investigating temperature and moisture profiles of seasonally frozen soil under different land covers using actively heated fiber Bragg grating sensors. Eng. Geol., 290 (2021), Article 106197

M. Chai, J. Zhang, H. Zhang, Y. Mu, G. Sun, Z. Yin. A method for calculating unfrozen water content of silty clay with consideration of freezing point. Appl. Clay Sci., 161 (2018), pp. 474-481

Chen, T., Guestrin, C., 2016. XGBoost: A scalable tree boosting system. In: Proceedings of the 22nd acm sigkdd international conference on knowledge discovery and data mining, pp. 785-794.

M. Christ, J.B. Park. Ultrasonic technique as tool for determining physical and mechanical properties of frozen soils. Cold Reg. Sci. Technol., 58 (3) (2009), pp. 136-142

M. Dall'Amico, S. Endrizzi, S. Gruber, R.J.T.C. Rigon. A robust and energy-conserving model of freezing variably-saturated soil. Cryosphere, 5 (2) (2011), pp. 469-484

J.G. Dash, H. Fu, J.S. Wettlaufer. The premelting of ice and its environmental consequences. Rep. Prog. Phys., 58 (1) (1995), p. 115

É.G. Devoie, S. Gruber, J.M. McKenzie. A repository of measured soil freezing characteristic curves: 1921 to 2021. Earth Syst. Sci. Data, 14 (7) (2022), pp. 3365-3377

S.N. Feng, J.R. Chen, S.B. Jones, G. Flerchinger, M. Dyck, V. Filipovic, Y. Hu, B. Si, J. Lv, Q. Wu, Hai. He. Miscellaneous methods for determination of unfrozen water content in frozen soils. J. Hydrol., 31 (2024), p. 130802

D.C. Feng, W.J. Wang, S. Mangalathu, E. Taciroglu. Interpretable XGBoost-SHAP machine-learning model for shear strength prediction of squat RC walls. J. Struct. Eng., 147 (11) (2021), p. 04021173

Z.T. Fu, Q.B. Wu, D. Miles, H.L. He. A new model to describe soil freezing and thawing characteristic curve. J. Glaciol. Geocryol., 43 (2021), pp. 437-452

X. Gu, L. Wang, Q. Ou, W. Zhang. Efficient stochastic analysis of unsaturated slopes subjected to various rainfall intensities and patterns. Geosci. Front., 14 (1) (2023), Article 101490

H. He, M. Dyck. Application of multiphase dielectric mixing models for understanding the effective dielectric permittivity of frozen soils. Vadose Zone J., 12 (1) (2013)

H. He, M. Dyck, J. Wang, J. Lv. Evaluation of TDR for quantifying heat-pulse-method-induced ice melting in frozen soils. Soil Sci. Soc. Am. J., 79 (5) (2015), pp. 1275-1288

Y. He, Y. Xu, Y. Lv, et al.. Characterization of unfrozen water in highly organic turfy soil during freeze–thaw by nuclear magnetic resonance. Eng. Geol., 312 (2023), Article 106937

G.B. Heuvelink, M.E. Angelini, L. Poggio, et al.. Machine learning in space and time for modelling soil organic carbon change. Eur. J. Soil Sci., 72 (4) (2021), pp. 1607-1623

G. Hu, L. Zhao, X. Zhu, et al.. Review of algorithms and parameterizations to determine unfrozen water content in frozen soil. Geoderma, 368 (2020), Article 114277

Y.W. Jame, D.I. Norum. . Phase composition of a partially frozen soil. Res. Paper II. Division of Hydrology, College of Engineering University of Saskatchewan, Saskatoon, Canada (1972)

L. Kong, Y. Wang, W. Sun, J. Qi. Influence of plasticity on unfrozen water content of frozen soils as determined by nuclear magnetic resonance. Cold Reg. Sci. Technol., 172 (2020), Article 102993

R.W.R. Koopmans, R.D. Miller. Soil freezing and soil water characteristic curves. Soil Sci. Soc. Am. J., 30 (6) (1966), pp. 680-685

T. Kozlowski. Soil freezing point as obtained on melting. Cold Reg. Sci. Technol., 38 (2–3) (2004), pp. 93-101

T. Kozlowski. A semi-empirical model for phase composition of water in clay–water systems. Cold Reg. Sci. Technol., 49 (3) (2007), pp. 226-236

T. Kozlowski, E. Nartowska. Unfrozen water content in representative bentonites of different origin subjected to cyclic freezing and thawing. Vadose Zone J., 12 (1) (2013), Article vzj2012-0057

B.L. Kurylyk, K. Watanabe. The mathematical representation of freezing and thawing processes in variably-saturated, non-deformable soils. Adv. Water Resour., 60 (2013), pp. 160-177

X. Li, X. Li. A soil freezing-thawing model based on thermodynamics. Cold Reg. Sci. Technol., 211 (2023), Article 103867

KQ. Li, ZY. Yin. State of the Art of Coupled Thermo -hydro-Mechanical -Chemical Modelling for Frozen Soils. Archives of Computational Methods in Engineering (2024),

Y. Liu, K.Q. Li, D.Q. Li, X.S. Tang, S.X. Gu. Coupled thermal–hydraulic modeling of artificial ground freezing with uncertainties in pipe inclination and thermal conductivity. Acta Geotech., 17 (2022), pp. 257-274

Z. Liu, X. Yu. Physically based equation for phase composition curve of frozen soils. Transp. Res. Rec., 2349 (1) (2013), pp. 93-99

N. Lu, W.J. Likos, S. Luo, H. Oh. Is the conventional pore water pressure concept adequate for fine-grained soils in geotechnical and geoenvironmental engineering?. J. Geotech. Geoenviron. Eng., 147 (10) (2021), Article 02521001

S. Luo, S. Lü, Y. Zhang. Development and validation of the frozen soil parameterization scheme in Common Land Model. Cold Reg. Sci. Technol., 55 (1) (2009), pp. 130-140

J.M. McKenzie, C.I. Voss, D.I. Siegel. Groundwater flow with energy transport and water–ice phase change: numerical simulations, benchmarks, and application to freezing in peat bogs. Adv. Water Resour., 30 (4) (2007), pp. 966-983

R.L. Michalowski. A constitutive model of saturated soils for frost heave simulations. Cold Reg. Sci. Technol., 22 (1) (1993), pp. 47-63

Q.Y. Mu. Hydro-mechanical behaviour of loess at elevated and subzero temperatures. The Hong Kong University of Science and Technology (HKUST), Hong Kong, China (2017)

Y. Nakano, A. Tice, J. Oliphant, T. Jenkins. Transport of water in frozen soil: I: Experimental determination of soil-water diffusivity under isothermal conditions. Adv. Water Resour., 5 (4) (1982), pp. 221-226

Z.A. Nersesova, N.A. Tsytovich. Unfrozen water in frozen soils. In Permafrost: Proceedings of 1st International Conference (1963), pp. 11-15

D.J. Nicolsky, V.E. Romanovsky, S.K. Panda, S.S. Marchenko, R.R. Muskett. Applicability of the ecosystem type approach to model permafrost dynamics across the Alaska North Slope. J. Geophys. Res. Earth, 122 (1) (2017), pp. 50-75

S. Nishimura, A. Gens, S. Olivella, R.J. Jardine. THM-coupled finite element analysis of frozen soil: formulation and application. Géotechnique, 59 (3) (2009), pp. 159-171

G.Y. Niu, Z.L. Yang. Effects of frozen soil on snowmelt runoff and soil water storage at a continental scale. J. Hydrometeorol., 7 (5) (2006), pp. 937-952

Oliphant, J.L., Tice, A.R., Nakano, Y., 1983. Water migration due to a temperature gradient in frozen soil. Proc. 4th Int. Conf. on Permafrost, Fairbanks, Alaska., vol. 1. National Academy Press, Washington, D.C, 95-956.

T.E. Osterkamp, V.E. Romanovsky. Freezing of the active layer on the coastal plain of the Alaskan Arctic. Permafr. Periglac. Process., 8 (1) (1997), pp. 23-44

D.E. Patterson, M.W. Smith. The measurement of unfrozen water content by time domain reflectometry: Results from laboratory tests. Can. Geotech. J., 18 (1) (1981), pp. 131-144

W. Peng, Y. Lu, M. Wang, T. Ren, R. Horton. Determining water content and bulk density: The heat-pulse method outperforms the thermo-tdr method in high-salinity soils. Geoderma, 407 (2022), Article 115564

Qin, Y., Li, G., Qu, G., 2009. A formula for the unfrozen water content and temperature of frozen soils. In Cold Regions Engineering 2009: Cold Regions Impacts on Research, Design, and Construction, pp. 155–161.

J. Ren, S.K. Vanapalli. Comparison of soil-freezing and soil-water characteristic curves of two Canadian soils. Vadose Zone J., 18 (1–14) (2019), Article 180185

J. Ren, S.K. Vanapalli, Z. Han. Soil freezing process and different expressions for the soil-freezing characteristic curve. Sciences in Cold and Arid Regions, 9 (3) (2018), pp. 221-228

R. Pusch. Unfrozen water as a function of clay microstructure. Engineering Geology, 13 (1–4) (1979), pp. 157-162

J. Ren, X. Fan, X. Yu, S. Vanapalli, S. Zhang. Use of an artificial neural network model for estimation of unfrozen water content in frozen soils. Can. Geotech. J., 60 (8) (2023), pp. 1234-1248

D.W. Riseborough. Exploring the parameters of a simple model of the permafrost-climate relationship. Carleton University (2004)

A. Robert. Dielectric permittivity of concrete between 50 MHz and 1 GHz and GPR measurements for building materials evaluation. J. Appl. Geophys., 40 (1–3) (1998), pp. 89-94

A. Shastri, M. Sánchez, X. Gai, M.Y. Lee, T. Dewers. Mechanical behavior of frozen soils: Experimental investigation and numerical modeling. Comput. Geotech., 138 (2021), Article 104361

A.Y. Sheshukov, J.L. Nieber. One-dimensional freezing of nonheaving unsaturated soils: Model formulation and similarity solution. Water Resour. Res., 47 (11) (2011), p. W11519

S.A. Shoop, S.R. Bigl. Moisture migration during freeze and thaw of unsaturated soils: modeling and large scale experiments. Cold Reg. Sci. Technol., 25 (1) (1997), pp. 33-45

E.J. Spaans, J.M. Baker. The soil freezing characteristic: Its measurement and similarity to the soil moisture characteristic. Soil Sci. Soc. Am. J., 60 (1) (1996), pp. 13-19

M. Stähli, D. Stadler. Measurement of water and solute dynamics in freezing soil columns with time domain reflectometry. J. Hydrol., 195 (1–4) (1997), pp. 352-369

M. Stähli, D. Bayard, H. Wydler, H. Flühler. Snowmelt infiltration into alpine soils visualized by dye tracer technique. Arct. Antarct. Alp. Res., 36 (1) (2004), pp. 128-135

S. Suzuki, S. Kitamura. Unfrozen water in amylosic molecules is dependent on the molecular structures—a differential scanning calorimetric study. Food Hydrocoll., 22 (5) (2008), pp. 862-867

J. Teng, Y. Zhong, S. Zhang, D. Sheng. A mathematic model for the soil freezing characteristic curve: the roles of adsorption and capillarity. Cold Reg. Sci. Technol., 181 (2021), Article 103178

H. Tian, C. Wei, H. Wei, J. Zhou. Freezing and thawing characteristics of frozen soils: Bound water content and hysteresis phenomenon. Cold Reg. Sci. Technol., 103 (2014), pp. 74-81

A.R. Tice, D.M. Anderson, K.F. Sterrett. Unfrozen water contents of submarine permafrost determined by nuclear magnetic resonance. Dev. Geotech. Eng., 28 (1982), pp. 135-146

P. Tziachris, V. Aschonitis, T. Chatzistathis, M. Papadopoulou, I.J.D. Doukas. Comparing machine learning models and hybrid geostatistical methods using environmental and soil covariates for soil pH prediction. ISPRS Int. J. Geo Inf., 9 (4) (2020), p. 276

A.M.C. Wadoux, A. Samuel-Rosa, L. Poggio, V.L. Mulder. A note on knowledge discovery and machine learning in digital soil mapping. Eur. J. Soil Sci., 71 (2) (2020), pp. 133-136

X. Wan, W. Pei, J. Lu, E. Qiu, Z. Yan, N. Pirhadi, J. Zhu. Analytical model to predict unfrozen water content based on the probability of ice formation in soils. Permafr. Periglac. Process., 33 (4) (2022), pp. 436-451

X.S. Wan, S.J. Zhu, W.S. Pei, F.X. Zhou, J.G. Lu, Z.R. Yan, D. Wa. A theoretical model on unfrozen water content in soils and verification. J. Hydrol., 622 (2023), Article 129675

C. Wang, Y. Lai, M. Zhang. Estimating soil freezing characteristic curve based on pore-size distribution. Appl. Therm. Eng., 124 (2017), pp. 1049-1060

K. Watanabe, Y. Osada. Simultaneous measurement of unfrozen water content and hydraulic conductivity of partially frozen soil near 0 C. Cold Reg. Sci. Technol., 142 (2017), pp. 79-84

K. Watanabe, T. Wake. Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR. Cold Reg. Sci. Technol., 59 (1) (2009), pp. 34-41

K. Watanabe, T. Kito, T. Wake, M. Sakai. Freezing experiments on unsaturated sand, loam and silt loam. Ann. Glaciol., 52 (58) (2011), pp. 37-43

H. Wen, J. Bi, D. Guo. Evaluation of the calculated unfrozen water contents determined by different measured subzero temperature ranges. Cold Reg. Sci. Technol., 170 (2020), Article 102927

Z. Wen, T. Zhang, Y. Sheng, W. Ma, Q. Wu, W. Feng, Z. Sun. Managing ice-rich permafrost exposed during cutting excavation along Qinghai-Tibetan railway: Experiences and implementation. Eng. Geol., 122 (3–4) (2011), pp. 316-327

Z. Wen, W. Ma, W. Feng, Y. Deng, D. Wang, Z. Fan, C. Zhou. Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibetan silty clay. Environ. Earth Sci., 66 (2012), pp. 1467-1476

L. Weng, Z. Wu, Q. Liu, Z. Chu, S. Zhang. Evolutions of the unfrozen water content of saturated sandstones during freezing process and the freeze-induced damage characteristics. Int. J. Rock Mech. Min. Sci., 142 (2021), Article 104757

S. Westermann, J. Boike, M. Langer, T.V. Schuler, B. Etzelmüller. Modeling the impact of wintertime rain events on the thermal regime of permafrost. Cryosphere, 5 (4) (2011), pp. 945-959

P.J. Williams. Unfrozen water content of frozen soils and soil moisture suction. Géotechnique, 14 (3) (1964), pp. 231-246

M. Wu, X. Tan, J. Huang, J. Wu, P.E. Jansson. Solute and water effects on soil freezing characteristics based on laboratory experiments. Cold Reg. Sci. Technol., 115 (2015), pp. 22-29

Y. Wu, Y. Wang, L. Hu. A theoretical model of the soil freezing characteristic curve for saline soil. J. Hydrol., 622 (2023), Article 129639

B. Wu, H.H. Zhu, D. Cao, L. Xu, B. Shi. Feasibility study on ice content measurement of frozen soil using actively heated FBG sensors. Cold Reg. Sci. Technol., 189 (2021), Article 103332

X.Z. Xu, J.C. Wang, L.X. Zhang. Frozen Soil Physics Science. Science Press, Beijing (2001)

L. Yang, H. Jia, L. Han, H. Zhang, L. Tang. Hysteresis in the ultrasonic parameters of saturated sandstone during freezing and thawing and correlations with unfrozen water content. J. Rock Mech. Geotech. Eng., 13 (5) (2021), pp. 1078-1092

C. Yang, Y. Yin, J. Zhang, P. Ding, J. Liu. A graph deep learning method for landslide displacement prediction based on global navigation satellite system positioning. Geosci. Front., 15 (1) (2024), Article 101690

M. Ye, L. Zhu, X. Li, et al.. Estimation of the soil arsenic concentration using a geographically weighted XGBoost model based on hyperspectral data. Sci. Total Environ., 858 (2023), Article 159798

K. Yoshikawa, P.P. Overduin. Comparing unfrozen water content measurements of frozen soil using recently developed commercial sensors. Cold Reg. Sci. Technol., 42 (3) (2005), pp. 250-256

F. Yu, J. Qi, Y. Lai, et al.. Typical embankment settlement/heave patterns of the Qinghai-Tibet highway in permafrost regions: Formation and evolution. Eng. Geol., 214 (2016), pp. 147-156

L. Yuan, L. Zhao, R. Li, G. Hu, E. Du, Y. Qiao, L. Ma. Spatiotemporal characteristics of hydrothermal processes of the active layer on the central and northern Qinghai-Tibet plateau. Sci. Total Environ., 712 (2020), Article 136392

T. Zhang, R.G. Barry, K. Knowles, J.A. Heginbottom, J. Brown. Statistics and characteristics of permafrost and ground-ice distribution in the Northern Hemisphere. Polar Geogr., 23 (2) (1999), pp. 132-154

Y. Zhang, S.K. Carey, W.L. Quinton. Evaluation of the algorithms and parameterizations for ground thawing and freezing simulation in permafrost regions. J. Geophys. Res. Atmos., 113 (2008), Article D17116

M. Zhang, W. Pei, S. Li, J. Lu, L. Jin. Experimental and numerical analyses of the thermo-mechanical stability of an embankment with shady and sunny slopes in a permafrost region. Appl. Therm. Eng., 127 (2017), pp. 1478-1487

X. Zhang, S.F. Sun, Y. Xue. Development and testing of a frozen soil parameterization for cold region studies. J. Hydrometeorol., 8 (4) (2007), pp. 690-701

M. Zhang, X. Zhang, J. Lu, W. Pei, C. Wang. Analysis of volumetric unfrozen water contents in freezing soils. Exp. Heat Transfer, 32 (5) (2019), pp. 426-438

N. Zhang, A. Zhou, Y.F. Jin, Z.Y. Yin, S.L. Shen. An enhanced deep learning method for accurate and robust modelling of soil stress–strain response. Acta Geotechnica, 18 (8) (2023), pp. 4405-4427

D. Zhao, J. Wang, X. Zhao, J. Triantafilis. Clay content mapping and uncertainty estimation using weighted model averaging. Catena, 209 (2022), Article 105791

J. Zhou, C. Wei, Y. Lai, H. Wei, H. Tian. Application of the generalized Clapeyron equation to freezing point depression and unfrozen water content. Water Resour. Res., 54 (11) (2018), pp. 9412-9431