Finite element models for the thermohydromechanical analysis of road embankments in areas with permafrost soils

Introduction. Modern construction practice in areas with permafrost soils (PS) shows that the most rational principle for the construction of foundations for highways in the area of prospective development of the territories of the Arctic zone is the preservation of soils in a frozen state (the so-called I design principle). This is primarily due to economic considerations, since soil thawing is a costly technology, and its use is justified to some extent only in the area of island occurrence of permafrost soils.

Materials and methods. In order to meet the regulatory requirements for the strength and deformations of the pavement in the PS areas, it is necessary to perform a joint calculation of three physical fields — thermal, hydraulic and mechanical, that is, to perform a thermohydromechanical (THM) calculation. Such calculations, which are absolutely necessary for the design and assessment of conformity during the construction of roads in permafrost areas. At the same time, only separate methods of calculating the thermal condition of roads at PS are currently used in practice, after which the usual methods of calculating the mechanics of multilayer road structures are further applied. In this paper, the authors used the Plaxis 2D finite element (FE) software package, which is widely used for calculations of building structures, to perform joint THM calculations.

Results. The paper presents the results of the conducted research, on the basis of which recommended FE models have been developed for the joint THM calculation of embankments of highways in the PS areas. Concrete examples show that these models make it possible, in particular, to determine the optimal location in the body of the embankment of the XPS thermal insulation board layers used for thermal insulation. The data from the FE model also make it possible to study the fields of deformations and fields of water filtration rates during the defrosting of the embankment – base structure.

Conclusions. This study shows the possibilities of developing FE models for the joint thermohydromechanical calculation of highway embankments in permafrost areas using the Plaxis 2D software package. Concrete examples show that these models make it possible, in particular, to determine the optimal design of a highway embankment in permafrost areas in the presence of PS when used for thermal stabilization of XPS-type insulating plates in the embankment body. The studies carried out on the developed FE models have shown that these models also make it possible to study the fields of deformations and fields of water filtration rates during the thawing of the embankment – base structure, which makes it possible to conduct research on various road structures designed to operate in the Arctic zones at PS.

1. Aukenthaler M. The Frozen & Unfrozen Barcelona Basic Model: A Verification and Validation of a New Constitutive Model : MSc thesis. Delft, Delft University of Technology, 2016.

2. Ghoreishian Amiri S.A., Grimstad G., Kadivar M., Nordal S. Constitutive model for rate-independent behavior of saturated frozen soils. Canadian Geotechnical Journal. 2016; 53(10):1646-1657. DOI: 10.1139/cgj-2015-0467

3. Aukenthaler M., Brinkgreve R.B. J., Haxaire A. A practical approach to obtain the soil freezing characteristic curve and the freezing/melting point of a soil-water system. Proceedings of the GeoVancouver 2016: the 69th Canadian Geotechnical Conference, Vancouver, Canada. 2016; 397-404.

4. Tuohino M., Solowski W., Abed A., Koivisto K., Lei X. Application of the Frozen and Unfrozen Soil model to modelling effects of freeze-thaw on low-volume roads. IOP Conference Series: Earth and Environmental Science. 2021; 710:012067. DOI: 10.1088/1755-1315/710/1/012067

5. Aukenthaler M., Brinkgreve R.B.J. Application of a Thermo-hydro-mechanical Model for Freezing and Thawing. Procedia Engineering. 2017; 191:74-81. DOI: 10.1016/j.proeng.2017.05.156

6. Rostami H. Finite element analysis of coupled thermo-hydro-mechanical processes in fully saturated, partially frozen soils. 2017; 103.

7. Lyu C., Nishimura S., Ghoreishian Amiri S.A., Zhu F., Eiksund G.R., Grimstad G. Pore-water pressure development in a frozen saline clay under isotropic loading and undrained shearing. Acta Geotechnica. 2021; 16(12):3831-3847. DOI: 10.1007/s11440-021-01338-y. EDN JDTCNY.

8. Li K.-Q., Yin Z.-Y. State of the Art of Coupled Thermo–hydro-Mechanical–Chemical Modelling for Frozen Soils. Archives of Computational Methods in Engineering. 2025; 32(2):1039-1096. DOI: 10.1007/s11831-024-10164-w. EDN XCWVXH.

9. Nishimura S. A model for freeze-thaw-induced plastic volume changes in saturated clays. Soils and Foundations. 2021; 61(4):1054-1070. DOI: 10.1016/j.sandf.2021.05.008. EDN XCWVXH.

10. Lu Y., Liu S., Alonso E., Wang L., Xu L., Li Z. Volume changes and mechanical degradation of a compacted expansive soil under freeze-thaw cycles. Cold Regions Science and Technology. 2019; 157:206-214. DOI: 10.1016/j.coldregions.2018.10.008

11. Nishimura S., Okajima S., Joshi B.R., Higo Y., Tokoro T. Volumetric behaviour of clays under freeze–thaw cycles in a mesoscopically uniform element. Géotechnique. 2021; 71(12):1150-1164. DOI: 10.1680/jgeot.20.p.047. EDN MZOSED.

12. Zheng H., Kanie S., Akagawa S. A method for obtaining radial stress in the freezing direction in frozen soil samples. Cold Regions Science and Technology. 2020; 169:102899. DOI: 10.1016/j.coldregions.2019.102899. EDN KJCYAL.

13. Cui W., Potts D.M., Zdravkovic L., Gawecka K.A., Taborda D.M.G. An alternative coupled thermo-hydro-mechanical finite element formulation for fully saturated soils. Computers and Geotechnics. 2018; 94:22-30. DOI: 10.1016/j.compgeo.2017.08.011

14. Nishimura S., Liang M., Lyu C. Analysis of freezing and thawing processes in clay with freeze-induced compression (FIC) model. Soils and Foundations. 2025; 65(1):101559. DOI: 10.1016/j.sandf.2024.101559. EDN RYADWR.

15. Yamazoe N., Tanaka H., Hayashi H., Nishimura S. A rational design approach to peat ground improvement by vertical drains. Soils and Foundations. 2020; 60(6):1387-1404. DOI: 10.1016/j.sandf.2020.08.009. EDN IXMETU.

16. Nishimura S., Wang J. A simple framework for describing strength of saturated frozen soils as multi-phase coupled system. Géotechnique. 2019; 69(8):659-671. DOI: 10.1680/jgeot.17.p.104

17. Dalla Santa G., Cola S., Secco M., Tateo F., Sassi R., Galgaro A. Multiscale analysis of freeze–thaw effects induced by ground heat exchangers on permeability of silty clays. Géotechnique. 2019; 69(2):95-105. DOI: 10.1680/jgeot.16.p.313

18. Shastri A., Sánchez M., Gai X., Lee M.Y., Dewers T. Mechanical behavior of frozen soils: Experimental investigation and numerical modeling. Computers and Geotechnics. 2021; 138:104361. DOI: 10.1016/j.compgeo.2021.104361. EDN OTDJFK.

19. Li Q., Zhang D., Li P., Cui K., Jing X. The small-strain stiffness of frozen clay soils at different temperatures and initial water contents: Experimental study and predicted model. Cold Regions Science and Technology. 2023; 215:103986. DOI: 10.1016/j.coldregions.2023.103986. EDN WSFZPO.

20. Zhelnin M.S., Kostina A.A., Prokhorov A.E., Plekhov O.A., Semin M.A., Agutin K.A. Validation of a thermo-hydro-mechanical model of freezing of water-saturated soil based on laboratory tests results. Computational Continuum Mechanics. 2021; 14(2):144-158. DOI: 10.7242/1999-6691/2021.14.2.12. EDN TJUHGV. (rus.).

21. Repina P.I., Sakharov I.I., Fadeev A.B. Numerical modeling of freezing and heaving processes in the foundation-base system. Soil Mechanics and Foundation Engineering. 1994; 5:6-9. (rus.).

22. Shashkin K.G. Using the structure of a universal finite element in the development of models within the framework of the FEM models program. Urban Reconstruction and Geotechnical Construction. 2000; 2:26-32. (rus.).

23. Sakharov I.I., Paramonov M.V. Numerical assessment of the effect of frost heaving on the VAT of reinforced walls of excavation pits. Numerical calculation methods in the practice of geotechnics : proceedings of a scientific and technical conference. 2012; 159-164. (rus.).

24. Maksimov I.A., Maksimova A.G. Forecast of artificial thawing of permafrost soils in the foundations of hydraulic structures. Materials of conferences and meetings on hydraulic engineering. Leningrad, Energo-atomizdat, 1988; 111-118. (rus.).

25. Kudriavtsev S.A. Numerical investigations of the thermophysical processes in seasonally freezing soils. Kriosfera Zemli. 2003; 7(4):76-81. EDN MPPZAH.

26. Karlov V.D. Principles of foundation design when using seasonally frozen soils in the foundations of structures. Geotechnics. Science and Practice : Collection of Scientific Papers. 2000; 15-24. (rus.).

27. Aspiz E.S., Vavrinyuk T.S. Reinforcement of deformable long-term exploited embankments on permafrost. Polytransport systems : proceedings of the IX International Scientific and Technical Conference. Siberian State University of Railway Transport. 2017; 86-90. EDN ZWVQJL. (rus.).

28. Zhang A.A., Aspiz E.S., Khrustalev L.N., Shesternev D.M. A new method of protecting frozen soils at the base of an embankment from thawing. Path and Track Management Journal. 2018; 1:6-9. (rus.).

29. Aspiz E.S., Khrustalev L.N. Prevention of degradation of permafrost soils at the base of embankments for the conditions of construction of the Salekhard – Nadym line. Modern problems of design, construction and operation of the railway track : proceedings of the XVI International Scientific and Technical Conference. Readings dedicated to the memory of Professor G.M. Shakhunyants. 2019; 49-54. (rus.).

30. Aspiz E.S., Vavrinyuk T.S. Protective layers of the earthbed for the conditions of the northern latitudinal course. Modern problems of railway track design, construction and operation : proceedings of the XVI International Scientific and Technical Conference. Readings dedicated to the memory of Professor G.M. Shakhunyants. 2019; 96-99.

31. Aspiz E. The subgrade in the conditions of permafrost soils of the northern latitudinal line. Railway Track and Facilities. 2021; 3:22-25. EDN PVTRAW. (rus.).

32. Passek V.V., Gerasimov V.A. Heat and stress-strain condition of embankment in culvert zone on permafrost. Railway Track and Facilities. 2015; 11:8-13. EDN VBCKYL. (rus.).

33. Passek V.V., Paskov M.V., Andreev V.S. The construction of embankments in difficult permafrost-soil conditions in the presence of buried ice and ice soils of the polar and circumpolar tundra. Oil and Gas of Western Siberia : Proceedings of the International Scientific and Technical Conference dedicated to the 90th anniversary of the birth of Anatoly Nikolaevich Kosukhin. 2015; 270-275. EDN UNJFCP. (rus.).

34. Kudryavtsev S.A., Kazharskiу A.V. Numerical modeling of freeze heaving and thawing process depending on velocity of soil freezing. Modern Technologies. System analysis. Modeling. 2012; 2(34):105-110. EDN PCGRPJ. (rus.).

35. Lanis A.L., Razuvaev D.A., Usov D.A. Influence of thawing soils on the deformation top of subgrade. Bulletin of the Siberian State University of Railway Communications. 2021; 3(58):104-111. DOI: 10.52170/1815-9265_2021_58_104. EDN FKKNWQ. (rus.).

36. Prokhorov A.E., Zhelnin M.S., Kostina A.A., Plekhov O.A. Investigation of non-equilibrium phase transition in freezing porous media. Bulletin of Perm University. Physics. 2018; 4(42):31-37. DOI: 10.17072/1994-3598-2018-4-31-37. EDN VQRDBQ. (rus.).

37. Zhelnin M.S., Prokhorov A.E., Kostina A.A., Plekhov O.A. Experimental and theoretical study of mechanical deformation of freezing saturated soil. PNRPU Mechanics Bulletin. 2019; 4:19-28. DOI: 10.15593/perm.mech/2019.4.02. EDN UOASYG. (rus.).

38. Belozerov A.G., Semenov E.V., Babakin B.S. Mathematical modelling of soil freezing on the basis of experimental data. Journal of International Academy of Refrigeration. 2021; 1:102-107. DOI: 10.17586/1606-4313-2021-20-1-102-107. EDN XXTTQU. (rus.).

39. Trapeznikov A.G., Becker A.T., Isaeva E.S., Tsimbelman N.Ya., Chernova T.I. Numerical modeling of the thermal regime of the frozen-type embankment dam of the Anadyr hydrosystem. FEFU: School of Engineering Bulletin. 2022; 1(50):81-93. DOI: 10.24866/2227-6858/2022-1/81-93. EDN UFIKXG. (rus.).