Technical Papers
Jan 17, 2024

Constitutive Model for Thermo–Hydro–Mechanical Behaviors of Saturated Partially Frozen Cohesionless Soils: A Theoretical Pore-Scale Study

Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 150, Issue 4

Abstract

The thermo–hydro–mechanical (THM) behaviors of frozen soils are often modeled based on the thermodynamic fluxes of moisture and heat. However, existing models disregard the pore-scale granular interaction between the soil grain and ice crystal for saturated partially frozen soils. The pore-scale mechanism of pore-filling and load-bearing for the ice phase in the loaded soil skeleton has not been explored. An alternative constitutive model is therefore proposed by considering the microscopic temperature-dependent distribution of the ice phase for pore-filling and load-bearing in the soil interpore. This reflects the influence of the ice phase on the soil stress states and the associated THM behaviors as interpreted based on the critical state framework. The model was validated by published experimental results and considerably captured undrained shearing behaviors of frozen soils at various temperatures and confining pressures. A numerical parametric study was conducted to investigate the dependency of the phase relationship, stress state, undrained shear strength, and soil stiffness on temperature. The modeling suggests that the ice crystals filling in the pore are partially load-bearing to affect the soil stiffness and partially unloaded to alter the stress state. It shows that freezing turns the soil into a heavily consolidated state by increasing the specific volume and decreasing the effective granular void ratio. The undrained shear strength of frozen soils increases with a decrease in temperature because the dilatancy is enhanced due to the ice invasion in the interpore. It also demonstrates that soil stiffness is influenced by not only the stress state but the freezing history. This study highlights the temperature-dependency of mechanical behaviors and the validity of using the concept of stress states to interpret the pore-scale mechanistic soil–water–ice interactions for frozen soils.

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Data Availability Statement

All data, models, and code generated or used during the study appear in the published article.

Acknowledgments

This research was funded by USDOE (United States Department of Education) GAANN (Graduate Assistance in Areas of National Need) Program (Grant No. P200A210109) and supported by the Broad Agency Announcement Program and the US Army Engineer Research and Development Center (ERDC) under Contract No. W913E523C0007. Any opinions, findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the Broad Agency Announcement Program and the US Army Engineer Research and Development Center (ERDC). The authors would also thank anonymous reviewers for their invaluable comments and insightful suggestions.

References

Aldaeef, A. A., and M. T. Rayhani. 2020. “Pull-out capacity and creep behavior of helical piles in frozen ground.” J. Geotech. Geoenviron. Eng. 146 (12): 04020140. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002405.
Amankwah, S. K., A. M. Ireson, C. Maulé, R. Brannen, and S. A. Mathias. 2021. “A model for the soil freezing characteristic curve that represents the dominant role of salt exclusion.” Water Resour. Res. 57 (8): e2021WR030070. https://doi.org/10.1029/2021WR030070.
Arenson, L. U., and S. M. Springman. 2005a. “Mathematical descriptions for the behaviour of ice-rich frozen soils at temperatures close to 0°C.” Can. Geotech. J. 42 (2): 431–442. https://doi.org/10.1139/t04-109.
Arenson, L. U., and S. M. Springman. 2005b. “Triaxial constant stress and constant strain rate tests on ice-rich permafrost samples.” Can. Geotech. J. 42 (2): 412–430. https://doi.org/10.1139/t04-111.
Arenson, L. U., S. M. Springman, and D. C. Sego. 2007. “The rheology of frozen soils.” Appl. Rheol. 17 (1): 12147. https://doi.org/10.1515/arh-2007-0003.
Bai, R., Y. Lai, M. Zhang, and F. Yu. 2018. “Theory and application of a novel soil freezing characteristic curve.” Appl. Therm. Eng. 129 (Jun): 1106–1114. https://doi.org/10.1016/j.applthermaleng.2017.10.121.
Been, K., and M. G. Jefferies. 1985. “A state parameter for sands.” Géotechnique 35 (2): 99–112. https://doi.org/10.1680/geot.1985.35.2.99.
Brugada, J., Y. P. Cheng, K. Soga, and J. C. Santamarina. 2010. “Discrete element modelling of geomechanical behaviour of methane hydrate soils with pore-filling hydrate distribution.” Granular Matter 12 (5): 517–525. https://doi.org/10.1007/s10035-010-0210-y.
Cudmani, R., W. Yan, and U. Schindler. 2022. “A constitutive model for the simulation of temperature-, stress-and rate-dependent behaviour of frozen granular soils.” Géotechnique 2022 (May): 1–13. https://doi.org/10.1680/jgeot.21.00012.
Dai, S., and J. C. Santamarina. 2017. “Stiffness evolution in frozen sands subjected to stress changes.” J. Geotech. Geoenviron. Eng. 143 (9): 04017042. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001713.
Ghoreishian Amiri, S. A., G. Grimstad, M. Kadivar, and S. Nordal. 2016. “Constitutive model for rate-independent behavior of saturated frozen soils.” Can. Geotech. J. 53 (10): 1646–1657. https://doi.org/10.1139/cgj-2015-0467.
Hazirbaba, K., Y. Zhang, and J. L. Hulsey. 2011. “Evaluation of temperature and freeze–Thaw effects on excess pore pressure generation of fine-grained soils.” Soil Dyn. Earthquake Eng. 31 (3): 372–384. https://doi.org/10.1016/j.soildyn.2010.09.006.
Huang, C., C. Zhu, Y. Ma, and S. A. Hewage. 2022. “Investigating mechanical behaviors of rocks under freeze–Thaw cycles using discrete element method.” Rock Mech. Rock Eng. 55 (Jun): 7517–7534. https://doi.org/10.1007/s00603-022-03027-y.
Ji, S., X. Chen, and A. Wang. 2020. “Influence of the loading direction on the uniaxial compressive strength of sea ice based on field measurements.” Ann. Glaciol. 61 (82): 86–96. https://doi.org/10.1017/aog.2020.14.
Kim, I., D. Lee, Y. Kim, T. Sup Yun, and J. Lee. 2021a. “Effects of pore water volume on K°0 for sand subject to freezing and thawing.” J. Geotech. Geoenviron. Eng. 147 (3): 04020173. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002468.
Kim, S. Y., W. T. Hong, and J. S. Lee. 2018. “Silt fraction effects of frozen soils on frozen water content, strength, and stiffness.” Constr. Build. Mater. 183 (Sep): 565–577. https://doi.org/10.1016/j.conbuildmat.2018.06.187.
Kim, S. Y., J. Park, W. Cha, J. S. Lee, and C. J. Santamarina. 2021b. “Soil response during globally drained and undrained freeze–thaw cycles under deviatoric loading.” J. Geotech. Geoenviron. Eng. 147 (2): 06020030. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002464.
Konrad, J. M., and N. R. Morgenstern. 1981. “The segregation potential of a freezing soil.” Can. Geotech. J. 18 (4): 482–491. https://doi.org/10.1139/t81-059.
Ladanyi, B. 1972. “An engineering theory of creep of frozen soils.” Can. Geotech. J. 9 (1): 63–80. https://doi.org/10.1139/t72-005.
Li, Q., and Z. Yang. 2017. “P–Y approach for laterally loaded piles in frozen silt.” J. Geotech. Geoenviron. Eng. 143 (5): 04017001. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001556.
Li, X. S., and Y. F. Dafalias. 2000. “Dilatancy for cohesionless soils.” Géotechnique 50 (4): 449–460. https://doi.org/10.1680/geot.2000.50.4.449.
Liao, M., Y. Lai, and C. Wang. 2016. “A strength criterion for frozen sodium sulfate saline soil.” Can. Geotech. J. 53 (7): 1176–1185. https://doi.org/10.1139/cgj-2015-0569.
Lide, D. R. 2004. CRC handbook of chemistry and physics. Boca Raton, FL: CRC Press.
Loria, A. R., B. Frigo, and B. Chiaia. 2017. “A non-linear constitutive model for describing the mechanical behaviour of frozen ground and permafrost.” Cold Reg. Sci. Technol. 133 (Jan): 63–69. https://doi.org/10.1016/j.coldregions.2016.10.010.
Lyu, C., S. A. G. Amiri, G. Grimstad, K. V. Høyland, and T. Ingeman-Nielsen. 2020. “Comparison of geoacoustic models for unfrozen water content estimation.” J. Geophys. Res. Solid Earth 125 (10): e2020JB019766. https://doi.org/10.1029/2020JB019766.
Lyu, C., G. Grimstad, and S. Nishimura. 2021. “Pore pressure coefficient in frozen soils.” Géotechnique 73 (6): 521–530. https://doi.org/10.1680/jgeot.21.00097.
Michalowski, R. L. 1993. “A constitutive model of saturated soils for frost heave simulations.” Cold Reg. Sci. Technol. 22 (1): 47–63. https://doi.org/10.1016/0165-232X(93)90045-A.
Miner, K. R., J. D’Andrilli, R. Mackelprang, A. Edwards, M. J. Malaska, M. P. Waldrop, and C. E. Miller. 2021. “Emergent biogeochemical risks from arctic permafrost degradation.” Nat. Clim. Change 11 (10): 809–819. https://doi.org/10.1038/s41558-021-01162-y.
Mu, Q. Y., C. Zhou, C. W. W. Ng, and G. G. D. Zhou. 2019. “Stress effects on soil freezing characteristic curve: Equipment development and experimental results.” Vadose Zone J. 18 (1): 1–10. https://doi.org/10.2136/vzj2018.11.0199.
Nishimura, S., A. Gens, S. Olivella, and R. J. Jardine. 2009. “THM-coupled finite element analysis of frozen soil: Formulation and application.” Géotechnique 59 (3): 159–171. https://doi.org/10.1680/geot.2009.59.3.159.
O’Neill, K., and R. D. Miller. 1985. “Exploration of a rigid ice model of frost heave.” Water Resour. Res. 21 (3): 281–296. https://doi.org/10.1029/WR021i003p00281.
Petrovic, J. J. 2003. “Review mechanical properties of ice and snow.” J. Mater. Sci. 38 (1): 1–6. https://doi.org/10.1023/A:1021134128038.
Potapowicz, J., D. Szumińska, M. Szopińska, and Ż. Polkowska. 2019. “The influence of global climate change on the environmental fate of anthropogenic pollution released from the permafrost: Part I. Case study of Antarctica.” Sci. Total Environ. 651 (Jun): 1534–1548. https://doi.org/10.1016/j.scitotenv.2018.09.168.
Rahman, M. M., S. R. Lo, and C. T. Gnanendran. 2008. “On equivalent granular void ratio and steady state behaviour of loose sand with fines.” Can. Geotech. J. 45 (10): 1439–1456. https://doi.org/10.1139/T08-064.
Shastri, A., M. Sánchez, X. Gai, M. Y. Lee, and T. Dewers. 2021. “Mechanical behavior of frozen soils: Experimental investigation and numerical modeling.” Comput. Geotech. 138 (Oct): 104361. https://doi.org/10.1016/j.compgeo.2021.104361.
Shelman, A., J. Tantalla, S. Sritharan, S. Nikolaou, and H. Lacy. 2014. “Characterization of seasonally frozen soils for seismic design of foundations.” J. Geotech. Geoenviron. Eng. 140 (7): 04014031. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001065.
Shin, H., and J. C. Santamarina. 2013. “Role of particle angularity on the mechanical behavior of granular mixtures.” J. Geotech. Geoenviron. Eng. 139 (2): 353–355. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000768.
Sinha, N. K. 1989. “Elasticity of natural types of polycrystalline ice.” Cold Reg. Sci. Technol. 17 (2): 127–135. https://doi.org/10.1016/S0165-232X(89)80003-5.
Sun, K., and A. Zhou. 2021. “A multisurface elastoplastic model for frozen soil.” Acta Geotech. 16 (11): 3401–3424. https://doi.org/10.1007/s11440-021-01391-7.
Teng, J., J. Kou, X. Yan, S. Zhang, and D. Sheng. 2020. “Parameterization of soil freezing characteristic curve for unsaturated soils.” Cold Reg. Sci. Technol. 170 (Apr): 102928. https://doi.org/10.1016/j.coldregions.2019.102928.
Teng, J., Y. Zhong, S. Zhang, and D. Sheng. 2021. “A mathematic model for the soil freezing characteristic curve: The roles of adsorption and capillarity.” Cold Reg. Sci. Technol. 181 (Jul): 103178. https://doi.org/10.1016/j.coldregions.2020.103178.
Thomas, H. R., P. Cleall, Y. C. Li, C. Harris, and M. Kern-Luetschg. 2009. “Modelling of cryogenic processes in permafrost and seasonally frozen soils.” Géotechnique 59 (3): 173–184. https://doi.org/10.1680/geot.2009.59.3.173.
Wang, J., S. Nishimura, and T. Tokoro. 2017. “Laboratory study and interpretation of mechanical behavior of frozen clay through state concept.” Soils Found. 57 (2): 194–210. https://doi.org/10.1016/j.sandf.2017.03.003.
Wood, D. M. 1990. Soil behaviour and critical state soil mechanics. Cambridge, UK: Cambridge University Press.
Yamamoto, Y., and S. M. Springman. 2014. “Axial compression stress path tests on artificial frozen soil samples in a triaxial device at temperatures just below 0°C.” Can. Geotech. J. 51 (10): 1178–1195. https://doi.org/10.1139/cgj-2013-0257.
Yao, X., M. Zhang, G. Xu, and F. Yu. 2020. “Influence of mechanical properties on the coefficient of lateral earth pressure at rest of frozen soils.” Cold Reg. Sci. Technol. 174 (Jun): 103057. https://doi.org/10.1016/j.coldregions.2020.103057.
Yu, F., P. Guo, and S. Na. 2022. “A framework for constructing elasto-plastic constitutive models for frozen and unfrozen soils.” Int. J. Numer. Anal. Methods Geomech. 46 (2): 436–466. https://doi.org/10.1002/nag.3306.
Zhang, Y., and R. L. Michalowski. 2015. “Thermal-hydro-mechanical analysis of frost heave and thaw settlement.” J. Geotech. Geoenviron. Eng. 141 (7): 04015027. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001305.

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Go to Journal of Geotechnical and Geoenvironmental Engineering
Journal of Geotechnical and Geoenvironmental Engineering
Volume 150Issue 4April 2024

History

Received: Jan 4, 2023
Accepted: Nov 3, 2023
Published online: Jan 17, 2024
Published in print: Apr 1, 2024
Discussion open until: Jun 17, 2024

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Graduate Research Assistant, Center for Research and Education in Advanced Transportation Engineering Systems, Dept. of Civil and Environmental Engineering, Rowan Univ., 201 Mullica Hill Rd., Glassboro, NJ 08028. ORCID: https://orcid.org/0000-0002-7946-3547. Email: [email protected]
Associate Professor, Center for Research and Education in Advanced Transportation Engineering Systems, Dept. of Civil and Environmental Engineering, Rowan Univ., 201 Mullica Hill Rd., Glassboro, NJ 08028 (corresponding author). ORCID: https://orcid.org/0000-0001-5382-1003. Email: [email protected]

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