Investigation and Modification of a CSSM-Based Elastic–Thermoviscoplastic Model for Clay
Publication: International Journal of Geomechanics
Volume 22, Issue 10
Abstract
This paper examines the accuracy of a new elastic–thermoviscoplastic (E-TVP) constitutive model developed based on critical state soil mechanics. The model can be used for simulating the temperature-dependent and strain-rate-dependent behavior of clay soils. The study compares the E-TVP behavior of a single soil element with previously published thermo-mechanical experimental results performed on saturated clay specimens at different temperatures. Suggestions regarding unloading and reloading at constant temperatures as well as thermal consolidation under constant loads are presented. A modification for unloading–reloading adds a new criterion to the volumetric thermoviscoplastic strain rate formulation. A physics-based term is added to the current specific volume of the soil to include the viscous effect induced by temperature change. These modifications improve the convergence of laboratory data and simulated model responses. Comparisons of results from an earlier E-TVP model and the newly improved model provide evidence of improved predictive capabilities.
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Acknowledgments
This research was supported by the New Frontiers in Research Fund - Exploration Grant [NFRFE-2018-00966] and a University of Manitoba Graduate Fellowship (2019–2020).
Notation
The following symbols are used in this paper:
- G′
- effective shear modulus;
- g
- plastic potential;
- M
- slope of critical state line;
- N
- location of isotropic normal compression line in V − ln(p′) plane at p′ = 1 kPa;
- p′
- mean effective stress;
- isotropic mean effective stress (reference size of plastic potential);
- mean effective stress on the normal compression line at its intersection with the URL;
- reference size of yield locus;
- q
- deviator stress;
- S
- scalar multiplier;
- sij
- deviator stress tensor;
- T
- temperature;
- t
- time elapsed from the end of primary consolidation;
- t0
- time corresponding to the end of primary consolidation;
- V
- specific volume;
- u
- pore water pressure;
- Vm
- isotropic specific volume;
- Z
- location of VPL in V − ln(p′) plane at p′ = 1 kPa;
- γ
- viscosity parameter;
- δij
- Kronecker delta;
- ɛp
- volumetric strain;
- ɛq
- deviator strain;
- ɛij
- strain tensor;
- viscoplastic volumetric strain rate;
- κ
- slope of URL in V − ln(p′) plane;
- λ
- slope of normal compression line in V − ln(p′) plane; and
- ψT
- temperature-dependent slope of secondary compression line in V − ln(p′).
References
Abuel-Naga, H. M. 2006. “Thermo-mechanical behavior of soft Bangkok clay: Experimental results and constitutive modeling.” Ph.D. thesis, Asian Institute of Technology.
Adachi, T., and F. Oka. 1982. “Constitutive equations for normally consolidated clay based on elasto-viscoplasticity.” Soils Found. 22 (4): 57–70. https://doi.org/10.3208/sandf1972.22.4_57.
Adachi, T., F. Oka, and M. Mimura. 1987. “Mathematical structure of an overstress elasto-viscoplastic model for clay.” Soils Found. 27 (3): 31–42. https://doi.org/10.3208/sandf1972.27.3_31.
Adachi, T., and M. Okano. 1974. “A constitutive equation for normally consolidated clay.” Soils Found. 14 (4): 55–73. https://doi.org/10.3208/sandf1972.14.4_55.
Anongphouth, A., P. Maghoul, and M. Alfaro. 2020. “Geothermal energy pile-soil interaction under mechanical loading and thermalcycles.” Int. J. GEOMATE 18 (70): 1–8.
Bjerrum, L. 1967. “Engineering geology of norwegian normally-consolidated marine clays as related to settlements of buildings.” Geotechnique 17 (2): 83–118. https://doi.org/10.1680/geot.1967.17.2.83.
Buisman, A. 1936. “Results of long duration settlement tests.” Vol. 1 of Proc., 1st Int. Conf. on Soil Mechanics and Foundation Engineering, 103–107. Cambridge, MA: Graduate School of Engineering.
Campanella, R. G., and J. K. Mitchell. 1968. “Influence of temperature variations on soil behavior.” J. Soil Mech. Found. Div. 94 (3): 709–734. https://doi.org/10.1061/JSFEAQ.0001136.
Cekerevac, C., and L. Laloui. 2004. “Experimental study of thermal effects on the mechanical behaviour of a clay.” Int. J. Numer. Anal. Methods Geomech. 28 (3): 209–228. https://doi.org/10.1002/(ISSN)1096-9853.
Crilly, T. 1996. “Unload-reload tests on saturated illite specimens at elevated temperature.” M.S. thesis, Dept. of Civil and Geological Engineering, Univ. of Manitoba.
Cui, Y.-J., X.-P. Nguyen, A. M. Tang, and X.-L. Li. 2013. “An insight into the unloading/reloading loops on the compression curve of natural stiff clays.” Appl. Clay Sci. 83 (5): 343–348. https://doi.org/10.1016/j.clay.2013.08.003.
Cui, Y. J., N. Sultan, and P. Delage. 2000. “A thermomechanical model for saturated clays.” Can. Geotech. J. 37 (3): 607–620. https://doi.org/10.1139/t99-111.
Delage, P., and G. Lefebvre. 1984. “Study of the structure of a sensitive champlain clay and of its evolution during consolidation.” Can. Geotech. J. 21 (1): 21–35. https://doi.org/10.1139/t84-003.
Feng, W.-Q., and J.-H. Yin. 2017. “A new simplified hypothesis B method for calculating consolidation settlements of double soil layers exhibiting creep.” Int. J. Numer. Anal. Methods Geomech. 41 (6): 899–917. https://doi.org/10.1002/nag.v41.6.
Fox, P. J., and T. B. Edil. 1996. “Effects of stress and temperature on secondary compression of peat.” Can. Geotech. J. 33 (3): 405–415. https://doi.org/10.1139/t96-062.
Gatmiri, B., P. Maghoul, and D. Duhamel. 2010. “Two-dimensional transient thermo-hydro mechanical fundamental solutions of multiphase porous media in frequency and time domains.” Int. J. Solids Struct. 47 (5): 595–610. https://doi.org/10.1016/j.ijsolstr.2009.10.022.
Ghahremannejad, B. 2003. “Thermo-mechanical behaviour of two reconstituted clays.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Sydney.
Graham, J., J. Crooks, and A. L. Bell. 1983. “Time effects on the stress-strain behaviour of natural soft clays.” Géotechnique 33 (3): 327–340.
Graham, J., N. Tanaka, T. Crilly, and M. Alfaro. 2001. “Modified Cam-Clay modelling of temperature effects in clays.” Can. Geotech. J. 38 (3): 608–621. https://doi.org/10.1139/t00-125.
Graham, J., and J.-H. Yin. 2001. “On the time-dependent stress-strain behaviour of soft soils.” In Proc., 3rd Int. Conf. on Soft Soil Engineering, 13–24. London: Taylor & Francis.
Green, W. J. 1969. “The influence of several factors on the rate of secondary compression of soil.” M.S. thesis. Dept. of Civil Engineering, Univ. of Missouri.
Gupta, B. 1964. “Creep of saturated soil at different temperatures.” M.S. thesis, Dept. of Civil Engineering, Univ. of British Columbia.
Hamidi, A. 2020. “A novel elasto-thermo-viscoplastic model for the isotropic compression of structured clays.” J. Hazard. Toxic Radioact. Waste 24 (4): 06020003. https://doi.org/10.1061/(ASCE)HZ.2153-5515.0000528.
Hueckel, T., and G. Baldi. 1990. “Thermoplasticity of saturated clays: Experimental constitutive study.” J. Geotech. Eng. 116 (12): 1778–1796. https://doi.org/10.1061/(ASCE)0733-9410(1990)116:12(1778).
Hueckel, T., B. François, and L. Laloui. 2009. “Explaining thermal failure in saturated clays.” Géotechnique 59 (3): 197–212.
Kelln, C., J. Sharma, and D. Hughes. 2008a. “A finite element solution scheme for an elastic–viscoplastic soil model.” Comput. Geotech. 35 (4): 524–536. https://doi.org/10.1016/j.compgeo.2007.10.003.
Kelln, C., J. Sharma, D. Hughes, and J. Graham. 2008b. “An improved elastic–viscoplastic soil model.” Can. Geotech. J. 45 (10): 1356–1376. https://doi.org/10.1139/T08-057.
Kelln, C. G. 2007. “An elastic-viscoplastic constitutive model for soil.” Ph.D. thesis, School of Planning, Architecture, and Civil Engineering, Queen's Univ. Belfast.
Kurz, D., J. Sharma, M. Alfaro, and J. Graham. 2016. “Semi-empirical elastic–thermoviscoplastic model for clay.” Can. Geotech. J. 53 (10): 1583–1599. https://doi.org/10.1139/cgj-2015-0598.
Kurz, D. R. 2014. “Understanding the effects of temperature on the behaviour of clay.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Manitoba.
Laloui, L., and C. Cekerevac. 2003. “Thermo-plasticity of clays: An isotropic yield mechanism.” Comput. Geotech. 30 (8): 649–660. https://doi.org/10.1016/j.compgeo.2003.09.001.
Laloui, L., and C. Cekerevac. 2008. “Numerical simulation of the non-isothermal mechanical behaviour of soils.” Comput. Geotech. 35 (5): 729–745. https://doi.org/10.1016/j.compgeo.2007.11.007.
Leroueil, S. 1996. “Importance of strain rate and temperature effects in geotechnical engineering.” In Measuring and modeling time dependent soil behavior, edited by T. C. Sheahan and V. N. Kaliakin. Reston, VA: ASCE.
Maghoul, P., B. Gatmiri, and D. Duhamel. 2010. “Three-dimensional transient thermo-hydro-mechanical fundamental solutions of unsaturated soils.” Int. J. Numer. Anal. Methods Geomech. 34 (3): 297–329.
Marques, M. E. S., S. Leroueil, and M. D. S. Soares de Almeida. 2004. “Viscous behaviour of St-Roch-de-l’Achigan clay, Quebec.” Can. Geotech. J. 41 (1): 25–38. https://doi.org/10.1139/t03-068.
Mašín, D., and N. Khalili. 2012. “A thermo-mechanical model for variably saturated soils based on hypoplasticity.” Int. J. Numer. Anal. Methods Geomech. 36 (12): 1461–1485. https://doi.org/10.1002/nag.1058.
Mesri, G., and Y. Choi. 1985. “The uniqueness of the end-of-primary (EOP): Void ratio-effective stress relationship.” In Proc., 11th Int. Conf. On Soil Mechanics And Foundation Engineering, 587–590. Rotterdam, Netherlands: Balkema.
Modaressi, H., and L. Laloui. 1997. “A thermo-viscoplastic constitutive model for clays.” Int. J. Numer. Anal. Methods Geomech. 21 (5): 313–335. https://doi.org/10.1002/(ISSN)1096-9853.
Olson, R. E., and G. Mesri. 1970. “Mechanisms controlling compressibility of clays.” J. Soil Mech. Found. Div. 96 (SM6): 1863–1878. https://doi.org/10.1061/JSFEAQ.0001475.
Perzyna, P. 1966. “Fundamental problems in viscoplasticity.” Vol. 9 of Advances in applied mechanics, 243–377. Amsterdam, Netherlands: Elsevier.
Qiao, Y., and W. Ding. 2017. “Acmeg-tvp: A thermoviscoplastic constitutive model for geomaterials.” Comput. Geotech. 81 (3): 98–111. https://doi.org/10.1016/j.compgeo.2016.08.003.
Saaly, M., K. Bobko, P. Maghoul, M. Kavgic, and H. Holländer. 2020. “Energy performance of below-grade envelope of an institutional building in cold regions.” J. Build. Eng. 27: 100911. https://doi.org/10.1016/j.jobe.2019.100911.
Sällfors, G. 1975. “Preconsolidation pressure of soft, high-plastic clays.” Ph.D. thesis, Dept. of Geotechnical, Chalmers Univ. of Technology.
Tanaka, N. 1995. “Thermal elastic plastic behaviour and modelling of saturated clays.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Manitoba.
Taylor, D. W. 1942. Vol. 82 of Research on consolidation of clays. Cambridge, MA: Massachusetts Institute of Technology.
Tsutsumi, A., and H. Tanaka. 2012. “Combined effects of strain rate and temperature on consolidation behavior of clayey soils.” Soils Found. 52 (2): 207–215. https://doi.org/10.1016/j.sandf.2012.02.001.
Wood, D. M. 1990. Soil behaviour and critical state soil mechanics. Cambridge, UK: Cambridge University Press.
Xiong, Y., G. Ye, H. Zhu, S. Zhang, and F. Zhang. 2016. “Thermo-elastoplastic constitutive model for unsaturated soils.” Acta Geotech. 11 (6): 1287–1302. https://doi.org/10.1007/s11440-016-0462-8.
Yashima, A., S. Leroueil, F. Oka, and I. Guntoro. 1998. “Modelling temperature and strain rate dependent behavior of clays: One dimensional consolidation.” Soils Found. 38 (2): 63–73. https://doi.org/10.3208/sandf.38.2_63.
Yin, J.-H. 1999. “Non-linear creep of soils in oedometer tests.” Geotechnique 49 (5): 699–707. https://doi.org/10.1680/geot.1999.49.5.699.
Yin, J.-H., and J. Graham. 1989. “Viscous–elastic–plastic modelling of one-dimensional time-dependent behaviour of clays.” Can. Geotech. J. 26 (2): 199–209. https://doi.org/10.1139/t89-029.
Yin, J.-H., and J. Graham. 1994. “Equivalent times and one-dimensional elastic viscoplastic modelling of time-dependent stress–strain behaviour of clays.” Can. Geotech. J. 31 (1): 42–52. https://doi.org/10.1139/t94-005.
Yin, J.-H., and J. Graham. 1999. “Elastic viscoplastic modelling of the time-dependent stress-strain behaviour of soils.” Can. Geotech. J. 36 (4): 736–745. https://doi.org/10.1139/t99-042.
Yin, J.-H., and F. Tong. 2011. “Constitutive modeling of time-dependent stress–strain behaviour of saturated soils exhibiting both creep and swelling.” Can. Geotech. J. 48 (12): 1870–1885. https://doi.org/10.1139/t11-076.
Yin, J.-H., J.-G. Zhu, and J. Graham. 2002. “A new elastic viscoplastic model for time-dependent behaviour of normally and overconsolidated clays: Theory and verification.” Can. Geotech. J. 39 (1): 157–173. https://doi.org/10.1139/t01-074.
Zhou, C., J.-H. Yin, J.-G. Zhu, and C.-M. Cheng. 2005. “Elastic anisotropic viscoplastic modeling of the strain-rate-dependent stress–strain behavior of K0-consolidated natural marine clays in triaxial shear tests.” Int. J. Geomech. 5 (3): 218–232. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:3(218).
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 22 • Issue 10 • October 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 25, 2021
Accepted: Mar 27, 2022
Published online: Jul 20, 2022
Published in print: Oct 1, 2022
Discussion open until: Dec 20, 2022
ASCE Technical Topics:
- Clays
- Elastic analysis
- Engineering fundamentals
- Geomechanics
- Geotechnical engineering
- Material mechanics
- Materials engineering
- Measurement (by type)
- Model accuracy
- Models (by type)
- Saturated soils
- Simulation models
- Soft soils
- Soil mechanics
- Soil properties
- Soils (by type)
- Strain
- Strain rates
- Structural analysis
- Structural engineering
- Temperature effects
- Temperature measurement
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