A Model of Undrained Stress–Strain Curves Considering Stress Path and Strain Softening
Publication: International Journal of Geomechanics
Volume 21, Issue 11
Abstract
The stress path and strain-softening effect have a great influence on the strength and deformation of soils. Former test results show that the strength and deformation behaviors under lateral unloading conditions are quite different from those under axial loading conditions, especially for the structured soils. Based on the deformation mechanism of structured soils and incremental linear elasticity theory, a four-parameter stress–strain curve model is proposed by analyzing the stress–strain curves of axial loading and lateral unloading consolidated undrained shear tests. The model contains four important parameters: ultimate residual strength, curve shape factor, initial tangent modulus parameter, and peak strength parameter. All the parameters can be determined easily by conventional triaxial tests. Besides, comparisons of predicted and measured results of shear tests of different sands and soft soils indicate that the newly built model can describe the stress–strain curves with extensive adaptability and high accuracy, and it provides a unified nonlinear elastic model for both strain-hardening and strain-softening soils.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was substantially supported by the National Natural Science Foundation of China (Grant No. 40972214) and the Research Project of Zhejiang Provincial Department of Transportation (Grant No. 2014H06). All supports are gratefully acknowledged.
Notation
The following symbols are used in this paper:
- a
- ultimate residual strength;
- Ei
- initial tangent modulus;
- e0
- initial void ratio;
- IL
- liquid index;
- IP
- plasticity index;
- k
- parameter that controls the initial tangential modulus;
- m
- parameter reflecting the peak strength and peak strain;
- patm
- atmospheric pressure;
- Rf
- damage ratio of remolded soil;
- Rr
- residual strength ratio;
- Sr
- saturation degree;
- wL
- liquid limit;
- wP
- plastic limit;
- w
- water content in weight;
- α
- peak index;
- Δɛ
- simulation deviation;
- ɛ
- strain;
- λ
- scale factor that controls curve shape; and
- ρ
- soil density.
References
Asaoka, A., N. Masaki, and N. Toshihiro. 2000. “Superloading yield surface concept for highly structured soil behavior.” Soils Found. 40 (2): 99–110. https://doi.org/10.3208/sandf.40.2_99.
Bai, B., G. Yang, T. Li, and C. Yang. 2019. “A thermodynamic constitutive model with temperature effect based on particle rearrangement for geomaterials.” Mech. Mater. 139: 103180. https://doi.org/10.1016/j.mechmat.2019.103180.
Chen, C., and Z. Zhou. 2013. “Nonlinear elastic model for soils incorporating both dilatancy and strain softening.” Chin. J. Geotech. Eng. 35 (1): 39–43.
Collins, I. F. 2005. “The concept of stored plastic work or frozen elastic energy in soil mechanics.” Géotechnique 55 (5): 373–382. https://doi.org/10.1680/geot.2005.55.5.373.
Collins, I. F., and T. Hilder. 2002. “A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests.” Int. J. Numer. Anal. Methods Geomech. 26 (13): 1313–1347. https://doi.org/10.1002/nag.247.
Collins, I. F., and B. Muhunthan. 2003. “On the relationship between stress–dilatancy, anisotropy and plastic dissipation for granular materials.” Géotechnique 53 (7): 611–618. https://doi.org/10.1680/geot.2003.53.7.611.
Costa, P. A., R. Calcada, A. S. Cardoso, and A. Bodare. 2010. “Influence of soil non-linearity on the dynamic response of high-speed railway tracks.” Soil Dyn. Earthquake Eng. 30 (4): 221–235. https://doi.org/10.1016/j.soildyn.2009.11.002.
Dong, T., L. Kong, M. Zhe, and Y. Zheng. 2018. “Nonlinear model of soils under complex stress paths.” Geotech. Geol. Eng. 36 (5): 3081–3089. https://doi.org/10.1007/s10706-018-0522-y.
Duncan, J. M., and C. Y. Chang. 1970. “Nonlinear analysis of stress and strain in soils.” J. Soil Mech. Found. Div. 96 (5): 1629–1653. https://doi.org/10.1061/JSFEAQ.0001458.
Hamidi, A., S. Tourchi, and F. Kardooni. 2017. “A critical state based thermo-elasto-plastic constitutive model for structured clays.” J. Rock Mech. Geotech. Eng. 9 (6): 1094–1103. https://doi.org/10.1016/j.jrmge.2017.09.002.
Katrina, R. 1997. “The stress–dilatancy behavior of sands: Pressure and density dependence in both monotonic and cyclic loading regime.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Calgary.
Kavvadas, M., and A. Kalos. 2019. “A time-dependent plasticity model for structured soils (TMS) simulating drained tertiary creep.” Comput. Geotech. 109: 130–143. https://doi.org/10.1016/j.compgeo.2019.01.022.
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.
Ranjbarnia, M., A. Fahimifar, and P. Oreste. 2015. “Analysis of non-linear strain-softening behavior around tunnels.” Proc. Inst. Civ. Eng. Geotech. Eng. 168 (1): 16–30. https://doi.org/10.1680/geng.13.00144.
Roscoe, K. H., and J. B. Burland. 1968. Engineering plasticity. Cambridge, UK: Cambridge University Press.
Roscoe, K. H., and A. N. Schofield. 1963. “Mechanical behavior of an idealised ‘wet clay’.” In Proc., 2nd European Conf. on Soil Mechanics and Foundation Engineering, 47–54. Essen, Germany: Deutsche Gesellschaft für Erd- und Grundbau.
Sánchez, M., A. Gens, M. V. Villar, and S. Olivella. 2016. “Fully coupled thermo-hydro-mechanical double-porosity formulation for unsaturated soils.” Int. J. Geomech. 16 (6): D4016015. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000728.
Schofield, A. N., and C. P. Wroth. 1968. Critical state soil mechanics. London: McGraw-Hill.
Shen, Z. 1986. “A nonlinear dilatant stress–strain model for soil sand rock materials.” Hydro-Sci. Eng. 4 (4): 3–16.
Wang, G., S. Xiao, and W. Zhou. 2003. “Determination of preconsolidation pressure and structural strength of undisturbed structural soils.” Chin. J. Geotech. Eng. 25 (2): 249–251. https://doi.org/10.3321/j.issn:1000-4548.2003.02.030.
Wang, W. 2006. “Study on soil–structure interface model based on potential energy dissipating principle and its application.” Ph.D. thesis, Institute of Geotechnical Engineering, Hohai Univ.
Yao, Y., W. Hou, and A.-N. Zhou. 2009. “UH model: Three-dimensional unified hardening model for overconsolidated clays.” Géotechnique 59 (5): 451–469. https://doi.org/10.1680/geot.2007.00029.
Yin, D., H. Wu, C. Cheng, and Y. Q. Chen. 2013. “Fractional order constitutive model of geomaterials under the condition of triaxial test.” Int. J. Numer. Anal. Methods Geomech. 37 (8): 961–972. https://doi.org/10.1002/nag.2139.
Yin, J.-H., J.-G. Zhu, and J. Graham. 2002. “A new elastic viscoplastic model for time-dependent behavior of normally and overconsolidated clays: Theory and verification.” Can. Geotech. J. 39 (1): 157–173. https://doi.org/10.1139/t01-074.
Zhang, C. 1983. “Geotechnical properties of two structural clays.” J. Nanjing Hydraul. Res. Inst. 4: 68–74.
Zhang, R., and S. Chen. 2002. “An experimental study on stress–strain behavior of soft clay along decreasing average normal stress.” Rock Soil Mech. 23 (5): 612–616. https://doi.org/10.3969/j.issn.1000-7598.2002.05.019.
Zhang, S., H. Li, and J. Teng. 2016. “New constructive model for structures soil.” Geomech. Eng. 11 (5): 725–738. https://doi.org/10.12989/gae.2016.11.5.725.
Zhou, Q., and X. Chen. 2009. “Test research on typical mechanical characteristics of soft clay under lateral unloading condition.” Chin. J. Rock Mech. Eng. 28 (11): 2215–2221. https://doi.org/10.3321/j.issn:1000-6915.2009.11.008.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 21 • Issue 11 • November 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Apr 8, 2020
Accepted: Jul 15, 2021
Published online: Sep 6, 2021
Published in print: Nov 1, 2021
Discussion open until: Feb 6, 2022
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Liqin Wang, Kaiyu Li, Zheng Wang, Lun Li, Description and prediction of stress-strain curve of loess, Engineering Geology, 10.1016/j.enggeo.2022.106827, 308, (106827), (2022).