Elastoplastic Modeling of Sandy Clays Based on Equivalent Void Ratio Concept
Publication: International Journal of Geomechanics
Volume 23, Issue 8
Abstract
Naturally sedimentary soils, such as marine clays, weathered residual soils, and glacial deposits, usually possess a certain amount of sand particles. These types of soils could be classified as sandy clay, because the coarse fraction is usually under the transitional content. Their mechanical properties (e.g., compressibility and shear strength) are dominated by the clay matrix and significantly affected by the evolving interparticle structure. Previous research into sandy clay is experimental or numerical, and theoretical investigations that considered the reinforcing effect of coarse inclusions have seldom been reported. Therefore, the effect of sand content was incorporated based on the equivalent void ratio (e*) and equivalent compression curve (ECC) of sandy clays. A unified structure parameter (χ) was introduced, which could capture the reinforcing effect of sand particles on the stiffness and shear strength of sandy clays well. The constitutive relationship was formulated by incorporating the equivalent void ratio concept into an elastoplastic framework. Validation of the proposed model was achieved by comparing the predicted results with experimental data that were compiled from the literature. This revealed a satisfactory prediction for the mechanical response of sandy clays and other gap-graded soils (i.e., gravel–clay mixtures) with a broad spectrum of coarse fractions.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was partially supported by the National Natural Science Foundation of China (under Grant No. 52278346; Grant No. 51909194), the Research Grants Council of Hong Kong (under RGC/GRF Grant No. 16201419), and the Funds for the Disciplinary Development (Research Starting Funds for High-level Talents: Grant No. 522020212).
References
Bolzon, G., B. A. Schrefler, and O. C. Zienkiewicz. 1996. “Elastoplastic soil constitutive laws generalized to partially saturated states.” Géotechnique 46 (2): 279–289. https://doi.org/10.1680/geot.1996.46.2.279.
Butterfield, R. 1979. “A natural compression law for soils (an advance on e-log p′).” Géotechnique 29 (4): 469–480. https://doi.org/10.1680/geot.1979.29.4.469.
Chandler, R. J. 2000. “The Third Glossop Lecture: Clay sediments in depositional basins: The geotechnical cycle.” Q. J. Eng. Geol. Hydrogeol. 33 (1): 7–39. https://doi.org/10.1144/qjegh.33.1.7.
Farhat, F., W. Q. Shen, and J. F. Shao. 2017. “A micro-mechanics based viscoplastic model for clayey rocks.” Comput. Geotech. 89: 92–102. https://doi.org/10.1016/j.compgeo.2017.04.014.
Gobbi, S., P. Reiffsteck, L. Lenti, M. P. S. d’Avila, and J. F. Semblat. 2022. “Liquefaction triggering in silty sands: Effects of non-plastic fines and mixture-packing conditions.” Acta Geotech. 17 (2): 391–410. https://doi.org/10.1007/s11440-021-01262-1.
Goudarzy, M., D. König, and T. Schanz. 2016. “Small strain stiffness of granular materials containing fines.” Soils Found. 56 (5): 756–764. https://doi.org/10.1016/j.sandf.2016.08.002.
Guo, J., Y. Cui, W. Xu, Y. Yin, Y. Li, and W. Jin. 2022. “Numerical investigation of the landslide-debris flow transformation process considering topographic and entrainment effects: A case study.” Landslides 19: 773–788. https://doi.org/10.1007/s10346-021-01791-6.
Herle, I., and G. Gudehus. 1999. “Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies.” Mech. Cohesive-frict. Mater. 4 (5): 461–486. https://doi.org/10.1002/(SICI)1099-1484(199909)4:5%3C461::AID-CFM71%3E3.0.CO;2-P.
Jafari, M. K., and A. Shafiee. 2004. “Mechanical behavior of compacted composite clays.” Can. Geotech. J. 41 (6): 1152–1167. https://doi.org/10.1139/t04-062.
Kavvadas, M., and A. Amorosi. 2000. “A constitutive model for structured soils.” Géotechnique 50 (3): 263–273. https://doi.org/10.1680/geot.2000.50.3.263.
Khalili, A., D. Wijewickreme, and G. W. Wilson. 2010. “Mechanical response of highly gap-graded mixtures of waste rock and tailings. Part I: Monotonic shear response.” Can. Geotech. J. 47 (5): 552–565. https://doi.org/10.1139/T09-126.
Kumar, G. V. 1996. Some aspects of the mechanical behaviour of mixtures of kaolin and coarse sand. Glasgow, UK: Univ. of Glasgow.
Liu, W. H., H. Y. Zhang, W. G. Li, G. Q. Kong, and X. Y. Lin. 2022. “An advanced critical state constitutive model for overconsolidated structured soils.” Int. J. Geomech. 22 (5): 06022004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002349.
McDowell, G. R., and K. W. Hau. 2004. “A generalised modified cam clay model for clay and sand incorporating kinematic hardening and bounding surface plasticity.” Granular Matter 6 (1): 11–16. https://doi.org/10.1007/s10035-003-0152-8.
Monkul, M. M., and G. Ozden. 2007. “Compressional behavior of clayey sand and transition fines content.” Eng. Geol. 89 (3–4): 195–205. https://doi.org/10.1016/j.enggeo.2006.10.001.
Mortara, G. 2015. “A constitutive framework for the elastoplastic modelling of geomaterials.” Int. J. Solids Struct. 63: 139–152. https://doi.org/10.1016/j.ijsolstr.2015.02.047.
Ng, T. T., W. Zhou, and G. Ma. 2022. “Numerical study of a binary mixture of similar ellipsoids of various particle shapes and fines contents.” Int. J. Geomech. 22 (4): 04022022. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002325.
Nie, J., et al. 2023. “Predicting residual friction angle of lunar regolith based on Chang’e-5 lunar samples.” Sci. Bull. 68 (7): 730–739. https://doi.org/10.1016/j.scib.2023.03.019.
Nikolinakou, M. A., A. J. Whittle, J. T. Germaine, and G. Zhang. 2022. “Consolidation properties and structural alteration of Old Alluvium.” Acta Geotech. 17: 15691584. https://doi.org/10.1007/s11440-021-01330-6.
Pastor, M., O. C. Zienkiewicz, and A. Chan. 1990. “Generalized plasticity and the modelling of soil behaviour.” Int. J. Numer. Anal. Methods Geomech. 14 (3): 151–190. https://doi.org/10.1002/nag.1610140302.
Peters, J. F., and E. S. Berney IV. 2010. “Percolation threshold of sand-clay binary mixtures.” J. Geotech. Geoenviron. Eng. 136 (2): 310–318. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000211.
Prashant, A., and D. Penumadu. 2005. “Effect of overconsolidation and anisotropy of kaolin clay using true triaxial testing.” Soils Found. 45 (3): 71–82. https://doi.org/10.3208/sandf.45.3_71.
Roscoe, K., and J. B. Burland. 1968. “On the generalized stress-strain behaviour of wet clay.” In Engineering plasticity, edited by J. Heyman and F. A. Leckie, 535–609. Cambridge, UK: Cambridge University Press.
Ruggeri, P., D. Segato, V. M. E. Fruzzetti, and G. Scarpelli. 2016. “Evaluating the shear strength of a natural heterogeneous soil using reconstituted mixtures.” Géotechnique 66 (11): 941–946. https://doi.org/10.1680/jgeot.15.P.022.
Schofield, A. N., and P. Wroth. 1968. Vol. 310 of Critical state soil mechanics. London: McGraw-Hill.
Scott, R. F. 1985. “Plasticity and constitutive relations in soil mechanics.” J. Geotech. Eng. 111 (5): 559–605. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:5(559).
Shafiee, A., H. R. Tavakoli, and M. K. Jafari. 2008. “Undrained behavior of compacted sand-clay mixtures under monotonic loading paths.” J. Appl. Sci. 8 (18): 3108–3118. https://doi.org/10.3923/jas.2008.3108.3118.
Shi, X. S., Y. Gao, and J. Ding. 2021a. “Estimation of the compression behavior of sandy clay considering sand fraction effect based on equivalent void ratio concept.” Eng. Geol. 280: 105930. https://doi.org/10.1016/j.enggeo.2020.105930.
Shi, X. S., K. Liu, and J. Yin. 2021b. “Effect of initial density, particle shape, and confining stress on the critical state behavior of weathered gap-graded granular soils.” J. Geotech. Geoenviron. Eng. 147 (2): 04020160. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002449.
Shi, X. S., and J. Zhao. 2020. “Practical estimation of compression behavior of clayey/silty sands using equivalent void-ratio concept.” J. Geotech. Geoenviron. Eng. 146 (6): 04020046. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002267.
Shi, X. S., J. Zhao, and Y. Gao. 2021c. “A homogenization-based state-dependent model for gap-graded granular materials with fine-dominated structure.” Int. J. Numer. Anal. Methods Geomech. 45 (8): 1007–1028. https://doi.org/10.1002/nag.3189.
Shi, X. S., J. Zhao, J. Yin, and Z. Yu. 2019. “An elastoplastic model for gap-graded soils based on homogenization theory.” Int. J. Solids Struct. 163: 1–14. https://doi.org/10.1016/j.ijsolstr.2018.12.017.
Silva, S. 2016. Three runway system project, contract 3206: Main reclamation works. Rep. for ZHECC-CCCC-CDC Joint Venture. 7076481/R00, Hong Kong.
Su, Y., Y. J. Cui, J. C. Dupla, and J. Canou. 2022. “Modeling the suction-and deviator stress-dependent resilient modulus of unsaturated fine/coarse soil mixture by considering soil-water retention curve.” Acta Geotech. 17 (9): 3747–3763. https://doi.org/10.1007/s11440-022-01452-5.
Sun, Y., Y. Gao, and Q. Zhu. 2018. “Fractional order plasticity modelling of state-dependent behaviour of granular soils without using plastic potential.” Int. J. Plast. 102: 53–69. https://doi.org/10.1016/j.ijplas.2017.12.001.
Sun, Y., and W. Sumelka. 2021. “Multiaxial stress-fractional plasticity model for anisotropically overconsolidated clay.” Int. J. Mech. Sci. 205: 106598. https://doi.org/10.1016/j.ijmecsci.2021.106598.
Thevanayagam, S. 2000. “Liquefaction potential and undrained fragility of silty soils.” In Proc., 12th World Conf. on Earthquake Engineering. Wellington, New Zealand: New Zealand Society of Earthquake Engineering.
Thevanayagam, S., and J. Liang. 2001. “Shear wave velocity relations for silty and gravely soils.” In Proc., 4th Int. Conf. on Soil Dynamics and Earthquake Engineering, 1–15. San Diego: Univ. of Missouri Rolla.
Thevanayagam, S., and G. R. Martin. 2002. “Liquefaction in silty soils—Screening and remediation issues.” Soil Dyn. Earthquake Eng. 22 (9–12): 1035–1042. https://doi.org/10.1016/S0267-7261(02)00128-8.
Thevanayagam, S., T. Shenthan, S. Mohan, and J. Liang. 2002. “Undrained fragility of clean sands, silty sands, and sandy silts.” J. Geotech. Geoenviron. Eng. 128 (10): 849–859. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:10(849).
Tiwari, B., and B. Ajmera. 2011. “Consolidation and swelling behavior of major clay minerals and their mixtures.” Appl. Clay Sci. 54 (3–4): 264–273. https://doi.org/10.1016/j.clay.2011.10.001.
Vallejo, L. E., and R. Mawby. 2000. “Porosity influence on the shear strength of granular material-clay mixtures.” Eng. Geol. 58 (2): 125–136. https://doi.org/10.1016/S0013-7952(00)00051-X.
Wang, S., G. Chen, L. Zhang, and J. Yuan. 2021. “Triaxial discrete element simulation of soil-rock mixture with different rock particle shapes under rigid and flexible loading modes.” Int. J. Geomech. 21 (8): 04021142. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002081.
Wang, X., B. Xu, X. Meng, and Q. Fan. 2022. “Experimental study on the dilatancy characteristics and equation of saturated sand-gravel composites during the whole shearing process.” Int. J. Geomech. 22 (3): 04021310. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002306.
Wickland, B. E. 2006. “Volume change and permeability of mixtures of waste rock and fine tailings.” Ph.D. thesis, The Norman B. Keevil Institute of Mining, Univ. of British Columbia.
Xu, D. S., M. Huang, and Y. Zhou. 2020. “One-dimensional compression behavior of calcareous sand and marine clay mixtures.” Int. J. Geomech. 20 (9): 04020137. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001763.
Xu, L., and M. R. Coop. 2017. “The mechanics of a saturated silty loess with a transitional mode.” Géotechnique 67 (7): 581–596. https://doi.org/10.1680/jgeot.16.P.128.
Yao, Y. P., 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, J. H. 1999. “Properties and behaviour of Hong Kong marine deposits with different clay contents.” Can. Geotech. J. 36 (6): 1085–1095. https://doi.org/10.1139/t99-068.
Zeng, Y., X. Shi, W. Chen, and W. Feng. 2023. “Equivalent compression curve for clay-sand mixtures using equivalent void-ratio concept.” Int. J. Geomech. 23 (2): 06022039. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002643.
Zhou, C., and C. W. W. Ng. 2018. “A new thermo-mechanical model for structured soil.” Géotechnique 68 (12): 1109–1115. https://doi.org/10.1680/jgeot.17.T.031.
Zhou, Z., H. Yang, X. Wang, and B. Liu. 2017. “Model development and experimental verification for permeability coefficient of soil-rock mixture.” Int. J. Geomech. 17 (4): 04016106. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000768.
Zuo, L., and B. A. Baudet. 2015. “Determination of the transitional fines content of sand-non plastic fines mixtures.” Soils Found. 55 (1): 213–219. https://doi.org/10.1016/j.sandf.2014.12.017.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 23 • Issue 8 • August 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Nov 11, 2022
Accepted: Mar 23, 2023
Published online: May 30, 2023
Published in print: Aug 1, 2023
Discussion open until: Oct 30, 2023
ASCE Technical Topics:
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.