Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Modelling the critical state behaviour of granular soils: Application of NorSand constitutive law to TP-Lisbon sand

  • Received : 2022.08.02
  • Accepted : 2023.07.06
  • Published : 2023.08.10
⟨ Previous Next ⟩

Abstract

The soil behaviour can be represented by numerical modelling of element testing using diverse constitutive models. However, not all constitutive models allow the simulation of the stress-strain response at the critical state in granular soils with both contractive and dilative behaviour. Moreover, the accuracy of these models depends highly on the quality of the experimental data used for their calibration. This study addresses the modelling of the critical state behaviour of an alluvial natural soil from the Lower Tagus Valley (south of Portugal), known as TP-Lisbon sand, using the NorSand constitutive law. For this purpose, a series of numerical simulations of element testing was carried out using two algorithms performed in Visual Basic (VB) and Fast Lagrangian Analysis of Continua (FLAC). Moreover, this study presents the characterisation of of NorSand parameters from an accurate experimental programme based on triaxial and bender element testing. This experimental program allowed defining: (i) the critical state locus, (ii) the stress-dilatancy, and (iii) the soil elasticity of TP-Lisbon sand -all fundamental to calibrate the contractive and dilative behaviour of such alluvial soil. The results revealed a good agreement between experimental data and NorSand simulations using VB and FLAC. Therefore, this study showed that the quality of laboratory testing procedures and its good interpretation enables NorSand constitutive law to capture representatively the non-associated plastic strains, often expressed by the state parameter, allowing a representation of soil behaviour of alluvial soils within the critical state soil mechanics framework for different state parameters.

Keywords

Acknowledgement

This work was financially supported by UIDB/04708/2020 and UIDP/04708/2020 of CONSTRUCT - Institute of R&D in Structures and Construction, Portugal funded by the national funds through the FCT/MCTES (PIDDAC). The second and fourth authors acknowledge the Portuguese Foundation for Science and Technology (FCT) for the support of the grants SFRH/BD/146265/2019 and SFRH/BD/143817/2019, respectively. Acknowledgements are especially due to Dr Cristina Raminhos from 'Metropolitano de Lisboa, E.P.E.' for providing the samples of TP-Lisbon sand. The authors also cknowledge the technical support given by Eng. Daniela Coelho and Mr. Armando Pinto of LabGeo during the development of the experimental program.

References

  1. Been, K. and Jefferies, M. (1985), "A state parameter for sands", Geotechnique, 35(2), 99-112. https://doi.org/10.1680/geot.1985.35.2.99.
  2. Been, K. and Jefferies, M. (2004), "Stress-dilatancy in very loose sand", Can. Geotech. J., 41(5), 972-989. https://doi.org/10.1139/T04-038.
  3. Boulanger, R.W. and Ziotopoulou, K. (2017), PM4SAND (version 3.1): A sand plasticity model for earthquake engineering applications. Davis, California, USA. Retrieved from https://ucdavis.app.box.com/s/wvyr69j5cmq3iu6o9fpzlmzif8r2bwv8.
  4. CEN. ISO 17892-9 (2018), Geotechnical investigation and testing - Laboratory testing of soil - Part 9, Consolidated triaxial compression tests on water saturated soils, International Organization for Standardization, Brussels.
  5. Cho, G.C., Dodds, J. and Santamarina, J.C. (2006), "Particle shape effects on packing density, stiffness, and strength: Natural and crushed sands", J. Geotech. Geoenviron. Eng., 132(5), 591-602. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:5(591).
  6. Desai, C.S. (2005), "Constitutive modeling for geologic materials: significance and directions", Int. J. Geomech., 5(2), 81-84. https://doi.org/10.1061/(ASCE)1532-3641(2005)5:2(81).
  7. Ferreira, C., Diaz-Duran, F., Viana da Fonseca, A. and Cascante, G. (2021), "New approach to concurrent Vs and Vp measurements using bender elements", Geotech. Test. J., 44(6), 1801. https://doi.org/10.1520/GTJ20200207.
  8. Ghafghazi, M. and Shuttle, D. (2008), "Interpretation of sand state from cone penetration resistance", Geotechnique, 58(8), 623-634. https://doi.org/10.1680/geot.2008.58.8.623.
  9. Giretti, D., Fioravante, V., Been, K. and Dickenson, S. (2018), "Mechanical properties of a carbonate sand from a dredged hydraulic fill", Geotechnique, 68(5), 410-420. https://doi.org/10.1680/jgeot.16.P.304.
  10. Gong, J., Cheng, L., Zhao, L., Zou, J., Li, L. and Nie, Z. (2021), "Study on the packing and shear characteristics of granular mixtures via the DEM", Geomech. Eng., 27(3), 223-237. https://doi.org/10.12989/gae.2021.27.3.223.
  11. Gouveia, F., Viana da Fonseca, A., Carrilho Gomes, R. and Teves-Costa, P. (2018), "Deeper Vs profile constraining the dispersion curve with the ellipticity curve: A case study in Lower Tagus Valley, Portugal", Soil Dyn. Earthq. Eng., 109, 188-198. https://doi.org/10.1016/J.SOILDYN.2018.03.010.
  12. Gu, X., Yang, J. and Huang, M. (2013), "Laboratory measurements of small strain properties of dry sands by bender element", Soils Found., 53(5), 735-745. https://doi.org/10.1016/j.sandf.2013.08.011.
  13. Jamil, I., Ahmad, I., Ullah, W., Junaid, M. and Khan, S.A. (2022), "Uniform large scale cohesionless soil sample preparation using mobile pluviator", Geomech. Eng., 28(5), 521-529. https://doi.org/10.12989/gae.2022.28.5.521.
  14. Jefferies, M. (1993), "Nor-Sand: a simple critical state model for sand", Geotechnique, 43(1), 91-103. https://doi.org/10.1680/geot.1993.43.1.91.
  15. Jefferies, M. and Been, K. (2015), Soil Liquefaction: A Critical State Approach (2nd ed.). Milton Park, Abingdon: CRC Press.
  16. Jefferies, M., Shuttle, D. and Been, K. (2015), "Principal stress rotation as cause of cyclic mobility", Geotech. Res., 2(2), 66-96. https://doi.org/10.1680/jgere.15.00002.
  17. Lee, J.S. and Santamarina, J.C. (2005), "Bender elements: performance and signal interpretation", J. Geotech. Geoenviron. Eng., 131(9), 1063-1070. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:9(1063).
  18. Mendoza, C. and Muniz de Farias, M. (2020), "Critical state model for structured soil", J. Rock Mech. Geotech. Eng., 12(3), 630-641. https://doi.org/10.1016/j.jrmge.2019.12.006.
  19. Miranda, L., Caldeira, L., Serra, J. and Gomes, R.C. (2020), "Dynamic behaviour of Tagus River sand including liquefaction", Bull. Earthq. Eng., 18(10), 4581-4604. https://doi.org/10.1007/s10518-020-00881-5.
  20. Molina-Gomez, F., Caicedo, B. and Viana da Fonseca, A. (2019), "Physical modelling of soil liquefaction in a novel micro shaking table", Geomech. Eng., 19(3), 229-240. https://doi.org/10.12989/gae.2019.19.3.229.
  21. Molina-Gomez, F. and Viana da Fonseca, A. (2021), "Key geomechanical properties of the historically liquefiable TP-Lisbon sand", Soils Found., 61(3), 836-856. https://doi.org/10.1016/j.sandf.2021.03.004.
  22. Molina-Gomez, F., Viana da Fonseca, A., Ferreira, C. and Caicedo, B. (2023), "Improvement of cyclic liquefaction resistance induced by partial saturation: An interpretation using wave-based approaches", Soil Dyn. Earthq. Eng., 167, 107819. https://doi.org/10.1016/j.soildyn.2023.107819.
  23. Molina-Gomez, F., Viana da Fonseca, A., Ferreira, C. and Camacho-Tauta, J. (2020), "Dynamic properties of two historically liquefiable sands in the Lisbon area", Soil Dyn. Earthq. Eng., 132, 106101. https://doi.org/10.1016/j.soildyn.2020.106101.
  24. Nieto-Leal, A. and Kaliakin, V.N. (2021), "Additional insight into generalized bounding surface model for saturated cohesive soils", Int. J. Geomech., 21(6). https://doi.org/10.1061/(ASCE)GM.1943-5622.0002012.
  25. Nova, R. (1982), "A constitutive model for soil under monotonic and cyclic loading", (Eds., G. Pande and O. Zienkiewicz), Soil Mechanics - Transient and Cyclic Loads, 343-373. Chichester, UK: Wiley.
  26. Nova, R. (1994), "Controllability of the incremental response of soil specimens subjected to arbitrary loading programmes", J. Mech. Behavior Mater., 5(2), 193-201. https://doi.org/10.1515/JMBM.1994.5.2.193.
  27. Petalas, A.L., Dafalias, Y.F. and Papadimitriou, A.G. (2020), "SANISAND-F: Sand constitutive model with evolving fabric anisotropy", Int. J. Solids Struct., 188-189, 12-31. https://doi.org/10.1016/j.ijsolstr.2019.09.005.
  28. Quinteros, V.S. and Carraro, J. A. H. (2023), "The initial fabric of undisturbed and reconstituted fluvial sand", Geotechnique, 73(1), 1-15. https://doi.org/10.1680/jgeot.20.P.121.
  29. Ramos, C., Viana da Fonseca, A. and Vaunat, J. (2015), "Modeling flow instability of an Algerian sand with the dilatancy rule in CASM", Geomech. Eng., 9(6), 729-742. https://doi.org/10.12989/gae.2015.9.6.729.
  30. Reid, D., Fourie, A., Ayala, J.L., Dickinson, S., Ochoa-Cornejo, F., Fanni, R. and Suazo, G. (2021). "Results of a critical state line testing round robin programme", Geotechnique, 71(7), 616-630. https://doi.org/10.1680/jgeot.19.p.373.
  31. Santamarina, J.C., Rinaldi, V.A., Fratta, D., Klein, K.A., Wang, Y.-H., Cho, G.C. and Cascante, G. (2005), "A survey of elastic and electromagnetic properties of near-surface soils", (Ed., D.K. Butler), Near-Surface Geophysics, 71-87. Society of Exploration Geophysicists. https://doi.org/10.1190/1.9781560801719.ch4
  32. Schofield, A.N. and Wroth, C.P. (1968), Critical State Soil Mechanics, 25, https://doi.org/10.1111/j.1475-2743.1987.tb00718.x.
  33. Shuttle, D. and Cunning, J. (2007), "Liquefaction potential of silts from CPTu", Can. Geotech. J., 44(1), 1-19. https://doi.org/10.1139/T06-086.
  34. Shuttle, D. and Jefferies, M. (2016), "Determining silt state from CPTu", Geotech. Res., 3(3), 90-118. https://doi.org/10.1680/jgere.16.00008.
  35. Soares, M. and Viana da Fonseca, A. (2016), "Factors affecting steady state locus in triaxial tests", Geotech. Test. J., 39(6), 20150228. https://doi.org/10.1520/GTJ20150228.
  36. Suwal, L.P. and Kuwano, R. (2013), "Statically and dynamically measured poisson's ratio of granular soils on triaxial laboratory specimens", Geotech. Test. J., 36(4), 20120108. https://doi.org/10.1520/GTJ20120108.
  37. Taiebat, M., Dafalias, Y.F., Taiebat, M. and Dafalias, Y.F. (2008), "SANISAND: Simple anisotropic sand plasticity model", Int. J. Numer. Anal. Method. Geomech., 32(8), 915-948. https://doi.org/10.1002/NAG.651.
  38. Verdugo, R. and Ishihara, K. (1996), "The steady state of sandy soils", Soils Found., 36(2), 81-91. https://doi.org/10.3208/sandf.36.2_81.
  39. Viana da Fonseca, A., Cordeiro, D. and Molina-Gomez, F. (2021), "Recommended procedures to assess critical state locus from triaxial tests in cohesionless remoulded samples", Geotechnics, 1(1), 95-127. https://doi.org/10.3390/GEOTECHNICS1010006.
  40. Viana da Fonseca, A., Cordeiro, D., Molina-Gomez, F., Besenzon, D., Fonseca, A. and Ferreira, C. (2022), "The mechanics of iron tailings from laboratory tests on reconstituted samples collected in post-mortem Dam I in Brumadinho", Soils Rocks, 45(2), 1-20. https://doi.org/10.28927/SR.2022.001122.
  41. Viana da Fonseca, A., Ferreira, C. and Fahey, M. (2009), "A framework interpreting bender element tests, combining time-domain and frequency-domain methods", Geotech. Test. J., 32(2), 100974. https://doi.org/10.1520/GTJ100974.
  42. Viana da Fonseca, A., Molina-Gomez, F. and Ferreira, C. (2023), "Liquefaction resistance of TP-Lisbon sand: a critical state interpretation using in situ and laboratory testing", Bull. Earthq. Eng., 21(2), 767-790. https://doi.org/10.1007/s10518-022-01577-8.
  43. Wichtmann, T., Fuentes, W. and Triantafyllidis, T. (2019), "Inspection of three sophisticated constitutive models based on monotonic and cyclic tests on fine sand: Hypoplasticity vs. Sanisand vs. ISA", Soil Dyn. Earthq. Eng., 124, 172-183. https://doi.org/10.1016/j.soildyn.2019.05.001.
  44. Wichtmann, T. and Triantafyllidis, T. (2010), "On the influence of the grain size distribution curve on P-wave velocity, constrained elastic modulus Mmax and Poisson's ratio of quartz sands", Soil Dyn. Earthq. Eng., 30(8), 757-766. https://doi.org/10.1016/j.soildyn.2010.03.006.
  45. Wood, D.M. (2004), Geotechnical Modelling (1st Ed.), Milton Park, Abingdon: CRC Press.
  46. Xu, L. and Coop, M.R. (2017). "The mechanics of a saturated silty loess with a transitional mode", Geotechnique, 67(7), 581-596. https://doi.org/10.1680/jgeot.16.P.128.
  47. Yang, Z., Elgamal, A. and Parra, E. (2003), "Computational model for cyclic mobility and associated shear deformation", J. Geotech. Geoenviron. Eng., 129(12), 1119-1127. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:12(1119).