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Thermodynamic basis of granular STZ model and its application in revealing shear resistance reduction mechanisms of granular soils under vibration

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Abstract

The granular shear-transformation-zone (STZ) model is an energy-based constitutive model for studying granular materials subjected to vibration. This paper provides a detailed analysis of the thermodynamic foundation of the granular STZ model and applies it to investigate the mechanism of vibration-induced shear resistance reduction (ViSRR) in granular soils. Firstly, using the principles of thermodynamics, an energy conversion equation for a mechanical-energy-governed granular soil system is derived, accounting for vibration energy, configurational energy, strain energy, and contact energy dissipation. Then, by incorporating the critical state concept from soil mechanics, the energy conversion function is used to develop the evolution law of configurational temperature, one of the three governing functions of the granular STZ model. The analysis shows that ViSRR is influenced by the rate of strain energy development and the input rate of vibration energy, and that a limitation in soil deformation during vibration is necessary for ViSRR to occur. Furthermore, the contact energy dissipation arising from inelastic contact deformation and particle collisions contributes to enhancing a granular soil’s shear resistance by absorbing part of the external energy applied to the soil.

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References

  1. Airey, D.W., Ghorbani, J.: Analysis of unsaturated soil columns with application to bulk cargo liquefaction in ships. Comput. Geotech. 140, 104402 (2021)

    Article  Google Scholar 

  2. Asmaei, S., Shourijeh, P.T., Binesh, S.M., Ghaedsharafi, M.H.: An Experimental Parametric Study of Segregation in Cohesionless Soils of Embankment Dams. Geotechn. Test. J. 41(3), 473–493 (2018)

    Google Scholar 

  3. Barkan, D.D.: Dynamics of Bases and Fundations. In: Drashevska, L. (ed.) Trans, pp. 207–210. McGraw-Hill, New, York (1962)

    Google Scholar 

  4. Bingham, C.M., Stone, D.A., Schofield, N., Howe, D., Peel, D.: Amplitude and frequency control of a vibratory pile driver. IEEE Trans. Indust. Electron. 47(3), 623–631 (2000)

    Article  Google Scholar 

  5. Blekhman, I.I.: Vibrational Mechanics, p. 509. World Scientific, Singapore (2000)

    Book  Google Scholar 

  6. Bouchbinder, E., Langer, J.S.: Nonequilibrium thermodynamics of driven amorphous materials. I. Internal degrees of freedom and volume deformation. Phys. Rev. E 80(3), 031131 (2009)

    Article  ADS  Google Scholar 

  7. Bouchbinder, E., Langer, J.S.: Nonequilibrium thermodynamics of driven amorphous materials. II. Effective-temperature theory. Phys. Rev. E 80(3), 031132 (2009)

    Article  ADS  Google Scholar 

  8. Chen, L., Ghorbani, J., Zhang, C., Dutta, T.T., Kodikara, J.: A novel unified model for volumetric hardening and water retention in unsaturated soils. Comput. Geotechn. 140, 104446 (2021)

    Article  Google Scholar 

  9. Denies, N.: Dynamic behavior of vibrated dry sand: sphere penetration experiments and discrete element modeling of vibrofluidization (Doctoral dissertation, UCL-Université Catholique de Louvain) (2010)

  10. Denies, N., Holeyman, A.: Shear strength loss of vibrated dry sand. Soil Dyn. Earthq. Eng. 95, 106–117 (2017)

    Article  Google Scholar 

  11. Edwards, S.F., Oakeshott, R.B.S.: Theory of powders. Phys. A Statist. Mechan. Appl. 157(3), 1080–1090 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  12. Edwards, S.F., Grinev, D.V.: Statistical mechanics of vibration-induced compaction of powders. Phys. Rev. E 58(4), 4758 (1998)

    Article  ADS  Google Scholar 

  13. Falk, M.L., Langer, J.S.: Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E 57(6), 7192 (1998)

    Article  ADS  Google Scholar 

  14. Ferdowsi, B., Griffa, M., Guyer, R.A., Johnson, P.A., Marone, C., Carmeliet, J.: Three-dimensional discrete element modeling of triggered slip in sheared granular media. Phys. Rev. E 89(4), 042204 (2014)

    Article  ADS  Google Scholar 

  15. Ferdowsi, B., Griffa, M., Guyer, R.A., Johnson, P.A., Marone, C., Carmeliet, J.: Acoustically induced slip in sheared granular layers: application to dynamic earthquake triggering. Geophys. Res. Lett. 42(22), 9750–9757 (2015)

    Article  ADS  Google Scholar 

  16. Griffa, M., Ferdowsi, B., Guyer, R.A., Daub, E.G., Johnson, P.A., Marone, C., Carmeliet, J.: Influence of vibration amplitude on dynamic triggering of slip in sheared granular layers. Phys. Rev. E 87(1), 012205 (2013)

    Article  ADS  Google Scholar 

  17. Haff, P.K.: A physical picture of kinetic granular fluids. J. Rheol. 30(5), 931–948 (1986)

    Article  ADS  Google Scholar 

  18. Heerema, E.P.: Predicting pile driveability: Heather as an illustration of the "friction fatigue" theory. In SPE European Petroleum Conference. Society of Petroleum Engineers (1978, January)

  19. Hosoi, A.E., Goldman, D.I.: Beneath our feet: strategies for locomotion in granular media. Ann. Rev. Fluid Mech. 47, 1023 (2015)

    Article  MathSciNet  Google Scholar 

  20. Jaeger, H.M., Nagel, S.R., Behringer, R.P.: Granular solids, liquids, and gases. Rev. Modern Phys. 68(4), 1259 (1996)

    Article  ADS  Google Scholar 

  21. Kothari, K.R., Elbanna, A.E.: Localization and instability in sheared granular materials: Role of friction and vibration. Phys. Rev. E 95(2), 022901 (2017)

    Article  ADS  Google Scholar 

  22. Kremer, G.M.: Entropy, entropy flux and entropy rate of granular materials. Phys. A Statist. Mechan. Appl. 389(19), 4018–4025 (2010)

    Article  ADS  Google Scholar 

  23. Krey, H.: Erddruck. Erdwiderstand und Tragfähigkeit des Baugrundes Berlin, Deutschland, Wilhelm Ernst ahd Sohn (1932)

  24. Lemaître, A.: Rearrangements and dilatancy for sheared dense materials. Phys. Rev. Lett. 89(19), 195503 (2002)

    Article  ADS  Google Scholar 

  25. Mehta, A., Edwards, S.F.: Statistical mechanics of powder mixtures. Phys. A Statist. Mechan. Appl. 157(3), 1091–1100 (1989)

    Article  MathSciNet  ADS  Google Scholar 

  26. Melosh, H.J.: The mechanics of large rock avalanches: Geological Society of America Review in Engineering Geology, v. 7 (1987)

  27. Melosh, H.J.: Dynamical weakening of faults by acoustic fluidization. Nature 379(6566), 601–606 (1996)

    Article  ADS  Google Scholar 

  28. Moriyasu, S., Kobayashi, S.I., Matsumoto, T.: Experimental study on friction fatigue of vibratory driven piles by in situ model tests. Soils Foundat. 58(4), 853–865 (2018)

    Article  Google Scholar 

  29. O’Neill, M.W., Vipulanadan, C., Wong, D.O.: Evaluation of bearing capacity of vibro-driven piles from laboratory experiments. Transportation Research Record, (1277) (1990)

  30. Osinov, V.A.: Application of a high-cycle accumulation model to the analysis of soil liquefaction around a vibrating pile toe. Acta Geotechn. 8(6), 675–684 (2013)

    Article  Google Scholar 

  31. Pestana, J.M., Hunt, C.E., Bray, J.D.: Soil deformation and excess pore pressure field around a closed-ended pile. J. Geotechn. Geoenviron. Eng. 128(1), 1–12 (2002)

    Article  Google Scholar 

  32. Roscoe, K.H., Schofield, A., Wroth, A.P.: On the yielding of soils. Geotechnique 8(1), 22–53 (1958). https://doi.org/10.1680/geot.1958.8.1.22

    Article  Google Scholar 

  33. Schofield, A.N., Wroth, P.: Critical state soil mechanics. Soil Use Manag. 25(3), 105–128 (1968). https://doi.org/10.1111/j.1475-2743.1987.tb00718.x

    Article  Google Scholar 

  34. Sharpe, S.S., Kuckuk, R., Goldman, D.I.: Controlled preparation of wet granular media reveals limits to lizard burial ability. Phys. Biol. 12(4), 046009 (2015)

    Article  ADS  Google Scholar 

  35. Taslagyan, K.A., Chan, D.H., Morgenstern, N.R.: Effect of vibration on the critical state of dry granular soils. Granular Matter 17(6), 687–702 (2015)

    Article  Google Scholar 

  36. Taslagyan, K.A., Chan, D.H., Morgenstern, N.R.: Vibrational fluidization of granular media. Int. J. Geomechan. 16(3), 04015080 (2016)

    Article  Google Scholar 

  37. Urata, S., Li, S.: A multiscale shear-transformation-zone (STZ) model and simulation of plasticity in amorphous solids. Acta Mater. 155, 153–165 (2018)

    Article  ADS  Google Scholar 

  38. Uzuoka, R., Sento, N., Kazama, M., Unno, T.: Landslides during the earthquakes on May 26 and July 26, 2003 in Miyagi Japan. Soils and Foundations 45(4), 149–163 (2005)

    Article  Google Scholar 

  39. White, D.J., Lehane, B.M.: Friction fatigue on displacement piles in sand. Géotechnique 54(10), 645–658 (2004)

    Article  Google Scholar 

  40. Xie, T., Guo, P.: A modified triaxial apparatus for soils under high-frequency. low-amplitude vibrations. Geotechnical Testing Journal 45(1), 203 (2021)

    Google Scholar 

  41. Xie, T., Guo, P., Stolle, D.: Experimental investigation of vibration-induced shear resistance reduction in sheared granular soils. Canada Geotechn. J. (2022). https://doi.org/10.1139/cgj-2021-0662

    Article  Google Scholar 

  42. Youd, T.L.: The engineering properties of cohesionless materials during vibration. PhD dissertation, Iowa State University (1967)

  43. Zhao, C.F., Salami, Y., Hicher, P.Y., Yin, Z.Y.: Multiscale modeling of unsaturated granular materials based on thermodynamic principles. Contin. Mechan. Thermodyn. 31(1), 341–359 (2019)

    Article  MathSciNet  ADS  Google Scholar 

  44. Pestana, J.M., Whittle, A.J.: Compression model for cohesionless soils. Géotechnique 45(4), 611–631 (1995)

    Google Scholar 

  45. Einav, I.: Breakage mechanics–part I: theory. J. Mechan. Phys. Solids 55(6), 1274–1297 (2007)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  46. Forterre, Y., Pouliquen, O.: Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 1–24 (2008)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  47. Xie, T., Guo, P., Stolle, D.: Development of extended STZ model for granular soils subjected to combined static loading and vibration. Géotechnique (2022). https://doi.org/10.1680/jgeot.22.00099

    Article  Google Scholar 

  48. Xie, T., Guo, P., Stolle, D.: Experimental and modelling investigation of vibration-induced fluidization in sheared granular soils. International Journal for Numerical and Analytical Methods in Geomechanics. https://doi.org/10.1002/nag.3520 (2023)

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Acknowledgements

Funding from the Natural Sciences and Engineering Research Council of Canada is greatly appreciated.

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  1. Department of Civil Engineering, McMaster University, 1280 Main St W, Hamilton, ON, L8S 4L7, Canada

    Tao Xie, Peijun Guo & Dieter Stolle

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  1. Tao Xie
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Correspondence to Tao Xie.

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Communicated by Andreas Öchsner.

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Xie, T., Guo, P. & Stolle, D. Thermodynamic basis of granular STZ model and its application in revealing shear resistance reduction mechanisms of granular soils under vibration. Continuum Mech. Thermodyn. 35, 2239–2253 (2023). https://doi.org/10.1007/s00161-023-01244-6

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