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Soil Mechanical Behaviour and Its Modelling

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Modelling of Soil Behaviour with Hypoplasticity

Part of the book series: Springer Series in Geomechanics and Geoengineering ((SSGG))

Abstract

In this chapter, the two features of soil (and particulate material in general) mechanical behaviour that distinguish it from most other materials are introduced: stiffness non-linearity and asymptotic behaviour. Supporting experimental evidence is outlined, along with various modelling concepts suggested by different researchers in the past. The aim of this Chapter is to present the background needed for understanding the merits of hypoplastic modelling compared to the more standard elasto-plastic approaches.

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Notes

  1. 1.

    Note that the isotropic asymptotic state is defined here by \(\psi _{\dot{\varepsilon }}=0^\circ \); the corresponding asymptotic \(\psi _{\sigma }\) may then differ from \(0^\circ \) in the case of an anisotropic soil.

  2. 2.

    OCR is traditionally defined as \(OCR=p_c/p\), where \(p_c\) is the preconsolidation pressure. In this book, definition (2.3) will be preferred, as no additional assumptions about the quasi-elastic soil behaviour are needed for its quantification.

References

  1. Tamagnini, C., Viggiani, G.: Constitutive modelling for rate-independent soils: a review. Revue Française de Génie Civil 6(6), 933–974 (2002)

    Google Scholar 

  2. Puzrin, A.: Constitutive Modelling in Geomechanics. Springer, Berlin (2012)

    Google Scholar 

  3. Tresca, H.: Sur l’ecoulement des corps solides soumis a de fortes pressions. C. R. Acas. Sci. (Paris) 59, 754 (1864)

    Google Scholar 

  4. von Mises, R.: Mechanik der festen Korper im plastisch deformation. Zustand. Nachr. Ges. Wiss. Gottigen p. 582 (1913)

    Google Scholar 

  5. Coulomb, C.A.: Essai sur une application des regeles de maximis & minimis a quelques problemes de statique relatifs a l’architecture. Mem. de Math. et de Phys., presentes a l’Acad. Roy des Sci., Paris 7, 343–382 (1776)

    Google Scholar 

  6. Mohr, O.: Welche umstände bedingen die elastizitätsgrenze und den bruch eines materials? Zeitschrift des Vereines Deutscher Ingenieure 44, 1524–1530, 1572–1577 (1900)

    Google Scholar 

  7. Drucker, D.C., Prager, W.: Soil mechanics and plastic analysis or limit design. Q. Appl. Math. 10, 157–165 (1952)

    MathSciNet  MATH  Google Scholar 

  8. von Mises, R.: Mechanik der plastischen Formaenderung von Kristallen. Z. Angew. Math. Mech. 8, 161–185 (1928)

    MATH  Google Scholar 

  9. Melan, E.: Ingenieur-Archiv. Zur Plastizität des räumlischen Kontinuums 9, 116–126 (1938)

    Google Scholar 

  10. Prager, W.: The theory of plasticity - a survey of recent achievements. Proc. Inst. Mech. Eng. 3–19 (1955)

    Google Scholar 

  11. Schofield, A.N., Wroth, C.P.: Critical State Soil Mechanics. McGraw-Hill, London (1968)

    Google Scholar 

  12. Roscoe, K.H., Burland, J.B.: On the generalised stress-strain behaviour of wet clay. In: Heyman, J., Leckie, F.A. (eds.) Engineering Plasticity, pp. 535–609. Cambridge University Press, Cambridge (1968)

    Google Scholar 

  13. Bishop, A.W., Wesley, L.D.: A hydraulic triaxial apparatus for controlled stress path testing. Géotechnique 25(4), 657–670 (1975)

    Google Scholar 

  14. Jardine, R.J., Symes, M.J., Burland, J.B.: The measurement of soil stiffness in the triaxial apparatus. Géotechnique 34(3), 323–340 (1984)

    Google Scholar 

  15. Atkinson, J.H.: Non-linear soil stiffness in routine design. Géotechnique 50(5), 487–508 (2000)

    Google Scholar 

  16. Symes, M.J., Burland, J.B.: Determination of local displacements on soil samples. Geotech. Test. J. 7, 49–59 (1984)

    Google Scholar 

  17. Cooke, R.W., Price, G.: Horisontal inclinometers for the measurement of vertical displacement in the soil around experimental foundations. Field Instrumentation in Geotechnical Engineering, pp. 112–125. Butterworths, London (1974)

    Google Scholar 

  18. Cuccovillo, T., Coop, M.R.: The measurement of local axial strains in tiaxial tests using LVDT’s. Géotechnique 47(1), 167–171 (1997)

    Google Scholar 

  19. Clayton, C.R.I., Khatrush, S.A.: A new device for measuring local axial strains on triaxial specimens. Géotechnique 36(4), 593–597 (1986)

    Google Scholar 

  20. Ezaoui, A., Di Benedetto, H.: Experimental measurements of the global anisotropic elastic behaviour of dry Hostun sand during triaxial tests, and effect of sample preparation. Géotechnique 57(7), 621–635 (2009)

    Google Scholar 

  21. White, D.J., Take, W.A., Bolton, M.D.: Soil deformation measurement using particle image velocimetry (piv) and photogrammetry. Géotechnique 53(7), 619–631 (2003)

    Google Scholar 

  22. Kung, G.T.C.: Equipment and testing procedures for small strain triaxial tests. J. Chin. Inst. Eng. 30(4), 579–591 (2007)

    Google Scholar 

  23. Gasparre, A.: Advanced laboratory characterisation of London clay. Ph.D. thesis, University of London, Imperial College of Science, Technology and Medicine (2005)

    Google Scholar 

  24. Gasparre, A., Nishimura, S., Minh, N.A., Coop, M.R., Jardine, R.J.: The stiffness of natural London clay. Géotechnique 57(1), 33–47 (2007)

    Google Scholar 

  25. Atkinson, J.H., Richardson, D., Stallebrass, S.E.: Effects of recent stress history on the stiffness of overconsolidated soil. Géotechnique 40(4), 531–540 (1990)

    Google Scholar 

  26. Lings, M.L., Pennington, D.S., Nash, D.F.T.: Anisotropic stiffness parameters and their measurement in a stiff natural clay. Géotechnique 50(2), 109–125 (2000)

    Google Scholar 

  27. Shirley, D.J., Hampton, L.D.: Shear-wave measurements in laboratory sediments. J. Acoust. Soc. Am. 63(2), 607–613 (1978)

    Google Scholar 

  28. Richart, F.E., Hall, J.R., Woods, R.D.: Vibrations of Soils and Foundations. Prentice Hall Inc, Englewood Cliffs (1970)

    Google Scholar 

  29. Hardin, B.O., Drnevich, V.P.: Modulus and damping of soils I: measurement and parameters effect. J. Soil Mech. Found. Div. ASCE 98(7), 667–692 (1972)

    Google Scholar 

  30. Kumar, J., Clayton, C.R.I.: Effect of sample torsional stiffness on resonant column test results. Can. Geotech. J. 44, 201–230 (2007)

    Google Scholar 

  31. Leong, E.C., Yeo, S.H., Rahardjo, H.: Measuring shear wave velocity using bender elements. Geotech. Test. J. 28(5), 488–498 (2005)

    Google Scholar 

  32. Jardine, R.J., Potts, D.M., Fourie, D.M., Burland, J.B.: Studies of the influence of non-linear stress-strain characteristics in soil-structure interaction. Géotechnique 36(3), 377–396 (1986)

    Google Scholar 

  33. Addenbrooke, T., Potts, D., Puzrin, A.: The influence of pre-failure soil stiffness on the numerical analysis of tunnel construction. Géotechnique 47(3), 693–712 (1997)

    Google Scholar 

  34. Franzius, J.N., Potts, D.M., Burland, J.B.: The influence of soil anisotropy and \(K_0\) on ground surface movements resulting from tunnel excavation. Géotechnique 55(3), 189–199 (2005)

    Google Scholar 

  35. Daffalias, Y.F.: Bounding surface plasticity. I: mathematical foundation and hypoplasticity. J. Eng. Mech. ASCE 112(9), 966–987 (1986)

    Google Scholar 

  36. Russell, A.R., Khalili, N.: A unified bounding surface plasticity model for unsaturated soils. Int. J. Numer. Anal. Methods Geomech. 30(3), 181–212 (2006)

    MATH  Google Scholar 

  37. Khalili, N., Habte, M.A., Valliapan, S.: A bounding surface plasticity model for cyclic loading of granular soils. Int. J. Numer. Methods Eng. 63, 1939–1960 (2005)

    MATH  Google Scholar 

  38. Hashiguchi, K.: Subloading surface model in unconventional plasticity. Int. J. Solids Struct. 25(8), 917–945 (1989)

    MATH  Google Scholar 

  39. Hashiguchi, K., Saitoh, K., Okayasu, T., Tsutsumi, S.: Evaluation of typical conventional and unconventional plasticity models in prediction of softening behaviour of soils. Géotechnique 52(8), 561–578 (2002)

    Google Scholar 

  40. Whittle, A.J.: Evaluation of a constitutive model for overconsolidated clays. Géotechnique 43(2), 289–313 (1993)

    Google Scholar 

  41. Whittle, A.J., Kavvadas, M.J.: Formulation of MIT-E3 constitutive model for overconsolidated clays. J. Geotech. Eng. ASCE 120(1), 173–198 (1994)

    Google Scholar 

  42. Pestana, J.M., Whittle, A.J.: Formulation of a unified constitutive model for clays and sands. Int. J. Numer. Anal. Methods Geomech. 23, 1215–1243 (1999)

    MATH  Google Scholar 

  43. Schanz, T., Vermeer, P.A., Bonnier, P.G.: The hardening soil model: formulation and verification. In: Beyond 2000 in Computational Geotechnics - 10 Years of PLAXIS, pp. 281–296. Balkema, Rotterdam (2000)

    Google Scholar 

  44. Pastor, M., Zienkiewicz, O.C., Chan, A.H.C.: Generalised plasticity and the modelling of soil behaviour. Int. J. Numer. Anal. Methods Geomech. 14, 151–190 (1990)

    MATH  Google Scholar 

  45. Rouainia, M., Muir Wood, D.: Implicit numerical integration for a kinematic hardening soil plasticity model. Int. J. Numer. Anal. Methods Geomech. 25, 1305–1325 (2001)

    MATH  Google Scholar 

  46. Mróz, Z.: On the description of anisotropic work-hardening. J. Mech. Phys. Solids 15, 163–175 (1967)

    Google Scholar 

  47. Mroz, Z., Norris, V.A., Zienkiewicz, O.C.: An anisotropic hardening model for soils and its application to cyclic loading. Int. J. Numer. Anal. Methods Geomech. 2, 203–221 (1978)

    MATH  Google Scholar 

  48. Mróz, Z., Norris, V.A., Zienkiewicz, O.C.: Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soil. Géotechnique 29(1), 1–34 (1979)

    Google Scholar 

  49. Al-Tabbaa, A., Muir Wood, D.: An experimentally based “bubble” model for clay. In: Proceedings of the 3th International Conference on Numerical Models in Geomechanics. Niagara Falls (1989)

    Google Scholar 

  50. Rouainia, M., Muir Wood, D.: A kinematic hardening constitutive model for natural clays with loss of structure. Géotechnique 50(2), 153–164 (2000)

    Google Scholar 

  51. Gajo, A., Muir Wood, D.: A new approach to anisotropic, bounding surface plasticity: general formulation and simulations of natural and reconstituted clay behaviour. Int. J. Numer. Anal. Methods Geomech. 25, 207–241 (2001)

    MATH  Google Scholar 

  52. Kavvadas, M., Amorosi, A.: A constitutive models for structured soils. Géotechnique 50(3), 263–273 (2000)

    Google Scholar 

  53. Manzari, M.T., Dafalias, Y.F.: A critical state two-surface plasticity model for sands. Int. J. Numer. Anal. Methods Geomech. 47(2), 255–272 (1997)

    Google Scholar 

  54. Gajo, A., Muir Wood, D.: Severn-Trent sand: a kinematic hardening constitutive model: the \(q\)-\(p\) formulation. Géotechnique 49(5), 595–614 (1999)

    Google Scholar 

  55. Taiebat, M., Dafalias, Y.F.: SANISAND: simple anisotropic sand plasticity model. Int. J. Numer. Anal. Methods Geomech. 32, 915–948 (2008)

    MATH  Google Scholar 

  56. Stallebrass, S.E., Taylor, R.N.: Prediction of ground movements in overconsolidated clay. Géotechnique 47(2), 235–253 (1997)

    Google Scholar 

  57. Baudet, B.A., Stallebrass, S.E.: A constitutive model for structured clays. Géotechnique 54(4), 269–278 (2004)

    Google Scholar 

  58. Grammatikopoulou, A., Zdravković, L., Potts, D.M.: General formulation of two kinematic hardening constitutive models with a smooth elastoplastic transition. Int. J. Geomech. 6(5), 291–302 (2006)

    Google Scholar 

  59. McDowell, G.R., Hau, K.W.: A simple non-associated three surface kinematic hardening model. Géotechnique 53(4), 433–437 (2003)

    Google Scholar 

  60. Puzrin, A.M., Burland, J.B.: Non-linear model of small-strain behaviour of soils. Géotechnique 48(2), 217–233 (1998)

    Google Scholar 

  61. Puzrin, A.M., Burland, J.B.: Kinematic hardening plasticity formulation of small strain behaviour of soils. Int. J. Numer. Anal. Methods Geomech. 24, 753–781 (2000)

    MATH  Google Scholar 

  62. Einav, I., Puzrin, A.M., Houlsby, G.T.: Numerical studies of hyperplasticity with single, multiple and a continuous field of yield surfaces. Int. J. Numer. Anal. Methods Geomech. 27, 837–858 (2003)

    MATH  Google Scholar 

  63. Einav, I., Puzrin, A.M.: Continuous hyperplastic critical state (CHCS) model derivation. Int. J. Solids Struct. 41, 199–226 (2004)

    MATH  Google Scholar 

  64. Einav, I., Puzrin, A.M.: Evaluation of continuous hyperplastic critical state (CHCS) model. Géotechnique 53(10), 901–913 (2003)

    MATH  Google Scholar 

  65. Simpson, B.: Retaining structures: displacement and design. Géotechnique 42(4), 539–576 (1992)

    Google Scholar 

  66. Vukadin, V., Likar, J., Jovičić, V.: Development of a conceptual material model for structured materials - \(\rm {S}\_\rm {BRICK}\). Acta Geotech. Slov. 2005(1), 33–43 (2005)

    Google Scholar 

  67. Ellison, K.C., Soga, K., Simpson, B.: A strain space soil model with evolving stiffness anisotropy. Géotechnique 62(7), 627–641 (2012)

    Google Scholar 

  68. Pande, G.N., Sharma, K.G.: Multi-laminate model for clays - a numerical evaluation of the influence of rotation of principal axes. Int. J. Numer. Anal. Methods Geomech. 7(4), 397–418 (1983)

    MATH  Google Scholar 

  69. Pietruszczak, S., Pande, G.N.: Multi-laminate framework of soil models - plasticity formulation. Int. J. Numer. Anal. Methods Geomech. 11(6), 651–658 (1987)

    MATH  Google Scholar 

  70. Cudny, M., Vermeer, P.A.: On the modelling of anisotropy and destruction of soft clays within the multi-laminate framework. Comput. Geotech. 31(1), 1–22 (2004)

    Google Scholar 

  71. Scharinger, F., Schweiger, H.F., Pande, G.N.: On a multilaminate model for soil incorporating small strain stiffness. Int. J. Numer. Anal. Methods Geomech. 33, 215–243 (2009)

    MATH  Google Scholar 

  72. Benz, T., Vermeer, P.A., Schwab, R.: A small-strain overlay model. Int. J. Numer. Anal. Methods Geomech. 33, 25–44 (2009)

    MATH  Google Scholar 

  73. Benz, T.: Small-strain stiffness of soils and its numerical consequences. Ph.D. thesis, University of Stuttgart (2007)

    Google Scholar 

  74. Hueckel, T., Nova, R.: Some hysteresis effects of the behaviour of geological media. Int. J. Solids Struct. 15(8), 625–642 (1979)

    MATH  Google Scholar 

  75. Niemunis, A., Prada Sarmiento, L.F., Grandas Tavera, C.E.: Paraelasticity. Acta Geotech. 6, 67–80 (2011)

    Google Scholar 

  76. Niemunis, A., Herle, I.: Hypoplastic model for cohesionless soils with elastic strain range. Mech. Cohesive-Frict. Mater. 2(4), 279–299 (1997)

    Google Scholar 

  77. Niemunis, A., Prada Sarmiento, L.F., Grandas Tavera, C.E.: Extended paraelasticity and its application to a boundary value problem. Acta Geotech. 6, 91–92 (2011)

    Google Scholar 

  78. Fuentes, W., Triantafyllidis, T.: ISA: a constitutive model for deposited sand. In: Schanz, T., Hettler, A. (eds.) Aktuelle Forschung in der Bodenmechanik 2015, pp. 169–187. Springer, Berlin (2015)

    Google Scholar 

  79. Casagrande, A.: Characteristics of cohesionless soils affecting the stability of slopes and earth fills. J. Boston Soc. Civ. Eng. 23, 257–276 (1936)

    Google Scholar 

  80. Hvorslev, M.J.: Über die Festigkeitseigenschaften gestörter bindiger Böden. Ph.D. thesis, Danmarks naturvidenskabelige samfund, Københaven (1937)

    Google Scholar 

  81. Taylor, D.W.: Fundamentals of Soil Mechanics. Wiley, New York (1948)

    Google Scholar 

  82. Gudehus, G., Goldscheider, M., Winter, H.: Mechanical properties of sand and clay and numerical intergration methods: some sources of errors and bounds of accuracy. In: Gudehus, G. (ed.) Finite Elements in Geomechanics, pp. 121–150. Wiley, Chichester (1977)

    Google Scholar 

  83. Gudehus, G.: Attractors for granular storage and flow. In: 3rd European Symposium – Storage and Flow of Particulate Solids, Paper for the conference ‘Partec 95’, pp. 333–345 (1995)

    Google Scholar 

  84. Gudehus, G.: Discussion of paper “Asymptotic behaviour of a granular soil in strain path testing” by Chu, J. and Lo, S.-C. R. Géotechnique 45(2), 337–338 (1995)

    Google Scholar 

  85. Gudehus, G., Mašín, D.: Graphical representation of constitutive equations. Géotechnique 59(2), 147–151 (2009)

    Google Scholar 

  86. Gudehus, G.: Physical Soil Mechanics. Springer, Berlin (2011)

    Google Scholar 

  87. Mašín, D.: Asymptotic behaviour of granular materials. Granul. Matter 14(6), 759–774 (2012)

    Google Scholar 

  88. Butterfield, R.: A natural compression law for soils. Géotechnique 29(4), 469–480 (1979)

    Google Scholar 

  89. Mašín, D., Herle, I.: State boundary surface of a hypoplastic model for clays. Comput. Geotech. 32(6), 400–410 (2005)

    Google Scholar 

  90. Goldscheider, M.: True triaxial tests on dense sand. In: Gudehus, G. (ed.) Constitutive Relations for Soils, pp. 11–54. Workshop Grenoble, Balkema (1982)

    Google Scholar 

  91. Chu, J., Lo, S.C.R.: Asymptotic behaviour of a granular soil in strain path testing. Géotechnique 44(1), 65–82 (1994)

    Google Scholar 

  92. Topolnicki, M., Gudehus, G., Mazurkiewicz, B.K.: Observed stress-strain behaviour of remoulded saturated clays under plane strain conditions. Géotechnique 40(2), 155–187 (1990)

    Google Scholar 

  93. Sitharam, T.G., Vinod, J.S.: Critical state behaviour of granular materials from isotropic and rebounded paths: DEM simulations. Granul. Matter 11, 33–42 (2009)

    MATH  Google Scholar 

  94. Salot, C., Gotteland, P., Villard, P.: Influence of relative density on granular materials behaviour: DEM simulations of triaxial tests. Granul. Matter 11, 221–236 (2009)

    MATH  Google Scholar 

  95. Wang, J., Yu, H.S., Langston, P., Fraige, F.: Particle shape effects in discrete element modelling of cohesive angular particles. Granul. Matter 13, 1–12 (2011)

    Google Scholar 

  96. Peña, A.A., Herrmann, H.J., Lizcano, A., Alonso-Marroquín, F.: Investigation of the asymptotic states of granular materials using discrete element model of anisotropic particles. In: H. García-Rojo, McNamara (eds.) Powders and Grains, pp. 697–700. Taylor and Francis, London (2005)

    Google Scholar 

  97. Cheng, Y.P., Bolton, M.D., Nakata, Y.: Crushing and plastic deformation of soils simulated using DEM. Géotechnique 54(2), 131–141 (2004)

    Google Scholar 

  98. Cheng, Y.P., Nakata, Y., Bolton, M.D.: Discrete element simulation of crushable soil. Géotechnique 53(7), 633–641 (2003)

    Google Scholar 

  99. Zhao, X., Evans, T.M.: Numerical analysis of critical state behaviors of granular soils under different loading conditions. Granul. Matter 13, 751–764 (2011)

    Google Scholar 

  100. Kozicki, J., Tejchman, J.: Numerical simulations of sand behaviour using DEM with two different descriptions of grain roughness. In: E. Oñate, D.R.J. Owen (eds.) II International Conference on Particle-based Methods - Fundamentals and Applications. PARTICLES 2011 (2011)

    Google Scholar 

  101. Ferellec, J.F., McDowell, G.R.: A method to model realistic particle shape and inertia in DEM. Granul. Matter 12, 459–467 (2010)

    MATH  Google Scholar 

  102. Lu, N., McDowell, G.R.: The importance of modelling ballast particle shape in the discrete element method. Granul. Matter 9, 69–80 (2007)

    Google Scholar 

  103. Markauskas, D., Kašianauskas, R., Džiugys, A., Navakas, R.: Investigation of adequacy of multi-sphere approximation of elliptical particles for DEM simulations. Granul. Matter 12, 107–123 (2010)

    MATH  Google Scholar 

  104. Stahl, M., Konietzky, H.: Discrete element simulation of ballast and gravel under special consideration of grain-shape, grain-size and relative density. Granul. Matter 13(4), 417–428 (2011)

    Google Scholar 

  105. Luding, S., Alonso-Marroquín, F.: The critical state yield stress (termination locus) of adhesive powders from a single numerical experiment. Granul. Matter 13, 109–119 (2011)

    Google Scholar 

  106. Walker, D.M., Tordesillas, A., Einav, I., Small, M.: Complex networks in confined comminution. Phys. Rev. E 84, 021,301–1/9 (2011)

    Google Scholar 

  107. Ben-Nun, O., Einav, I., Tordesillas, A.: Force attractor in confined comminution of granular materials. Phys. Rev. Lett. 104, 108,001–1/4 (2010)

    Google Scholar 

  108. McDowell, G.R., Harireche, O.: Discrete element modelling of yielding and normal compression of sand. Géotechnique 52(4), 299–304 (2002)

    Google Scholar 

  109. McDowell, G.R., Humpreys, A.: Yielding of granular materials. Granul. Matter 4, 1–8 (2002)

    Google Scholar 

  110. McDowell, G.R., Bolton, M.D.: On micromechanics of crushable aggregates. Géotechnique 48(5), 667–679 (1998)

    Google Scholar 

  111. Jerman, J., Mašín, D.: Discrete element investigation of rate effects on the asymptotic behaviour of granular materials. In: V. Rinaldi, M. Zeballos, J. Clari (eds.) Proceedings of the 6th International Symposium on Deformation Characteristics of Geomaterials, IS-Buenos Aires 2015, 15–18 November 2015, pp. 695–702. Buenos Aires, Argentina (2015)

    Google Scholar 

  112. Kolymbas, D.: Introduction to barodesy. Géotechnique 65(1), 52–65 (2015)

    Google Scholar 

  113. Kolymbas, D., Medicus, G.: Genealogy of hypoplasticity and barodesy. Int. J. Numer. Anal. Methods Geomech. 40, 2532–2550 (2016)

    Google Scholar 

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    David Mašín

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Mašín, D. (2019). Soil Mechanical Behaviour and Its Modelling. In: Modelling of Soil Behaviour with Hypoplasticity. Springer Series in Geomechanics and Geoengineering. Springer, Cham. https://doi.org/10.1007/978-3-030-03976-9_2

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