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Modelling and Testing: Implementation of Numerical Models and Their Application in Practice

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Numerical Methods and Constitutive Modelling in Geomechanics

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 311))

Abstract

The complexity of many geomechanical systems necessitates the use of modern numerical methods such as the finite element, boundary element and finite difference procedures. With the almost unlimited power of the current and future computers, these methods can provide extremely powerful tools for analysis and design of engineering systems with complex factors that was not possible or very difficult with the use of the conventional methods, often based on closed-form analytical solutions.

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References

  1. Argyris, J. H., L. E. Vaz and K. J. Willam: Higher order methods for transient diffusion analysis, Comp. Meth. Appl. Mech. Eng., 12 (1977), 243–278.

    Article  MATH  MathSciNet  Google Scholar 

  2. Armaleh, S.: Disturbed state modelling approach for cohesionless soils,” Ph.D. Dissertation, University of Arizona, Tucson (1989), in progress.

    Google Scholar 

  3. Arthur, J.R.F., K. S. Chua, T. Dunstant and J. I. Rodriguez del C.: Principal stress rotation: a missing parameter, J. Geotech. Eng. Div., ASCE, 106, GT4 (1980), 419–433.

    Google Scholar 

  4. Baker, R. and C. S. Desai: Induced anisotropy during plastic straining, Int. J. Num. Analyt. Meth. in Geomech., 8, 2 (1984), 167–185.

    Article  MATH  Google Scholar 

  5. Baseghi, B. and C. S. Desai: Laboratory verification and applications of residual flow procedure for three-dimensional seepage, J. Water Resources Research, in press.

    Google Scholar 

  6. Biot, M.A.: General theory of three-dimensional consolidation, J. App. Physics, 12 (1941), 155–164.

    Article  MATH  Google Scholar 

  7. Biot, M.A.: Theory of propagation of elastic waves in a fluid saturated porous solid I & II, J. Acoustical Soc. of America, 28 (1956), 168–191.

    Article  MathSciNet  Google Scholar 

  8. Biot, M.A.: Mechanics of deformation and acoustic propagation in porous media, J. App. Physics, 33 (1962), 1482–1498.

    Article  MATH  MathSciNet  Google Scholar 

  9. Dafalias, Y.F.: Initial and induced anisotropy of cohesive soils by means of a varying nonassociated flow rule, Colloque Internationale du C.N.R.S., 319, Villard-du-Lans, Grenoble, France, June (1981).

    Google Scholar 

  10. Dafalias, Y.F.: On Rate Dependence and Anisotropy in Soil Constitutive Modelling, in: Constitutive Relations for Soils, (Eds. G. Duehus, F. Darve and I. Vardoulakis), A.A. Balkema Publishers, 1984, 457–462.

    Google Scholar 

  11. Desai, C.S.: Finite element residual schemes for unconfined flow, Int. J. Num. Meth. Engng, 10 (1976), 1415.

    Article  MATH  Google Scholar 

  12. Desai, C.S.: Effect of driving and subsequent consolidation on driven piles, Int. J. Num. Analyt. Meth. in Geomech., 2 (1978), 283–301.

    Article  Google Scholar 

  13. Desai, C.S.: A general basis for yield, failure and potential functions in plasticity, Int. J. Num. Analyt. Meth. in Geomech., 4 (1980), 361–375.

    Article  MATH  Google Scholar 

  14. Desai, C.S.: A dynamic multi-degree-of-freedom shear device, Report No. 8–36, Department of Civil Engineering, Virginia Tech, Blacksburg, Virginia (1980).

    Google Scholar 

  15. Desai, C.S.: Behavior of interfaces between structural and geologic media. A State-of-the-Art Paper for Int. Conf. on Recent Advances in Geotech. Earthquake Engrg. and Soil Dyn., St. Louis, Missouri (1981).

    Google Scholar 

  16. Desai, C.S.: Further on unified hierarchical models based on alternative correction of “damage” approach, Report, Dept. of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, Arizona (1987).

    Google Scholar 

  17. Desai, C.S.: Single surface yield and potential function plasticity models: a review, Letter to Editor, J. Comp. and Geotechnics, 7 (1989) 319–335.

    Article  Google Scholar 

  18. Desai, C.S.: Computer Code HISSDOD1 for Computation of constants and back predictions of hierarchical single surface models, Report, Tucson, AZ (1990).

    Google Scholar 

  19. Desai, C.S. and J. F. Abel: Introduction to the Finite Element Method, Van Nostrand Reinhold Co., New York (1972).

    MATH  Google Scholar 

  20. Desai, C.S. and G. C. Appel: 3-D analysis of laterally wooded structures, Proc. 2nd Int. Conf. on Num. Meth. Geomech., ASCE, Blacksburg, Virginia (1976).

    Google Scholar 

  21. Desai, C.S. and B. Baseghi: Theory and verification of residual flow procedure for 3-D free surface seepage, Ad. Water Resources, 11 (1988), 195–203.

    Google Scholar 

  22. Desai, C.S., E.C. Drumm and M.M. Zaman: Cyclic testing and modeling of interfaces, J. of Geotech. Engrg., ASCE, 111, 6 (1985), 793–815.

    Article  Google Scholar 

  23. Desai, C.S., I.M. Eitani and C. Haycocks: An application of finite element procedure for underground structures with nonlinear analysis and joints, Proc., 5th Int. Conf. Soc. of Rock Mech., Melbourne, Australia (1983).

    Google Scholar 

  24. Desai, C.S. and M.O. Faruque: Constitutive model for geologic materials, J. Eng. Mech. Div., ASCE, 110, 9, September (1984), 1391–1408.

    Article  Google Scholar 

  25. Desai, C.S. and K.L. Fishman: Constitutive models for rocks and discontinuities (joints), Proc., 28th Symp. on Rock Mech., Tucson, Arizona (1987).

    Google Scholar 

  26. Desai, C.S. and K. L. Fishman: Plasticity based constitutive model with associated testing for joints, Int. J. Rock Mech. and Min. Sc (1988), accepted for publication.

    Google Scholar 

  27. Desai, C.S., G.N. Frantziskonis and S. Somasundaram: Constitutive modelling for geologic materials, Proc., 5th Intl. Conf. on Num. Meth. in Geomech., Nagoya, Japan, April (1985), 19–34.

    Google Scholar 

  28. Desai, C.S. and H.M. Galagoda: Earthquake analysis with generalized plasticity model for saturated soils, J. Earthquake Eng. and Struct. Dyn., 18, 6 (1989), 903–919.

    Article  Google Scholar 

  29. Desai, C.S., H.M. Galagoda and G.W. Wathugala: Hierarchical modelling for geologic materials and discontinuities — joints and interfaces, Proc., 2nd Int. Conf. on Constitutive Laws for Eng. Mat., Tucson, AZ (1987), Elsevier, N.Y.

    Google Scholar 

  30. Desai, C.S. and Q.S.E. Hashmi: Analysis, evaluation and implementation of a nonassociative model for geologic materials, Int. J. Plasticity, 5 (1989),

    Google Scholar 

  31. Desai, C.S. and L.D. Johnson: Evaluation of two finite element formulations for one-dimensional consolidation, J. Computers and Structures, 2, 4 (1972).

    Article  Google Scholar 

  32. Desai, C.S. and L.D. Johnson Evaluation of some numerical schemes for consolidation, Int. J. Num. Meth. Eng., 7 (1973).

    Google Scholar 

  33. Desai, C.S., J. Kujawski, C. Miedzialowski and W. Ryzynski: Improved time integration of nonlinear dynamic problems, Comp. Meth. in Appl. Mech. and Eng., 62 (1987), 155–168.

    Article  MATH  MathSciNet  Google Scholar 

  34. Desai, C.S. and G. C. Li: A residual flow procedure and application for free surface flow in porous media, Adv. in Water resources, 6 (1983), 27.

    Article  Google Scholar 

  35. Desai, C.S. and J.G. Lightner: Mixed finite element procedure for soil-structure interaction and construction sequences, J. Num. Meth. in Eng., 21 (1985), 801–814.

    Article  MATH  Google Scholar 

  36. Desai, C.S. and R.L. Lytton: Stability criteria for two finite element schemes for parabolic equations, Int. J. Num. Meth. Eng., 9 (1975).

    Google Scholar 

  37. Desai, C.S., A. Muqtadir and F. Scheele: Interaction analysis of anchor-soil systems, J. Geotech. Eng., ASCE, 112, 5 (1985), 537–553.

    Article  Google Scholar 

  38. Desai, C.S. and B.K. Nagaraj: Modeling for cyclic normal and shear behavior of interfaces, J. of Eng. Mech., ASCE, 114 (1988), 1198–1217.

    Article  Google Scholar 

  39. Desai, C.S. and M.R. Salami: A constitutive model and associated testing for soft rock, Int. J. Rock Mech. Min. Sc., 24 (1987), 299–307.

    Article  Google Scholar 

  40. Desai, C.S. and M.R. Salami: A constitutive model for rocks, J. Geotech. Eng., ASCE, 113, 5 (1987).

    Article  Google Scholar 

  41. Desai, C.S. and S.M. Sargand: Hybrid finite element procedure for soil-structure interaction, J. Geotech. Eng., ASCE, 110 (1984), 473–486.

    Article  Google Scholar 

  42. Desai, C.S. and S.K. Saxena: Consolidation analysis of layered anisotropic foundations, Int. J. Num. Analyt. Meth. in Geomech., 1 (1977).

    Google Scholar 

  43. Desai, C.S. and W.C Sherman: Unconfined transient seepage in sloping banks, J. Soil Mech. and Found. Engg. Div., ASCE, 97, SM2 (1971), 357.

    Google Scholar 

  44. Desai, C.S. and H.J. Siriwardane: Numerical models for track support structures, J. of Geotech. Eng., ASCE, 108, 3 (1982).

    Google Scholar 

  45. Desai, C. S., S. Somasundaram and G.N. Frantziskonis: A hierarchical approach for constitutive modelling of geologic materials, Int. J. Num. Meth. in Geomech., 10, 3 (1986).

    Google Scholar 

  46. Desai, C.S. and A. Varadarajan: A constitutive model for quasistatic behavior of rock salt, J. of Geophys. Research, Manuscript No. 6136091 (October 1987).

    Google Scholar 

  47. Desai, C.S. and G. W. Wathugala: Hierarchical and unified models for solids and discontinuities (joints/interfaces), Notes for Short Course, Tucson, AZ (1987).

    Google Scholar 

  48. Desai, C.S., M.M. Zaman, J.G. Lightner and H.J. Siriwardane: Thin-layer element for interfaces and joints, Int. J. Num. Analyt. Meth. Geomech., 8, 1 (1984).

    Google Scholar 

  49. Desai, C.S. and D. Zhang: Viscoplastic model (for rocks) with generalized yield function, Int. J. Num. Analyt. Meth. Geomech., 11 (1987), 603–620.

    Article  MATH  Google Scholar 

  50. DiMaggio, F.L. and I. Sandler: Material model for granular soils, J. of Eng. Mech. Div., ASCE, 97 (1971), 935–950.

    Google Scholar 

  51. Drucker, D.C., R.E. Gibson and D.J. Henkel: Soil mechanics and work-hardening theories of plasticity, Trans. ASCE Eng. Mech. Div., Paper No. 2864 (1955), 81.

    Google Scholar 

  52. Drumm, E.E. and C.S. Desai: Determination of parameters for a model for the cyclic behavior of interfaces, J. of Earthq. Engrg. and Struct. Dyn., 16, 1 (1986), 1–18.

    Article  Google Scholar 

  53. The Earth Technology Corp: Pile segment tests-Sabine pass, some aspects of the fundamental behavior of axially loaded piles in clay soils, ETC Report No. 85–007, Long Beach, CA (1986).

    Google Scholar 

  54. Fishman, K.L. and C. S. Desai: A constitutive model for hardening behavior of rock joints, Proc., 2nd Int. Conf. on Const. Laws for Eng. Mat., Elsevier, New York (1987).

    Google Scholar 

  55. Fishman, K.L. and C.S. Desai: Measurements of normal deformations in joints during shear using inductance devices, Geotech. Testing J., 12, 4 (1989), 297–301.

    Article  Google Scholar 

  56. Frantziskonis, G. and C.S. Desai: Constitutive model with strain softening, Int. J. of Solids Structures, 23, 6 (1987).

    Google Scholar 

  57. Frantziskonis, G., C.S. Desai and S. Somasundaram: Constitutive model for nonassociative behavior, J. of Eng. Mech., ASCE, 112 (1986), 932–946.

    Article  Google Scholar 

  58. Galagoda, H.M.: Nonlinear analysis of porous soil media and application, Ph.D. Dissertation, University of Arizona, Tucson, AZ (1986).

    Google Scholar 

  59. Ghaboussi, J. and K.J. Kim: Quasi-static and dynamic analysis of saturated soils, in: Mechanics of Engineering Materials (Eds. C.S. Desai and R.H. Gallagher), John Wiley & Sons Ltd. (1984).

    Google Scholar 

  60. Hashmi, Q.S.E.: Modelling for nonassociative behavior and implementation, Ph.D. Dissertation, University of Arizona, Tucson, Arizona (1987).

    Google Scholar 

  61. Hogge, M.A.: Accuracy and cost of integration techniques for nonlinear heat transfer, in: Finite Element Methods in the Commerical Environment (Ed. J. Robinson), Robinson Assoc, Wimborne, U.K. (1978).

    Google Scholar 

  62. Hogge, M.A.: A comparison of two- and three-level integration schemes for non-linear heat conduction, in: Numerical Methods in Heat Transfer (Eds. R.W. Lewis, K. Morgan and O.C. Zienkiewicz), Wiley (1981).

    Google Scholar 

  63. Hughes, T.J.R.: Analysis of transient algorithms with particular reference to stability behavior, in: Computational Methods in Transient Analysis (Eds. T. Belytschko and T.J.R. Hughes), North-Holland Publishing Co., Amsterdam, The Netherlands (1983).

    Google Scholar 

  64. Hvorslev, M.J.: Über die Festigkeitsei genschaffen gestorter bindiger Boden (on physical properties of disturbed cohesive soils), Ingeniorvidenskabelige Skrifter, No. 45, Austria (1937), 159 p.

    Google Scholar 

  65. Jelinek, R. and F. Scheele: Tragfahigkert und tragverhalten von verpressanken, Bundes Ministerium fur Raumordnung, Bauwesan und Statebau (1977).

    Google Scholar 

  66. Katti, D.R.: Disturbed state approach for cyclic behavior of clays, Ph.D. Dissertation, University of Arizona, Tucson, Arizona (1989), in progress.

    Google Scholar 

  67. Kim, M.K. and P.V. Lade: Single hardening constitutive model for frictional materials: I. Plastic potential function, Computers and Geotechnics, 5 (1988), 307–324.

    Article  Google Scholar 

  68. Kujawski, J. and C.S. Desai: Unconditionally stable time finite element family of schemes for time integration in linear and non-linear dynamic problems, Rept. 2/KD/83, Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, AZ (1983).

    Google Scholar 

  69. Kujawski, J. and C.S. Desai: Generalized time finite element algorithm for non-linear dynamic problems, Engrg. Comput., 1, 3 (1984), 247–251.

    Article  Google Scholar 

  70. Kujawski, J. and C.S. Desai: A quasi-explicit modification of two time level family of schemes for nonlinear transient analysis, Int. J. Num. Analyt. Meth. in Geomech., 9, 5 (1985).

    Google Scholar 

  71. Kujawski, J. and C.S. Desai: Construction of highly stable explicit algorithms for transient field problems, J. of Tech. Physics, 28, 1 (1987).

    Google Scholar 

  72. Lade, P.V.: Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces, Int. J. Solids Struct., 13 (1977), 1019–1035.

    Article  MATH  Google Scholar 

  73. Lade, P.V. and J.M. Duncan: Elasto-plastic stress-strain theory of cohesionless soils, J. Geot. Eng., ASCE, 101 (1975), 1037–1053.

    Google Scholar 

  74. Lade, P.V. and M.K. Kim: Single hardening constitutive model for frictional materials: II. Yield criterion and plastic work contours, Computers and Geotechnics, 6 (1988), 13–29.

    Article  Google Scholar 

  75. Lade, P.V. and M.K. Kim: Single hardening constitutive model for frictional materials: III. Comparison with experimental data, Computers and Geotechnics, 6 (1988), 31–47.

    Article  Google Scholar 

  76. Lewin, P.I.: The deformation of soft clay under generalized stress conditions, Ph.D. Thesis, Kings College, University of London (1978).

    Google Scholar 

  77. Li, G. C. and C.S. Desai: Stress and seepage analysis of earth dams, J. Geotech. Eng., ASCE, 109 (1983), 946–960.

    Article  Google Scholar 

  78. Ma, Y.: Hierarchical single surface model for rock joints, Ph.D. Dissertation, University of Arizona, Tucson, Arizona (1989), under preparation.

    Google Scholar 

  79. Matsuoka, H. and T. Nakai: Stress-deformation and strength characteristics of soil under three different principal stresses, Soils & Found., J. Jap. Soc. of Soil Mech. & Found. Eng., 232 (1974), 59–70.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  81. Navayogarajah, N.: Hierarchical single surf ace model for interfaces, Ph.D. Dissertation, University of Arizona, Tucson, AZ (1989), under preparation.

    Google Scholar 

  82. Norrie, D.H. and G. DeVries: Application of the pseudo-functional finite element method to nonlinear problems, in: Finite Elements in Fluids (Eds. Gallagher et al.), John Wiley & Sons, U.K. (1974), 2, Ch.3.

    Google Scholar 

  83. Nova, R. and D.M. Wood: An experimental program to define the yield function for sand, Soils and Foundations, 18, 4 (1978), 77–86.

    Article  Google Scholar 

  84. Ostemayer, H. and F. Scheele: Research on ground anchors in noncohesive soils, Sp. Session 4, at Int. Conf. on Soil Mech. and Found. Eng., Tokyo, Japan (1977).

    Google Scholar 

  85. Poorooshasb, H.B.: Deformation of sand in triaxial compression, Proc., 4th Asian Conf. SMFE, Bangkok, 1 (1971), 63–66.

    Google Scholar 

  86. Poorooshasb, H.B., I. Holubec and A.N. Sherbourne: Yielding and flow of sand in triaxial compression, Part 2 and 3, Can. Geot. Journal, 4 (1967), 376–397.

    Article  Google Scholar 

  87. Potts, D.M. and A. Gens: A critical assessment of methods of corrections for drift from the yield surface in elasto-plastic finite element analysis, Int. J. Num. Analyt. Meth. in Geomech., 9 (1985), 149–159.

    Article  Google Scholar 

  88. Prevost, J.H.: Plasticity theory for soil stress-strain behavior, J. Eng. Mech. Div., ASCE, 104, EM5, October (1978), 1177–1194.

    Google Scholar 

  89. Prevost, J.H.: Nonlinear transient phenomena in elastic-plastic solids, J. of Eng. Mech. Div., ASCE, 108 (1982), 1297–1311.

    Google Scholar 

  90. Roscoe, K.H., A.N. Schofield and A. Thurairajah: Yielding of clays in states wetter than critical, Geotechnique, 13 (1963), 211–240.

    Article  Google Scholar 

  91. Roscoe, K.H., A.N. Schofield and C.P. Wroth: On yielding of soils, Geotechnique, 8 (1958), 22–53.

    Article  Google Scholar 

  92. Sandhu, R.S., I.S. Rai and C.S. Desai: Variable time-step analysis of unconfined seepage, Proc. Int. Symp. on Finite Element Meth. in Flow Problems, Univ. of Wales, Swansea, U.K. (1974).

    Google Scholar 

  93. Sandhu, R.S. and E.L. Wilson: Finite element analysis of seepage in elastic media, J. Eng. Mech. Div., ASCE, Proc, No. EM3 (1969) 641–652.

    Google Scholar 

  94. Scheele, F. and C.S. Desai: Laboratory Behavior of Munich Sand, Report, Dept. of Civil Eng. & Eng. Mech., Univ. of Arizona, Tucson, AZ (1983).

    Google Scholar 

  95. Scheele, F.: Tragfaigkeit von verpressanken in nichtbinddigen boden, Neue Erkemnt-nisien durah dehnungsmessungen in veran-Kernungsbereich, Ph.D. Disseration, University of Munich, West Germany (1981).

    Google Scholar 

  96. Scheele, F., C.S. Desai and A. Muqtadir: Testing and modelling of “Munich” sand, Soils & Found. J. of JSMFE, 26 (1986), 1–18.

    Article  Google Scholar 

  97. Schreyer, H.L.: A third-invariant plasticity theory for frictional materials, J. of Structural Mech., June (1983).

    Google Scholar 

  98. Siriwardane, H.J. and C.S. Desai: Two numerical schemes for nonlinear consolidation, Int. J. Num. Meth. in Engg., 5 (1981).

    Google Scholar 

  99. Somasundaram, S.: Constitutive modelling for anisotropic hardening behavior with applications to cohesionless soils, Ph.D. Thesis, University of Arizona, Tucson, AZ (1986).

    Google Scholar 

  100. Somasundaram, S. and C.S. Desai: Modelling and testing for anisotropic behavior of soils, J. Eng. Mech., ASCE, 114 (1988), 1177–1194.

    Article  Google Scholar 

  101. Sugio, S. and C.S. Desai: Residual flow procedure for sea water intrusion in unconfined aquifers, Int. J. Num. Meth. Eng., 24 (1987), 1439–1450.

    Article  MATH  Google Scholar 

  102. Tatsuoka, F. and K. Ishihara: Drained deformation of sand under cyclic stresses reversing direction, Soils and Foundations, 14, 3, December (1974), 51–65.

    Article  Google Scholar 

  103. Tatsuoka, F. and K. Ishihara: Yielding of sand in triaxial compression, Soils and Foundations, 14, 2 (1974), 63–76.

    Article  Google Scholar 

  104. Uesugi, M. and H. Kishida: Influence factors of friction between steel and dry sands, Soils and Foundations, 26 2 (1986) 33–46.

    Article  Google Scholar 

  105. Uesugi, M. and H. Kishida: Frictional resistance at yield between dry sand mild steel, Soils and Foundations, 26, 4 (1986) 139–149.

    Article  Google Scholar 

  106. Varadarajan, A. and C.S. Desai: Constitutive modelling for some sands from India, Report, Dept. of Civil Eng. & Eng. Mech., Univ. of Arizona, Tucson, AZ, (1987).

    Google Scholar 

  107. Wathugala, G.W.: Dynamic soil-structure interaction analysis with anisotropic hardening model, Ph.D. Dissertation, Dept. of Civil Eng. & Eng. Mech., University of Arizona, Tucson, AZ (1989), under preparation.

    Google Scholar 

  108. Wathugala, G.W. and C.S. Desai: “Damage” based constitutive model for soils, Proc., 12th Canadian Congress of Appl. Mech., Ottawa, Canada (1987).

    Google Scholar 

  109. Wathugala, G.W. and C.S. Desai: An analysis of piles in Maine clay under cyclic axial loading, Offshore Technology Conf., OTC paper 6002, Houston, Texas (1989).

    Google Scholar 

  110. Westbrook, D.R.: Analysis of inequality and residual flow procedures and an iterative scheme for free surface seepage, Int. J. for Num. Meth. in Eng., 21 (1985), 1791.

    Article  MATH  MathSciNet  Google Scholar 

  111. Zaman, M.M., C.S. Desai and E.C. Drumm: An interface model for dynamic soil-structure interaction. J. Geotech. Div., ASCE, 110, 4 (1984), 1257–1273.

    Article  Google Scholar 

  112. Zienkiewicz, O.C., K.H. Leung and E. Hinton: Earthquake response behavior of soils with damage, Proc. Num. Meth. in Geomech., (Ed. Z. Eizenstein), Edmonton (1982).

    Google Scholar 

  113. Zienkiewicz, O.C. and T. Shiomi: Dynamic behavior of saturated porous media: the generalized Biot formulation and its numerical solution, J. Num. Analyt. Meth. in Geomech., 8 (1984), 71–96.

    Article  MATH  Google Scholar 

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Desai, C.S. (1990). Modelling and Testing: Implementation of Numerical Models and Their Application in Practice. In: Desai, C.S., Gioda, G. (eds) Numerical Methods and Constitutive Modelling in Geomechanics. International Centre for Mechanical Sciences, vol 311. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2832-9_1

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