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Effect of seismic wave propagation in massed medium on rate-dependent anisotropic damage growth in concrete gravity dams

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Abstract

Seismic modeling of massive structures requires special caution, as wave propagation effects significantly affect the responses. This becomes more crucial when the path-dependent behavior of the material is considered. The coexistence of these conditions renders numerical earthquake analysis of concrete dams challenging. Herein, a finite element model for a comprehensive nonlinear seismic simulation of concrete gravity dams, including realistic soil-structure interactions, is introduced. A semi-infinite medium is formulated based on the domain reduction method in conjunction with standard viscous boundaries. Accurate representation of radiation damping in a half-space medium and wave propagation effects in a massed foundation are verified using an analytical solution of vertically propagating shear waves in a viscoelastic half-space domain. A rigorous nonlinear finite element model requires a precise description of the material response. Hence, a microplane-based anisotropic damage-plastic model of concrete is formulated to reproduce irreversible deformations and tensorial degeneration of concrete in a coupled and rate-dependent manner. Finally, the Koyna concrete gravity dam is analyzed based on different assumptions of foundation, concrete response, and reservoir conditions. Comparison between responses obtained based on conventional assumptions with the results of the presented comprehensive model indicates the significance of considering radiation damping and employing a rigorous constitutive material model, which is pursued for the presented model.

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References

  1. Ghaemian M, Ghobarah A. Staggered solution schemes for dam-reservoir interaction. Journal of Fluids and Structures, 1998, 12(7): 933–948

    Article  Google Scholar 

  2. Ghaemian M, Ghobarah A. Nonlinear seismic response of concrete gravity dams with dam-reservoir interaction. Engineering Structures, 1999, 21(4): 306–315

    Article  Google Scholar 

  3. Chopra K, Chakrabarti P. Earthquake analysis of concrete gravity dams including dam-water-foundation rock interaction. Earthquake Engineering & Structural Dynamics, 1981, 9(4): 363–383

    Article  Google Scholar 

  4. Fenves G, Chopra A K. Earthquake analysis of concrete gravity dams including reservoir bottom absorption and dam-waterfoundation rock interaction. Earthquake Engineering & Structural Dynamics, 1984, 12(5): 663–680

    Article  Google Scholar 

  5. Fenves G, Chopra A K. Simplified earthquake analysis of concrete gravity dams. Journal of Structural Engineering, 1987, 113(8): 1688–1708

    Article  Google Scholar 

  6. Bouaanani N, Lu F Y. Assessment of potential-based fluid finite elements for seismic analysis of dam-reservoir systems. Computers & Structures, 2009, 87(3–4): 206–224

    Article  Google Scholar 

  7. Samii V L, Lotfi V. Application of H-W boundary condition in dam-reservoir interaction problem. Finite Elements in Analysis and Design, 2012, 50: 86–97

    Article  Google Scholar 

  8. Clough R. Non-linear mechanisms in the seismic response of arch dams. In: Proceedings of the International Conference on Earthquake Engineering. Skopje, 1980, 1: 669–684

  9. Tan H, Chopra A K. Earthquake analysis of arch dams including dam-water-foundation rock interaction. Earthquake Engineering & Structural Dynamics, 1995, 24(11): 1453–1474

    Article  Google Scholar 

  10. Tan H, Chopra A K. Dam-foundation rock interaction effects in frequency-response functions of arch dams. Earthquake Engineering & Structural Dynamics, 1995, 24(11): 1475–1489

    Article  Google Scholar 

  11. Chopra K. Earthquake analysis of arch dams: Factors to be considered. Journal of Structural Engineering, 2012, 138(2): 205–214

    Article  Google Scholar 

  12. Lysmer J, Kuhlemeyer R L. Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division, 1969, 95(4): 859–878

    Article  Google Scholar 

  13. Givoli D. High-order local non-reflecting boundary conditions: A review. Wave Motion, 2004, 39(4): 319–326

    Article  MathSciNet  MATH  Google Scholar 

  14. Katz D, Thiele E, Taffove A. A perfectly matched layer for the absorbing of electromagnetic waves. IEEE Microwave and Guided Wave Letters, 1994, 4: 268270

    Google Scholar 

  15. Basu U, Chopra A K. Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: Theory and finite-element implementation. Computer Methods in Applied Mechanics and Engineering, 2003, 192(11–12): 1337–1375

    Article  MATH  Google Scholar 

  16. Basu U, Chopra A K. Perfectly matched layers for transient elastodynamics of unbounded domains. International Journal for Numerical Methods in Engineering, 2004, 59(8): 1039–1074

    Article  MathSciNet  MATH  Google Scholar 

  17. Ungless R F. Infinite finite element. Dissertation for the Doctoral Degree. Vancouver: University of British Columbia, 1973

    Google Scholar 

  18. Bettess P. Infinite elements. International Journal for Numerical Methods in Engineering, 1977, 11(1): 53–64

    Article  MathSciNet  MATH  Google Scholar 

  19. Zienkiewicz O, Bicanic N, Shen F. Advances in Computational Nonlinear Mechanics. Vienna: Springer, 1989, 109–138

    Book  Google Scholar 

  20. Wolf J, Hall W. Soil-structure-interaction analysis in time domain. Nuclear Engineering and Design, 1989, 111(3): 381–393

    Article  Google Scholar 

  21. Léger P, Boughoufalah M. Earthquake input mechanisms for timedomain analysis of dam-foundation systems. Engineering Structures, 1989, 11(1): 37–46

    Article  Google Scholar 

  22. Wang J, Zhang C, Jin F. Nonlinear earthquake analysis of high arch dam-water-foundation rock systems. Earthquake Engineering and Structural Dynamics, 2012, 41(7):1157–1176

    Article  Google Scholar 

  23. Wang J, Chopra A K. EACD-3D-2008: A Computer Program for Three-Dimensional Earthquake Analysis of Concrete Dams Considering Spatially-Varying Ground Motion. Berkeley, CA: Earthquake Engineering Research Center, University of California, 2008

    Google Scholar 

  24. Bielak J, Christiano P. On the effective seismic input for non-linear soil-structure interaction systems. Earthquake Engineering & Structural Dynamics, 1984, 12(1): 107–119

    Article  Google Scholar 

  25. Bielak J, Loukakis K, Hisada Y, Yoshimura C. Domain reduction method for three-dimensional earthquake modeling in localized regions, part I: Theory. Bulletin of the Seismological Society of America, 2003, 93(2): 817–824

    Article  MathSciNet  Google Scholar 

  26. Yoshimura C, Bielak J, Hisada Y, Fernandez A. Domain reduction method for three-dimensional earthquake modeling in localized regions, part II: Verification and applications. Bulletin of the Seismological Society of America, 2003, 93(2): 825–841

    Article  MathSciNet  Google Scholar 

  27. Ayari M L, Saouma V E. A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Engineering Fracture Mechanics, 1990, 35(1–3): 587–598

    Article  Google Scholar 

  28. Pekau O, Chuhan Z, Lingmin F. Seismic fracture analysis of concrete gravity dams. Earthquake Engineering & Structural Dynamics, 1991, 20(4): 335–354

    Article  Google Scholar 

  29. Pekau O, Batta V. Seismic crack propagation analysis of concrete structures using boundary elements. International Journal for Numerical Methods in Engineering, 1992, 35(8): 1547–1564

    Article  MATH  Google Scholar 

  30. El-Aidi B, Hall J F. Non-linear earthquake response of concrete gravity dams part 1: Modelling. Earthquake Engineering & Structural Dynamics, 1989, 18(6): 837–851

    Article  Google Scholar 

  31. Bhattacharjee S, Leger P. Seismic cracking and energy dissipation in concrete gravity dams. Earthquake Engineering & Structural Dynamics, 1993, 22(11): 991–1007

    Article  Google Scholar 

  32. Guanglun W, Pekau O, Chuhan Z, Shaomin W. Seismic fracture analysis of concrete gravity dams based on nonlinear fracture mechanics. Engineering Fracture Mechanics, 2000, 65(1): 67–87

    Article  Google Scholar 

  33. Hillerborg M, Modéer M, Petersson P E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976, 6(6): 773–781

    Article  Google Scholar 

  34. Bazant Z P, Oh B H. Crack band theory for fracture of concrete. Mat’eriaux et construction, 1983, 16(3): 155–177

    Article  Google Scholar 

  35. Mirzabozorg H, Ghaemian M. Non-linear behavior of mass concrete in three-dimensional problems using a smeared crack approach. Earthquake Engineering & Structural Dynamics, 2005, 34(3): 247–269

    Article  Google Scholar 

  36. Areias P, Rabczuk T. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122

    Article  MathSciNet  MATH  Google Scholar 

  37. Areias P, Rabczuk T, Dias-da Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137

    Article  Google Scholar 

  38. Areias P, Rabczuk T. Steiner-point free edge cutting of tetrahedral meshes with applications in fracture. Finite Elements in Analysis and Design, 2017, 132: 27–41

    Article  Google Scholar 

  39. Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics, 2002, 69(7): 813–833

    Article  Google Scholar 

  40. Daneshyar S M, Mohammadi S. Strong tangential discontinuity modeling of shear bands using the extended finite element method. Computational Mechanics, 2013, 52(5): 1023–1038

    Article  MathSciNet  MATH  Google Scholar 

  41. Afshar A, Daneshyar A, Mohammadi S. XFEM analysis of fiber bridging in mixed-mode crack propagation in composites. Composite Structures, 2015, 125: 314–327

    Article  Google Scholar 

  42. Song J H, Belytschko T. Cracking node method for dynamic fracture with finite elements. International Journal for Numerical Methods in Engineering, 2009, 77(3): 360–385

    Article  MathSciNet  MATH  Google Scholar 

  43. Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782

    Article  MathSciNet  MATH  Google Scholar 

  44. Sluys L. Wave propagation, localisation and dispersion in softening solids. Dissertation for the Doctoral Degree. Delft: Delft University of Technology, 1992

    Google Scholar 

  45. Bažant Z P, Jir’asek M. Nonlocal integral formulations of plasticity and damage: Survey of progress. Journal of Engineering Mechanics, 2002, 128(11): 1119–1149

    Article  Google Scholar 

  46. Ren H, Zhuang X, Rabczuk T. A nonlocal operator method for solving partial differential equations. Computer Methods in Applied Mechanics and Engineering, 2020, 358: 112621

    Article  MathSciNet  MATH  Google Scholar 

  47. Løland K. Continuous damage model for load-response estimation of concrete. Cement and Concrete Research, 1980, 10(3): 395–402

    Article  Google Scholar 

  48. Krajcinovic D, Fonseka G. The continuous damage theory of brittle materials. Journal of Applied Mechanics, 1981, 48(4): 809–815

    Article  MATH  Google Scholar 

  49. Lee J, Fenves G L. A plastic-damage concrete model for earthquake analysis of dams. Earthquake Engineering & Structural Dynamics, 1998, 27(9): 937–956

    Article  Google Scholar 

  50. Cervera M, Oliver J, Manzoli O. A rate-dependent isotropic damage model for the seismic analysis of concrete dams. Earthquake Engineering & Structural Dynamics, 1996, 25(9): 987–1010

    Article  Google Scholar 

  51. Bourdin G A, Francfort G A, Marigo J J. The variational approach to fracture. Journal of Elasticity, 2008, 91(1–3): 5–148

    Article  MathSciNet  MATH  Google Scholar 

  52. Miehe F, Welschinger F, Hofacker M. Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations. International Journal for Numerical Methods in Engineering, 2010, 83(10): 1273–1311

    Article  MathSciNet  MATH  Google Scholar 

  53. Zhou S, Rabczuk T, Zhuang X. Phase field modeling of quasi-static and dynamic crack propagation: Comsol implementation and case studies. Advances in Engineering Software, 2018, 122: 31–49

    Article  Google Scholar 

  54. Zhou S, Zhuang X, Zhu H, Rabczuk T. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96: 174–192

    Article  Google Scholar 

  55. Zhou S, Zhuang X, Rabczuk T. Phase field modeling of brittle compressive-shear fractures in rock-like materials: A new driving force and a hybrid formulation. Computer Methods in Applied Mechanics and Engineering, 2019, 355: 729–752

    Article  MathSciNet  MATH  Google Scholar 

  56. Ren H, Zhuang X, Anitescu C, Rabczuk T. An explicit phase field method for brittle dynamic fracture. Computers & Structures, 2019, 217: 45–56

    Article  Google Scholar 

  57. Zhou S, Zhuang X, Rabczuk T. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240: 189–203

    Article  Google Scholar 

  58. Zhou S, Zhuang X, Rabczuk T. Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 169–198

    Article  MathSciNet  MATH  Google Scholar 

  59. Zhuang X, Zhou S, Sheng M, Li G. On the hydraulic fracturing in naturally-layered porous media using the phase field method. Engineering Geology, 2020, 266: 105306

    Article  Google Scholar 

  60. Goswami S, Anitescu C, Chakraborty S, Rabczuk T. Transfer learning enhanced physics informed neural network for phase-field modeling of fracture. Theoretical and Applied Fracture Mechanics, 2020, 106: 102447

    Article  Google Scholar 

  61. Daneshyar M G, Ghaemian M. Coupling microplane-based damage and continuum plasticity models for analysis of damage-induced anisotropy in plain concrete. International Journal of Plasticity, 2017, 95: 216–250

    Article  Google Scholar 

  62. Daneshyar M G, Ghaemian M. Seismic analysis of arch dams using anisotropic damage-plastic model for concrete with coupled adhesivefrictional joints response. Soil Dynamics and Earthquake Engineering, 2019, 125: 105735

    Article  Google Scholar 

  63. Kachanov L. On creep rupture time. Bulletin of the Academy of Sciences of the USSR, 1958, 8: 26–31

    Google Scholar 

  64. Brara J K, Klepaczko J R. Experimental characterization of concrete in dynamic tension. Mechanics of Materials, 2006, 38(3): 253–267

    Article  Google Scholar 

  65. Bischoff P, Perry S. Compressive behaviour of concrete at high strain rates. Materials and Structures, 1991, 24(6): 425–450

    Article  Google Scholar 

  66. Duvaut G, Lions J. Inequalities in Mechanics and Physics. New York: Springer-Verlag, 1977

    MATH  Google Scholar 

  67. Gálvez J, Elices M, Guinea G, Planas J. Mixed mode fracture of concrete under proportional and nonproportional loading. International Journal of Fracture, 1998, 94(3): 267–284

    Article  Google Scholar 

  68. Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495

    Article  MATH  Google Scholar 

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Correspondence to Mohsen Ghaemian.

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Daneshyar, A., Mohammadnezhad, H. & Ghaemian, M. Effect of seismic wave propagation in massed medium on rate-dependent anisotropic damage growth in concrete gravity dams. Front. Struct. Civ. Eng. 15, 346–363 (2021). https://doi.org/10.1007/s11709-021-0694-z

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