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

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.

Graphical abstract

Keywords

soil–structure interaction / massed foundation / radiation damping / anisotropic damage

References

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

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

[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

[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

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

[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

[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

[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

[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

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

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

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

[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

[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

[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

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

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

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

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

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

[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

[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

[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

[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

[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

[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

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

[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

[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

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

[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

[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

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

[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

[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

[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

[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

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

[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

[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

[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

[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

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

[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

[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

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

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

[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

[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

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

[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

[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

[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

[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

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

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

[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

[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

[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

[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

[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

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

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

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

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

[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

[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

RIGHTS & PERMISSIONS

2021 Higher Education Press