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Capacity Functions

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Aging, Shaking, and Cracking of Infrastructures

Abstract

Structural analyses are an important part of safety assessment. In this chapter, the concept of a “capacity function” is explained in the context of existing structural analysis techniques. Loading due to seismic, hydrologic, and aging hazard are studied from a probabilistic point of view. Single, multiple, and combined capacity functions are derived. Moreover, the summarized capacity functions and their confidence intervals are presented.

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References

  1. M. Alembagheri, M. Ghaemian, Damage assessment of a concrete arch dam through nonlinear incremental dynamic analysis. Soil Dyn. Earthq. Eng. 44, 127–137 (2013)

    Article  Google Scholar 

  2. M. Alembagheri, M. Ghaemian, Incremental dynamic analysis of concrete gravity dams including base and lift joints. Earthq. Eng. Eng. Vib. 12(1), 119–134 (2013)

    Article  Google Scholar 

  3. M. Alembagheri, M. Ghaemian, Seismic assessment of concrete gravity dams using capacity estimation and damage indexes. Earthq. Eng. Struct. Dyn. 42, 123–144 (2013)

    Article  Google Scholar 

  4. A. Andonov, K Apostolov, Displacement-based seismic capacity assessment of concrete dams, in Proceedings of the 15th World Conference on Earthquake Engineering (Lisbon, 2012)

    Google Scholar 

  5. A. Andonov, K Apostolov, Displacement-based seismic capacity assessment of concrete dams, in Proceedings of the 15th World Conference on Earthquake Engineering. (Lisbon, 2012)

    Google Scholar 

  6. A. Andonov, A. Iliev, K. Apostolov, Towards displacement-based seismic assessment of concrete dams using non-linear static and dynamic procedures. Struct. Eng. Int. 23(2), 132–140 (2013)

    Article  Google Scholar 

  7. S. Antoniou, R. Pinho, Advantages and limitations of adaptive and non-adaptive force-based pushover procedures. J. Earth-Quake Eng. 8, 497–522 (2004)

    Article  Google Scholar 

  8. S. Antoniou, R. Pinho, Development and verification of a displacement-based adaptive pushover procedure. J. Earthq. Eng. 8, 643–661 (2004)

    Article  Google Scholar 

  9. ASCE/SEI-41-13, Seismic Evaluation and Retrofit of Existing Buildings. Tech. rep. American Society of Civil Engineers, Reston, 2014

    Google Scholar 

  10. A. Azarbakht, M. Dolšek, Prediction of the median IDA curve by employing a limited number of ground motion records. Earthq. Eng. Struct. Dyn. 36, 2401–2421 (2007)

    Article  Google Scholar 

  11. A. Azarbakht, M. Dolšek, Progressive incremental dynamic analysis for first-mode dominated structures. J. Struct. Eng. 137, 445–455 (2011)

    Article  Google Scholar 

  12. J. Baker, C. Cornell, A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthq. Eng. Struct. Dyn. 34, 1193–1217 (2005)

    Article  Google Scholar 

  13. M. Barbato et al., Performance-based hurricane engineering (PBHE) frame-work. Struct. Saf. 45, 24–35 (2013)

    Article  Google Scholar 

  14. Ž. Bažant, Mathematical Modeling of Creep and Shrinkage of Concrete (Wiley, New York, 1988)

    Google Scholar 

  15. R. Bertero, V. Bertero, Performance-based seismic engineering: the need for a reliable conceptual comprehensive approach. Earthq. Eng. Struct. Dyn. 31, 627–652 (2002)

    Article  Google Scholar 

  16. E. Bojorquez et al., Comparing vector-valued intensity measures for fragility analysis of steel frames in the case of narrow-band ground motions. Eng. Struct. 45, 472–480 (2012)

    Article  Google Scholar 

  17. C. Casarotti, R. Pinho, An adaptive capacity spectrum method for assessment of bridges subjected to earthquake action. Bull. Earthq. Eng. 5, 377–390 (2007)

    Article  Google Scholar 

  18. D. Celarec, M. Dolšek, The impact of modelling uncertainties on the seismic performance assessment of reinforced concrete frame buildings. Eng. Struct. 52, 340–354 (2013)

    Article  Google Scholar 

  19. O. Celik, B. Ellingwood, Seismic fragilities for non-ductile reinforced concrete frames-role of aleatoric and epistemic uncertainties. Struct. Saf. 32, 1–12 (2010)

    Article  Google Scholar 

  20. P. Cheung, T. Pauley, R. Park, New Zealand tests on full-scale reinforced concrete beam-column-slab sub-assemblages designed for earth-quake resistance, in ACI Special Publication SP-123, Design of Beam-Column Joints for Seismic Resistance (Detroit, 1991), pp. 1–37

    Google Scholar 

  21. A. Chopra, R. Goel, Capacity-demand-diagram methods based on inelastic design spectrum. Earthq. Spectra 15, 637–656 (1999)

    Article  Google Scholar 

  22. A. Chopra, R. Goel, A modal pushover analysis procedure for estimating seismic demands for buildings. Earthq. Eng. Struct. Dyn. 31, 561–582 (2002)

    Article  Google Scholar 

  23. A. Chwang, Hydrodynamic pressures on sloping dams during earthquakes. Part 2. Exact theory. J. Fluid Mech. 87(2), 343–348 (1978)

    Google Scholar 

  24. A. Chwang, G. Housner, Hydrodynamic pressures on sloping dams during earthquakes. Part 1. Momentum method. J. Fluid Mech. 87(2), 335–341 (1978)

    Google Scholar 

  25. M. Ciampoli, F. Petrini, G. Augusti, Performance-based wind engineering: towards a general procedure. Struct. Saf. 33(6), 367–378 (2011)

    Article  Google Scholar 

  26. P. Clark et al., Protocol for Fabrication, Inspection, Testing and Documentation of Beam-Column Connection and Other Experimental Specimens. Tech. rep. SAC/BD-97/02. SAC Joint Venture, Sacramento, 1997

    Google Scholar 

  27. R. Clough, J. Penzien, Dynamics of Structures (McGraw-Hill, London, 1993)

    MATH  Google Scholar 

  28. C. Comi, R. Fedele, U. Perego, A chemo-thermo-damage model for the analysis of concrete dams affected by alkali-silica reaction. Mech. Mater. 41, 210–230 (2009)

    Article  Google Scholar 

  29. A.T. Council, Guidelines for Cyclic Seismic Testing of Components for Steel Structures. Tech. rep. Redwood City, Applied Technology Council, 1992

    Google Scholar 

  30. A. D’Ambrisi, M. Mezzi, An energy-based approach for nonlinear static analysis of structures. Bull. Earthq. Eng. 13(5), 1513–1530 (2015)

    Article  Google Scholar 

  31. M. Dolšek, Incremental dynamic analysis with consideration of modeling uncertainties, Earthq. Eng. Struct. Dyn. 38, 805–825 (2009)

    Article  Google Scholar 

  32. M. Dolšek, Estimation of seismic response parameters through extended incremental dynamic analysis, in Computational Methods in Earthquake Engineering, ed. by M. Papadrakakis, M. Fragiadakis, N.D. Lagaros. Computational Methods in Applied Sciences, vol. 21 (Springer Netherlands, 2011), pp. 285–304

    Google Scholar 

  33. M. Dolšek, Simplified method for seismic risk assessment of buildings with consideration of aleatory and epistemic uncertainty. Struct. Infrastruct. Eng. 8, 939–953 (2012)

    Google Scholar 

  34. Y. Dong, D. Frangopol, D. Saydam, Time-variant sustainability assessment of seismically vulnerable bridges subjected to multiple hazards. Earthq. Eng. Struct. Dyn. 42, 1451–1467 (2013)

    Article  Google Scholar 

  35. H. Estekanchi, A. Vafai, M. Sadeghazar, Endurance time method for seismic analysis and design of structures. Sci. Iran. 11, 361–370 (2004)

    Google Scholar 

  36. P. Fajfar, A nonlinear analysis method for performance based seismic design. Earthq. Spectra 16, 573–592 (2000)

    Article  Google Scholar 

  37. FEMA, Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Tech. rep. Federal Emergency Management Agency, Washington, 2000

    Google Scholar 

  38. G. Fenves, A. Chopra, Earthquake analysis of concrete gravity dams including reservoir bottom absorption and dam-water-foundation rock interaction. Earthq. Eng. Struct. Dyn. 12, 663–680 (1984)

    Article  Google Scholar 

  39. G. Fenves, A. Chopra, Simplified earthquake analysis of concrete gravity dams. J. Struct. Eng. 113(8), 1688–1708 (1987)

    Article  Google Scholar 

  40. FERC, FERC Guidance Document: Potential Failure Mode Analysis. Tech. rep. Federal Energy Regulatory Committee, 2005

    Google Scholar 

  41. A. Filiatrault, A. Wanitkorkul, M. Constantinou, Development and Appraisal of a Numerical Cyclic Loading Protocol for Quantifying Building System Performance. Tech. rep. MCEER-08-0013. University at Buffalo, State University of New York, 2008

    Google Scholar 

  42. S. Freeman, Prediction of response of concrete buildings to severe earthquake motion, in Proceedings of Douglas McHenry International Symposium on Concrete and Concrete Structures, ed. by A.C. Institute. Detroit, 1978

    Google Scholar 

  43. S. Freeman, The capacity spectrum method, in Proceedings of the 11th European Conference on Earthquake Engineering (Paris, 1998)

    Google Scholar 

  44. A. Ghaemmaghami, M. Ghaemian, Experimental seismic investigation of Sefid-rud concrete buttress dam model on shaking table. Earthq. Eng. Struct. Dyn. 37, 809–823 (2008)

    Article  Google Scholar 

  45. A. Ghobarah, M. Ghaemian, Experimental study of small scale dam models. J. Eng. Mech. ASCE 124, 1241–1248 (1998)

    Article  Google Scholar 

  46. J. Ghosh, J. Padgett, Aging considerations in the development of time-dependent seismic fragility curves. J. Struct. Eng. 136, 1497–1511 (2010)

    Article  Google Scholar 

  47. P. Giorgi, R. Scotta, Validation and improvement of {N1} method for pushover analysis. Soil Dyn. Earthq. Eng. 55, 140–147 (2013)

    Article  Google Scholar 

  48. S. Gunay, K. Mosalam, PEER performance-based earthquake engineering methodology, revisited. J. Earthq. Eng. 17(6), 829–858 (2013)

    Article  Google Scholar 

  49. A. Guo et al., Time-dependent seismic demand and fragility of deteriorating bridges for their residual service life. Bull. Earthq. Eng. 13, 2389–2409 (2015)

    Article  Google Scholar 

  50. M. Hariri-Ardebili, M. Kianoush, Seismic analysis of a coupled dam-reservoir foundation system considering pressure effects at opened joints. Struct. Infrastruct. Eng. 11, 833–850 (2015)

    Article  Google Scholar 

  51. M. Hariri-Ardebili, H. Mirzabozorg, Estimation of probable damages in arch dams subjected to strong ground motions using endurance time acceleration functions. KSCE J. Civil Eng. 18, 574–586 (2014)

    Article  Google Scholar 

  52. M. Hariri-Ardebili, V. Saouma, Quantitative failure metric for gravity dams. Earthq. Eng. Struct. Dyn. 44, 461–480 (2015)

    Article  Google Scholar 

  53. M. Hariri-Ardebili, V. Saouma, Collapse fragility curves for concrete dams: comprehensive study. ASCE J. Struct. Eng. 142(10), 04016075 (2016)

    Google Scholar 

  54. M. Hariri-Ardebili, V. Saouma, Probabilistic seismic demand model and optimal intensity measure for concrete dams. Struct. Saf. 59, 67–85 (2016)

    Article  Google Scholar 

  55. M. Hariri-Ardebili, V. Saouma, Single and multi-hazard capacity functions for concrete dams. Soil Dyn. Earthq. Eng. 101, 234–249 (2017)

    Article  Google Scholar 

  56. M. Hariri-Ardebili, V. Saouma, K. Porter, Quantification of seismic potential failure modes in concrete dams. Earthq. Eng. Struct. Dyn. 45(6), 979–997 (2016)

    Article  Google Scholar 

  57. T. Hastie, R. Tibshirani, Generalized Additive Models (Chapman and Hall, New York, 1990)

    MATH  Google Scholar 

  58. E. Hernandez-Montes, O. Kwon, M. Aschheim, An energy-based formulation for first-and multiple-mode nonlinear static (pushover) analyses. J. Earthq. Eng. 8, 69–88 (2004)

    Article  Google Scholar 

  59. F. Jalayer, Direct Probabilistic Seismic Analysis: Implementing Non-Linear Dynamic Assessments. Ph.D. thesis. Stanford University, Palo-Alto, 2003

    Google Scholar 

  60. S. Jankovic, B. Stojadinovic, Probabilistic performance-based seismic demand model for {R/C} frame buildings, in Proceeding of the 13th World Conference on Earthquake Engineering (Vancouver, 2004)

    Google Scholar 

  61. F. Javanmardi, P. Leger, R. Tinawi, Seismic water pressure in cracked concrete gravity dams: experimental study and theoretical modeling. ASCE J. Struct. Eng. 131(1), 139–150 (2005)

    Article  Google Scholar 

  62. E. Karacabeyli, Lateral resistance of nailed shear walls subjected to static and cyclic displacements, in Research Report, FPS 49th Annual Meeting. Portland, 1998

    Google Scholar 

  63. A. Kazantzi, D. Vamvatsikos, D. Lignos, Seismic performance of a steel moment-resisting frame subject to strength and ductility uncertainty. Eng. Struct. 78, 69–77 (2014)

    Article  Google Scholar 

  64. I. Koutromanos et al., Numerical modeling of masonry-infilled RC frames subjected to seismic loads. Comput. Struct. 89, 1026–1037 (2011)

    Article  Google Scholar 

  65. Q. Li, Q. Ren, Research on determining solid structure critical load and failure mode. Eng. Fail. Anal. 32, 113–123 (2013)

    Article  Google Scholar 

  66. A. Liel et al., Incorporating modeling uncertainties in the assessment of seismic collapse risk of buildings. Struct. Saf. 31, 197–211 (2009)

    Article  Google Scholar 

  67. J. Liu et al., Stability assessment of the three-gorges dam foundation, china, using physical and numerical modeling—Part I: physical model tests. Int. J. Rock Mech. Mining Sci. 40, 609–631 (2003)

    Article  Google Scholar 

  68. A. Løkke, A. Chopra, Response spectrum analysis of concrete gravity dams including dam-water-foundation interaction. J. Struct. Eng. 141(8), 04014202 (2014)

    Google Scholar 

  69. J. Mander et al., Incremental dynamic analysis applied to seismic financial risk assessment of bridges. Eng. Struct. 29, 2662–2672 (2007)

    Article  Google Scholar 

  70. M. Mashayekhi, H. Estekanchi, Investigation of strong-motion duration consistency in endurance time excitation functions. Sci. Iran. 20, 1085–1093 (2013)

    Google Scholar 

  71. MATLAB, Version 9.1 (R2016b) (The MathWorks, Natick, 2016)

    Google Scholar 

  72. R. McGuire, Probabilistic seismic hazard analysis and design earth-quakes: closing the loop. Bull. Seismol. Soc. Am. 85, 1275–1284 (1995)

    Article  Google Scholar 

  73. A. Nozari, H. Estekanchi, Optimization of endurance time acceleration functions for seismic assessment of structures. Int. J. Optim. Civil Eng. 1, 257–277 (2011)

    Google Scholar 

  74. J. Padgett, R. DesRoches, Sensitivity of seismic response and fragility to parameter uncertainty. J. Struct. Eng. 133, 1710–1718 (2007)

    Article  Google Scholar 

  75. J. Padgett, B. Nielson, R. DesRoches, Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios. Earthq. Eng. Struct. Dyn. 37, 711–725 (2008)

    Article  Google Scholar 

  76. J. Pan, Y. Xu, F. Jin, Seismic performance assessment of arch dams using incremental nonlinear dynamic analysis. Eur. J. Environ. Civil Eng. 19(3), 305–326 (2015)

    Article  Google Scholar 

  77. P. Panyakapo, Cyclic pushover analysis procedure to estimate seismic demands for buildings. Eng. Struct. 66, 10–23 (2014)

    Article  Google Scholar 

  78. V. Papanikolaou, A. Elnashai, Evaluation of conventional and adaptive pushover analysis I: methodology. J. Earthq. Eng. 9, 923–941 (2005)

    Article  Google Scholar 

  79. K. Pitilakis, S. Karapetrou, S. Fotopoulou, Consideration of aging and SSI effects on seismic vulnerability assessment of RC buildings. Bull. Earthq. Eng. 12, 1755–1776 (2014)

    Article  Google Scholar 

  80. L.G. Pujades et al., Parametric model for capacity curves. Bull. Earthq. Eng. 13(5), 1347–1376

    Google Scholar 

  81. S. Ramamoorthy, P. Gardoni, J. Bracci, Probabilistic demand models and fragility curves for reinforced concrete frames. J. Struct. Eng. 132, 1563–1572 (2006)

    Article  Google Scholar 

  82. R. Riddell, On ground motion intensity indices. Earthq. Spectra 23, 147–173 (2007)

    Article  Google Scholar 

  83. J. Salamon, Seismic Induced Loads on Spillway Gates, Phase I—Literature Review. Tech. rep. DSO-11-06. U.S. Bureau of Reclamation, Denver, 2011

    Google Scholar 

  84. V. Saouma, L. Perotti, T. Shimpo, Stress analysis of concrete structures subjected to alkali-aggregate reactions. ACI Struct. J. 104, 532–541 (2007)

    Google Scholar 

  85. V. Saouma et al., A mathematical model for the kinetics of the alkali-silica chemical reaction. Cement Concr. Res. 68, 184–195 (2015)

    Article  Google Scholar 

  86. Saouma, V.E, Numerical Modeling of AAR (CRC Press, 2014), p. 324

    Google Scholar 

  87. N. Shome, Probabilistic Seismic Demand Analysis of Nonlinear structures. Ph.D. thesis. Stanford University, Stanford, 1999

    Google Scholar 

  88. V. Slowik, V. Saouma, Water pressure in propagating concrete cracks. ASCE Struct. Eng. 126, 235–242 (2000)

    Article  Google Scholar 

  89. B. Soysal, B. Binici, Y. Arici, Investigation of the relationship of seismic intensity measures and the accumulation of damage on concrete gravity dams using incremental dynamic analysis. Earthq. Eng. Struct. Dyn. 45(5), 719–737 (2015)

    Article  Google Scholar 

  90. R. Swain et al., Hydrologic Hazard Curve Estimating Procedures. Tech. rep. U.S. Department of the Interior Bureau of Reclamation, 2004

    Google Scholar 

  91. USACE, Earthquake Design and Evaluation of Concrete Hydraulic Structures. Tech. rep. EM 1110-2-6053. Department of the Army, U.S. Army Corps of Engineers, Washington, 2007

    Google Scholar 

  92. D. Vamvatsikos, C. Cornell, Incremental dynamic analysis. Earthq. Eng. Struct. Dyn. 31, 491–514 (2002)

    Article  Google Scholar 

  93. D. Vamvatsikos, C. Cornell, Applied incremental dynamic analysis. Earthq. Spectra 20, 523–553 (2004)

    Article  Google Scholar 

  94. D. Vamvatsikos, C. Cornell, Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information. Earthq. Eng. Struct. Dyn. 34(13), 1573–1600 (2005)

    Article  Google Scholar 

  95. D. Vamvatsikos, M. Fragiadakis, Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty. Earthq. Eng. Struct. Dyn. 39, 141–163 (2010)

    Google Scholar 

  96. M. Vořechovský, D. Novák, Correlation control in small-sample Monte Carlo type simulations I: a simulated annealing approach. Probab. Eng. Mech. 24, 452–462 (2009)

    Article  Google Scholar 

  97. W. Wang, C. Gu, T. Bao, Safety monitoring index of high concrete gravity dam based on failure mechanism of instability. Math. Prob. Eng. 2013, 732325 (2013)

    Article  Google Scholar 

  98. Y. Wang et al., Performance-Based Fire Engineering of Structures (CRC Press, Boca Raton, 2012)

    Book  Google Scholar 

  99. Z. Wei et al., Failure analysis of high-concrete gravity dam based on strength reserve factor method. Comput. Geotech. 35, 627–636 (2008)

    Article  Google Scholar 

  100. H. Westergaard, Water pressures on dams during earthquakes. Trans. Am. Soc. Civil Eng. 98, 418–433 (1933)

    Article  Google Scholar 

  101. A. Whittaker, R. Hamburger, A. Mahoney, Performance-based engineering of buildings for extreme events, in Proceedings of the Steel Building Symposium on Blast and Progressive Collapse Resistance (2003), pp. 55–66

    Google Scholar 

  102. C. Zangar, Hydrodynamic pressures on dams due to horizontal earthquakes. Proc. Soc. Exp. Stress Anal. 10, 93–102 (1953)

    Google Scholar 

  103. H. Zhu et al., Physical modelling of sliding failure of concrete gravity dam under overloading condition. Geomech. Eng. 2, 89–106 (2010)

    Article  Google Scholar 

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Saouma, V.E., Hariri-Ardebili, M.A. (2021). Capacity Functions. In: Aging, Shaking, and Cracking of Infrastructures. Springer, Cham. https://doi.org/10.1007/978-3-030-57434-5_24

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