Expected seismic performance of gravity dams using machine learning techniques


  • Rocio Segura University of Sherbrooke, QC, Canada
  • Jamie Padgett Rice University, Houston, TX, USA
  • Patrick Paultre University of Sherbrooke, QC, Canada




Methods for the seismic analysis of dams have improved extensively in the last several decades. Advanced numerical models have become more feasible and constitute the basis of improved procedures for design and assessment. A probabilistic framework is required to manage the various sources of uncertainty that may impact system performance and fragility analysis is a promising approach for depicting conditional probabilities of limit state exceedance under such uncertainties. However, the effect of model parameter variation on the seismic fragility analysis of structures with complex numerical models, such as dams, is frequently overlooked due to the costly and time-consuming revaluation of the numerical model. To improve the seismic assessment of such structures by jointly reducing the computational burden, this study proposes the implementation of a polynomial response surface metamodel to emulate the response of the system. The latter will be computationally and visually validated and used to predict the continuous relative maximum base sliding of the dam in order to build fragility functions and show the effect of modelling parameter variation. The resulting fragility functions are used to assess the seismic performance of the dam and formulate recommendations with respect to the model parameters. To establish admissible ranges of the model parameters in line with the current guidelines for seismic safety, load cases corresponding to return periods for the dam classification are used to attain target performance limit states.


Schleiss AJ and Pougatsch H (2011). “Les Barrages, du Project a la mise en Service”. Volume 17 of the Civil Engineering Treaty of the Swiss Federal Institute of Technology in Lausanne. Editor: PPUR Presses Polytechniques, ISBN 2880748313, 9782880748319. 714pp. (in French)

Lave LB, Resendiz-Carrillo D and McMichael FC (1990). “Safety goals for high-hazard dams: are dams too safe?”. Water Resources Research, 26: 1383–1391. https://doi.org/10.1029/WR026i007p01383 DOI: https://doi.org/10.1029/WR026i007p01383

Schultz MT, Gouldby BP, Simm JD and Wibowo JL (2010). “Beyond the Factor of Safety: Developing Fragility Curves to Characterize System Reliability”. Technical Report ERDC SR-10-01, U.S. Army Corps of Engineers. DOI: https://doi.org/10.21236/ADA525580

Tekie PB and Ellingwood BR (2001). “Fragility analysis of concrete gravity dams”. Journal of Infrastructure Systems, 127(8): 41–48. https://doi.org/10.1061/(ASCE)1076-0342(2001)7:2(41) DOI: https://doi.org/10.1061/(ASCE)1076-0342(2001)7:2(41)

Kreuzer H and Léger P (2013). “The adjustable factor of safety: A reliability-based approach to assess the factor of safety for concrete dams”. International Journal on Hydropower and Dams, 20(1): 67–80.

Westberg Wilde M and Johansson F (2013). “Probability-based guidelines for design and assessment of concrete dams”. Safety, Reliability, Risk and Life-Cycle Performance of Structures & Infrastructures, Deodatis EF, Ed., Taylor and Francis Group, 5187–5210. DOI: https://doi.org/10.1201/b16387-753

Hariri-Ardebili M (2017). “Analytical failure probability model for generic gravity dam classes”. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 1–12. https://doi.org/10.1177/1748006X17712663 DOI: https://doi.org/10.1177/1748006X17712663

Cordier M and Léger P (2018). “Structural stability of gravity dams: a progressive assessment considering uncertainties in shear strength parameters”. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 12(2): 109–122. https://doi.org/10.1080/17499518.2017.1395464 DOI: https://doi.org/10.1080/17499518.2017.1395464

Segura RL, Bernier C, Durand C and Paultre P (2019). “Modelling and characterizing a concrete gravity dam for fragility analysis”. Infrastructures, 4: 1–19. https://doi.org/10.3390/infrastructures4040062 DOI: https://doi.org/10.3390/infrastructures4040062

USBR and USACE (2019). “Best Practices in Dam and Levee Safety Risk Analysis.” Technical Report Version 4.1, U.S. Bureau of Reclamation and U.S. Army Corps of Engineer.

Kalinina A, Spada M, Marelli S, Burgherr P and Sudret B (2016). “Uncertainties in the Risk Assessment of Hydropower Dams: State-of-the-Art and Outlook”. Technical Report RSUQ-2016-008, ETH Zurich.

FERC (2016). “Risk-informed Decision Making Guidelines”. Technical Report Version 4.1, Federal Energy Regulatory Commission.

FEMA (2015). “Federal Guidelines for Dam Safety Risk Management”. Report No. P-1025. Federal Guidelines for Dam Safety Risk Management, Federal Emergency Management Agency.

Hariri Ardebili M and Saouma V (2016). “Seismic fragility analysis of concrete dams: A state-of-the-art review”. Engineering Structures, 128: 374–399. https://doi.org/10.1016/j.engstruct.2016.09.034 DOI: https://doi.org/10.1016/j.engstruct.2016.09.034

Alembagheri M (2018). “Investigating efficiency of vector-valued intensity measures in seismic demand assessment of concrete dams”. Advances in Civil Engineering, 12. https://doi.org/10.1155/2018/5675032 DOI: https://doi.org/10.1155/2018/5675032

Ghosh J, Padgett JE and Duenas Osorio L (2013). “Surrogate modelling and failure surface visualization for efficient seismic vulnerability assessment of highway bridges”. Probabilistic Engineering Mechanics, 34: 189–199. https://doi.org/10.1016/j.probengmech.2013.09.003 DOI: https://doi.org/10.1016/j.probengmech.2013.09.003

Forrester AIJ, Sobester A and Keane AJ (2008). “Engineering Design via Surrogate Modelling: A Practical Guide”. Chichester: Wiley. DOI: https://doi.org/10.1002/9780470770801

Yu J, Qin X and Larsen O (2014). “Uncertainty analysis of flood inundation modelling using GLUE with surrogate models in stochastic sampling”. Hydrological. Processes, 29(6): 1267–1279. https://doi.org/10.1002/hyp.10249 DOI: https://doi.org/10.1002/hyp.10249

Sudret B (2012). “Meta-models for structural reliability and uncertainty quantification”. Proceedings of the 5th Asian-Pacific Symposium on Structural Reliability (APSSRA 2012), Wuhan, China: Scientific Research Publishing. https://hal-enpc.archives-ouvertes.fr/hal-00683179/document DOI: https://doi.org/10.3850/978-981-07-2219-7_P321

Simpson W, Peplinski J, Koch P and Allen J (2001). “Metamodels for computer-based engineering design: Survey and recommendations”. Engineering Computation, 17(Jul): 129–150. https://doi.org/10.1007/PL00007198 DOI: https://doi.org/10.1007/PL00007198

Mangalathu S and Jeon J-S (2018). “Stripe-based fragility analysis of multispan concrete bridge classes using machine learning techniques”. Earthquake Engineering and Structural Dynamics, 48(11): 1238-1255. https://doi.org/10.1002/eqe.3183 DOI: https://doi.org/10.1002/eqe.3183

Sichani E, Padgett JE and Bisadi V (2017). “Probabilistic seismic analysis of concrete dry cask structures”. Structural Safety, 73(Jul): 87–98. https://doi.org/10.1016/j.strusafe.2018.03.001 DOI: https://doi.org/10.1016/j.strusafe.2018.03.001

Kameshwar S and Padgett JE (2014). “Multi-hazard risk assessment of highway bridges subjected to earthquake and hurricane hazards”. Engineering Structures, 78(Nov): 154–166. https://doi.org/10.1016/j.engstruct.2014.05.016 DOI: https://doi.org/10.1016/j.engstruct.2014.05.016

Salazar F, Toledo MA, Onate T and Moran R (2015). “Data-based models for the prediction of dam behaviour: A review and some methodogical considerations”. Archives of Computational Methods in Engineering, 24 (1): 1–21. https://doi.org/10.1007/s11831-015-9157-9 DOI: https://doi.org/10.1007/s11831-015-9157-9

Hariri-Ardebili M and Pourkamali-Anaraki F (2017). “Simplified reliability analysis of multi hazard risk in gravity dams via machine learning techniques”. Archives of Civil and Mechanical Engineering, 18(2): 592–610. https://doi.org/10.1016/j.acme.2017.09.003 DOI: https://doi.org/10.1016/j.acme.2017.09.003

Hariri-Ardebili M (2018). “MCS-based response surface metamodels and optimal design of experiments for gravity dams”. Structure and Infrastructure Engineering, 14(12): 1641–1663. https://doi.org/10.1080/15732479.2018.1469650 DOI: https://doi.org/10.1080/15732479.2018.1469650

Segura RL, Padgett JE and Paultre P (2020). “Metamodel-based seismic fragility analysis of concrete gravity dams”. ASCE Journal of Structural Engineering, 46: 04020121. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002629 DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0002629

Murphy KP (2012). Machine Learning a Probabilistic Perspective. Cambridge, MA: MIT Press.

Segura RL, Bernier C, Monteiro R and Paultre P (2018). “On the seismic fragility assessment of concrete gravity dams in eastern Canada”. Earthquake Spectra, 35(1):211– 231. https://doi.org/10.1193/012418EQS024M DOI: https://doi.org/10.1193/012418EQS024M

Westberg M and Johansson F (2016). “Probabilistic Model Code for Concrete Dams.” Rapport Technique 2016:292, Energiforsk.

Ghanaat Y, Patev RC and Chudgar AK (2012). “Seismic fragility analysis of concrete gravity dams”. 15th World Conference on Earthquake Engineering, Lisbon.

Proulx J and Paultre P (1997). “Experimental and numerical investigation of dam-reservoir-foundation interaction for a large gravity dam”. Canadian Journal of Civil Engineering, 24: 90–105. https://doi.org/10.1139/l96-086 DOI: https://doi.org/10.1139/l96-086

Mills-Bria B, Koltuniuk R and Percell P (2013). “State-of-Practice for the Nonlinear Analysis of Concrete Dams”. Technical Report, U.S Department of the interior Bureau of Reclamation. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:12(1710)

Padgett JE and DesRoches R (2007). “Sensitivity of seismic response and fragility to parameter uncertainty”. Journal of Structural Engineering, 133: 1710–1718. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:12(1710) DOI: https://doi.org/10.1061/(ASCE)0733-9445(2007)133:12(1710)

Natural Resources Canada, NRC (2015). Simplified Seismic Hazard Map for Canada. http://www.earthquakescanada.nrcan.gc.ca/hazard-alea/simphaz-eng.php. Visited on 2016-02-08.

Atkinson G and Adams J (2013). “Ground motion prediction equations for application to the 2015 Canadian national seismic hazard maps”. Canadian Journal of Civil Engineering, 40: 988–998. https://doi.org/10.1139/cjce-2012-0544 DOI: https://doi.org/10.1139/cjce-2012-0544

Bradley BA (2010). “A generalized conditional intensity measure approach and holistic ground motion selection”. Earthquake Engineering and Structural Dynamics, 56: 1321–1342. https://doi.org/10.1002/eqe.995 DOI: https://doi.org/10.1002/eqe.995

Hariri Ardebili M and Saouma V (2016). “Probabilistic seismic demand model and optimal intensity measure for concrete dams”. Structural Safety, 59: 67–85. https://doi.org/10.1016/j.strusafe.2015.12.001 DOI: https://doi.org/10.1016/j.strusafe.2015.12.001

Baker JW (2011). “Conditional mean spectrum: Tool for ground-motion selection”. Journal of Structural Engineering, 220: 1–8. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000215 DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0000215

Ancheta TD, Darragh RB, Stewart JP, Seyhan E, Silva WJ, Chiou KE, Brian SJ, Wooddell J, Graves RW, Kottke AR, Boore DM, Kishida T and Donahue JL (2013). “PEER NGA-West2 Database”. Pacific Earthquake Engineering Research Center. DOI: https://doi.org/10.1193/070913EQS197M

Goulet CA, Kishida T, Ancheta TD, Cramer CH, Darragh RB, Silva WJ, Hashash Y, Harmon J, Stewart JP, Wooddell KE and Youngs RR (2014). “PEER NGA-East Database”. Pacific Earthquake Engineering Research Center.

Hurtado JE (2012). “Dimensionality reduction and visualization of structural reliability problems using polar features”. Probabilistic Engineering Mechanics, 29: 16–31. https://doi.org/10.1016/j.probengmech.2011.12.004 DOI: https://doi.org/10.1016/j.probengmech.2011.12.004

Hasofer AM and Lind NC (1974). “Exact and invariant second-moment code format”. Journal of Engineering Mechanics Division, 100: 111–121. https://doi.org/10.1061/JMCEA3.0001848 DOI: https://doi.org/10.1061/JMCEA3.0001848

Bernier C, Padgett JE, Proulx J and Paultre P (2016). “Seismic fragility of concrete gravity dams with modelling parameter uncertainty and spatial variation”. ASCE Journal of Structural Engineering, 142(5): 05015002. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001441 DOI: https://doi.org/10.1061/(ASCE)ST.1943-541X.0001441

Baker JW (2015). “Efficient analytical fragility function fitting using dynamic structural analysis”. Earthquake Spectra, 31: 579–599. https://doi.org/10.1193/021113EQS025M DOI: https://doi.org/10.1193/021113EQS025M

CDA (2007). “Dam Safety Guidelines, 2013 Revision”. Canadian Dam Association (CDA), Edmonton, AB, Canada.

Vick SG (2002). “Degrees of Belief, Subjective Probability and Engineering Judgment”. American Society of Civil Engineers, Reston, Virginia. 455 pp.

ASCE (2016). “Minimum Design Loads for Buildings and Other Structures”. Technical Report, American Society of Civil Engineers, Reston, Virginia.




How to Cite

Segura, R., Padgett, J., & Paultre, P. (2021). Expected seismic performance of gravity dams using machine learning techniques. Bulletin of the New Zealand Society for Earthquake Engineering, 54(2), 58–68. https://doi.org/10.5459/bnzsee.54.2.58-68