{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T23:49:40Z","timestamp":1768261780779,"version":"3.49.0"},"reference-count":84,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T00:00:00Z","timestamp":1669334400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation for Science and Technology (FCT)","award":["PTDC\/ECI-EGC\/5332\/2020"],"award-info":[{"award-number":["PTDC\/ECI-EGC\/5332\/2020"]}]},{"name":"Foundation for Science and Technology (FCT)","award":["UIDB\/04625\/2020"],"award-info":[{"award-number":["UIDB\/04625\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Water"],"abstract":"<jats:p>The seismic safety assessment of large concrete dams remains a significant challenge in dam engineering, as it requires appropriate analysis methods, modern performance criteria, and advanced numerical models to simulate the dam seismic behavior. This paper presents a method for seismic safety assessment of arch dams based on Endurance Time Analysis (ETA), using tensile and compressive damage results from a robust formulation for seismic analysis considering joint opening\/sliding and concrete non-linear behavior (finite element program DamDySSA, under development in LNEC). The seismic performance is evaluated by controlling the evolution of the damage state of the dam, according to predefined performance criteria, to estimate acceleration endurance limits for tensile and compressive damage. These acceleration limits are compared, respectively, with the peak ground accelerations prescribed for the Operating Basis Earthquake (OBE) and Safety Evaluation Earthquake (SEE), aiming to evaluate the dam seismic performance relative to both earthquake levels efficiently, using a single intensifying acceleration time history. The ETA-based method is applied to the cases of Cabril Dam (132 m-high) and Cahora Bassa Dam (170 m-high), confirming its usefulness for future seismic safety studies, while the potential of DamDySSA for non-linear seismic analysis of arch dams is highlighted.<\/jats:p>","DOI":"10.3390\/w14233835","type":"journal-article","created":{"date-parts":[[2022,11,25]],"date-time":"2022-11-25T03:34:24Z","timestamp":1669347264000},"page":"3835","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Seismic Safety Assessment of Arch Dams Using an ETA-Based Method with Control of Tensile and Compressive Damage"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8324-7559","authenticated-orcid":false,"given":"Andr\u00e9","family":"Alegre","sequence":"first","affiliation":[{"name":"Civil Engineering Department, Instituto Superior de Engenharia de Lisboa, Instituto Polit\u00e9cnico de Lisboa (ISEL-IPL), R. Conselheiro Em\u00eddio Navarro 1, 1959-007 Lisboa, Portugal"},{"name":"Concrete Dams Department, National Laboratory for Civil Engineering (LNEC), Av. do Brasil 101, 1700-075 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3309-5897","authenticated-orcid":false,"given":"S\u00e9rgio","family":"Oliveira","sequence":"additional","affiliation":[{"name":"Concrete Dams Department, National Laboratory for Civil Engineering (LNEC), Av. do Brasil 101, 1700-075 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4833-5091","authenticated-orcid":false,"given":"Paulo","family":"Mendes","sequence":"additional","affiliation":[{"name":"Civil Engineering Department, Instituto Superior de Engenharia de Lisboa, Instituto Polit\u00e9cnico de Lisboa (ISEL-IPL), R. Conselheiro Em\u00eddio Navarro 1, 1959-007 Lisboa, Portugal"}]},{"given":"Jorge","family":"Proen\u00e7a","sequence":"additional","affiliation":[{"name":"CERIS, Instituto Superior T\u00e9cnico, Universidade de Lisboa (IST-ULisboa), Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"given":"Rafael","family":"Ramos","sequence":"additional","affiliation":[{"name":"Concrete Dams Department, National Laboratory for Civil Engineering (LNEC), Av. do Brasil 101, 1700-075 Lisboa, Portugal"},{"name":"CERIS, Instituto Superior T\u00e9cnico, Universidade de Lisboa (IST-ULisboa), Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal"}]},{"given":"Ezequiel","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Hidroel\u00e9trica de Cahora Bassa, Office Headquarters, Songo 2304, Mozambique"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,25]]},"reference":[{"key":"ref_1","unstructured":"(2016). ICOLD Bulletin 169: Global Climate Change, Dams, Reservoirs and Related Water Sources, Technical Committee Y, International Commission on Large Dams."},{"key":"ref_2","unstructured":"(2019). ICOLD Bulletin Preprint 185: Challenges and Needs for Dams in the 21st Century. Technical Committee on Global Climate Change and Dams, Reservoirs and the Associated Water Resources, International Commission on Large Dams."},{"key":"ref_3","unstructured":"UNESCO (2020). UN-Water United Nations World Water Development Report 2020: Water and Climate Change, United Nations Educational, Scientific, and Cultural Organization."},{"key":"ref_4","unstructured":"(2019). ICOLD World Declaration on Dam Safety, International Commission on Large Dams."},{"key":"ref_5","unstructured":"(2021). IJHD World Atlas & Industry Guide, Aqua Media Int. Ltd."},{"key":"ref_6","unstructured":"Wieland, M., and Chen, H. Leassons Learnt from the Wenchuan Earthquake. Int. Water Power Dam Constr., 2009."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1007\/s11709-010-0005-6","article-title":"Features of Seismic Hazard in Large Dam Projects and Strong Motion Monitoring of Large Dams","volume":"4","author":"Wieland","year":"2010","journal-title":"Front. Archit. Civ. Eng. China"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ansal, A. (2014). Seismic Hazard and Seismic Design and Safety Aspects of Large Dam Projects. Perspectives on European Earthquake Engineering and Seismology, Springer.","DOI":"10.1007\/978-3-319-07118-3"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/J.ENG.2016.03.011","article-title":"Safety Aspects of Sustainable Storage Dams and Earthquake Safety of Existing Dams","volume":"2","author":"Wieland","year":"2016","journal-title":"Engineering"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/j.wse.2019.01.002","article-title":"Seismic Design of Xiluodu Ultra-High Arch Dam","volume":"11","author":"Wang","year":"2018","journal-title":"Water Sci. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/J.ENG.2016.03.012","article-title":"Key Technologies in the Design and Construction of 300 M Ultra-High Arch Dams","volume":"2","author":"Wang","year":"2016","journal-title":"Engineering"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1546","DOI":"10.1002\/1096-9845(200010)29:10<1547::AID-EQE979>3.0.CO;2-N","article-title":"Non-Linear Seismic Response of Arch Dams with Contraction Joint Opening and Joint Reinforcements","volume":"29","author":"Zhang","year":"2000","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_13","unstructured":"Zhang, C., Xu, Y., Jin, F., and Wang, G. (2004, January 1\u20136). Studies on Seismic Behaviour of Xiaowan Arch Dam and Earthquake Resistance Measures. Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada."},{"key":"ref_14","first-page":"22","article-title":"Seismic Safety Evaluation of Large Dams in Switzerland: Lessons Learned","volume":"70","author":"Darbre","year":"2019","journal-title":"Int. Water Power Dam Constr."},{"key":"ref_15","unstructured":"Alegre, A., Carvalho, E., Matsinhe, B., Mendes, P., Oliveira, S., and Proen\u00e7a, J. (2019, January 16\u201319). Monitoring Vibrations in Large Dams. Proceedings of the HYDRO 2019\u2014Concept to closure: Practical Steps, Porto, Portugal."},{"key":"ref_16","unstructured":"Alegre, A., Oliveira, S., Carvalho, E., Mendes, P., Proen\u00e7a, J., and Matsinhe, B. (2022, January 25\u201327). Continuous Dynamic Monitoring of Large Arch Dams and Vibration-Based Damage Detection. Proceedings of the HYDRO 2022\u2014Roles of Hydro in the Global Recovery, Strasbourg, France."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4483","DOI":"10.1007\/s10518-022-01392-1","article-title":"Seismic and Structural Health Monitoring Systems for Large Dams: Theoretical, Computational and Practical Innovations","volume":"20","author":"Oliveira","year":"2022","journal-title":"Bull. Earthq. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1061\/(ASCE)ST.1943-541X.0000431","article-title":"Earthquake Analysis of Arch Dams: Factors to Be Considered","volume":"138","author":"Chopra","year":"2012","journal-title":"J. Struct. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11803-014-0237-x","article-title":"Seismic Safety of High Concrete Dams","volume":"13","author":"Chen","year":"2014","journal-title":"Earthq. Eng. Eng. Vib."},{"key":"ref_20","unstructured":"(2016). ICOLD Bulletin 148: Selecting Seismic Parameters for Large Dams\u2014Guidelines (Revision of Bulletin 72), Committee on Seismic Aspects of Dam Design, International Commission on Large Dams."},{"key":"ref_21","unstructured":"(2017). ICOLD Bulletin 168: Recommendations for Operation, Maintenance and Rehabilitation, International Comission on Large Dams."},{"key":"ref_22","unstructured":"(2018). ICOLD Bulletin 158: Dam Surveillance Guide, International Comission on Large Dams."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.scient.2011.05.039","article-title":"Application of the Endurance Time Method in Seismic Analysis of Concrete Gravity Dams","volume":"18","author":"Valamanesh","year":"2011","journal-title":"Sci. Iran."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1002\/eqe.2697","article-title":"Quantification of Seismic Potential Failure Modes in Concrete Dams","volume":"45","author":"Saouma","year":"2016","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_25","unstructured":"Meghella, M., and Furgani, L. (2014, January 4\u20135). Application of Endurance Time Analysis Method to the NonLinear Seismic Analysis of Dams: Potentialities and Limitations. Proceedings of the ICOLD 82nd Annual Meeting, Banff, AB, Canada."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1007\/s12205-013-0264-6","article-title":"Estimation of Probable Damages in Arch Dams Subjected to Strong Ground Motions Using Endurance Time Acceleration Functions","volume":"18","author":"Mirzabozorg","year":"2014","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3599","DOI":"10.1007\/s13369-014-1027-5","article-title":"Nonlinear Seismic Assessment of Arch Dams and Investigation of Joint Behavior Using Endurance Time Analysis Method","volume":"39","author":"Mirzabozorg","year":"2014","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"108402","DOI":"10.1016\/j.ress.2022.108402","article-title":"An Uncertainty-Aware Dynamic Shape Optimization Framework: Gravity Dam Design","volume":"222","author":"Abdollahi","year":"2022","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.engstruct.2015.11.021","article-title":"A New Class of Seismic Damage and Performance Indices for Arch Dams via ETA Method","volume":"110","author":"Furgani","year":"2016","journal-title":"Eng. Struct."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Furgani, L., Hariri-Ardebili, M.A., Meghella, M., and Seyed-Kolbadi, S.M. (2019). On the Dynamic Capacity of Concrete Dams. Infrastructures, 4.","DOI":"10.3390\/infrastructures4030057"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hariri-Ardebili, M., Mahdavi, G., Abdollahi, A., and Amini, A. (2021). An RF-PCE Hybrid Surrogate Model for Sensitivity Analysis of Dams. Water, 13.","DOI":"10.3390\/w13030302"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Segura, R.L., Miquel, B., Paultre, P., and Padgett, J.E. (2021). Accounting for Uncertainties in the Safety Assessment of Concrete Gravity Dams: A Probabilistic Approach with Sample Optimization. Water, 13.","DOI":"10.3390\/w13060855"},{"key":"ref_33","unstructured":"Pedro, J.O., and C\u00e2mara, R. (1986, January 7\u201312). Coupled Models for Dynamic Analysis of Arch Dams. Proceedings of the 8th European Conference on Earthquake Engineering, Lisbon, Portugal."},{"key":"ref_34","unstructured":"Chopra, A.K., and Tan, H. (1992, January 19\u201324). Modelling Dam-Foundation Interaction in Analysis of Arch Dams. Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, Spain."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1061\/TACEAT.0004496","article-title":"Water Pressures on Dams during Earthquakes","volume":"98","author":"Westergaard","year":"1933","journal-title":"Trans. Am. Soc. Civ. Eng."},{"key":"ref_36","unstructured":"Tiliouine, B., and Seghir, A. (1998, January 6\u201311). Fluid-Structure Models for Dynamic Studies of Dam-Water Systems. Proceedings of the 11th European Conference on Earthquake Engineering, Paris, France."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1810","DOI":"10.1061\/(ASCE)0733-9445(1986)112:8(1810)","article-title":"Hydrodynamic and Foundation Flexibility Effects in Earthquake Response of Arch Dams","volume":"112","author":"Fok","year":"1986","journal-title":"J. Struct. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/nme.1620130102","article-title":"Fluid-Structure Dynamic Interaction and Wave Forces. An Introduction to Numerical Treatment. An Introduction to Numerical Treatment","volume":"13","author":"Zienkiewicz","year":"1978","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.compstruc.2008.10.006","article-title":"Assessment of Potential-Based Fluid Finite Elements for Seismic Analysis of Dam-Reservoir Systems","volume":"87","author":"Bouaanani","year":"2009","journal-title":"Comput. Struct."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1002\/eqe.3019","article-title":"Direct Finite Element Method for Nonlinear Earthquake Analysis of 3-Dimensional Semi-Unbounded Dam\u2013water-Foundation Rock Systems","volume":"47","author":"Lokke","year":"2018","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_41","unstructured":"Clough, R.W. (July, January 30). Non-Linear Mechanisms in the Seismic Response of Arch Dams. Proceedings of the International Research Conference on Earthquake Engineering, Skopje, Yugoslavia."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1002\/eqe.4290140202","article-title":"Earthquake Analysis of Arch Dams Including Dam-Water Interaction, Reservoir Boundary Absorption and Foundation Flexibility","volume":"14","author":"Fok","year":"1986","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1002\/eqe.968","article-title":"Linear Analysis of Concrete Arch Dams Including Dam-Water-Foundation Rock Interaction Considering Spatially Varying Ground Motions","volume":"39","author":"Wang","year":"2010","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1002\/eqe.576","article-title":"Generation of Spatially Nonuniform Ground Motion for Nonlinear Analysis of a Concrete Arch Dam","volume":"35","author":"Alves","year":"2006","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1016\/j.soildyn.2009.03.003","article-title":"Influence of Seismic Input Mechanisms and Radiation Damping on Arch Dam Response","volume":"29","author":"Zhang","year":"2009","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_46","unstructured":"Dominguez, J., and Maeso, O. (1992, January 19\u201324). Model for the Seismic Analysis of Arch Dams Including Interaction Effects. Proceedings of the 10th World Conference on Earthquake Engineering, Madrid, Spain."},{"key":"ref_47","unstructured":"Alves, S.W. (2004). Nonlinear Analysis of Pacoima Dam with Spatially Non-Uniform Ground Motion. [Ph.D. Thesis, California Institute of Technology]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.soildyn.2013.02.006","article-title":"Earthquake Damage Analysis of Arch Dams Considering Dam\u2013water\u2013foundation Interaction","volume":"49","author":"Wang","year":"2013","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"63","DOI":"10.56748\/ejse.12153","article-title":"Seismic Response of Concrete Arch Dams Including Dam-Reservoir-Foundation Interaction Using Infinite Elements","volume":"12","author":"Mirzabozorg","year":"2012","journal-title":"Electron. J. Struct. Eng."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1350032","DOI":"10.1142\/S0219455413500326","article-title":"A Comparative Study of Seismic Stability of Coupled Arch Dam-Foundation-Reservoir Systems Using Infinite Elements and Viscous Boundary Models","volume":"13","author":"Mirzabozorg","year":"2013","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1080\/13632469.2011.638697","article-title":"An Investigation into the Influence of Damping on the Earthquake Response Analysis of a High Arch Dam","volume":"16","author":"Chen","year":"2012","journal-title":"J. Earthq. Eng."},{"key":"ref_52","unstructured":"Robbe, E., Kashiwayanagi, M., and Yamane, Y. (2017, January 9\u201313). Seismic Analyses of Concrete Dam, Comparison between Finite-Element Analyses and Seismic Records. Proceedings of the 16th World Conference on Earthquake Engineering, Santiago, Chile."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1002\/eqe.974","article-title":"Earthquake Response of Arch Dams to Spatially Varying Ground Motion","volume":"39","author":"Chopra","year":"2010","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_54","unstructured":"Proulx, J., and Darbre, G.R. (2008, January 12\u201317). Earthquake Response of Large Arch Dams Observational Evidence and Numerical Modelling. Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1061\/(ASCE)0733-9445(1992)118:4(1039)","article-title":"Effect of Contraction Joints on Earthquake Response of an Arch Dam","volume":"118","author":"Fenves","year":"1992","journal-title":"J. Struct. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1002\/eqe.4290100208","article-title":"Non-Linear Seismic Response of Arch Dams","volume":"10","author":"Niwa","year":"1982","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.1002\/eqe.4290240905","article-title":"Seismic Evaluation of Concrete Dams via Continuum Damage Models","volume":"24","author":"Cervera","year":"1995","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1002\/(SICI)1097-0207(19990820)45:11<1695::AID-NME651>3.0.CO;2-2","article-title":"Seismic Analysis of Arch Dams\u2014A Continuum Damage Mechanics Approach","volume":"45","author":"Valliappan","year":"1999","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_59","first-page":"681350","article-title":"Seismic Performance Evaluation and Analysis of Major Arch Dams Considering Material and Joint Nonlinearity Effects","volume":"2012","author":"Mirzabozorg","year":"2012","journal-title":"ISRN Civ. Eng."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"1157","DOI":"10.1002\/eqe.1178","article-title":"Nonlinear Earthquake Analysis of High Arch Dam-Water-Foundation Rock Systems","volume":"41","author":"Wang","year":"2012","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1080\/19648189.2014.960950","article-title":"Seismic Performance Assessment of Arch Dams Using Incremental Nonlinear Dynamic Analysis","volume":"19","author":"Pan","year":"2015","journal-title":"Eur. J. Environ. Civ. Eng."},{"key":"ref_62","unstructured":"Alegre, A. (2021). Modelling and Monitoring the Dynamic Behaviour of Concrete Dams. Modal Analysis and Seismic Response. [Ph.D. Thesis, Instituto Superior T\u00e9cnico, University of Lisbon]."},{"key":"ref_63","unstructured":"Goldgruber, M. (2015). Non-Linear Seismic Modelling of Concrete Dams. [Ph.D. Thesis, Graz University of Technology]."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1080\/13632460409350521","article-title":"The Use of Real Earthquake Accelerograms as Input to Dynamic Analysis","volume":"8","author":"Bommer","year":"2004","journal-title":"J. Earthq. Eng."},{"key":"ref_65","unstructured":"Clough, R.W., and Penzien, J. (2003). Dynamics of Structures, Computers & Structures, Inc.. [3rd ed.]."},{"key":"ref_66","unstructured":"Gasparini, D.A., and Vanmarcke, E.H. (1976). Simulated Earthquake Motions Compatible with Prescribed Response Spectra. Dept. of Civil Engineering, Massachusetts Institute of Technology. Research Report R76-4."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1007\/PL00012553","article-title":"Simulation of Ground Motion Using the Stochastic Method","volume":"160","author":"Boore","year":"2003","journal-title":"Pure Appl. Geophys."},{"key":"ref_68","unstructured":"Carvalho, A. (2007). Modela\u00e7\u00e3o Estoc\u00e1stica Da Ac\u00e7\u00e3o S\u00edsmica Em Portugal Continental [Stochastic Modelling of the Seismic Action in Continental Portugal]. [Ph.D. Thesis, Instituto Superior T\u00e9cnico, University of Lisbon]."},{"key":"ref_69","first-page":"361","article-title":"Endurance Time Method for Seismic Analysis and Design of Structures","volume":"11","author":"Estekanchi","year":"2004","journal-title":"Sci. Iran."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"2069","DOI":"10.1080\/0305215X.2019.1567724","article-title":"An Evolutionary Optimization-Based Approach for Simulation of Endurance Time Load Functions","volume":"51","author":"Mashayekhi","year":"2019","journal-title":"Eng. Optim."},{"key":"ref_71","first-page":"257","article-title":"Optimization of Endurance Time Acceleration Functions for Seismic Assessment of Structures","volume":"1","author":"Nozari","year":"2011","journal-title":"Int. J. Optim. Civ. Eng."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/s40999-018-0339-3","article-title":"Models of Earthquake Ground Shaking Used in Seismic Design and Safety Checks of Large Dams","volume":"17","author":"Wieland","year":"2019","journal-title":"Int. J. Civ. Eng."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1002\/eqe.141","article-title":"Incremental Dynamic Analysis","volume":"31","author":"Vamvatsikos","year":"2002","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.soildyn.2012.09.010","article-title":"Damage Assessment of a Concrete Arch Dam through Nonlinear Incremental Dynamic Analysis","volume":"44","author":"Alembagheri","year":"2013","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_75","unstructured":"Oliveira, S., Silvestre, A., and C\u00e2mara, R. (2014). Barragem de Ribeiradio. Obra Constr\u00faida. Verifica\u00e7\u00e3o Da Seguran\u00e7a Estrutural Para A\u00e7\u00f5es Est\u00e1ticas E Din\u00e2micas. Cen\u00e1rios Correntes E de Rotura [Ribeiradio Dam. Built Structure. Structural Safety Verification under Static and Dynamic Loads. Current and Fail], Concrete Dams Department, LNEC. Report."},{"key":"ref_76","unstructured":"LNEC (2009). Cahora Bassa Hydroelectric Scheme. Analysis of the Seismic Dam Behaviour, Concrete Dams Department, National Laboratory for Civil Engineering."},{"key":"ref_77","unstructured":"Oliveira, S., Alegre, A., Silvestre, A., Espada, M., and C\u00e2mara, R. (2015, January 9\u201311). Seismic Safety Evaluation of Luzzone Dam. Use of a 3DFEM State Formulation in Pressures and Displacements. Proceedings of the 13th ICOLD International Benchmark Workshop on Numerical Analysis of Dams, EPFL, Lausanne, Switzerland."},{"key":"ref_78","unstructured":"Gunn, R.M., Balissat, M., Manso, P., Mouvet, L., and Schleiss, A. (2016). Proceedings of the 13th ICOLD International Benchmark Workshop on the Numerical Analysis of Dams, Swiss Committee on Dams."},{"key":"ref_79","unstructured":"Zienkiewicz, O.C., Taylor, R.L., and Zhu, J.Z. (2013). The Finite Element Method: Its Basis and Fundamentals, Elsevier Butterworth-Heinemann. [7th ed.]."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1061\/JMCEA3.0000098","article-title":"A Method of Computation for Structural Dynamics","volume":"85","author":"Newmark","year":"1959","journal-title":"J. Eng. Mech. Div."},{"key":"ref_81","unstructured":"(2014). The Finite Element Method for Solid and Structural Mechanics, Elsevier. [7th ed.]."},{"key":"ref_82","unstructured":"Oliveira, S. (2002). Continuous Monitoring Systems for the Dynamic Performance Assessment of Arch Dams. Sub-Program D, in Study of Evolutive Deterioration Processes in Concrete Dams. Safety Control over Time, Aqua~Media International Ltd."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"1430","DOI":"10.1016\/j.engstruct.2006.01.012","article-title":"Numerical Simulation of Collapse Scenarios in Reduced Scale Tests of Arch Dams","volume":"28","author":"Oliveira","year":"2006","journal-title":"Eng. Struct."},{"key":"ref_84","unstructured":"Planning and Infrastructure Ministry (2018). Regulamento de Seguran\u00e7a de Barragens [Dam Safety Regulation], Decree-law No. 21\/2018 of March 28."}],"container-title":["Water"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4441\/14\/23\/3835\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:26:31Z","timestamp":1760145991000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4441\/14\/23\/3835"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,25]]},"references-count":84,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["w14233835"],"URL":"https:\/\/doi.org\/10.3390\/w14233835","relation":{},"ISSN":["2073-4441"],"issn-type":[{"value":"2073-4441","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,25]]}}}