Center and Characteristic Seismic Reliability as new indexes for accounting uncertainties in seismic reliability analysis

Abstract Seismic reliability analysis is a powerful tool to assess structural safety against ground shaking actions induced by earthquake occurrences. The classic approach for computing seismic reliability of a structural system requires a seismic hazard curve and a fragility function and leads to the estimation of the failure probability of the investigated damage state. However, resulting failure probability is strongly related to the preliminary assumptions in both hazard and fragility analyses, and slight changes in the input model parameters may cause relevant variability of seismic reliability estimates. The present work formalizes a general approach to be followed when dealing with seismic reliability assessment of structural systems, aimed at taking into account the whole uncertainties of the input parameters within hazard and fragility models. In the proposed approach, probability of failure becomes in turn a random variable and therefore new indexes are introduced, namely Expected Failure Rate, Failure Rate Dispersion, Characteristic Failure Rate, Center of Seismic Reliability and Characteristic Seismic Reliability. Lastly, such approach is applied to a case study, where seismic reliability of an existing open-spandrel reinforced concrete arch bridge is analyzed, and results are discussed highlighting some relevant issues.

[1]  Jack W. Baker,et al.  Incorporating modeling uncertainties in the assessment of seismic collapse risk of buildings , 2009 .

[2]  H. Crowley,et al.  Seismic Hazard Assessment (2003–2009) for the Italian Building Code , 2011 .

[3]  Julian J. Bommer,et al.  Why Do Modern Probabilistic Seismic-Hazard Analyses Often Lead to Increased Hazard Estimates? , 2006 .

[4]  P. Bazzurro,et al.  Disaggregation of Probabilistic Ground-Motion Hazard in Italy , 2009 .

[5]  Jamie E. Padgett,et al.  Comparison between the Seismic Performance of Integral and Jointed Concrete Bridges , 2015 .

[6]  Julian J. Bommer,et al.  The Use and Misuse of Logic Trees in Probabilistic Seismic Hazard Analysis , 2008 .

[7]  Jihong Ye,et al.  Seismic Risk Assessment of a 2-storey Steel-sheathed CFS Building Considering Different Sources of Uncertainty , 2018, Structures.

[8]  Julian J. Bommer,et al.  Challenges of Building Logic Trees for Probabilistic Seismic Hazard Analysis , 2012 .

[9]  Julian J. Bommer,et al.  Uncertainty about the uncertainty in seismic hazard analysis , 2003 .

[10]  A. Rebez,et al.  Introducing epistemic uncertainties into seismic hazard assessment for the broader Vittorio Veneto area (N.E. Italy) , 2004 .

[11]  A. Harbitz.  An efficient sampling method for probability of failure calculation , 1986 .

[12]  J. Mander,et al.  Theoretical stress strain model for confined concrete , 1988 .

[13]  Paolo Castaldo,et al.  Seismic reliability-based ductility demand for hardening and softening structures isolated by friction pendulum bearings , 2018, Structural Control and Health Monitoring.

[14]  Andrea Dall'Asta,et al.  Seismic risk sensitivity of structures equipped with anti-seismic devices with uncertain properties , 2019 .

[15]  Jack W. Baker,et al.  Efficient Analytical Fragility Function Fitting Using Dynamic Structural Analysis , 2015 .

[16]  Thomas Most.  Assessment of structural simulation models by estimating uncertainties due to model selection and model simplification , 2011 .

[17]  L. Ibarra.  Global collapse of frame structures under seismic excitations , 2003 .

[18]  J. Wolfowitz,et al.  Introduction to the Theory of Statistics. , 1951 .

[19]  Reginald DesRoches,et al.  Sensitivity of Seismic Response and Fragility to Parameter Uncertainty , 2007 .

[20]  C. Cornell.  Engineering seismic risk analysis , 1968 .

[21]  C. Allin Cornell,et al.  The Case for Using Mean Seismic Hazard , 2005 .

[22]  Roger M.W. Musson.  On the Nature of Logic Trees in Probabilistic Seismic Hazard Assessment , 2012 .

[23]  Terje Haukaas,et al.  Model Uncertainty in Finite-Element Analysis: Bayesian Finite Elements , 2011 .

[24]  Thomas H. Jordan,et al.  A Unified Probabilistic Framework for Seismic Hazard Analysis , 2017 .

[25]  Dimitrios Vamvatsikos,et al.  Applied Incremental Dynamic Analysis , 2004 .

[26]  Giuseppe Mancini,et al.  Seismic reliability-based robustness assessment of three-dimensional reinforced concrete systems equipped with single-concave sliding devices , 2018 .

[27]  Warner Marzocchi,et al.  Accounting for Epistemic Uncertainty in PSHA: Logic Tree and Ensemble Modeling , 2014 .

[28]  B. Gutenberg,et al.  Frequency of Earthquakes in California , 1944, Nature.

[29]  Bruce R. Ellingwood,et al.  Seismic fragilities for non-ductile reinforced concrete frames – Role of aleatoric and epistemic uncertainties , 2010 .

[30]  Jorge M. Gaspar-Escribano,et al.  Uncertainty assessment for the seismic hazard map of Spain , 2015 .

[31]  Aleš Florian,et al.  An efficient sampling scheme: Updated Latin Hypercube Sampling , 1992 .

[32]  Paolo Castaldo,et al.  Probabilistic analysis of excavation-induced damages to existing structures , 2013 .

[33]  Julian J. Bommer,et al.  Sensitivity of PSHA results to ground motion prediction relations and logic-tree weights , 2005 .

[34]  R. Mcguire.  Probabilistic seismic hazard analysis and design earthquakes: Closing the loop , 1995, Bulletin of the Seismological Society of America.

[35]  Jean-Claude Mitteau.  Error evaluations for the computation of failure probability in static structural reliability problems , 1999 .

[36]  Fatemeh Jalayer,et al.  Probabilistic assessment of groundwater leakage in diaphragm wall joints for deep excavations , 2018 .

[37]  P. Castaldo,et al.  Partial safety factor for resistance model uncertainties in 2D non-linear finite element analysis of reinforced concrete structures , 2018, Engineering Structures.

[38]  D. Bindi,et al.  Ground motion prediction equations derived from the Italian strong motion database , 2011 .

[39]  Fatemeh Jalayer,et al.  Direct probabilistic seismic analysis: Implementing non-linear dynamic assessments , 2003 .

[40]  Humberto Varum,et al.  Hazard Disaggregation and Record Selection for Fragility Analysis and Earthquake Loss Estimation , 2017 .

[41]  Robert E. Bachman,et al.  Creating Fragility Functions for Performance-Based Earthquake Engineering , 2007 .

[42]  Massimiliano Stucchi,et al.  A seismic source zone model for the seismic hazard assessment of the Italian territory , 2008 .

[43]  Amr S. Elnashai,et al.  The effect of material and ground motion uncertainty on the seismic vulnerability curves of RC structure , 2006 .

[44]  B. E. Shaw,et al.  Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time‐Independent Model , 2014 .

[45]  Henrik O. Madsen,et al.  Structural Reliability Methods , 1996 .

[46]  Gian Paolo Cimellaro,et al.  On the selection and scaling of ground motions for fragility analysis of structures , 2014 .

[47]  G. Schuëller,et al.  A critical appraisal of methods to determine failure probabilities , 1987 .

[48]  D. Huntington,et al.  Improvements to and limitations of Latin hypercube sampling , 1998 .

[49]  Julian J. Bommer,et al.  Probability and Uncertainty in Seismic Hazard Analysis , 2005 .

[50]  C. Allin Cornell,et al.  Three Proposals for Characterizing MDOF Nonlinear Seismic Response , 1998 .

[51]  Patrick Paultre,et al.  Fragility curves of typical as-built highway bridges in eastern Canada , 2012 .

[52]  Mohsen Ghafory-Ashtiany,et al.  Strong ground motion record selection for the reliable prediction of the mean seismic collapse capacity of a structure group , 2011 .