Structural reliability evaluation considering capacity degradation over time

Abstract Due to the ageing of the existing infrastructure on a worldwide scale and to the lack of codes for the continued safety management of structures during their lifetime, it is necessary to develop mathematical tools to evaluate their structural reliability over a time interval taking into consideration the reduction in their structural capacities. In this paper, an approach to evaluating structural reliability that takes into account capacity degradation over time by means of closed mathematical expressions is proposed. Two alternative indicators of structural reliability are considered: (1) The expected number of failures over a time interval, taking into account the uncertainty due to both aleatory and epistemic uncertainties; (2) The confidence factor, λ conf ( t ) , and the confidence level, K x ( t ) , as functions of time ( t ) are presented within a Demand-and-Capacity-Factor Design format (as used in FEMA 351). Both indicators are extended (based on the approach proposed by Cornell and collaborators) to estimate the reliability of a structure over a time interval. This reliability analysis takes into account events of different intensities (all possible events at the site) by means of environmental hazard curves. It is assumed that the structural capacity decreases linearly with time. The proposed expressions can be applied to different types of structures and can consider different conditions and levels of cumulative damage. An illustrative example is presented using a simplified model of a fixed steel jacket platform located at Campeche Bay in the Gulf of Mexico. The damage condition considered is the fatigue crack sizes at the critical joints caused by service and storm waves. The environmental hazard is represented in this example by means of exceedance rate curves of the maximum wave heights. The results obtained from the proposed expression are analyzed and compared with those obtained from numerical integration.

[1]  Pacific Earthquake.  A Technical Framework for Probability-Based Demand and Capacity Factor Design (DCFD) Seismic Formats , 2003 .

[2]  Yasuhiro Mori,et al.  Time-dependent system reliability analysis by adaptive importance sampling , 1993 .

[3]  Michael P. Enright,et al.  Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion , 1998 .

[4]  C. Allin Cornell,et al.  Probabilistic Basis for 2000 SAC Federal Emergency Management Agency Steel Moment Frame Guidelines , 2002 .

[5]  Henrik O. Madsen,et al.  Methods for Time‐Dependent Reliability and Sensitivity Analysis , 1990 .

[6]  S. Winterstein,et al.  Random Fatigue: From Data to Theory , 1992 .

[7]  Luis Esteva,et al.  Reliability Basis for Some Mexican Codes , 1972 .

[8]  Bruce R. Ellingwood,et al.  Probability Based Load Criteria: Load Factors and Load Combinations , 1982 .

[9]  Sonia E. Ruiz,et al.  Design Algorithm Based on Probabilistic Seismic Demands for Buildings Rehabilitated with Hysteretic Energy-Dissipating Devices , 2004 .

[10]  W. Pierson,et al.  A proposed spectral form for fully developed wind seas based on the similarity theory of S , 1964 .

[11]  Sonia E. Ruiz,et al.  Seismic Design Method for Reliability-Based Rehabilitation of Buildings , 2006 .

[12]  Y. K. Wen,et al.  Response Surface Method for Time-Variant Reliability Analysis , 1996 .

[13]  James O. Jirsa,et al.  A Damage Model for Practical Seismic Design that Accounts for Low Cycle Fatigue , 2005 .

[14]  P. C. Paris,et al.  A Critical Analysis of Crack Propagation Laws , 1963 .

[15]  R. Melchers,et al.  On the ensemble crossing rate approach to time variant reliability analysis of uncertain structures , 2004 .

[16]  Min Liu,et al.  Optimal seismic design of steel frame buildings based on life cycle cost considerations , 2003 .

[17]  R. Rackwitz.  Reliability analysis—a review and some perspectives , 2001 .

[18]  Palle Thoft-Christensen,et al.  Assessment of the Reliability of Concrete Bridges , 1996 .

[19]  James C. Newman,et al.  An empirical stress-intensity factor equation for the surface crack , 1981 .

[20]  Ming-Te Liang,et al.  Reliability analysis for the existing reinforced concrete pile corrosion of bridge substructure , 2005 .

[21]  C. Hofmayer,et al.  Degradation assessment of structures and passive components at nuclear power plants , 2004 .

[22]  Helmut Krawinkler,et al.  Cumulative damage in steel structures subjected to earthquake ground motions , 1983 .

[23]  Dan M. Frangopol,et al.  Minimum expected cost-oriented optimal maintenance planning for deteriorating structures: application to concrete bridge decks , 2001, Reliab. Eng. Syst. Saf..

[24]  Bruce Ellingwood.  RELIABILITY BASIS OF LOAD AND RESISTANCE FACTORS FOR REINFORCED CONCRETE DESIGN , 1978 .

[25]  Bruce R. Ellingwood,et al.  Stochastic fatigue crack growth in steel structures subjected to random loading , 1998 .

[26]  Fatemeh Jalayer,et al.  The probabilistic basis for the 2000 SAC/FEMA steel moment frame guidelines , 2002 .

[27]  C. Allin Cornell,et al.  Probabilistic seismic demand analysis of nonlinear structures , 1999 .

[28]  Bahman Lashkari,et al.  Seismic risk evaluation of steel structures based on low-cycle fatigue , 1988 .

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

[30]  Luis Esteva Maraboto,et al.  Bases para la formulacion de decisiones de diseño sismico , 1999 .

[31]  Daniel Straub,et al.  Risk Based Acceptance Criteria for Joints Subject to Fatigue Deterioration , 2004 .

[32]  Luis Esteva,et al.  Life-Cycle Optimization of Structures with Seismic Energy-Dissipating Devices , 1999 .

[33]  W. J. Hall,et al.  Recommended Seismic Evaluation and Upgrade Criteria for Existing Welded Steel Moment-Frame Buildings , 2000 .

[34]  Dan M. Frangopol.  Case Studies in Optimal Design and Maintenance Planning of Civil Infrastructure Systems , 1999 .

[35]  Palle Thoft-Christensen,et al.  Reliability and Optimization of Structural Systems , 2019 .

[36]  Ernesto Heredia-Zavoni,et al.  Effect of Uncertainties on the Reliability of Fatigue Damaged Systems , 2004 .

[37]  C. Allin Cornell,et al.  Probability Based Load Criteria: Assessment of Current Design Practice , 1982 .

[38]  Emilio Rosenblueth,et al.  Optimum Design for Infrequent Disturbances , 1976 .

[39]  R. A. Burton.  Effects of Two-Dimensional, Sinusoidal Roughness on the Load Support Characteristics of a Lubricant Film , 1963 .

[40]  Robert E. Melchers.  Load‐Space Formulation for Time‐Dependent Structural Reliability , 1992 .