A stochastic computational framework for the joint transportation network fragility analysis and traffic flow distribution under extreme events

Abstract This paper deals with a novel technique that jointly uses structural fragility analysis, network flow analysis, and random field theory to assess the correlation among the damage levels of bridges in a transportation network under extreme events, and to estimate the sensitivity of the network performance to the correlation distance. A stochastic computational framework for the combined use of the individual bridge damage level due to extreme events and the bridge network performance evaluation is presented. Random field theory is used to simulate the bridge damage level, so that it is possible to directly control its correlation and perform a parametric analysis. Two numerical examples that involve bridges in parallel and series configurations subject to extreme events (e.g. earthquakes) show that the correlation distance of the damage can strongly affect the network performance indicators. Therefore, this correlation should be taken into account for every analysis that involves the network performance assessment.

[1]  Dan M. Frangopol,et al.  Generalized bridge network performance analysis with correlation and time-variant reliability , 2011 .

[2]  Barry J. Goodno,et al.  Interdependent Response of Networked Systems , 2007 .

[3]  Dan M. Frangopol,et al.  Computationally Efficient Simulation Techniques for Bridge Network Maintenance Optimization under Uncertainty , 2011 .

[4]  Dan M. Frangopol,et al.  Probabilistic models for life‐cycle performance of deteriorating structures: review and future directions , 2004 .

[5]  J. Baker,et al.  Correlation model for spatially distributed ground‐motion intensities , 2009 .

[6]  Frank Rubin,et al.  A Search Procedure for Hamilton Paths and Circuits , 1974, JACM.

[7]  Alan T. Murray,et al.  A Methodological Overview of Network Vulnerability Analysis , 2008 .

[8]  Dan M. Frangopol,et al.  Computational Platform for Predicting Lifetime System Reliability Profiles for Different Structure Types in a Network , 2004 .

[9]  Suzanne P. Evans,et al.  DERIVATION AND ANALYSIS OF SOME MODELS FOR COMBINING TRIP DISTRIBUTION AND ASSIGNMENT , 1976 .

[10]  Angela Lee,et al.  Perspectives on … Environmental Systems Research Institute, Inc , 1997 .

[11]  Leonardo Dueñas-Osorio,et al.  Cascading failures in complex infrastructure systems , 2009 .

[12]  Paolo Bocchini,et al.  Advanced analysis of uncertain cracked structures , 2006 .

[13]  J. Mander,et al.  Seismic Fragility Curve Theory for Highway Bridges , 1999 .

[14]  A. Gibbons.  Algorithmic Graph Theory , 1985 .

[15]  Dan M. Frangopol,et al.  On the applicability of random field theory to transportation network analysis , 2010 .

[16]  David A. Hensher,et al.  Handbook of Transport Modelling , 2000 .

[17]  Maarten-Jan Kallen,et al.  Optimal periodic inspection of a deterioration process with sequential condition states , 2006 .

[18]  Dan M. Frangopol,et al.  Bridge Maintenance, Safety, Management and Life-Cycle Optimization , 2010 .

[19]  Pol D. Spanos,et al.  Computational Stochastic Mechanics , 2011 .

[20]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

[21]  Stephanie E. Chang,et al.  Probabilistic Earthquake Scenarios: Extending Risk Analysis Methodologies to Spatially Distributed Systems , 2000 .

[22]  David M Levinson,et al.  MULTIMODAL TRIP DISTRIBUTION: STRUCTURE AND APPLICATION , 1994 .

[23]  F. Sibel Salman,et al.  Pre-disaster investment decisions for strengthening a highway network , 2010, Comput. Oper. Res..

[24]  Paolo Gardoni,et al.  Matrix-based system reliability method and applications to bridge networks , 2008, Reliab. Eng. Syst. Saf..

[25]  Michel Bruneau,et al.  A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities , 2003 .

[26]  Philip Wolfe,et al.  An algorithm for quadratic programming , 1956 .

[27]  Michael G. McNally,et al.  The Four Step Model , 2007 .

[28]  Junho Song,et al.  System reliability and sensitivity under statistical dependence by matrix-based system reliability method , 2009 .

[29]  Paolo Bocchini.  Probabilistic approaches in civil engineering: generation of random fields and structural identification with genetic algorithms , 2008 .

[30]  Dan M. Frangopol,et al.  A probabilistic computational framework for bridge network optimal maintenance scheduling , 2011, Reliab. Eng. Syst. Saf..

[31]  A. Zerva,et al.  SPATIAL VARIATION OF SEISMIC GROUND MOTIONS , 2002 .

[32]  Erik H. Vanmarcke,et al.  Random Fields: Analysis and Synthesis. , 1985 .

[33]  R. Machemehl,et al.  Combined traffic signal control and traffic assignment: algorithms, implementation and numerical results , 1998 .

[34]  Masanobu Shinozuka,et al.  Socio-economic effect of seismic retrofit of bridges for highway transportation networks: a pilot study , 2010 .

[35]  Masanobu Shinozuka,et al.  Modeling, synthetics and engineering applications of strong earthquake wave motion 1 This paper is d , 1999 .

[36]  W A Martin,et al.  Travel estimation techniques for urban planning , 1998 .

[37]  Stuart E. Dreyfus,et al.  An Appraisal of Some Shortest-Path Algorithms , 1969, Oper. Res..

[38]  Gian Paolo Cimellaro,et al.  Seismic resilience of a hospital system , 2010 .

[39]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[40]  Marco Tomassini,et al.  a Survey of Genetic Algorithms , 1995 .

[41]  Paolo Bocchini,et al.  Critical review and latest developments of a class of simulation algorithms for strongly non-Gaussian random fields , 2008 .

[42]  Dan M. Frangopol,et al.  Probability-Based Bridge Network Performance Evaluation , 2006 .