Loss estimation of steel buildings to earthquake mainshock–aftershock sequences

Abstract Following a large earthquake numerous aftershocks can be triggered due to the complex stress interaction between and within tectonic plates. Although aftershocks are normally smaller in magnitude, their ground motion intensity can be large and have different energy content than the mainshock. Even seemingly undamaged buildings may be damaged as a result of aftershocks. The mainshock-damaged buildings with deteriorated structural properties are more susceptible to damage. This paper proposes a framework for loss estimation of steel structures subjected to mainshock–aftershock sequences. The analysis is based on a typical 4-story steel frame with a deterioration model. Mainshocks are modeled as a homogeneous Poisson process, while aftershocks are simulated from non-homogeneous Poisson process, magnitudes of which are characterized by the Gutenberg–Richter relationship. The proposed framework is applied to examine the effects of aftershocks on seismic loss. The expected seismic loss of the building subjected to two levels of earthquakes, the Design Earthquake (DE) and the Maximum Considered Earthquake (MCE), followed by aftershocks are examined considering both transition cost and downtime cost. Monte Carlo Simulation (MCS) with Latin Hypercube Sampling (LHS) is applied to examine the uncertainty in the loss estimation. Uncertainty in earthquake ground motions, structural model, damage and loss are all considered. It was found that even if aftershocks have little effect on structural response, they may still have a significant impact on seismic loss due to the uncertainty of the damage state and cost estimation. This methodology can be used to mitigate seismic loss and evaluate the current building design.

[1]  Jonathan P. Stewart,et al.  An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced-Concrete Moment-Frame Building , 2008 .

[2]  Jon C. Helton,et al.  An Approach to Sensitivity Analysis of Computer Models: Part II - Ranking of Input Variables, Response Surface Validation, Distribution Effect and Technique Synopsis , 1981 .

[3]  F. Omori,et al.  On the after-shocks of earthquakes , 1894 .

[4]  Reginald DesRoches,et al.  Post‐repair effect of column jackets on aftershock fragilities of damaged RC bridges subjected to successive earthquakes , 2016 .

[5]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[6]  Quanwang Li,et al.  Performance evaluation and damage assessment of steel frame buildings under main shock–aftershock earthquake sequences , 2007 .

[7]  Curt B. Haselton,et al.  Expected earthquake damage and repair costs in reinforced concrete frame buildings , 2012 .

[8]  P. Reasenberg,et al.  Earthquake Hazard After a Mainshock in California , 1989, Science.

[9]  Farzin Zareian,et al.  Assessment of probability of collapse and design for collapse safety , 2007 .

[10]  P. Reasenberg,et al.  Earthquake aftershocks: update. , 1994, Science.

[11]  Helmut Krawinkler,et al.  Deterioration Modeling of Steel Components in Support of Collapse Prediction of Steel Moment Frames under Earthquake Loading , 2011 .

[12]  Dimitrios Vamvatsikos,et al.  Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty , 2010 .

[13]  Dimitrios G. Lignos,et al.  An efficient method for estimating the collapse risk of structures in seismic regions , 2013 .

[14]  N. Null.  Minimum Design Loads for Buildings and Other Structures , 2003 .

[15]  Bruce R. Ellingwood,et al.  Earthquake risk assessment of building structures , 2001, Reliab. Eng. Syst. Saf..

[16]  Jonathan P. Stewart,et al.  Evaluation of the seismic performance of a code‐conforming reinforced‐concrete frame building—from seismic hazard to collapse safety and economic losses , 2007 .

[17]  John W. van de Lindt,et al.  Seismic risk of base isolated non-ductile reinforced concrete buildings considering uncertainties and mainshock–aftershock sequences , 2014 .

[18]  Miles Parker,et al.  The Economic Impact of the Canterbury Earthquakes , 2012 .

[19]  Gee Liek Yeo,et al.  Post‐quake decision analysis using dynamic programming , 2009 .

[20]  John W. van de Lindt,et al.  Impact of earthquake ground motion characteristics on collapse risk of post-mainshock buildings considering aftershocks , 2014 .

[21]  B. Gutenberg,et al.  Seismicity of the Earth and associated phenomena , 1950, MAUSAM.

[22]  John W. van de Lindt,et al.  Impact of aftershocks and uncertainties on the seismic evaluation of non-ductile reinforced concrete frame buildings , 2015 .

[23]  James E. Campbell,et al.  An Approach to Sensitivity Analysis of Computer Models: Part I—Introduction, Input Variable Selection and Preliminary Variable Assessment , 1981 .

[24]  Dimitrios G. Lignos,et al.  Sidesway collapse of deteriorating structural systems under seismic excitations , 2008 .

[25]  Mauricio Sánchez-Silva,et al.  Life-cycle performance of structures subject to multiple deterioration mechanisms , 2011 .

[26]  N. Abrahamson,et al.  Summary of the Abrahamson & Silva NGA Ground-Motion Relations , 2008 .

[27]  Yue Li,et al.  Quantifying Changes in Structural Design Needed to Account for Aftershock Hazard , 2015 .

[28]  Y. Ogata,et al.  The Centenary of the Omori Formula for a Decay Law of Aftershock Activity , 1995 .

[29]  Carlos Marcelo Ramirez.  Building-specific loss estimation methods & tools for simplified performance-based earthquake engineering , 2009 .

[30]  Yue-Jun Yin,et al.  Seismic collapse risk of light-frame wood construction considering aleatoric and epistemic uncertainties , 2010 .

[31]  S. C. Liu,et al.  A cost optimization model for seismic design of structures , 1972 .

[32]  J. V. D. Lindt,et al.  Collapse Fragility of Steel Structures Subjected to Earthquake Mainshock-Aftershock Sequences , 2014 .

[33]  Andrew S. Whittaker,et al.  Prediction and validation of sidesway collapse of two scale models of a 4‐story steel moment frame , 2011 .

[34]  C. Cornell,et al.  Building life-cycle cost analysis due to mainshock and aftershock occurrences , 2009 .

[35]  Judith Mitrani-Reiser,et al.  AN OUNCE OF PREVENTION: PROBABILISTIC LOSS ESTIMATION FOR PERFORMANCE - BASED EARTHQUAKE ENGINEERING , 2007 .

[36]  Shiling Pei,et al.  Methodology for earthquake-induced loss estimation: An application to woodframe buildings , 2009 .

[37]  Bruce R. Ellingwood,et al.  Reliability of woodframe residential construction subjected to earthquakes , 2007 .

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

[39]  Jorge Ruiz-García,et al.  Nonlinear response analysis of SDOF systems subjected to doublet earthquake ground motions: A case study on 2012 Varzaghan–Ahar events , 2016 .

[40]  Changhai Zhai,et al.  Damage spectra for the mainshock–aftershock sequence-type ground motions , 2013 .

[41]  Katsuichiro Goda,et al.  Effects of aftershocks on peak ductility demand due to strong ground motion records from shallow crustal earthquakes , 2012 .

[42]  Luis Ibarra,et al.  Hysteretic models that incorporate strength and stiffness deterioration , 2005 .

[43]  Krzysztof Burnecki,et al.  An introduction to simulation of risk processes , 2003 .

[44]  Jack W. Baker,et al.  Uncertainty propagation in probabilistic seismic loss estimation , 2008 .

[45]  Paul Bratley,et al.  A guide to simulation , 1983 .

[46]  Yue-Jun Yin,et al.  Loss Estimation of Light-Frame Wood Construction Subjected to Mainshock-Aftershock Sequences , 2011 .

[47]  Dimitrios Vamvatsikos,et al.  Incremental dynamic analysis , 2002 .

[48]  Brendon A. Bradley,et al.  Accuracy of approximate methods of uncertainty propagation in seismic loss estimation , 2010 .