Multivariate Fragility Models for Earthquake Engineering

This paper employs a logistic regression technique to develop multivariate damage models. The models are intended for performance assessments that require the probability that structural components are in one of several damage states. As such, the developments represent an extension of the univariate fragility functions that are omnipresent in contemporary performance-based earthquake engineering. The multivariate logistic regression models that are put forward here eliminate several of the limitations of univariate fragility functions. Furthermore, the new models are readily substituted for existing fragility functions without any modifications to the existing performance-based analysis methodologies. To demonstrate the proposed modeling approach, a large number of tests of reinforced concrete shear walls are employed to develop multivariate damage models. It is observed that the drift ratio and aspect ratio of concrete shear walls are among the parameters that are most influential on the damage probabilities.

[1]  Yunfeng Zhang,et al.  Seismic Behavior of Reinforced Concrete Shear Walls Subjected to High Axial Loading , 2000 .

[2]  Anne S. Kiremidjian,et al.  Method for Probabilistic Evaluation of Seismic Structural Damage , 1996 .

[3]  Amr S. Elnashai,et al.  Cyclic Behavior of RC Cantilever Walls, Part I: Experimental Results , 1995 .

[4]  A. Kiureghian.  Non‐ergodicity and PEER's framework formula , 2005 .

[5]  Martin S. Williams,et al.  Seismic Damage Indices for Concrete Structures: A State-of-the-Art Review , 1995 .

[6]  C. Ledezma,et al.  Seismic Behavior of Squat Reinforced Concrete Shear Walls , 2002 .

[7]  Paolo Gardoni,et al.  Story-specific demand models and seismic fragility estimates for multi-story buildings , 2011 .

[8]  Paolo Gardoni,et al.  Seismic Fragility Estimates for Reinforced Concrete Buildings , 2007 .

[9]  Bruce R. Ellingwood,et al.  Seismic fragility assessment of steel frames for consequence-based engineering: A case study for Memphis, TN , 2007 .

[10]  Bruce R. Ellingwood,et al.  The Role of Fragility Assessment in Consequence-Based Engineering , 2005 .

[11]  Ahmet Yakut,et al.  Deformation Limits for Structural Walls with Confined Boundaries , 2012 .

[12]  Terje Haukaas,et al.  Multivariate probabilistic damage models for performance-based earthquake engineering , 2014 .

[13]  Phadeon-Stelios Koutsourelakis,et al.  Assessing structural vulnerability against earthquakes using multi-dimensional fragility surfaces: A Bayesian framework , 2010 .

[14]  Eric R. Ziegel,et al.  Generalized Linear Models , 2002, Technometrics.

[15]  John W. Wallace,et al.  Shear Strength of Lightly Reinforced Wall Piers and Spandrels , 2009 .

[16]  Thomas P. Ryan,et al.  Modern Regression Methods , 1996 .

[17]  Terje Haukaas,et al.  Application of a Probabilistic Drift Capacity Model for Shear-Critical Columns , 2006 .

[18]  Reginald DesRoches,et al.  Methodology for the development of analytical fragility curves for retrofitted bridges , 2008 .

[19]  Anne S. Kiremidjian,et al.  Assembly-Based Vulnerability of Buildings and Its Use in Performance Evaluation , 2001 .

[20]  Katrin Beyer,et al.  Quasi-static cyclic tests and plastic hinge analysis of RC structural walls , 2009 .

[21]  Paolo Gardoni,et al.  Probabilistic Demand Models and Fragility Curves for Reinforced Concrete Frames , 2006 .

[22]  Y Kabeyasawa,et al.  TEST ANALYSES OF HIGH-STRENGTH REINFORCED CONCRETE SHEAR WALLS IN JAPAN , 1998 .

[23]  C. V. Anderson,et al.  The Federal Emergency Management Agency (FEMA) , 2002 .

[24]  Jack P. Moehle,et al.  Seismic Performance Evaluation of Facilities: Methodology and Implementation , 2009 .

[25]  Terje Haukaas,et al.  NEW DAMAGE MODELS FOR PERFORMANCE-BASED EARTHQUAKE ENGINEERING , 2014 .

[26]  Mjn Priestley,et al.  Ductility in Earthquake Resisting Squat Shearwalls , 1982 .

[27]  A. Agresti.  An introduction to categorical data analysis , 1997 .

[28]  Fatemeh Jalayer,et al.  A scalar damage measure for seismic reliability analysis of RC frames , 2007 .

[29]  Armen Der Kiureghian,et al.  Probabilistic Capacity Models and Fragility Estimates for Reinforced Concrete Columns based on Experimental Observations , 2002 .

[30]  H Y Kim,et al.  STATISTICAL ANALYSIS OF FRAGILITY CURVES , 2000 .

[31]  N. Luco,et al.  Developing fragilities for mainshock-damaged structures through incremental dynamic analysis , 2011 .

[32]  A. Ang,et al.  Mechanistic Seismic Damage Model for Reinforced Concrete , 1985 .

[33]  Paolo Gardoni,et al.  Probabilistic Assessment of Structural Damage due to Earthquakes for Buildings in Mid-America , 2009 .

[34]  Sharon L. Wood,et al.  Cyclic Behavior of Reinforced Concrete Structural Walls with Diagonal Web Reinforcement , 2001 .

[35]  Howard H. M. Hwang,et al.  Generation of hazard-consistent fragility curves , 1994 .

[36]  A. Ibrahim,et al.  Test of high-rise core wall : Effective stiffness for seismic analysis , 2007 .

[37]  Howard H. M. Hwang,et al.  Probabilistic Damage Analysis of Structures , 1990 .

[38]  Anne S. Kiremidjian.  Subjective probabilities for earthquake damage and loss , 1985 .

[39]  Fumio Yamazaki,et al.  A simplified method of constructing fragility curves for highway bridges , 2003 .

[40]  Armen Der Kiureghian,et al.  PROBABILISTIC SEISMIC DEMAND MODELS AND FRAGILITY ESTIMATES FOR RC BRIDGES , 2003 .

[41]  David W. Hosmer,et al.  Applied Logistic Regression , 1991 .

[42]  Andreas J. Kappos,et al.  Cyclic Load Behavior of Low-Slenderness Reinforced Concrete Walls: Design Basis and Test Results , 1999 .

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

[44]  Paolo Gardoni,et al.  Seismic Fragility and Confidence Bounds for Gravity Load Designed Reinforced Concrete Frames of Varying Height , 2008 .

[45]  Fumio Yamazaki,et al.  Effect of earthquake ground motions on fragility curves of highway bridge piers based on numerical simulation , 2001 .

[46]  Abbas Javaherian Yazdi.  Damage modelling for performance-based earthquake engineering , 2015 .

[47]  James K. Wight,et al.  RC Structural Walls with Staggered Door Openings , 1991 .

[48]  Wilson H. Tang,et al.  Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering , 2006 .

[49]  C. J. Stone,et al.  A Course in Probability and Statistics , 1995 .