Seismic Fragility Using Response Surface Methodology
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Seismic Fragility Analysis Using Response Surface MethodologyCourse Project ReportbyAditya Jhunjhunwala(Roll No. 130040006)[pic 1]Department of Civil EngineeringIndian Institute of Technology BombayMumbai 400076 (India)AbstractSeismic risk assessment of buildings is important for calculating the loss of functionality of the building in the event of an earthquake. Seismic fragility functions for a building are an important part of the process of risk assessment as they present the probability of a damage level at given intensity of earthquake. Conventional methods for developing fragility functions are based on use of Monte Carlo simulation with a non-linear model of the building. Monte Carlo technique usually requires a relatively large number of simulations in order to obtain a sufficiently reliable estimate of the fragilities, and it becomes computationally impractical to simulate the required thousands of non-linear analyses. The use of Response Surface Methodology in connection with the Monte Carlo simulations simplifies the process. A response surface predicts the structural response calculated from complex non-linear dynamic analyses. Computational cost required in a Monte Carlo simulation will be significantly reduced since the simulation is performed on a polynomial response surface function, rather than a complex non-linear model. The methodology is applied to develop fragility functions of a low rise 2D concrete moment resisting frame detailed as per modern seismic code i.e. as per capacity design principles. Response surface equations for predicting peak drift are generated and used in the Monte Carlo simulation.Table of ContentsChapter 1 Introduction 1Chapter 2 Conventional Fragility Functions 22.1 Analytical Fragility Curves 32.1.1 Elastic Spectral Analysis Method 42.1.2 Nonlinear Static Analysis Method 42.1.3 Non-linear Time History Analysis Method 52.2 Probabilistic Seismic Demand Model 62.3 Limit States or Capacity 72.4 Issues with the Conventional Method 7Chapter 3 Metamodels 83.1 Metamodels 83.2 Experimental Design 103.2.1 Factorial Design 113.2.2 Central Composite Design (CCD) 123.3 Model Choice and Model Fitting 13
3.3.1 Response Surfaces 13Chapter 4 Model and Analysis 154.1 Model Details 154.2 Analysis Method 16Chapter 5 Results and Discussions 21References 29List of FiguresFigure 2-1 : Example fragility curve [1] 2Figure 2-2 : Demand and capacity spectra probabilistic distribution 5Figure 2-3 : PSDM in lognormal space [1] 6Figure 3-1: design for two and three factors ( are the coded variables) 11[pic 2][pic 3]Figure 4-1 : Details of sections of the moment resisting frame 15Figure 4-2 : Process of computing seismic fragility function using metamodel 17Figure 4-3 : Input data points 18Figure 4-4 : Response surface metamodel. The error term is not depicted here, only is shown 20[pic 4]Figure 5-1 : for 25 input data points for 30 ground motions 21[pic 5]Figure 5-2 : in log space 21[pic 6]Figure 5-3 : vs. 23[pic 7][pic 8]Figure 5-4 : vs. input parameters obtained from response surface model 25[pic 9]Figure 5-5 : Fragility functions for different damage state 26Figure 5-6 : Actual vs. predicted 27[pic 10]Figure 5-7 : Sorted actual vs. sorted predicted 27[pic 11]List of TablesTable 3-1 : Steps involved in development of metamodel 9Table 3-2 : Techniques for metamodeling 9Table 3-3 : Combination of techniques for metamodeling 9Table 4-1 : Input parameters 18Table 4-2 : Ground motions detail 19Table 4-3 : IDR values for various limit states of low-rise moment resisting buildings designed and detailed as per modern seismic codes (Capacity design) [2] 20