Seismic Fragility Using Response Surface Methodology

Seismic Fragility Analysis Using Response Surface Methodology

Course Project Report
by

Aditya Jhunjhunwala
(Roll No. 130040006)

[pic 1]

Department of Civil Engineering
Indian Institute of Technology Bombay
Mumbai 400076 (India)

Abstract

Seismic 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 Contents

Chapter 1        Introduction        1

Chapter 2        Conventional Fragility Functions        2

2.1        Analytical Fragility Curves        3

2.1.1        Elastic Spectral Analysis Method        4

2.1.2        Nonlinear Static Analysis Method        4

2.1.3        Non-linear Time History Analysis Method        5

2.2        Probabilistic Seismic Demand Model        6

2.3        Limit States or Capacity        7

2.4        Issues with the Conventional Method        7

Chapter 3        Metamodels        8

3.1        Metamodels        8

3.2        Experimental Design        10

3.2.1        Factorial Design        11

3.2.2        Central Composite Design (CCD)        12

3.3        Model Choice and Model Fitting        13

3.3.1        Response Surfaces        13

Chapter 4        Model and Analysis        15

4.1        Model Details        15

4.2        Analysis Method        16

Chapter 5        Results and Discussions        21

References        29

List of Figures

Figure 2-1 : Example fragility curve [1]        2

Figure 2-2 : Demand and capacity spectra probabilistic distribution        5

Figure 2-3 : PSDM in lognormal space [1]        6

Figure 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        15

Figure 4-2 : Process of computing seismic fragility function using metamodel        17

Figure 4-3 : Input data points        18

Figure 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        26

Figure 5-6 : Actual vs. predicted         27[pic 10]

Figure 5-7 : Sorted actual vs. sorted predicted         27[pic 11]

List of Tables

Table 3-1 : Steps involved in development of metamodel        9

Table 3-2 : Techniques for metamodeling        9

Table 3-3 : Combination of techniques for metamodeling        9

Table 4-1 : Input parameters        18

Table 4-2 : Ground motions detail        19

Table 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