ROSE SCHOOL AN INVESTIGATIVE STUDY ON THE MODELLING OF EARTHQUAKE HAZARD FOR LOSS ASSESSMENT

Transcription

1 I.U.S.S. Istituto Universitario di Studi Superiori Università degli Studi di Pavia EUROPEAN SCHOOL FOR ADVANCED STUDIES IN REDUCTION OF SEISMIC RISK ROSE SCHOOL AN INVESTIGATIVE STUDY ON THE MODELLING OF EARTHQUAKE HAZARD FOR LOSS ASSESSMENT An Individual Study Submitted in Partial Fulfilment of the Requirements for the Doctor of Philosophy Degree in EARTHQUAKE ENGINEERING By HELEN CROWLEY Supervisor: Dr JULIAN BOMMER April, 2005

2 The individual study entitled An investigative study on the modelling of earthquake hazard for loss assessment, by Helen Crowley, has been approved in partial fulfilment of the requirements for the Doctor of Philosophy Degree in Earthquake Engineering. Julian Bommer Rui Pinho

3 Abstract ABSTRACT Earthquake loss modelling based on a single earthquake scenario can be very useful, particularly for communicating seismic risk to the public and to decision makers. Nevertheless, for many applications, including decision-making processes within the insurance and reinsurance industries, and in seismic code drafting committees, it is necessary to estimate the effects of many, or even all, possible future earthquake scenarios that could impact upon the urban areas under consideration. In such cases, the purpose of the loss calculations is to estimate the annual frequency of exceedance (or the return period) of different levels of loss due to earthquakes: so-called loss exceedance curves. An attractive, cost-effective option for generating loss exceedance curves is to perform independent PSHA calculations at several locations simultaneously and to combine the losses at each site for each annual frequency of exceedance. An alternative, more time-consuming method involves the use of multiple earthquake scenarios to generate the ground motions at all sites of interest, defined through Monte Carlo simulations based on the seismicity model. The two procedures are applied to a loss model herein and it is shown that the latter is conceptually sounder and leads to a more realistic representation of the seismic hazard and associated aleatory variability when a number of sites are considered simultaneously in a loss model. Keywords: earthquake loss modelling; seismic hazard; scenario earthquakes; ground-motion variability; spatial correlation i

4 Acknowledgements ACKNOWLEDGEMENTS The author wishes to express sincere gratitude to Dr Julian Bommer for his excellent and invaluable guidance and support throughout the duration of this individual study. The author has particularly enjoyed working with him and looks forward to further collaboration in the future. Special mention is also due to Dr Rui Pinho and Dr Juliet Bird for their help and advice on many of the aspects of this study. The author is also especially grateful to Prof. Mustafa Erdik for providing data for the probabilistic seismic hazard assessment of the Marmara region (Turkey) and also to Shigeko Tabuchi and Oliver Peteken of Willis for providing building stock data for the same region. Selamet Yazici of the General Directorate of Insurance, the Prime Ministry, Turkey also deserves particular acknowledgement for authorising the use of the building stock data. The author also wishes to thank Arun Menon for his help with the probabilistic seismic hazard analysis and the use of the program EZ-FRISK. Thanks are also due to Dr Damian Grant for useful comments and observations made during discussions on many aspects of risk assessment. ii

5 Index AN INVESTIGATIVE STUDY ON THE MODELLING OF EARTHQUAKE HAZARD FOR LOSS ASSESSMENT INDEX Page ABSTRACT... i ACKNOWLEDGEMENTS...ii INDEX...iii LIST OF FIGURES... vi LIST OF TABLES... x 1. INTRODUCTION Foreword Outline of study SEISMIC HAZARD ASSESSMENT General requirements for a seismic hazard assessment Deterministic seismic hazard assessment (DSHA) Conventional probabilistic seismic hazard assessment (PSHA) Uncertainty in seismic hazard assessment... 9 iii

6 Index 2.5. Disaggregation of PSHA SIMULATION OF SYNTHETIC EARTHQUAKE CATALOGUES Spatial and temporal distributions and completeness Modified historical catalogue Stochastic catalogues using Monte Carlo simulations The Monte Carlo method The generation of stochastic earthquake catalogues THE MECHANICS OF EARTHQUAKE LOSS CALCULATIONS Basic elements of loss calculations Definition of the earthquake hazard Definition of the inventory characteristics Estimation of the inventory damage Calculation of economic loss Scenario losses versus rates of losses Loss exceedance curves from PSHA-based calculations Loss exceedance curves from catalogue-based calculations The influence of uncertainty in loss calculations LOSS MODEL FOR THE MARMARA REGION, TURKEY Building stock characteristics Exposure of buildings in the Marmara region Vulnerability of the RC buildings Input to the seismic hazard assessment The tectonics of the Marmara region Seismicity of the earthquake sources Selection of ground-motion prediction model LOSS CALCULATIONS FOR THE MARMARA REGION PSHA-based loss calculations Hazard curves, maps and spectra for the Marmara region Loss exceedance curves at selected municipalities Catalogue-based loss calculations Hazard curves from stochastic catalogues iv

7 Index Loss exceedance curves Influence of inter- and intra-event variability Sensitivity to the corner period of the demand spectra Sensitivity to duration-dependence of damping reduction factors Comparison of loss calculations CONCLUSIONS Summary Future research REFERENCES v

8 Index LIST OF FIGURES Page Figure 2.1: The four-step process to a typical DSHA (after Reiter, 1990)... 5 Figure 2.2: The four-step process to a typical PSHA (after Reiter, 1990)... 6 Figure 2.3: Recurrence relationship for faults that fit the characteristic earthquake model (Reiter, 1990)... 8 Figure 2.4: Logic-tree formulation for a probabilistic seismic hazard study of the Mississippi embayment (Toro et al., 1992) Figure 2.5: Contributions to the total aleatory variability of the predicted values of PGA and spectral acceleration (defined as the larger horizontal component) from inter- and intra-event variability, as presented in Bommer et al. (2003) Figure 2.6: 4D disaggregation plot of M, d, ε produced using the software from USGS ( 13 Figure 3.1: Illustrative diagram showing the modification of historical earthquakes to eliminate spatial incompleteness Figure 3.2: a) Illustration of the workings of the Monte Carlo method for a uniform distribution of random numbers b) Illustration of the workings of the Monte Carlo method for a normal distribution of random numbers (adapted from 17 Figure 3.3: Illustration to show how Monte Carlo method can be used to generate earthquakes. If a random number is generated between P max and P min then an earthquake occurs Figure 4.1: Components of an earthquake loss assessment Figure 4.2: A deformation-based seismic vulnerability procedure (Pinho et al., 2002). (LS stands for limit state.) Figure 4.3: a) CDFs of the demand displacement at each period, with median, 16-percentile and 84- percentile values of displacement response indicated at 3 seconds, b) Example JPDF of capacity for a 4 storey column-sway RC building class, (Crowley et al., 2004) vi

9 Index Figure 4.4: Typical loss exceedance curves for two sites. The curve for site 2 has a longer tail than site 1, which indicates that site 2 is affected by high-severity, low frequency earthquakes more than site 1. (Khater et al., 2003) Figure 4.5: Average annual loss (or Annual Estimated Loss, AEL) at county level, as documented in FEMA 366 (FEMA, 2001)...30 Figure 4.6: Example hazard curves for different period ordinates of spectral acceleration Figure 5.1: Location of study area showing boundaries of the provinces (from right to left) of Kocaeli, Istanbul and Tekirdag, and the co-ordinates of the 150 municipalities/urban areas within these provinces Figure 5.2: Proportions of good and poor RC frame buildings in the three provinces for each number of storeys Figure 5.3: Fault segmentation model for the Sea of Marmara region (Erdik et al., 2004) Figure 5.4: The long-term seismicity of the Marmara region, from 32AD to 1983 (Ambraseys and Finkel, 1991). The numbers represent the year of the earthquake and the size of the circle represents the size of the earthquake, as shown in the key in the figure Figure 5.5: Four zones used to model background seismicity in the Marmara region and the location of earthquakes from catalogue Figure 5.6: Output of Wizmap showing the Gutenberg-Richter relations of background seismicity for the four area sources obtained using Maximum Likelihood regression and a fixed b-value of Figure 5.7: Median displacement spectra predicted using the Boore et al. (1997) equations for site classes B, C, D and E at a distance of 15km from the fault rupture of an M w 7.2 earthquake. The dashed lines represent the ordinates obtained by linear extrapolation of the short-period ordinates Figure 6.1: PGA at municipalities for NEHRP B (rock) site class for a return period of 2500 years Figure 6.2: PGA contour map produced by Erdik et al. (2004) for NEHRP B/C boundary site class for a return period of 2500 years (Poisson model) Figure 6.3: Hazard curves for three sites in the Marmara region from conventional PSHA using the program EZ-FRISK Figure 6.4: Location of the three municipalities of Golcuk, Adalar and Saray considered in loss calculations herein Figure 6.5: Loss exceedance curves for three municipalities in the Marmara region (note that the annual frequency of exceedance is the reciprocal of the return period) Figure 6.6: Combined loss exceedance curve for the three municipalities using two different formulae for the mean damage ratio (MDR) vii

10 Index Figure 6.7: Comparison of hazard curves for spectral acceleration at 2 seconds using conventional PSHA with EZ-FRISK and by generating a synthetic catalogue of 100,000 yrs with Monte Carlo simulation Figure 6.8: Comparison of hazard curves for spectral acceleration at 2 seconds using conventional PSHA with EZ-FRISK and by generating a synthetic catalogue of 500,000 yrs with Monte Carlo simulation Figure 6.9: Comparison of loss exceedance curves for each of the three municipalities calculated using the FEMA 366 procedure (PSHA) with a procedure using a catalogue of earthquake scenarios spanning 100,000yrs Figure 6.10: Comparison of loss exceedance curves for each of the three municipalities calculated using the FEMA 366 procedure (PSHA) with a procedure using a catalogue of earthquake scenarios spanning 500,000yrs Figure 6.11: Combined loss exceedance curves for the three sites calculated using the scenarios from earthquake catalogues spanning 100,000 years and 500,000 years Figure 6.12: The influence of modelling the ground motion variability as all inter-event or all intraevent on the loss exceedance curves. (The curve for 100,000 yrs scenarios has been derived assuming a combination of inter- and intra-event variability as defined in the Boore et al. (1997) attenuation equation.) Figure 6.13: Plot of correlation (ρ = 0.68) between spectral displacement at 2 seconds at Adalar and Saray for each scenario (M-D-ε inter ) using the total variability defined in Boore et al. (1997) as all inter-event Figure 6.14: Illustration to explain how two earthquakes may produce the same ground motions at Adalar but very different ground motions from each other at Saray Figure 6.15: Plot of correlation (ρ = 0.49) between spectral displacement at 2 seconds at Adalar and Saray for each scenario (M-D-ε inter, ε intra ) using the proportions of inter- and intra-event variability defined in Boore et al. (1997) Figure 6.16: Plot of correlation (ρ = 0.43) between spectral displacement at 2 seconds at Adalar and Saray for each scenario (M-D-ε intra ) using the total variability defined in Boore et al. (1997) as all intra-event Figure 6.17: Comparison of loss exceedance curves at the site of Saray with multiple scenario earthquakes when the demand spectra have a constant corner period and when the corner period depends on the magnitude of the event Figure 6.18: The distribution of median secant period of vibration for each building class at the collapse limit state (each data marker represents a distinct number of storeys) and the distribution of corner period with M w using Equation viii

11 Index Figure 6.19: Magnitude disaggregation plot for an annual frequency of exceedance (AFOE) of 0.05 (return period = 20 years) and an AFOE of (return period = 200 years) from Monte Carlo simulations for the municipality of Saray Figure 6.20: Variation in the spectral ratio with magnitude and distance between (bottom) 20% and 5% damping and (top) 10% and 5% damping Figure 6.21: Regression curves fit to the variation of spectral ratio with distance for different levels of equivalent viscous damping. (The straight grey lines show the spectral ratios predicted using the equation provided in EC8.) Figure 6.22: Regression curves fit to the variation of the coefficients with viscous damping in equation Figure 6.23: Comparison of loss exceedance curve obtained by varying the spectral ratio for the distance of each scenario (Equation 6.6) with that obtained using a constant spectral ratio (Equation 6.2) Figure 6.24: Comparison of loss exceedance curves obtained following the FEMA 366 procedure (PSHA) and through the use of multiple earthquake scenarios from a stochastic catalogue of 100,000 years length Figure 6.25: Comparison of loss exceedance curves obtained using PSHA hazard curves with those from the hazard curves obtained from stochastically generated ground motions ix

12 Index LIST OF TABLES Page Table 4.1: Comparison of damage ratios for the US (HAZUS) and Turkey (Smyth et al., 2004; Crowley et al., 2005) Table 5.1: Adopted geometrical, material and limit state properties for poor buildings Table 5.2: Adopted geometrical, material and limit state properties for good buildings Table 5.3: Poisson model characteristic earthquake parameters associated with fault segments shown in Figure 5.3 (from Erdik et al., 2004) Table 6.1: Correlation coefficients for the ground motions between sites for different degrees of interand intra-event variability x

13 Chapter 1. Introduction 1. INTRODUCTION 1.1. Foreword The representation of the effects of future earthquakes using probabilistic seismic hazard analysis (PSHA) has been almost universally adopted for the site-specific design and assessment of engineered structures since its establishment (Cornell, 1968). Many improvements to the original procedure have subsequently been made, such that nowadays sophisticated models of the seismic hazard in a given region of interest can easily be produced. This individual study is concerned with the representation of seismic hazard for earthquake loss modelling, wherein ground motions with a given return period need to be simultaneously defined at multiple sites. Conventional PSHA was not derived for this purpose and so its use in loss modelling has recently been called into question (e.g. Leonard and Steinberg, 2002; Rhoades and McVerry, 2001). Nevertheless, the direct implementation of hazard curves from PSHA has been used to calculate the Annual Estimated Loss (AEL) in the USA, as documented in FEMA 366 (FEMA, 2001). Alternative procedures have been suggested which use a more physical, realistic representation of the seismic activity in the form of multiple earthquake scenarios varying in magnitude, location and recurrence (e.g. Bommer et al., 2002; Grossi, 2000). The main aim of this study is to produce an earthquake loss model and to compare the loss results using PSHA-derived hazard curves with the results from multiple earthquake scenarios. The assumption is that the latter procedure is conceptually sounder and the objective is therefore to determine the error in using the former. The sensitivity of the loss 1

14 Chapter 1. Introduction calculations to the number of earthquake scenarios triggered, the modelling of the aleatory variability and the scenario-dependence of the demand spectra are also studied Outline of study The basics of seismic hazard assessment are described in the second chapter of this study. Particular focus is paid to the uncertainties in hazard assessment as it will be seen herein that these play an important role in the prediction of future ground motions for loss modelling. The third chapter describes the various options for generating complete earthquake catalogues either through modification of the historical catalogue to account for spatial incompleteness or through stochastic modelling of earthquake occurrence using Monte Carlo simulations. In the fourth chapter, the mechanics of earthquake loss calculations are presented and discussed. A new methodology for earthquake loss assessment (DBELA) is introduced; this method is used in the calculations made in subsequent chapters. The procedures to generate loss curves using the demand modelled from PSHA maps and from earthquake catalogues are both described and the influence of uncertainty in the two methods is summarised. The Marmara region in Turkey has been chosen as the case study for which the loss calculations are to be made; the fifth chapter of this study describes the model. The inventory and characteristics of the building stock in the Marmara region are described and the input for the seismic hazard assessment is presented. The sixth chapter describes the main results of this study through the presentation and comparison of loss exceedance curves using the two procedures outlined in the fourth chapter. The sensitivity of the results from multiple earthquake scenarios to the modelling of aleatory variability and the scenario-dependence of the demand spectra is also studied. Finally, the conclusions of the study are presented in the seventh chapter and suggestions are made for additional future improvements of the representation of seismic hazard for earthquake loss modelling. 2

15 Chapter 2. Seismic Hazard Assessment 2. SEISMIC HAZARD ASSESSMENT Seismic hazards encompass all the potentially destructive effects of earthquakes (e.g. strong ground-motion, liquefaction, landslides) and seismic hazard analysis is concerned with the prediction of the severity and likelihood of occurrence of these effects at a particular site. A brief introduction into the elements of a seismic hazard assessment (SHA) is provided in this chapter and the main methods used in practice for SHA are presented: deterministic SHA, probabilistic SHA and disaggregation of probabilistic SHA General requirements for a seismic hazard assessment The main requirement for any seismic hazard assessment is a seismicity model of the region of interest wherein the occurrence in time and space of earthquakes of different sizes are modelled. There are three components that are generally combined in a seismicity model: earthquake catalogues, seismic source zones and recurrence relations. Earthquake catalogues report the origin time, location (i.e. epicentral co-ordinates and focal depths) and magnitude of earthquakes that have occurred in or near to the region of interest. Instrumentally, earthquakes have been measured and recorded for around 100 years, though reports of historical seismicity spanning several hundreds of years are available in many countries. Seismic source zones capture the spatial aspect of a seismicity model by defining regions within which future earthquakes are expected to occur at any location with an equal likelihood (i.e. the seismicity is uniform). Tectonics, observed seismicity and a degree of judgement are all called upon in the determination of source zones. Once the earthquake catalogue is compiled and the source zones have been defined, the temporal element of the seismicity model can be provided by recurrence relationships. Within each source zone, a recurrence relationship can be derived through the extraction of the number of earthquakes of different 3

16 Chapter 2. Seismic Hazard Assessment magnitudes from the earthquake catalogue. Effectively, the recurrence relationship provides information on the annual rate of exceedance of earthquakes of different magnitudes; recurrence relationships will be discussed further in Section 2.3. Once the seismicity model has been derived for the study area, a choice of whether to implement a deterministic or a probabilistic seismic hazard assessment needs to be made. As will be seen in Sections 2.2 and 2.3, there are actually many similarities between the two methods and both have their advantages and disadvantages. An important aspect of both procedures, which cannot be ignored, is the treatment of uncertainty; the origin of different types of uncertainty is discussed in Section Deterministic seismic hazard assessment (DSHA) In general, deterministic analyses use discrete, single-valued events or models to arrive at scenario-like descriptions of seismic hazard. Three basic elements are required to carry out the assessment: an earthquake source, a controlling earthquake of a specified size and a means of estimating the resulting ground motions. Deterministic seismic hazard assessment (DSHA) involves four basic steps, as illustrated in Figure 2.1. The first step involves the identification of the seismic sources capable of generating future earthquakes that could cause significant seismic hazard at the site (e.g. strong ground motion). Shallow continental earthquakes are commonly generated from source zones that delineate active geological faults, whilst many sources of earthquakes are less well-defined geological structures or even areas whose relationship to the generating process of earthquakes is not fully understood, though earthquakes are observed to occur therein. The controlling earthquake is selected, usually termed the Maximum Credible Earthquake (MCE), which is defined as the largest earthquake that can be reasonably expected to occur within each source zone (Krinitzsky, 2002). The magnitude of this earthquake can be determined on the basis of geological evidence through the use of empirical equations to relate magnitude to fault rupture dimensions (e.g. Wells and Coppersmith, 1994), though a common approach is to add 0.5 magnitude units to the size of the largest historical 4

17 Chapter 2. Seismic Hazard Assessment earthquake. The scenario earthquakes are placed at the closest location within each source with respect to the site. Figure 2.1: The four-step process to a typical DSHA (after Reiter, 1990) Once the scenario earthquake magnitude and distance for each source zone have been defined, the ground motions at the site can be estimated using a ground-motion prediction equation. These equations provide estimates of ground motion (e.g. peak acceleration, peak velocity, response spectrum ordinates) for an earthquake of a given magnitude at different distances by means of a curve fitted to observed data. As will be described in Section 2.4, there is a large amount of scatter in the data (see Figure 2.1) and whilst many studies use the median values from the predictive equations, the current trend is to use the 84-percentile motions, corresponding to one logarithmic standard deviation above the logarithmic mean (Krinitzsky, 2002). 5

18 Chapter 2. Seismic Hazard Assessment The motions at the site for each of the controlling earthquakes from the various sources are considered in the design, unless one scenario is seen to dominate the seismic hazard at all response frequencies Conventional probabilistic seismic hazard assessment (PSHA) In the previous section it was shown how a few isolated M-D-ε triplets (i.e. magnitude, distance, and number of logarithmic standard deviations) are considered in a deterministic seismic hazard assessment for a single site. In a probabilistic seismic hazard assessment (PSHA), the fundamental difference is that all possible M-D-ε triplets are considered in the calculation of hazard (see e.g. Cornell, 1968; Reiter, 1990; Kramer, 1995). Another difference is that the results of a PSHA have units of time, though it is arguable that units of time can also be applied to a deterministic assessment through the assignment of recurrence intervals to the scenario earthquakes. Figure 2.2: The four-step process to a typical PSHA (after Reiter, 1990) 6

19 Chapter 2. Seismic Hazard Assessment A PSHA comprises four basic stages, as illustrated in Figure 2.2. The first step involves the identification and characterisation of the earthquake sources in much the same way as has been described for a DSHA. The main difference, however, is that a probability distribution of potential rupture locations within each source is defined. This distribution is usually uniform, leading to an equal likelihood of earthquake occurrence at any point within the source. In a DSHA, on the other hand, it is assumed that the probability of an earthquake is 1 at the point on the source closest to the site. The second step of a PSHA involves the description of the temporal distribution of earthquake recurrence through the use of a recurrence relationship. These relationships specify the average rate at which an earthquake of some magnitude will be exceeded and the first was proposed by Gutenberg and Richter (1944): log( N m ) = a bm (2.1) where N m is the mean annual rate of exceedance of the magnitude M, 10 a is the mean yearly rate of earthquakes of magnitude greater than or equal to zero, and b describes the relative likelihood of large and small earthquakes. The a and b values can be obtained through regression analysis of a historical earthquake catalogue which must be corrected for completeness in magnitude and the removal of fore- and aftershocks. The conventional leastsquares regression method is violated in the case of the Gutenberg-Richter log-linear relationship, when N m is the cumulative event count. Weichert (1980) discusses how the least-squares method dates back to Gauss who realised that it was the maximum likelihood method for independent data and whose error distributions follow the Gaussian or normal error law. Cumulative event counts are not independent, and the number of earthquake occurrences is better represented by a Poisson rather than a Gaussian distribution, and thus the maximum likelihood method should be used directly in the regression. The validity of the Gutenberg-Richter law for an individual fault has been questioned by Schwarz and Coppersmith (1984): it has been observed through paleoseismic studies that points on fault segments tend to move by approximately the same distance in each earthquake, thus suggesting that individual fault segments generate earthquakes of a characteristic magnitude that is close to their maximum magnitude. A modified recurrence 7

20 Chapter 2. Seismic Hazard Assessment relationship is required for fault segments, as illustrated in Figure 2.3; the characteristic earthquakes are shown to occur more frequently than would be predicted from extrapolation of the seismicity data from low to high magnitude. The next step in the PSHA process is the definition of the ground motions at a site; this is carried out in a similar fashion to deterministic seismic hazard assessment whereby ground motion prediction equations are used. However, with PSHA a range of earthquakes is considered and so a family of ground-motion prediction curves is required for each magnitude, as illustrated in Figure 2.2. The aleatory uncertainty that arises when the data are fit to a particular curve is accounted for in PSHA, as will be described in the next step. Figure 2.3: Recurrence relationship for faults that fit the characteristic earthquake model (Reiter, 1990). The fourth step lies in determining the hazard at a particular site through the integration of the effects of all earthquakes of different sizes, occurring at different locations in different source zones at different probabilities of occurrence. A hazard curve is produced which shows the probability of exceeding different levels of ground motion at the site during a specified period of time. The annual expected number of exceedances of ground motion level λ(z) can be calculated from: 8

21 Chapter 2. Seismic Hazard Assessment λ ( z ) = = N mu r α i fm i= 1 mo r= 0 ( m ) f R ( r )P( Z > z / m,r )drdm (2.2) where α i is the mean rate of occurrence of earthquakes between lower and upper bound magnitudes (m o and m u ) being considered in the i th source, f M (m) is the probability density function (PDF) of magnitude (recurrence relationship) within source i, f R (r) is the PDF of distance between the various locations within source i and the site, and P(Z>z/m,r) is the probability that a given earthquake of magnitude m and distance r will exceed ground motion level z (due to the aleatory variability in the prediction equation). In practice, the integral shown in Eq. 2.2 is computed numerically and the range of values of M and R, are divided into bins or segments of width m, and r respectively and so the integrals in Eq. 2.2 are replaced by summations. An assumption often made in PSHA is that each earthquake occurs independently of any other earthquake, such that the annual frequency of exceedance λ(z) can be used in conjunction with the Poisson model to calculate the probability of exceedance of a given ground motion level q(z), during the design life L of a project placed at the site: q( z ) L λ( z ) =1 e (2.3) 2.4. Uncertainty in seismic hazard assessment There are two sources of uncertainty in all seismic hazard assessment: aleatory and epistemic. The former is a random source of uncertainty, a significant proportion of which is due to the scatter in ground motion prediction equations. This scatter results from randomness in rupture mechanisms and from variability and heterogeneity of the source, travel path and site conditions and is quantified using the standard deviation of the predicted ground-motion parameter. The latter uncertainty is due to the considerable degree of subjective judgement required in the definition of a seismicity model, and is the result of incomplete knowledge therein. Uncertainties related to the subjective decisions that are inevitably made as part of the process of carrying out the assessment include the following (adapted from Bommer, 2002): 9

22 Chapter 2. Seismic Hazard Assessment o The definition of the boundaries of the seismic source zones. o Assumptions regarding the completeness of the earthquake catalogue, which affect the b- value of the recurrence relationship. o The determination of the M max value for each seismic source zone. o The selection of a ground-motion prediction equation. o The assignment of recurrence intervals to characteristic earthquakes. Figure 2.4: Logic-tree formulation for a probabilistic seismic hazard study of the Mississippi embayment (Toro et al., 1992) Unlike aleatory uncertainty, which can be measured by statistical distributions and is incorporated directly into the hazard calculations (see Section 2.3), the epistemic uncertainty needs to be considered through the simultaneous consideration of different options for the various input parameters. A logic tree is generally used to handle the epistemic uncertainty in such a way, as illustrated in Figure 2.4. At each branch tip, a hazard estimate is obtained along with an associated relative weight that is calculated by multiplying the weights of the branches in that particular calculation. Hazard curves for any fractile (confidence level) can be drawn using these pairs of hazard estimates and weights; it is common engineering practice to then use the mean hazard curve from the logic tree, however, Abrahamson and Bommer (2005) discuss how this is the least appropriate choice, and they suggest that the fractile should reflect the desired degree of confidence that the safety level implied by the selected annual frequency of exceedance (or return period) is being achieved in light of the uncertainty in the estimation of the hazard. 10

23 Chapter 2. Seismic Hazard Assessment The inclusion of the aleatory uncertainty in hazard calculations is fundamental to PSHA because in any strong-motion data set, ground motions with amplitudes at least two or three standard deviations above the median values from predictive equations are encountered. In addition, the aleatory variability has a significant impact on the ground motions and this impact grows with return period. There are two components to the aleatory variability (which will be referred to as sigma hereafter), the first being from one earthquake to another with the same magnitude and rupture mechanism, the second being from one location to another at the same distance and with the same site classification during one earthquake. Herein the former is referred to as inter-event variability and the latter as intra-event variability; the total sigma is the square root of the sum of the squares of the inter- and intra-event sigma values. Whilst sigma cannot, by definition, be reduced for a particular model, refinement of the predictive model can lead to lower values of sigma, although efforts to date have not resulted in large reductions of the total aleatory variability (Douglas, 2003). Bommer et al. (2003) present an equation for the prediction of horizontal peak ground acceleration (PGA) and spectral acceleration which accounts for the style-of-faulting. For the larger component of the recorded horizontal components of motion, the values of the interand intra-event variability are reported, and from Figure 2.5 it can be seen that the proportion of the total randomness due to the earthquake-to-earthquake variability grows with response period. For each earthquake scenario, the inter-event variability will cause the ground motions at all locations to be lower or higher than the median estimates from the predictive equation. For a given earthquake event, the intra-event variability, which Figure 2.5 shows is larger than the inter-event variability, will lead to large fluctuations of the ground motion from one location to another. Figure 2.5 indicates that the maximum difference in ground-motion amplitudes at different sites with the same surface geology and located at the same distance from the source of the earthquake, will be appreciably larger than the difference between their median (for the scenario earthquake) and the median estimate (from the predictive equation) for the specific combination of magnitude, style-of-faulting, distance and site classification. The distinction 11

24 Chapter 2. Seismic Hazard Assessment between inter- and intra-event variability of ground motion is of obvious relevance in earthquake loss assessment, since the larger intra-event component will tend to lead to greater damage and higher losses in some locations and reduced earthquake impact in others. The influence of modelling the aleatory variability as intra- or inter-event is studied in detail in Chapter Logarithmic Standard Deviation σlogy Inter-event Intra-event Total variability Period (s) Figure 2.5: Contributions to the total aleatory variability of the predicted values of PGA and spectral acceleration (defined as the larger horizontal component) from inter- and intra-event variability, as presented in Bommer et al. (2003) 2.5. Disaggregation of PSHA Disaggregation of the PSHA is a process which allows the individual earthquake scenarios that contribute most to the hazard to be identified for a given ground motion parameter at a selected annual frequency of exceedance (e.g. McGuire, 1995; Bazzurro and Cornell, 1998). The proportion of the total hazard that is contributed by different M-D-ε triplets (defined in ranges of values or bins) can be identified and plotted on a 4-D plot as shown in Figure 2.6. This plot has been obtained from an Internet site maintained by the US Geological Survey ( and gives the proportion of the total hazard on the z-axis as a function of the distance and magnitude on the x- and y- axes, whilst the contribution of the scatter ε is plotted as a different colour on the vertical axis, for each M- D bin. The most dominant scenarios can be selected from this plot and used to produce realistic response spectra or to select appropriate accelerograms for the design of structures. 12

25 Chapter 2. Seismic Hazard Assessment Improvements to the disaggregation process have been proposed (Bazzurro and Cornell, 1998) such that the hazard is disaggregated to provide a plot of longitude, latitude, magnitude and ε. The advantage of this method is that specific sources and faults which have the greatest influence at a particular site for a M-ε pair can be identified and thus seismic source characteristics such as rupture mechanism and directivity effects can be accounted for during the selection of accelerograms. One problem of disaggregation highlighted by Bommer et al. (2002) is when the M-D-ε triplet needs to be matched to many ground motion parameters together, such as the spectral response at differing periods. Figure 2.6: 4D disaggregation plot of M, d, ε produced using the software from USGS ( The use of disaggregated scenarios in earthquake loss modelling would first require a PSHA of the whole region to be carried out. At each site within the study, and at each annual frequency of exceedance (AFOE) of interest (of which there will most likely be more than 10), the hazard estimate would need to be disaggregated to obtain a plot of magnitudedistance-ε (Figure 2.6). Each scenario in the plot would then be used to produce demand spectra and these would be convolved with the vulnerability and the loss calculated (the mechanics of loss calculations are discussed further in Chapter 4). The loss found for each 13

26 Chapter 2. Seismic Hazard Assessment scenario would then need to be multiplied by the contribution of that scenario to the hazard estimate and then the losses from all scenarios would then be integrated. This would then need to be repeated for each AFOE; when hundreds of sites are to be considered, the computational effort required to produce loss versus AFOE curves using disaggregated scenarios would most likely render the loss study unfeasible. Additionally, the use of scenario earthquakes generated from a PSHA that has been computed for each site independently is theoretically flawed, as will be discussed in detail in Chapter 6. 14

27 Chapter 3. Simulation of synthetic earthquake catalogues 3. SIMULATION OF SYNTHETIC EARTHQUAKE CATALOGUES 3.1. Spatial and temporal distributions and completeness The simulation of earthquake catalogues that are compatible with the seismicity of a given area is necessary to determination multiple scenario earthquakes that can be used in loss calculations. The historical catalogue cannot be used for the definition of such event sets as it does not describe the full range of events in time and space that could occur within a specified region. Various possibilities for the definition of a complete catalogue of earthquakes, either through modification of the historical catalogue or through stochastic generation of synthetic catalogues, are presented herein Modified historical catalogue Bommer et al. (2002) modified the historical catalogue to eliminate spatial incompleteness for their Turkish loss model based on multiple earthquake scenarios. A total of 1039 earthquake scenarios were triggered with a minimum magnitude of 5.5. Each scenario in the catalogue had an annual frequency of occurrence assigned to it, calculated from the recurrence relationship. A projected fault rupture plane was used as the model of each earthquake event source based on the predominant mechanism and average dip angle for each source zone. For an event of given magnitude, slip type and dip angle, surface fault rupture length and width were calculated from relationships provided by Wells and Coppersmith (1994). Each event was triggered with an epicentral location chosen randomly: anywhere within a source zone for magnitude < 7 and along a mapped fault of a certain minimum length for magnitude 7. The estimated length of the fault rupture for a given magnitude defined the selection of available 15

28 Chapter 3. Simulation of synthetic earthquake catalogues faults within a zone; it was assumed that the rupture would not exceed the mapped fault length. For a given (sub-)zone multiple events were triggered for a given magnitude and the event annual frequency was calculated by dividing the frequency for that magnitude by the number of events triggered in the (sub-)zone, so as to maintain the temporal description of the seismicity (see Figure 3.1). Rupture length Historical earthquake Annual rate of occurrence = 1/1000 years Identified fault Repetitions of historical earthquake, spatially distributed Annual rate of occurrence = 1/3000 years for each of the three segments Figure 3.1: Illustrative diagram showing the modification of historical earthquakes to eliminate spatial incompleteness A similar method is presented in the next section which uses the Monte Carlo method such that a simple program can be coded to calculate the magnitude and location of earthquakes in a synthetic catalogue using a seismicity model as the input Stochastic catalogues using Monte Carlo simulations The Monte Carlo simulation method, also known as stochastic modelling, can be used to generate large numbers of synthetic earthquake catalogues or stochastic event sets. Although the use of stochastic catalogues is not widely documented in scientific journals, their use for earthquake risk assessment appears to be common in the commercial sector (e.g. Zolfaghari, 1998; Eugster et al., 1999; Liechti et al., 2000; Windeler et al., 2004). However, Musson (1998, 1999) has provided an insight for earthquake engineers into the mechanism of the 16

29 Chapter 3. Simulation of synthetic earthquake catalogues Monte Carlo method for the generation of stochastic earthquake catalogues and their use in probabilistic seismic hazard analysis The Monte Carlo method The basic concept behind the Monte Carlo method is the generation of random numbers according to specified distributions. A simple example of how the Monte Carlo method works is illustrated in Figure 3.2. Suppose we wish to compute the area bounded by some arbitrary closed curve in a plane which is bounded by a unit square. If we select N random points inside the unit square, and n points fall within the area bounded by the closed curve, then if our points are randomly and uniformly distributed over the unit square, the ratio n/n will be approximately equal to the area bounded by our closed curve (Figure 3.2a). It is apparent that the approximation of the area approaches the actual area as the number of generated random points, N, increases and the ratio n/n gives the probability of a point falling within the closed curve a) b) 1 Figure 3.2: a) Illustration of the workings of the Monte Carlo method for a uniform distribution of random numbers b) Illustration of the workings of the Monte Carlo method for a normal distribution of random numbers (adapted from Random numbers can also be generated using a non-uniform distribution, as illustrated in Figure 3.2b. Suppose we place a target at the centre of our unit square and ask a marksman to shoot arrows at the target. Every arrow that hits the square represents a point: provided the marksman is experienced, most points will be located near the centre, with fewer points 17

30 Chapter 3. Simulation of synthetic earthquake catalogues scattered towards the boundaries. These points are still random but they are not uniformly distributed over the unit square. They are more likely to be scattered according to the Gaussian or normal distribution The generation of stochastic earthquake catalogues A seismic source zone model prepared for a conventional probabilistic seismic hazard analysis, as discussed in Section 2.3, describes with a certain degree of completeness the spatial and temporal distribution of earthquakes within a given region. The temporal distribution is modelled using recurrence relationships; in general a Gutenberg-Richter relationship is used for area sources and a characteristic magnitude recurrence relationship is used for active faults. The seismicity model of a region can be used to generate synthetic earthquake catalogues using the Monte Carlo method. The method described herein assumes a Poisson model, such that the occurrence of earthquakes is independent of the time elapsed since the last event, although time-dependent models can also be used. For active faults modelled using a characteristic magnitude recurrence relationship, the procedure to define a stochastic catalogue for each fault segment is as follows: 1) For each year in the catalogue, a random number between 0 and 1 is generated from a uniform distribution. 2) If the random number is less than the annual probability of earthquakes on that fault then this implies an earthquake in that year, otherwise no earthquakes occur. 3) The spatial distribution of the earthquakes is already determined from the fault segmentation model and the characteristic magnitude is as defined for that fault segment. If the whole process is repeated for a very large number of years (e.g years of data), then the ratio between the number of times that the random number falls below the annual rate of earthquakes and the total number of simulations should be equal to the annual probability of earthquakes on the fault. For distributed seismicity in area sources, a two-step random number process is required to define the catalogue for each source zone: 1) For each year in the catalogue, a random number, P random, between 0 and 1 is generated from a uniform distribution. 2) If the random number is less than the annual probability of events above a chosen minimum magnitude, M min, (i.e. P min, obtained from the annual rate N min by assuming a 18

31 Chapter 3. Simulation of synthetic earthquake catalogues Poisson model) and greater than the annual probability of events, P max, below a chosen maximum magnitude, M max, then there is an earthquake within the source zone in that year: N N min max ( a bm ) min =10 (3.1) ( a bm ) max =10 (3.2) N min P min =1 e (3.3) N max P max =1 e (3.4) If P > P > P earthquake (3.5) min random max where a and b are calculated for the area source from the historical catalogue, using the Gutenberg Richter relationship, as described in Section 2.3. The concept is illustrated in Figure 3.3; random numbers between 0 and 1 are generated, and the number of times that these fall between P max and P min divided by the total number of generated numbers will approximate the annual probability of earthquakes between the minimum and maximum magnitude range for the area under consideration. PDF P max P min 0 1 Annual probability of exceedance Figure 3.3: Illustration to show how Monte Carlo method can be used to generate earthquakes. If a random number is generated between P max and P min then an earthquake occurs. 3) When an earthquake is randomly generated, the magnitude is determined using the random number P random (using the Poisson model) and the recurrence relationship: N random = ln( 1 P ) (3.6) random M a log( N random ) = (3.7) b 19

32 Chapter 3. Simulation of synthetic earthquake catalogues In this way, even though the random numbers are uniformly distributed between 0 and 1, the magnitudes are exponentially distributed between M min and M max. 4) Each epicentre within the source zone is located by a random latitude and longitude coordinate (N, E ) by generating uniformly distributed numbers within the latitude and longitude bounds of the source. The assumption is thus that any location within the source zone has an equal probability of being the epicentre of the next earthquake, though this does not have to be the case and other assumptions can be incorporated into the model. The use of these stochastically-generated earthquake scenarios to define the ground motions, and ultimately the loss, at multiple sites is discussed in Section

33 Chapter 4. The mechanics of earthquake loss calculations 4. THE MECHANICS OF EARTHQUAKE LOSS CALCULATIONS 4.1. Basic elements of loss calculations Seismic risk can be defined as the possibility or probability of losses due to an earthquake, whether these losses are human, social or economic; seismic risk can be quantified through the convolution of four individual factors: Seismic Risk = Seismic Hazard * Exposure * Vulnerability * Specific Cost (4.1) The seismic hazard represents the effects that earthquakes can produce at the site of a structure or other engineering project whilst exposure refers to the extent of human activity located in the zones of seismic hazard. The vulnerability represents the susceptibility of the exposed elements to earthquake effects and the specific cost represents the cost of the repair and restoration of a structure as a proportion of the cost of demolition and replacement of the structure. There are thus four basic components to an earthquake loss assessment: (1) define the earthquake hazard, (2) define the inventory characteristics, (3) estimate the inventory damage, and (4) calculate the economic losses. The combination of these components in an earthquake loss model is illustrated in Figure 4.1 and further discussion of each is provided in the following sections. 21

34 Chapter 4. The mechanics of earthquake loss calculations SITE EARTHQUAKE OCCURRENCE Single scenario/ PSHA / Stochastic event set? HAZARDS Ground shaking Ground failure DIRECT PHYSICAL DAMAGE INVENTORY Building classes BUILDING CLASS CAPACITY/ VULNERABILITY LOSS Direct economic impact Indirect economic impact Figure 4.1: Components of an earthquake loss assessment Definition of the earthquake hazard Traditionally, the assessment of damage for loss estimation studies has been based on macroseismic intensity or peak ground acceleration (PGA). Both parameters, however, have their shortcomings: intensity, although directly related to building damage (Musson, 2000), is erroneously treated as a continuous variable in predictive relationships when in fact it is a discrete index with non-uniform intervals, whilst PGA shows almost no correlation with the damage potential of the ground motion. In addition, neither parameter accounts for the relationship between the frequency content of the ground motion and the fundamental period of the buildings. Nonetheless, these parameters are typically applied in damage matrix methods such as that developed by the Applied Technology Council (ATC, 1985) wherein damage ratios or factors, defined as the ratio between the cost of repair and the replacement value of the structure, are related to the intensity of shaking through the post-processing of field data collected following damaging earthquakes. The development of the damage matrices is subjective, however, since the determination of the intensity of shaking, as well as the level of observed damage in a structure, are based on expert opinion and thus cannot be judged as exact procedures. Another pitfall in this approach is that changing practices in construction may make observations of past events of little relevance to the prediction of damage in future earthquakes. Furthermore, the validity of applying statistics gathered from events that may be fundamentally distinct from the area under assessment, both in terms of seismic demand and supply, is debatable. 22

35 Chapter 4. The mechanics of earthquake loss calculations In order to compensate for the aforementioned shortcomings in traditional loss estimation procedures, recent proposals (e.g. Calvi, 1999; FEMA, 2003) have made use of response spectra, in particular the displacement (or acceleration-displacement) spectrum, to represent the destructive capacity of the ground motion. The rationale for using displacement spectra in assessment arises from the movement towards deformation-based philosophy in seismic design, which reflects the much closer correlation of displacements, as opposed to transient forces, with structural damage Definition of the inventory characteristics The initial step required in any loss model is the division of the building population into separate building classes. A building class is to be considered as a group of buildings which share the same construction material, failure mechanism and number of storeys. Reinforced concrete building classes might comprise the following structural types: 1) Reinforced concrete beam-sway moment resisting frames 2) Reinforced concrete column-sway moment resisting frames 3) Reinforced concrete structural wall buildings 4) Reinforced concrete dual (wall-frame) system buildings Within each structural type, further building classes need to be defined to separate, for example, buildings with different number of storeys, buildings designed with distinct steel grades or those built without adequate confining reinforcement. A decision regarding whether a moment resisting frame will exhibit a beam-sway (class 1) or a column-sway (class 2) mechanism may be made considering the construction type, construction year and evidence of a weak ground floor storey. Many buildings built before the inclusion of sound seismic design philosophy (i.e. capacity design) into a country s seismic design code and those with a weak ground floor storey will generally adopt a soft-storey (column-sway) mechanism Estimation of the inventory damage Various methods are available for the characterisation of building stock vulnerability; however, as mentioned previously, methods which utilise displacements provide a more rigorous approach for the estimation of structural vulnerability due to the strong correlation between displacement demand and damage. Two methods which predict the displacement 23

36 Chapter 4. The mechanics of earthquake loss calculations capacity of structures include HAZUS (e.g. Kircher et al., 1999; FEMA, 2003) and a more recently proposed method, DBELA (Crowley et al., 2004). The background to the derivation of DBELA for the prediction of damage for a scenario earthquake is described in some detail in what follows as this method will be used in the loss calculations carried out in subsequent chapters. Nevertheless, it should be noted that this methodology is still under development and various improvements (such as the influence of infill panels) will need to be included in the methodology before it is applied for actual loss modelling purposes. The underlying principles of the Direct Displacement-Based Design methodology (e.g. Priestley, 2003) were used by Calvi (1999) in the derivation of a displacement-based method for deriving the capacity of column-sway (soft-storey) reinforced concrete frames, starting from basic principles of structural mechanics and seismic response to arrive at an estimation of seismic vulnerability of classes of buildings. As a follow up to this proposal, which featured displacements as the fundamental indicator for damage and a spectral representation of the earthquake demand, Pinho et al. (2002) introduced a displacement-based vulnerability assessment methodology that was then developed by Glaister and Pinho (2003), and subsequently by Crowley et al. (2004). This probabilistic displacement-based loss assessment procedure (DBELA) uses mechanics-derived formulae to describe the displacement capacity of classes of buildings at three different structural and non-structural limit states. These expressions are given in terms of material and geometrical properties, as observed in Equation 4.2 which defines the post-yield displacement capacity of a RC beam-sway frame: lb SLsi = 0.5ef hhtεy + 0.5( εc ( Lsi) + εs ( Lsi) 1.7 εy ) efhht (4.2) h b where, SLsi is the structural limit state i (2 or 3) displacement capacity; ef h is the effective height coefficient; H T is the total height of the original structure; ε y is the yield strain of the reinforcement; l b is the length of beam; h b is the depth of beam section; ε C(Lsi) is the maximum allowable concrete strain for limit state i; and ε S(Lsi) is the maximum allowable steel strain for limit state i. 24

37 Chapter 4. The mechanics of earthquake loss calculations displacement LS3 LS2 LS1 η LS1 η LS2 P LS1 cumulative frequency P LSi percentage of buildings failing LSi η LS3 P LS2 Demand Spectra P LS3 T LS3 T LS2 T LS1 effective period 0 H LS3 H LS2 H LS1 Height H LSi = f (T Lsi, LSi) Figure 4.2: A deformation-based seismic vulnerability procedure (Pinho et al., 2002). (LS stands for limit state.) By substitution of the height of buildings in the class through a formula relating height to the limit state period (Crowley and Pinho, 2004), displacement capacity functions in terms of period are attained; the advantage being that a direct comparison can now be made at any period between the displacement capacity of a building class and the displacement demand predicted from a response spectrum. The concept is illustrated in Figure 4.2, whereby the range of structural periods with displacement capacity below the displacement demand is obtained and transformed into a range of heights using the aforementioned relationship between limit state period and height. From a purely deterministic and conceptual viewpoint, this range of heights could then be superimposed onto the cumulative distribution function of building stock to find the proportion of buildings failing the given limit state. However, considering that actual applications are generally carried out within a probabilistic framework, a slightly more refined methodology is required. The translation of the above procedure to a probabilistic framework was carried out by Crowley et al. (2004), building upon the work of Restrepo-Velez and Magenes (2004) who adapted the classical time-invariant reliability formulation described in Pinto et al. (2004). In this way, the method can duly cater for the uncertainty in the displacement demand spectrum and the uncertainty in the displacement capacity that arises when a group of buildings, which may have different geometrical and material properties, is considered together. The aleatory variability in the demand is modelled using the widely accepted assumption of a log-normal distribution of residuals. The cumulative distribution function (CDF) of the displacement demand can be found for a given earthquake scenario using the median displacement demand 25

38 Chapter 4. The mechanics of earthquake loss calculations values and their associated logarithmic standard deviation at each period. The cumulative distribution function gives the probability that the displacement demand exceeds a certain value, x, given a response period, T Lsi, for a given magnitude-distance scenario. In Figure 4.3a, an illustrative example of a displacement demand CDF is shown, cut-off at 3 seconds to allow the indication of the 50-percentile (median), 16-percentile and 84-percentile values of the displacement response. (a) (b) Figure 4.3: a) CDFs of the demand displacement at each period, with median, 16-percentile and 84- percentile values of displacement response indicated at 3 seconds, b) Example JPDF of capacity for a 4 storey column-sway RC building class, (Crowley et al., 2004) The probability density functions (PDF) of the limit state displacement capacity and period are found using the first-order reliability method (FORM). Essentially, FORM can be used to compute the approximate cumulative distribution function of a non-linear relationship of correlated parameters, such as the limit state displacement capacity equation and limit state period equation. The uncertainty in Lsi and in T Lsi is accounted for by constructing a matrix composed of their mean values and standard deviations. By assigning probability distributions to each parameter, FORM can be used to find both the PDF of the limit state displacement capacity, conditioned to a period, and the PDF of the limit state period. For a given number of storeys, the probability density of the periods may be multiplied by the probability density function of the corresponding displacement capacity so that the joint probability density function (JPDF) of period and displacement can be obtained, as exemplified in Figure 4.3b, for a four-storey column-sway building class. The joint probability density function can then be used in conjunction with the demand cumulative distribution function in the classical time 26

39 Chapter 4. The mechanics of earthquake loss calculations invariant reliability formulation to find the probability of exceeding the limit state for each number of storeys for a given scenario earthquake Calculation of economic loss Economic losses from an earthquake might be direct in that they are caused by structural and non-structural damage, or they may be indirect and are caused by downtime and other knock-on effects of the earthquake. Only direct losses are considered herein, but the reader is referred to the HAZUS manual (FEMA, 2003) for further information on the calculation of indirect losses. In the DBELA methodology, once the probability of failure of each structural limit state has been found, the proportion of buildings, P, within distinct damage bands (slight moderate, extensive and complete) can be calculated as follows: P P slight mod erate P extensive = (4.3) 1 Pf 1 = P P (4.4) f 1 f 2 = P P (4.5) f 2 f 3 P complete = P f (4.6) 3 A composite measure of the damage (mean damage ratio, MDR) that relates the estimated cost of loss to the rebuilding cost can be calculated by applying damage ratios to the proportion of buildings in each damage band, and the results are then integrated. The choice of damage ratios should ideally be based on detailed local data on insurance claims rates for different damage states of distinct building types. The variation in the damage ratios for different parts of the world is illustrated in Table 4.1, where the ratios used in HAZUS are compared with those suggested recently for Turkey (Smyth et al., 2004; Crowley et al., 2005). In addition, it might be justifiable to use a ratio greater than 100% for complete damage as the possible cost of demolishing a partly-collapsed building and removing the debris from a collapsed building would add to the cost of rebuilding the structure. 27

40 Chapter 4. The mechanics of earthquake loss calculations Table 4.1: Comparison of damage ratios for the US (HAZUS) and Turkey (Smyth et al., 2004; Crowley et al., 2005) Damage Band HAZUS Smyth et al. (2004) Crowley et al. (2005) Slight 2% 1% 10% Moderate 10% 10% 30% Extensive 50% 100% 100% Complete 100% 100% 100% 4.2. Scenario losses versus rates of losses Although estimation of the impact of a single earthquake scenario can be very useful, particularly for communicating seismic risk to the public and to decision makers, for many applications, including decision-making processes within the insurance and reinsurance industries and in seismic code drafting committees, it is necessary to estimate the effects of many, or even all, possible future earthquake scenarios that could impact upon the urban areas under consideration. In such cases, the purpose of the loss calculations is to estimate the annual frequency of exceedance (or the return period) of different levels of loss due to earthquakes. The annual frequency of exceedance can then be transformed into the annual probability of exceedance using an occurrence distribution such as the Poisson model. A loss exceedance probability distribution or curve is a graphical representation of the probability that a certain level of loss will be equalled or exceeded on an annual basis, as illustrated in Figure 4.4. Once a loss curve has been derived, the Average Annual Loss (AAL) can be found: the AAL is the expected value of a loss exceedance distribution and can be thought of as the product of the loss for a given event i (Loss i ) with the probability of at least one occurrence of event i (OP i ), summed over all events: = ( OP AAL (4.7) i i Lossi ) For insurance purposes, the AAL is of particular importance to help set annual premiums; however, for the design of any insurance scheme the shape of the loss exceedance probability curve for the whole exposure is of equal importance. 28

41 Chapter 4. The mechanics of earthquake loss calculations Figure 4.4: Typical loss exceedance curves for two sites. The curve for site 2 has a longer tail than site 1, which indicates that site 2 is affected by high-severity, low frequency earthquakes more than site 1. (Khater et al., 2003) 4.3. Loss exceedance curves from PSHA-based calculations An attractive option for representing the demand in a loss model for multiple earthquakes is to first perform a probabilistic seismic hazard analysis (PSHA) and then convolute the hazard curves at different locations with the exposure and vulnerability of the building stock. This approach was used, for example, by Cao et al. (1999), representing the shaking in the form of macroseismic intensity, and was also employed in FEMA 366 (FEMA, 2001) to calculate the Annual Estimated Loss (AEL) in the USA. In FEMA 366, the probabilistic seismic hazard data developed for the entire USA by the USGS ( was utilised to model the hazard curves and the capacity spectrum-based program HAZUS (FEMA, 2003) was used to predict the loss to the building stock. Figure 4.5 shows the AEL (which is equivalent to AAL, as described in Section 4.2) for all the states in the USA. Whilst it is evident that California accounts for a large proportion of the national AEL (74% or $3.3 billion), the regional distribution of annual loss demonstrates that seismic risk is a national concern and that seismic risk is not just a function of the level of hazard, but also of the value of the building inventory and the vulnerability of the building stock (Equation 4.1). 29

42 Chapter 4. The mechanics of earthquake loss calculations Figure 4.5: Average annual loss (or Annual Estimated Loss, AEL) at county level, as documented in FEMA 366 (FEMA, 2001) Following the procedure documented in FEMA 366 (FEMA, 2001), the methodology to calculate an aggregate loss exceedance probability curve, and subsequently the AAL, at a collection of sites using the DBELA methodology (Crowley et al., 2004) is described in what follows. 1) Produce hazard curves of annual exceedance frequency (λ) of spectral acceleration for appropriate period ordinates, as illustrated in Figure 4.6, at each site by carrying out a PSHA with the site conditions accounted for in the ground motion prediction equation. 1 Annual Frequency of Exceedance SA(0.3 s) SA(1.0 s) SA(2.0 s) Spectral Acceleration (g) Figure 4.6: Example hazard curves for different period ordinates of spectral acceleration 30

43 Chapter 4. The mechanics of earthquake loss calculations At each site: 2) Choose a number of return periods (= 1/annual exceedance frequency) at which the loss calculations will be carried out (e.g. 10, 50, 100, years etc.). 3) For each return period, calculate the annual exceedance frequency and obtain the spectral acceleration at each response period from the hazard curves. 4) The acceleration spectra are transformed into displacement spectra via the pseudo-spectral relationships: 2 T 2 S a = S D (4.8) π The displacement spectrum should be extrapolated past 2 seconds up to a corner period, T VD. This period can be calculated following the guidelines in HAZUS (FEMA, 2003) where the Joyner and Boore (1988) formulation is adopted: ( 5) M w 2 1 T VD = = 10 (4.9) f c However, when a PSHA is used to define the hazard, a scenario earthquake of moment magnitude M w cannot be defined and HAZUS (FEMA, 2003) recommends one use a corner period of 10 seconds which corresponds to a magnitude of 7. 5) For each building class (e.g. 3 storey, reinforced concrete, beam-sway frame), the probability of failing each limit state, P fn, is calculated using the DBELA methodology, as described in Section 4.1 and these probabilities are used to calculate the proportion of buildings in each damage band (slight, moderate, extensive or complete). An important point to note is that the aleatory variability needs to be removed from the reliability formulation (as it is already considered in the hazard curves), such that the CDF of the demand presented previously in Figure 4.3a becomes a step curve with 0 for displacement demands less than the median values, and 1 at displacement demands greater than the median. 6) The mean damage ratio (MDR) is calculated as discussed in Section ) The annual exceedance probability, q, is calculated from the annual exceedance frequency by assuming a Poisson process: 31

44 Chapter 4. The mechanics of earthquake loss calculations λ q = 1 e (4.10) 8) For each q, the MDR at each site is integrated. 9) A plot of annual exceedance probability versus combined MDR can now be produced and once rebuilding costs for each building type have been defined, MDR can be directly transformed into loss. 10) The AAL can be computed using Equation Loss exceedance curves from catalogue-based calculations Another option to model the seismic demand is through the triggering of large numbers of earthquake scenarios that are compatible with the seismicity model. Procedures to obtain a catalogue of scenario earthquakes that matches the seismicity of the historical catalogue but compensates for the temporal and spatial incompleteness of the latter have been described in Chapter 3. Examples of the use of multiple earthquake scenarios, or stochastic event sets, can be found in the technical literature (e.g. Grossi, 2000; Zolfaghari, 2000; Liechti et al., 2000); however, it is not made clear in these papers how and where the aleatory variability in the ground motion is being accounted for: different loss curves will be obtained depending on where the aleatory variability (sigma) is included in the calculations. The various possibilities for the treatment of sigma in the derivation of loss curves are discussed in Bommer and Crowley (2005). The most rigorous approach identified by Bommer and Crowley (2005) for the production of loss/mdr exceedance curves using multiple earthquake scenarios (which can be directly compared with those from the FEMA 366 method) is described below: 1) Once a synthetic earthquake catalogue of sufficient length has been generated (following the procedure in Section 3.3.2), then for each earthquake generated, the ground shaking at each site can be simulated using a ground-motion prediction equation and the aleatory variability in the equation. For each earthquake generated: i) A random number is picked using the standard normal probability distribution to obtain a random number of standard deviations (ε): this represents the number of inter-event standard deviations, ε inter, which is multiplied by the inter-event logarithmic standard deviation in the ground motion parameter (σ inter ). 32

45 Chapter 4. The mechanics of earthquake loss calculations ii) A ground motion prediction equation is used to calculate the logarithmic mean value of the ground shaking parameter (e.g. the spectral ordinate at a given period) at the site using the magnitude and distance from source to site. iii) At each site, a second random draw from the standard normal probability distribution is made to define the number of intra-event standard deviations, ε intra, which is multiplied by the intra-event logarithmic standard deviation in the ground motion parameter (σ intra ). iv) The two random measures of logarithmic scatter are then added to the logarithmic mean of the ground motion parameter and the exponential is taken to find the predicted ground motion at each site. 2) For each earthquake, the displacement spectra at each site are produced and these are convoluted with the capacity to calculate the probability of failing each of the three limit states and thus the proportion of buildings in each damage band. An important point to note is that the aleatory variability needs to be removed from the reliability formulation (as it is already considered in the ground motion), such that the CDF of the demand presented previously in Figure 4.3a becomes a step curve with 0 for displacement demands less than the median values, and 1 at displacement demands greater than the median. 3) For each earthquake, the mean damage ratio (MDR) at each site is combined. 4) The list of combined MDR is sorted in order of size and when, for example, 100,000 years of data have been generated, the MDR with a 10-3 annual probability of being exceeded can be found by picking the value which is exceeded 100 times in 100,000 years, i.e. the 101 st value in the sorted list. Each value of MDR is plotted against its annual frequency of exceedance to give a loss/mdr exceedance curve The influence of uncertainty in loss calculations The treatment of uncertainties in the input parameters defining both the seismic demand (ground motions) and seismic capacity (structural resistance) is an integral part of earthquake loss modelling. Crowley et al. (2005) presented a systematic exploration of the sensitivity of a loss model for the Sea of Marmara region to variations reflecting epistemic uncertainties in the parameters defining the model. The conclusion of that study was that the impact of epistemic uncertainties in the capacity model was greater than that of the epistemic uncertainty in the seismic demand. This finding is actually rather encouraging since although in theory all epistemic uncertainties can be reduced, there is far greater scope for reducing the 33

46 Chapter 4. The mechanics of earthquake loss calculations uncertainty in the capacity parameters (mainly through field investigations) than the epistemic uncertainty in ground-motion predictions, since the latter depends on the accumulation of new data for which it is necessary to wait for future earthquakes. There is even less scope for the reduction of the aleatory variability in ground-motion predictions in the short or even medium term, hence it is important to identify appropriate procedures for the treatment of sigma in earthquake loss models. As discussed in Section 2.4, the aleatory variability in ground-motion predictions cannot be neglected in the calculation of seismic hazard and consequently in the estimation of seismic risk. The need to model the aleatory variability has direct implications on the way in which seismicity and ground motions are modelled in earthquake loss estimation for extended urban areas. In effect, the PSHA estimates at each individual location are the calculated response to the question of how large could the ground motions become if a sufficiently low frequency of exceedance is considered. The answer comes from considering larger magnitude earthquakes (which occur less frequently) at shorter source-to-site distances (and hence are less common because the proportion of the seismic sources in which they can be triggered is reduced) and ground motions with larger epsilon values (i.e. greater exceedance of the median estimates from the predictive equations). For consideration of a single site, this does not present any problems, but when the method is used for loss estimation over a large urban area the same question is being asked simultaneously at all locations and this effectively means that all of the variability is being treated as inter-event variability resulting in uniformly high ground motions from the dominant earthquake scenarios, without spatial variability. This conversion of spatial (intra-event) variability into temporal (inter-event) variability is the ergodic assumption challenged by Anderson and Brune (1999). In the next chapter the input to a loss model is described and the results are presented in Chapter 6, wherein the influence of modelling the aleatory variability as temporal (via PSHA) is compared with the more rigorous approach of modelling both temporal and spatial variability (via multiple earthquake scenarios of M-D-ε inter -ε intra ). 34

47 Chapter 5. Loss model for the Marmara region, Turkey 5. LOSS MODEL FOR THE MARMARA REGION, TURKEY The region to the north of the Sea of Marmara in Turkey (Figure 5.1) has been chosen as the test case for this individual study because of the high levels of hazard and exposure in this area, and also to take advantage of the data and experience of previous earthquake loss modelling work in Turkey (Bommer et al., 2002; Spence et al., 2002; Spence et al., 2003). This earlier study was carried out to develop a national earthquake loss model for the Turkish Catastrophe Insurance Pool (TCIP), and was based on an adaptation of the HAZUS (FEMA, 2003) methodology to Turkish conditions. This area was also used in a sensitivity study of a loss model for a single earthquake scenario, carried out by Crowley et al. (2005). The results presented herein should not be taken as loss model for the Marmara region, however, as the DBELA methodology used still requires further development and calibration Longitude Latitude Figure 5.1: Location of study area showing boundaries of the provinces (from right to left) of Kocaeli, Istanbul and Tekirdag, and the co-ordinates of the 150 municipalities/urban areas within these provinces. 35

48 Chapter 5. Loss model for the Marmara region, Turkey 5.1. Building stock characteristics Exposure of buildings in the Marmara region Details of the exposed building stock in the three provinces of Istanbul, Kocaeli and Tekirdag for 150 municipalities (Figure 5.1) have been obtained from the 2000 Turkish Building Census data. All reinforced concrete frames up to 9 storeys are considered in this study, with a total of just over 750,000 buildings. The building count is given for each number of storeys up to 6, whereas buildings with between 7 and 9 storeys were already grouped together in the data provided. Thus, in this model, calculations of the proportion of damaged buildings are carried out for each number of storeys from 1 to 6, and for an assumed average of 8 storeys for the grouped 7 to 9 storey buildings Vulnerability of the RC buildings The buildings have been separated into good and poor classes. Poor buildings are defined through considerations of the construction year, evidence of poor construction quality derived from construction type, and the presence of a weak ground floor. The construction year and construction type were explicitly provided in the census data whereas the presence of a weak floor was determined by considering the use of the building: a high proportion of buildings that are mostly-residential, commercial or industrial have commercial premises on the ground floor, with large openings, and so were assumed to feature weak ground floors. A small proportion of the building stock was considered to be good : those buildings of good construction quality, built after 1975 and situated in zone 1 of the seismic code introduced at that time (Ergünay, 1973). Good buildings are assumed to exhibit a beam-sway response mechanism, whereas two-thirds of those classified as poor are expected to exhibit a columnsway (soft-storey) response mechanism and one-third a beam-sway mechanism. On the basis of the available data, good buildings constitute 10% of the building stock in the three provinces whilst the poor buildings constitute 90% (Figure 5.2). 36

49 Chapter 5. Loss model for the Marmara region, Turkey 0.25 Proportion of RC Frame Building Stock 'Good'_Beam-sway 'Poor'_Beam-sway 'Poor'_Column-sway Number of Storeys Figure 5.2: Proportions of good and poor RC frame buildings in the three provinces for each number of storeys Table 5.1 and Table 5.2 present the geometrical, material and limit state strain properties that have been assumed for poor and good Turkish buildings respectively. This information has been based to some extent on Turkish construction practice following the guidance of local engineers as well as the EERI reconnaissance report from the 1999 Kocaeli earthquake (EERI, 2000) and the World Housing Encyclopaedia ( Table 5.1: Adopted geometrical, material and limit state properties for poor buildings Capacity Parameter Mean value Coefficient of variation Probabilistic Distribution Ground floor storey height 3.6 m 35% Lognormal Column section depth 0.6 m 35% Lognormal Beam length 4.0 m 25% Lognormal Beam depth 0.55 m 10% Lognormal Steel yield strength 263 MPa 10% Normal Limit state 2 concrete strain, ε c % 50% Lognormal Limit state 2 steel strain, ε s % 50% Lognormal Limit state 3 concrete strain, ε c % 50% Lognormal Limit state 3 steel strain, ε s % 50% Lognormal 37

50 Chapter 5. Loss model for the Marmara region, Turkey Table 5.2: Adopted geometrical, material and limit state properties for good buildings Capacity Parameter Mean value Coefficient of variation Probabilistic Distribution Storey height 2.85m 10% Lognormal Beam length 4.0 m 25% Lognormal Beam depth 0.55 m 10% Lognormal Steel yield strength 503 MPa 10% Normal Limit state 2 concrete strain, ε c % 50% Lognormal Limit state 2 steel strain, ε s % 50% Lognormal Limit state 3 concrete strain, ε c % 50% Lognormal Limit state 3 steel strain, ε s % 50% Lognormal The dimensions shown in Table 5.1 and Table 5.2 are adopted for buildings of any number of storeys. Beam depths will generally be dictated by floor weights (assumed constant for each floor of a building) and so it is reasonable to assume the same values for buildings of different heights. On the other hand, the column depth reported in the tables refers to the ground floor columns of the building, which would generally increase with the height of the building. For simplicity, the same column depth statistics have been used for all building heights due to a lack of detailed data upon which to base the variation of statistics with height. The coefficient of variation of the geometrical properties in the good structures is generally assumed to be lower than that used in the poor structures, as observed by Crowley et al. (2004); this accounts for the fact that structures built to more recent design codes are more likely to comply with more uniform dimension standards. Two reinforcing steel grades are used in Turkey, S220 and S420; the 5% characteristic strength is 220MPa for the former and 420MPa for the latter. For the base model it has been assumed that all existing poor buildings have been constructed with grade S220 steel whilst the good buildings have been constructed with grade S420. The confinement of reinforced concrete members in existing Turkish building stock is, to a large extent, deficient, as observed from the damage following the 1999 Kocaeli earthquake (EERI, 2000), and so the attainment of high levels of steel and concrete strains is highly unlikely, even in the buildings that have been assigned to the good category. Hence, although it would generally be considered that buildings that are good would be able to achieve higher levels of sectional strains, in this study of Turkish buildings the sectional strain limits for both good and poor buildings are assumed to be the same. The only difference 38

51 Chapter 5. Loss model for the Marmara region, Turkey between these two building classes is thus in the steel strength and the geometrical properties, presented in Table 5.1 and Table 5.2. Furthermore, it is assumed that good buildings never attain a soft-storey (column-sway) failure mechanism, which in 60% of the buildings is assumed to occur through stiffness/strength irregularities within the structure or by an inadequate strength hierarchy between beams and columns Input to the seismic hazard assessment A PSHA for the Marmara Region has been carried out using the conventional procedure described in Section 2.3. Stochastic earthquake catalogues have also been generated using the procedure discussed in Section 3.3. The data on the tectonics and seismicity of the region required for both of these hazard assessments are described in the following sections The tectonics of the Marmara region Erdik et al. (2004) describe the tectonic regime of the Marmara Sea region and the work of many researchers to develop tectonic models using low resolution bathymetric data and the occurrences of earthquakes. The western portion of the North Anatolian Fault zone (NAFZ) dominates the tectonic regime of the Marmara Sea area: the NAFZ displays a single fault line character east of 31.5 E whereas to the west it splays into a complex fault system (Figure 5.3). Figure 5.3: Fault segmentation model for the Sea of Marmara region (Erdik et al., 2004) 39

52 Chapter 5. Loss model for the Marmara region, Turkey Erdik et al. (2004) have used many of the recent findings regarding the fault system below the Sea of Marmara (e.g. Le Pichon, et al., 1999; Pinar, 1943; Ergun and Ozel, 1995) to develop a fault segmentation model (Figure 5.3). The most significant tectonic element in the region is the Main Marmara fault: a through-going dextral strike-slip fault system Seismicity of the earthquake sources The study area for the PSHA is confined to N, E. This area has been divided into four rectangular area sources (Figure 5.5) to model the background seismicity for earthquakes of 5.5 < M w < 7.0. All earthquakes greater than M w = 7 are assumed to occur on faults through characteristic earthquakes, and the fault segmentation model proposed by Erdik et al. (2004) (Figure 5.3) has been used to model the location of these characteristic earthquakes. The long-term seismicity is illustrated in Figure 5.4 wherein it can be noted that the location of large magnitude earthquakes coincides with the fault segmentation model proposed by Erdik et al. (2004). Figure 5.4: The long-term seismicity of the Marmara region, from 32AD to 1983 (Ambraseys and Finkel, 1991). The numbers represent the year of the earthquake and the size of the circle represents the size of the earthquake, as shown in the key in the figure. The GSHAP catalogue ( has been used to model the historical and instrumental seismicity of the Marmara region. The catalogue is comprised of events of M w 5.5. The data of earthquakes of M w 5.5 are assumed to be complete from The removal of fore- and after-shocks was not considered necessary as these are rarely of magnitude 5.5. The Gutenberg-Richter recurrence relationship has been calculated using Maximum Likelihood regression for the four area sources using the events of magnitude 5.5 < 40

53 Chapter 5. Loss model for the Marmara region, Turkey M w < 7.0 from 1900 until 1999 from the earthquake catalogue using the program Wizmap ( (Figure 5.6). The b-value was calculated for the whole area due to a lack of data in some zones and was found to be 0.69; this was then fixed for all zones and the a-value was calculated accordingly. Zone 1 (NW) Zone 2 (NE) Zone 3 (SW) Zone 4 (SE) Figure 5.5: Four zones used to model background seismicity in the Marmara region and the location of earthquakes from catalogue Figure 5.6: Output of Wizmap showing the Gutenberg-Richter relations of background seismicity for the four area sources obtained using Maximum Likelihood regression and a fixed b-value of

54 Chapter 5. Loss model for the Marmara region, Turkey The characteristic magnitudes of the fault segments (Figure 5.3) were determined using the empirical relationship between magnitude, subsurface rupture length and rupture area for strike-slip faults (Wells and Coppersmith, 1994). The historical seismicity, the tectonic models and the known slip rates along the faults were the main data used by Erdik et al. (2004) to assign the recurrence times to the fault segments (from which the annual rates of occurrence are calculated, as shown in Table 5.3). Although the use of a time-dependent stochastic model would lead to a more rigorous assessment of the probabilistic hazard when characteristic magnitude fault models are used, the influence of the stochastic model on the PSHA of the Marmara region is outside the scope of this study, and the Poisson model will be used herein. All faults are assumed to be strike-slip with a dip of 90 and the minimum magnitude has been taken as the characteristic magnitude minus 0.1 units and the maximum magnitude was assumed to be the characteristic magnitude plus 0.1 units. Table 5.3: Poisson model characteristic earthquake parameters associated with fault segments shown in Figure 5.3 (from Erdik et al., 2004) Fault Segment Characteristic Magnitude (M w ) Annual Rate of occurrence Fault Segment Characteristic Magnitude (M w ) Annual Rate of occurrence S S S S S S S S S S S S S S S S S S S S S S S S A FORTRAN program has been coded to produce the stochastic earthquake catalogues, whilst the program EZ-FRISK Version 4.1 (Risk Engineering Inc., 1998) has been used to carry out the PSHA Selection of ground-motion prediction model The DBELA methodology used in the loss calculations presented in Chapter 6 uses an equivalent linearization approach for modelling the non-linear response of reinforced concrete structures, whereby the structure is represented by a single degree of freedom oscillator with 42

55 Chapter 5. Loss model for the Marmara region, Turkey secant stiffness properties. The use of secant stiffness properties leads to long structural periods of vibration which need to be accounted for in the displacement demand spectrum. There are very few ground-motion prediction equations for very long-period spectral ordinates, and these are sometimes not consistent with the frequency range for which reliable ordinates can be obtained from accelerograms, especially when these are obtained from analogue instruments (Boore and Bommer, 2005). For this study the equations of Boore et al. (1997) are used and the spectral accelerations are converted to displacements via the pseudospectral relationships. Local site effects are modelled using the equations, where site classes are represented by V s30 values. The following V s30 values were adopted for NEHRP classes B, C and D respectively, as recommended by Boore et al. (1997): 1070, 520 and 250 m/s; for site class E a value of 150 m/s has been assumed. The resulting spectra are essentially linear from 0.15 s up to 2 s, with the spectral displacement almost zero below 0.15 s. Therefore the simplifying assumption has been made that the spectra can be constructed as straight lines, following the 2003 NEHRP guidelines, passing through the ordinate attained from the hazard curve at 2 s and anchored to zero at 0.15 s, as presented in Figure E: Soft soil Spectral Displacement (m) D: Stiff soil C: Very dense soil Soft rock B: Rock Period (s) Figure 5.7: Median displacement spectra predicted using the Boore et al. (1997) equations for site classes B, C, D and E at a distance of 15km from the fault rupture of an M w 7.2 earthquake. The dashed lines represent the ordinates obtained by linear extrapolation of the short-period ordinates. 43

56 Chapter 6. Loss calculations for the Marmara region 6. LOSS CALCULATIONS FOR THE MARMARA REGION 6.1. PSHA-based loss calculations Hazard curves, maps and spectra for the Marmara region In order to follow the FEMA 366 (FEMA, 2001) procedure for the generation of loss curves, as described in Section 4.3, a PSHA of the Marmara region has been carried out using the program EZ-FRISK (Risk Engineering Inc., 1998) with the input data presented in Section 5.2. A hazard map depicting the peak ground acceleration (PGA) with a return period of 2500 years at each of the 150 municipalities in the three provinces of Kocaeli, Istanbul and Tekirdag is presented in Figure Longitude Political Boundary Province Boundary g g g g g Latitude Figure 6.1: PGA at municipalities for NEHRP B (rock) site class for a return period of 2500 years 44

57 Chapter 6. Loss calculations for the Marmara region A similar hazard map produced for the Marmara region by Erdik et al. (2004) is presented in Figure 6.2. Close inspection of Figure 6.1 and Figure 6.2 shows that the same bands of PGA are present, though the values of the latter map are slightly higher which is probably due a combination of factors: softer ground conditions were assumed in that hazard analysis, the average of the results obtained from Boore et al. (1997), Sadigh et al. (1997) and Campbell (1997) were used to predict the ground motions, and the program SEISRISK III was used. Figure 6.2: PGA contour map produced by Erdik et al. (2004) for NEHRP B/C boundary site class for a return period of 2500 years (Poisson model) 0.1 Annual Frequency of Exceedance EZFrisk - Saray EZFrisk - Adalar EZFrisk - Golcuk Spectral Acceleration (g) at 2 seconds Figure 6.3: Hazard curves for three sites in the Marmara region from conventional PSHA using the program EZ-FRISK 45