Uncertainty Quantification and Sensitivity Analysis of Earthquake Casualties
Large earthquake events can lead to a significant number of injuries and fatalities which in turn... more Large earthquake events can lead to a significant number of injuries and fatalities which in turn can contribute considerably to the overall financial loss of the insurance and reinsurance companies managing large life-risk portfolios. In this context, the number of injuries is calculated for six increasingly severe injury levels, as defined by the National Council of Compensation Insurance (NCCI), ranging from medical-only to fatal injuries. In order to estimate the number of injuries and their associated financial losses, in each one of the six injury levels, a proper earthquake casualty vulnerability model must be developed, calibrated and validated against historical data¬. Such a model aims at providing, in probabilistic terms, the distribution of the injured population impacted by the earthquake event among the six NCII-based injury levels aforementioned. In other words, the model predicts what portion (or rate) of the impacted population falls into each injury level, with the...
8th ACSE Specialty Conference on Probabilistic Mechanics and Structural Reliability PMC2000-119 1 Structural Seismic Demand Analysis: Consideration of “Collapse”
It is well known that a structure generally responds well beyond its elastic capacity at high sei... more It is well known that a structure generally responds well beyond its elastic capacity at high seismic loading; nonlinear time-history analysis is therefore the most accurate procedure for the seismic demand calculations. Such analyses are being used systematically, for example, in the current SAC steel moment-resisting frame project. There is apparently no methodology currently available to characterize the seismic-demand calculations when we observe that in some cases structures, especially tall structures, “collapse” because of strength degradation and/or significant effects. In this paper we will propose a novel way to calculate the seismic demand by considering a three-parameter probability distribution model. The parameters of the distribution at any ground-motion intensity level can be calculated easily from the response results when the ground-motion records are scaled to that intensity level. More generally, the parameters can be estimated economically from (1) a conventiona...
The 2011 Tohoku megathrust earthquake of magnitude 9.0 (MW) showed the potential of significant l... more The 2011 Tohoku megathrust earthquake of magnitude 9.0 (MW) showed the potential of significant loss to insurance industry due to tsunami. Large magnitude earthquakes at the Cascadia Subduction Zone (CSZ) can cause the most devastating tsunami hazard in the pacific basin to the west coast of USA including Washington, Oregon, and north California coastlines. The perception of tsunami risk in the industry has been small compared to the risk from the shake damage. To improve managing the tsunami risk for USA coastal cities, Risk management Solution (RMS) first modeled the historical 1700 Cascadia tsunami event and evaluated the maximum tsunami waves at different stations offshore of west coast of USA as well as coastal inundation. Then we developed a set of stochastic slip distributions along the CSZ corresponding to the large earthquakes with moment magnitude (MW) higher than 8.0 and modeled the tsunami wave propagation and coastal inundation. Each tsunami event is built based on seis...
Fire-Following Earthquake (FFEQ) is a secondary disaster to earthquakes which can cause significa... more Fire-Following Earthquake (FFEQ) is a secondary disaster to earthquakes which can cause significant losses and, in some cases, may comprise a large portion of the total loss by developing into large conflagrations (e.g., 1906 San Francisco earthquake). In order to estimate fire losses, conditioned on the occurrence of an earthquake, a probabilistic conflagration model is required. Such a model predicts the burnt areas based on the three-phases of the FFEQ process: fire ignition, fire spread and fire suppression. The first phase, fire ignition, estimates the number of fires that can occur in the aftermath of an earthquake and is a function of the intensity and time of occurrence of the earthquake, the square footage of the buildings in the impacted region, and the mix of construction and occupancy classes. The second phase, fire spread, estimates the propagation of each of the initial fires within a building, to other buildings, and among city blocks. This process is in general a fun...
The RMS catastrophe earthquake model has been used to assess the cost-effectiveness of a public C... more The RMS catastrophe earthquake model has been used to assess the cost-effectiveness of a public Californian earthquake early warning system. Taking a thirty year time frame, there is a reasonable expectation that the safety investment would be warranted by the number of lives saved and the reduced fire loss following earthquake. Significant additional early warning benefits also accrue to a number of corporate stakeholders. Given the balance between societal and corporate benefits, it would be equitable if the private sector supported this investment in public safety.
Earthquake Engineering & Structural Dynamics, 2015
This study presents a novel approach for evaluating ground motion selection and modification (GMS... more This study presents a novel approach for evaluating ground motion selection and modification (GMSM) procedures in the context of probabilistic seismic demand analysis. In essence, synthetic ground motions are employed to derive the benchmark seismic demand hazard curve (SDHC), for any structure and response quantity of interest, and to establish the causal relationship between a GMSM procedure and the bias in its resulting estimate of the SDHC. An example is presented to illustrate how GMSM procedures may be evaluated using synthetic motions. To demonstrate the robustness of the proposed approach, two significantly different stochastic models for simulating ground motions are considered. By quantifying the bias in any estimate of the SDHC, the proposed approach enables the analyst to rank GMSM procedures in their ability to accurately estimate the SDHC, examine the sufficiency of intensity measures employed in ground motion selection, and assess the significance of the conditioning intensity measure in probabilistic seismic demand analysis.
The output of risk analyses is used by insurance and reinsurance companies for critical decision-... more The output of risk analyses is used by insurance and reinsurance companies for critical decision-making that can have a profound effect on the business. As more companies use and rely on the results of catastrophe risk analyses, it is important for companies to have a good understanding of the uncertainties associated with the risk loss metrics. Loss risk models are complex combinations of components, which in turn have uncertainties that are difficult to evaluate. This paper presents a simplified framework to incorporate uncertainties in the different components that can be combined using logic trees. Specific cases for evaluating the effects of the seismic hazard uncertainties are given. The treatment of the epistemic and aleatory uncertainty of the ground motion models within the framework and the resulting uncertainties in the portfolio loss metrics are presented. Additional source of uncertainties can also be accommodated within the framework.
Performance based earthquake engineering often involves dynamic structural analysis of buildings ... more Performance based earthquake engineering often involves dynamic structural analysis of buildings using a set of input ground motions. This manuscript describes statistical analyses performed to evaluate the similarity of the response of tall buildings to comparable recorded and simulated ground motions. Structural response measures of a 40 story steel moment frame building designed based on the 2006 IBC are estimated under comparable sets of 40 recorded and simulated ground motions selected from the NGA database and the 2009 broadband Loma Prieta simulations by Dr. Rob Graves. Commonly used response measures such as peak story drift ratio, peak floor acceleration, residual drift ratio and beam plastic rotation are considered. Hypothesis testing is used to compare and contrast the response measures obtained using the selected recorded and simulated ground motions. Overall, this study provides a statistical basis to test simulated ground motions and identify applications where simulated ground motions can be used.
Aftershock Risk in Japan Following Tohoku Earthquake
Recent Tohuku earthquake has clearly showed that aftershocks following large magnitude earthquake... more Recent Tohuku earthquake has clearly showed that aftershocks following large magnitude earthquakes are a source of significant risk. In this study, we have followed the Reasenberg and Jones (1989) approach to describe the aftershock activity based on: 1) Gutenberg-Richter model (GRM) specifying the relationship between the magnitude and total number of earthquakes in any region and time period, and 2) modified Omori model (MOM) defining the decay of the aftershock activity with time. The aftershock occurrence is represented by a non-stationary Poisson process whose rate varies with time after the main shock. Since Tohoku earthquake occurred in a seismically active region, it is practically impossible to differentiate the aftershocks from the regular background earthquakes in the catalog. Hence this study fitted the MOM and GRM to all the events in the catalog in order to estimate the post-Tohoku seismicity (conventional study considers only the aftershocks). We have used the JMA cat...
The 22 February 2011 Lyttelton earthquake is one of the devastating natural catastrophes worldwid... more The 22 February 2011 Lyttelton earthquake is one of the devastating natural catastrophes worldwide, causing a large number of casualties and severe damage to the city of Christchurch, New Zealand. Though the magnitude of 6.3 was relatively low, the ground motions of the Lyttelton earthquake were unexpectedly strong. To understand the uniqueness of the Lyttelton event, this paper focuses on the investigation and characterization of the ground motions from the recent 2010-2011 earthquakes, including the February 2011 Lyttelton and September 2010 Darfield events. By analyzing the ground motion records at selected GeoNet stations in the vicinity of the city of Christchurch, the characteristics of spectral demands at ground motion recording stations from both events were discussed. Then we examine the empirical New Zealand ground motion models to investigate if the ground motion prediction models can explain the unusual destructiveness of the strong ground motions. This study can be help...
In the last two decades, significant progress in science and technology has driven major advances... more In the last two decades, significant progress in science and technology has driven major advances in the modeling of natural hazards and their impact on the built environment. In addition, several major catastrophe events over the same period highlighted important issues that could affect the underwriting and decision-making processes for selecting and managing risk. In many cases, these events had a profound impact on insurance and reinsurance practices, expanding the use of models, analytics, and exposure-data quality analysis to understand the sources of risk and to model loss uncertainty. Furthermore, since the development of earlier versions of catastrophe models, technology and computing power have advanced enormously, allowing modelers to address key elements of model and loss uncertainty in a more systematic way. Most catastrophe models implicitly account for the uncertainty associated with various model components. These uncertainties can be characterized as aleatory or epi...
Recent earthquakes in New Zealand and Japan show that it is important to consider the spatial and... more Recent earthquakes in New Zealand and Japan show that it is important to consider the spatial and temporal distribution of aftershocks following large magnitude events since the probability of high intensity ground motions from aftershocks, which are capable of causing significant societal impact, can be considerable. This is due to the fact that a mainshock will have many aftershocks, some of which may occur closer to populated areas and may be large enough to cause damage. When a large magnitude event strikes a region, the chance that aftershocks will cause damage can be significant as was observed after the 2011 Tohoku and 2010 Canterbury earthquakes (e.g., damage caused by Mw6.6 April 11, 2011 Fukushima-Hamadori earthquake following Tohoku earthquake or by Mw6.3 February 22, 2011 Christchurch earthquake following Canterbury earthquake). Aftershock events may further damage already damaged buildings, thereby further complicating assessments of risk to the built environment. In th...
It is well known that a structure generally responds well beyond its elastic capacity at high sei... more It is well known that a structure generally responds well beyond its elastic capacity at high seismic loading; nonlinear time-history analysis is therefore the most accurate procedure for the seismic demand calculations. Such analyses are being used systematically, for example, in the current SAC steel momentresisting frame project. There is apparently no methodology currently available to characterize the seismicdemand calculations when we observe that in some cases structures, especially tall structures, “collapse” because of strength degradation and/or significant effects. In this paper we will propose a novel way to calculate the seismic demand by considering a three-parameter probability distribution model. The parameters of the distribution at any ground-motion intensity level can be calculated easily from the response results when the ground-motion records are scaled to that intensity level. More generally, the parameters can be estimated economically from (1) a conventional-...
Insurance companies typically estimate earthquake losses for buildings using catastrophe loss mod... more Insurance companies typically estimate earthquake losses for buildings using catastrophe loss models. In this study, we analyze the insurance loss data from the Northridge earthquake to improve existing loss models. Conventionally, the distribution of loss is modelled using the Beta distribution. The claims data, however, show that the Beta distribution combined with Dirac-delta functions at 0 and 1 to model the probabilities of zero and complete loss improves the fit to the observed loss distribution. In addition, the spatial correlation between the losses at two locations is developed for modelling the loss distribution for a portfolio of buildings. The components of the correlation model are estimated using claims data and earthquake intensity data. Finally, the loss assessment for a portfolio of buildings is carried out using the improved uncertainty and spatial correlation models in order to demonstrate the importance of these models in assessing and managing seismic risks.
Probabilistic seismic demand analysis of nonlinear structures
Recent earthquakes in California have initiated improvement in current design philosophy and at p... more Recent earthquakes in California have initiated improvement in current design philosophy and at present the civil engineering community is working towards development of performance-based earthquake engineering of structures. The objective of this study is to develop efficient, but accurate procedures for probabilistic analysis of nonlinear seismic behavior of structures. The proposed procedures help the near-term development of seismic-building assessments which require an estimation of seismic demand at a given intensity level. We also develop procedures to estimate the probability of exceedance of any specified nonlinear response level due to future ground motions at a specific site. This is referred as Probabilistic Seismic Demand Analysis (PSDA). The latter procedure prepares the way for the next stage development of seismic assessment that consider the uncertainties in nonlinear response and capacity. The proposed procedures require structure-specific nonlinear analyses for a ...
This paper reviews, compares, and contrasts the three methodologies proposed by C. A. Cornell, by... more This paper reviews, compares, and contrasts the three methodologies proposed by C. A. Cornell, by Y. K. Wen, and by FEMA 273 (as proposed by H. Krawinkler) for predicting the postelastic response of buildings subject to seismic excitation. All three methods have the potential to contribute effectively to the problem of improving the practical prediction of seismic response of structures. Applications include preliminary design, routine (code) use, calibration of codes, and specific structure assessment. These methods appear different because their authors did not share the same objectives or information bases. The methods by Cornell and Wen are decisively prediction-oriented in explicitly probabilistic frameworks. The approach suggested by Krawinkler has instead the goal of understanding in some average sense the seismic response of structures at various performance levels. This last method has been adopted, however, for prediction purposes by the FEMA 273 Guidelines for rehabilitation of existing buildings. Despite the differences, the work proposed by these researchers is profitably brought under the same perspective here.
The U.S. National Seismic Hazard Model (NSHM) is composed of multiple logic trees that capture th... more The U.S. National Seismic Hazard Model (NSHM) is composed of multiple logic trees that capture the epistemic uncertainty inherent in any estimate of seismic hazard at a site. Logic trees and associated weights describe, but are not limited to, variability of fault geometry, maximum magnitude, and regional seismicity rate. They are also used to represent different models of ground motion. With each new edition of the NSHM, the number of logic trees and associated branches grows. While this does not pose insurmountable computational demands, the computation of mean hazard maps does grow proportionally, particularly when computing associated uncertainties on a map scale, and it is difficult to determine which branches are the most influential. It is also increasingly important that the NSHM program produce maps of uncertainty; to this end, any reductions in computation time are a benefit. Using the California component of the NHSM, the Uniform California Earthquake Rupture Forecast ver...
Uncertainty Quantification and Sensitivity Analysis of Earthquake Casualties
Large earthquake events can lead to a significant number of injuries and fatalities which in turn... more Large earthquake events can lead to a significant number of injuries and fatalities which in turn can contribute considerably to the overall financial loss of the insurance and reinsurance companies managing large life-risk portfolios. In this context, the number of injuries is calculated for six increasingly severe injury levels, as defined by the National Council of Compensation Insurance (NCCI), ranging from medical-only to fatal injuries. In order to estimate the number of injuries and their associated financial losses, in each one of the six injury levels, a proper earthquake casualty vulnerability model must be developed, calibrated and validated against historical data¬. Such a model aims at providing, in probabilistic terms, the distribution of the injured population impacted by the earthquake event among the six NCII-based injury levels aforementioned. In other words, the model predicts what portion (or rate) of the impacted population falls into each injury level, with the...
8th ACSE Specialty Conference on Probabilistic Mechanics and Structural Reliability PMC2000-119 1 Structural Seismic Demand Analysis: Consideration of “Collapse”
It is well known that a structure generally responds well beyond its elastic capacity at high sei... more It is well known that a structure generally responds well beyond its elastic capacity at high seismic loading; nonlinear time-history analysis is therefore the most accurate procedure for the seismic demand calculations. Such analyses are being used systematically, for example, in the current SAC steel moment-resisting frame project. There is apparently no methodology currently available to characterize the seismic-demand calculations when we observe that in some cases structures, especially tall structures, “collapse” because of strength degradation and/or significant effects. In this paper we will propose a novel way to calculate the seismic demand by considering a three-parameter probability distribution model. The parameters of the distribution at any ground-motion intensity level can be calculated easily from the response results when the ground-motion records are scaled to that intensity level. More generally, the parameters can be estimated economically from (1) a conventiona...
The 2011 Tohoku megathrust earthquake of magnitude 9.0 (MW) showed the potential of significant l... more The 2011 Tohoku megathrust earthquake of magnitude 9.0 (MW) showed the potential of significant loss to insurance industry due to tsunami. Large magnitude earthquakes at the Cascadia Subduction Zone (CSZ) can cause the most devastating tsunami hazard in the pacific basin to the west coast of USA including Washington, Oregon, and north California coastlines. The perception of tsunami risk in the industry has been small compared to the risk from the shake damage. To improve managing the tsunami risk for USA coastal cities, Risk management Solution (RMS) first modeled the historical 1700 Cascadia tsunami event and evaluated the maximum tsunami waves at different stations offshore of west coast of USA as well as coastal inundation. Then we developed a set of stochastic slip distributions along the CSZ corresponding to the large earthquakes with moment magnitude (MW) higher than 8.0 and modeled the tsunami wave propagation and coastal inundation. Each tsunami event is built based on seis...
Fire-Following Earthquake (FFEQ) is a secondary disaster to earthquakes which can cause significa... more Fire-Following Earthquake (FFEQ) is a secondary disaster to earthquakes which can cause significant losses and, in some cases, may comprise a large portion of the total loss by developing into large conflagrations (e.g., 1906 San Francisco earthquake). In order to estimate fire losses, conditioned on the occurrence of an earthquake, a probabilistic conflagration model is required. Such a model predicts the burnt areas based on the three-phases of the FFEQ process: fire ignition, fire spread and fire suppression. The first phase, fire ignition, estimates the number of fires that can occur in the aftermath of an earthquake and is a function of the intensity and time of occurrence of the earthquake, the square footage of the buildings in the impacted region, and the mix of construction and occupancy classes. The second phase, fire spread, estimates the propagation of each of the initial fires within a building, to other buildings, and among city blocks. This process is in general a fun...
The RMS catastrophe earthquake model has been used to assess the cost-effectiveness of a public C... more The RMS catastrophe earthquake model has been used to assess the cost-effectiveness of a public Californian earthquake early warning system. Taking a thirty year time frame, there is a reasonable expectation that the safety investment would be warranted by the number of lives saved and the reduced fire loss following earthquake. Significant additional early warning benefits also accrue to a number of corporate stakeholders. Given the balance between societal and corporate benefits, it would be equitable if the private sector supported this investment in public safety.
Earthquake Engineering & Structural Dynamics, 2015
This study presents a novel approach for evaluating ground motion selection and modification (GMS... more This study presents a novel approach for evaluating ground motion selection and modification (GMSM) procedures in the context of probabilistic seismic demand analysis. In essence, synthetic ground motions are employed to derive the benchmark seismic demand hazard curve (SDHC), for any structure and response quantity of interest, and to establish the causal relationship between a GMSM procedure and the bias in its resulting estimate of the SDHC. An example is presented to illustrate how GMSM procedures may be evaluated using synthetic motions. To demonstrate the robustness of the proposed approach, two significantly different stochastic models for simulating ground motions are considered. By quantifying the bias in any estimate of the SDHC, the proposed approach enables the analyst to rank GMSM procedures in their ability to accurately estimate the SDHC, examine the sufficiency of intensity measures employed in ground motion selection, and assess the significance of the conditioning intensity measure in probabilistic seismic demand analysis.
The output of risk analyses is used by insurance and reinsurance companies for critical decision-... more The output of risk analyses is used by insurance and reinsurance companies for critical decision-making that can have a profound effect on the business. As more companies use and rely on the results of catastrophe risk analyses, it is important for companies to have a good understanding of the uncertainties associated with the risk loss metrics. Loss risk models are complex combinations of components, which in turn have uncertainties that are difficult to evaluate. This paper presents a simplified framework to incorporate uncertainties in the different components that can be combined using logic trees. Specific cases for evaluating the effects of the seismic hazard uncertainties are given. The treatment of the epistemic and aleatory uncertainty of the ground motion models within the framework and the resulting uncertainties in the portfolio loss metrics are presented. Additional source of uncertainties can also be accommodated within the framework.
Performance based earthquake engineering often involves dynamic structural analysis of buildings ... more Performance based earthquake engineering often involves dynamic structural analysis of buildings using a set of input ground motions. This manuscript describes statistical analyses performed to evaluate the similarity of the response of tall buildings to comparable recorded and simulated ground motions. Structural response measures of a 40 story steel moment frame building designed based on the 2006 IBC are estimated under comparable sets of 40 recorded and simulated ground motions selected from the NGA database and the 2009 broadband Loma Prieta simulations by Dr. Rob Graves. Commonly used response measures such as peak story drift ratio, peak floor acceleration, residual drift ratio and beam plastic rotation are considered. Hypothesis testing is used to compare and contrast the response measures obtained using the selected recorded and simulated ground motions. Overall, this study provides a statistical basis to test simulated ground motions and identify applications where simulated ground motions can be used.
Aftershock Risk in Japan Following Tohoku Earthquake
Recent Tohuku earthquake has clearly showed that aftershocks following large magnitude earthquake... more Recent Tohuku earthquake has clearly showed that aftershocks following large magnitude earthquakes are a source of significant risk. In this study, we have followed the Reasenberg and Jones (1989) approach to describe the aftershock activity based on: 1) Gutenberg-Richter model (GRM) specifying the relationship between the magnitude and total number of earthquakes in any region and time period, and 2) modified Omori model (MOM) defining the decay of the aftershock activity with time. The aftershock occurrence is represented by a non-stationary Poisson process whose rate varies with time after the main shock. Since Tohoku earthquake occurred in a seismically active region, it is practically impossible to differentiate the aftershocks from the regular background earthquakes in the catalog. Hence this study fitted the MOM and GRM to all the events in the catalog in order to estimate the post-Tohoku seismicity (conventional study considers only the aftershocks). We have used the JMA cat...
The 22 February 2011 Lyttelton earthquake is one of the devastating natural catastrophes worldwid... more The 22 February 2011 Lyttelton earthquake is one of the devastating natural catastrophes worldwide, causing a large number of casualties and severe damage to the city of Christchurch, New Zealand. Though the magnitude of 6.3 was relatively low, the ground motions of the Lyttelton earthquake were unexpectedly strong. To understand the uniqueness of the Lyttelton event, this paper focuses on the investigation and characterization of the ground motions from the recent 2010-2011 earthquakes, including the February 2011 Lyttelton and September 2010 Darfield events. By analyzing the ground motion records at selected GeoNet stations in the vicinity of the city of Christchurch, the characteristics of spectral demands at ground motion recording stations from both events were discussed. Then we examine the empirical New Zealand ground motion models to investigate if the ground motion prediction models can explain the unusual destructiveness of the strong ground motions. This study can be help...
In the last two decades, significant progress in science and technology has driven major advances... more In the last two decades, significant progress in science and technology has driven major advances in the modeling of natural hazards and their impact on the built environment. In addition, several major catastrophe events over the same period highlighted important issues that could affect the underwriting and decision-making processes for selecting and managing risk. In many cases, these events had a profound impact on insurance and reinsurance practices, expanding the use of models, analytics, and exposure-data quality analysis to understand the sources of risk and to model loss uncertainty. Furthermore, since the development of earlier versions of catastrophe models, technology and computing power have advanced enormously, allowing modelers to address key elements of model and loss uncertainty in a more systematic way. Most catastrophe models implicitly account for the uncertainty associated with various model components. These uncertainties can be characterized as aleatory or epi...
Recent earthquakes in New Zealand and Japan show that it is important to consider the spatial and... more Recent earthquakes in New Zealand and Japan show that it is important to consider the spatial and temporal distribution of aftershocks following large magnitude events since the probability of high intensity ground motions from aftershocks, which are capable of causing significant societal impact, can be considerable. This is due to the fact that a mainshock will have many aftershocks, some of which may occur closer to populated areas and may be large enough to cause damage. When a large magnitude event strikes a region, the chance that aftershocks will cause damage can be significant as was observed after the 2011 Tohoku and 2010 Canterbury earthquakes (e.g., damage caused by Mw6.6 April 11, 2011 Fukushima-Hamadori earthquake following Tohoku earthquake or by Mw6.3 February 22, 2011 Christchurch earthquake following Canterbury earthquake). Aftershock events may further damage already damaged buildings, thereby further complicating assessments of risk to the built environment. In th...
It is well known that a structure generally responds well beyond its elastic capacity at high sei... more It is well known that a structure generally responds well beyond its elastic capacity at high seismic loading; nonlinear time-history analysis is therefore the most accurate procedure for the seismic demand calculations. Such analyses are being used systematically, for example, in the current SAC steel momentresisting frame project. There is apparently no methodology currently available to characterize the seismicdemand calculations when we observe that in some cases structures, especially tall structures, “collapse” because of strength degradation and/or significant effects. In this paper we will propose a novel way to calculate the seismic demand by considering a three-parameter probability distribution model. The parameters of the distribution at any ground-motion intensity level can be calculated easily from the response results when the ground-motion records are scaled to that intensity level. More generally, the parameters can be estimated economically from (1) a conventional-...
Insurance companies typically estimate earthquake losses for buildings using catastrophe loss mod... more Insurance companies typically estimate earthquake losses for buildings using catastrophe loss models. In this study, we analyze the insurance loss data from the Northridge earthquake to improve existing loss models. Conventionally, the distribution of loss is modelled using the Beta distribution. The claims data, however, show that the Beta distribution combined with Dirac-delta functions at 0 and 1 to model the probabilities of zero and complete loss improves the fit to the observed loss distribution. In addition, the spatial correlation between the losses at two locations is developed for modelling the loss distribution for a portfolio of buildings. The components of the correlation model are estimated using claims data and earthquake intensity data. Finally, the loss assessment for a portfolio of buildings is carried out using the improved uncertainty and spatial correlation models in order to demonstrate the importance of these models in assessing and managing seismic risks.
Probabilistic seismic demand analysis of nonlinear structures
Recent earthquakes in California have initiated improvement in current design philosophy and at p... more Recent earthquakes in California have initiated improvement in current design philosophy and at present the civil engineering community is working towards development of performance-based earthquake engineering of structures. The objective of this study is to develop efficient, but accurate procedures for probabilistic analysis of nonlinear seismic behavior of structures. The proposed procedures help the near-term development of seismic-building assessments which require an estimation of seismic demand at a given intensity level. We also develop procedures to estimate the probability of exceedance of any specified nonlinear response level due to future ground motions at a specific site. This is referred as Probabilistic Seismic Demand Analysis (PSDA). The latter procedure prepares the way for the next stage development of seismic assessment that consider the uncertainties in nonlinear response and capacity. The proposed procedures require structure-specific nonlinear analyses for a ...
This paper reviews, compares, and contrasts the three methodologies proposed by C. A. Cornell, by... more This paper reviews, compares, and contrasts the three methodologies proposed by C. A. Cornell, by Y. K. Wen, and by FEMA 273 (as proposed by H. Krawinkler) for predicting the postelastic response of buildings subject to seismic excitation. All three methods have the potential to contribute effectively to the problem of improving the practical prediction of seismic response of structures. Applications include preliminary design, routine (code) use, calibration of codes, and specific structure assessment. These methods appear different because their authors did not share the same objectives or information bases. The methods by Cornell and Wen are decisively prediction-oriented in explicitly probabilistic frameworks. The approach suggested by Krawinkler has instead the goal of understanding in some average sense the seismic response of structures at various performance levels. This last method has been adopted, however, for prediction purposes by the FEMA 273 Guidelines for rehabilitation of existing buildings. Despite the differences, the work proposed by these researchers is profitably brought under the same perspective here.
The U.S. National Seismic Hazard Model (NSHM) is composed of multiple logic trees that capture th... more The U.S. National Seismic Hazard Model (NSHM) is composed of multiple logic trees that capture the epistemic uncertainty inherent in any estimate of seismic hazard at a site. Logic trees and associated weights describe, but are not limited to, variability of fault geometry, maximum magnitude, and regional seismicity rate. They are also used to represent different models of ground motion. With each new edition of the NSHM, the number of logic trees and associated branches grows. While this does not pose insurmountable computational demands, the computation of mean hazard maps does grow proportionally, particularly when computing associated uncertainties on a map scale, and it is difficult to determine which branches are the most influential. It is also increasingly important that the NSHM program produce maps of uncertainty; to this end, any reductions in computation time are a benefit. Using the California component of the NHSM, the Uniform California Earthquake Rupture Forecast ver...
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