This paper presents a proposed method of aftershock probabilistic seismic hazard analysis (APSHA) similar to conventional ‘mainshock’ PSHA in that it estimates the likelihoods of ground motion intensity (in terms of peak ground accelerations, spectral accelerations or other ground motion intensity measures) due to aftershocks following a mainshock occurrence. This proposed methodology differs from the conventional mainshock PSHA in that mainshock occurrence rates remain constant for a conventional (homogeneous Poisson) earthquake occurrence model, whereas aftershock occurrence rates decrease with increased elapsed time from the initial occurrence of the mainshock. In addition, the aftershock ground motion hazard at a site depends on the magnitude and location of the causative mainshock, and the location of aftershocks is limited to an aftershock zone, which is also dependent on the location and magnitude of the initial mainshock. APSHA is useful for post‐earthquake safety evaluation where there is a need to quantify the rates of occurrence of ground motions caused by aftershocks following the initial rupture. This knowledge will permit, for example, more informed decisions to be made for building tagging and entry of damaged buildings for rescue, repair or normal occupancy. Copyright © 2008 John Wiley & Sons, Ltd.

The objective of this paper is to develop formal stochastic expected financial loss estimation models over the lifetime of the building due to mainshocks and their subsequent aftershock sequences. Mainshocks are typically modeled as a homogeneous Poisson process with constant mean rate of occurrence, while the resulting aftershocks are modeled as a nonhomogeneous Poisson process with random magnitudes which has parameters (mainshock magnitude, mm, and location) that are conditional on the random mainshock. The initial model to compute expected losses is the simplified homogeneous Poisson mainshock process and nonhomogeneous Poisson aftershock process with “immediate” repair of the building to the initial building state. We then develop a more general Markov and semi-Markov framework where we consider both Poisson and renewal processes for modeling mainshock occurrences with various building damage progression scenarios. Finally, we will incorporate the random aftershock losses into pre-mainshock financial loss estimation. The ability to compute the expected building life-cycle cost due to both mainshocks and aftershocks will be useful as an input to seismic decision making (both post- and pre-mainshock).

Alternative non‐linear dynamic analysis procedures, using real ground motion records, can be used to make probability‐based seismic assessments. These procedures can be used both to obtain parameter estimates for specific probabilistic assessment criteria such as demand and capacity factored design and also to make direct probabilistic performance assessments using numerical methods. Multiple‐stripe analysis is a non‐linear dynamic analysis method that can be used for performance‐based assessments for a wide range of ground motion intensities and multiple performance objectives from onset of damage through global collapse. Alternatively, the amount of analysis effort needed in the performance assessments can be reduced by performing the structural analyses and estimating the main parameters in the region of ground motion intensity levels of interest. In particular, single‐stripe and double‐stripe analysis can provide local probabilistic demand assessments using minimal number of structural analyses (around 20 to 40). As a case study, the displacement‐based seismic performance of an older reinforced concrete frame structure, which is known to have suffered shear failure in its columns during the 1994 Northridge Earthquake, is evaluated. Copyright © 2008 John Wiley & Sons, Ltd.

We introduce a general decision analysis procedure based on stochastic dynamic programming in the post‐quake aftershock environment. The damage sustained by the building due to the mainsheet, the time‐varying aftershock rates and the potential for further damage progression in the post‐quake environment are all factors taken into consideration in the proposed methodology. This procedure enables the optimal decision after the mainshock to be selected based on the minimization of expected financial losses, subject to a constraint on a minimal level of individual life‐safety, using a consistent probabilistic framework to explicitly quantify the uncertainties in the variables. Copyright © 2008 John Wiley & Sons, Ltd.

Near-source ground motion records affected by "directivity" may show unusual features resulting in low frequency pulses in the velocity time-history, especially in the fault-normal component. Although not all near-source recordings show pulses, such an effect is of particular interest for practitioners as it may cause the seismic demand for structures to deviate from that of, so-called, "ordinary" records. Consequently many seismology and earthquake engineering researchers have tried to parameterize the causes and the effects of directivity pulses. In the framework of the probabilistic seismic assessment of structures in near-source conditions, a quantification of the pulse threat is required. In fact, the recently developed probabilistic seismic hazard analysis for near-source sites requires a probabilistic model for the occurrence of pulses in ground motion. Herein this issue is investigated and models are obtained via logistic regression of a set of pulse-like records from the NGA database. Analyses are limited to ground motions recorded within 30km from the source and to strike-slip events. Occurrence probability of velocity pulses is computed as conditional in respect to those factors considered by seismologists to affect the amplitude of directivity effects.

Near-source ground-motion records affected by directivity may show unusual features in the signal resulting in low-frequency cycle pulses in the velocity time history, especially in the fault-normal component. Such an effect causes the seismic demand for structures to deviate from that of so-called ordinary records. This circumstance may be particularly hazardous for structural engineering applications if it is not properly accounted for. In fact, current attenuation laws are not able to capture such effects well, if at all, and therefore current probabilistic seismic hazard analysis (PSHA) is not able to predict this peculiar spectral shape. This failure may possibly lead to an underestimation of, in particular, the nonlinear demand. Accounting for pulse-type records in earthquake engineering practice should be reflected both in the PSHA and in the record selection for seismic assessment of structures. These applications require a model for the probability of occurrence of pulselike records. Herein such a model is proposed on an empirical basis. A set of pulselike fault-normal ground motions from the Next Generation Attenuation of Ground Motions (NGA) Project dataset, as systematically identified by Baker (2007), is used. The independent variables studied are chosen from those considered by seismologists to affect the amplitude of directivity pulses. Issues related to the dataset and the explanatory power of the proposed models are also discussed.

The disaggregation of output from Probabilistic Seismic Hazard Analysis (PSHA) has become a frequently used tool in recent years. The output from this procedure allows one to understand the condi- tional probability distribution of the earthquake scenarios that contribute to seismic hazard at a specified ground motion level. In this paper, the concept of disaggregation is extended to Probabilistic Seismic Demand Analysis (PSDA)—a performance-based engineering procedure that combines ground motion hazard infor- mation with probabilistic structural response. Disaggregation of this analysis provides the distribution of ground motion intensities contributing to exceedance of a given structural response level. This information provides additional insight to the engineer, and is also useful for verifying that a sufficient range of ground motion levels has been considered the assessment of a structure. PSDA disaggregation is combined with a PSHA disaggregation to determine the distribution of Magnitude-Distance pairs (i.e., scenarios) that contrib- ute to the exceedance of a given structural response level. A procedure is also presented for disaggregation with a vector-valued measure of ground motion intensity. The disaggregation methodology is outlined and an example analysis is performed to demonstrate the information provided.

iii ACKNOWLEDGMENTS iv CONTENTS v LIST OF FIGURES vii LIST OF TABLES xi 1 GUIDELINES AND PROCEDURE 1 1.1 Objective 1 1.2 PG&E Building Inventory 3 1.3 Procedure 4 1.4 Discussion of the Six Steps 7 1.4.1 Step 1: Nonlinear Static Procedure (NSP) Curve for Intact Building 7 1.4.2 Step 2: NSP Curves for Damaged Building 11 1.4.3 Step 3: Inferring Dynamic Response from Static Response 13 1.4.3.1 Intact Structure 15 1.4.3.2 Damaged Structure 16 1.4.4 Step 4: Occupancy Status for Damaged Building 24 1.4.5 Step 5: Ground Motion Level Associated with Structural Limit State 36 1.4.6 Step 6: Computation of Fragility Curves 45 2 APPLICATION OF THE GUIDELINES 51 2.1 Case Study No. 1: Three-Story Steel Moment-Resisting Frame (SMRF) Building...... 51 2.1.1 Structural Model 52 2.1.2 Connection Model 52 2.1.3 Application of the Guidelines 53 2.1.3.1 Step 1: NSP of Intact Structure and Identification of Damage States.... 53 2.1.3.2 Step 2: NSP Curves for Damaged Structure 54 2.1.3.3 Step 3: From SPO to IDA 56 2.1.3.4 Step 4: Occupancy Status for Damaged Building 64 2.1.3.5 Step 5: Ground Motion Level at Incipient Structural Limit State 65 2.1.3.6 Step 6: Computation of Fragility Curves 66 2.1.4 Validation 67 2.2 Case Study No. 2: Tilt-up Building 69 2.2.1 Structural Model 70

Probabilistic prediction of structural and nonstructural damage costs due to future earthquakes is one component of loss estimation currently being developed for use in performance-based earthquake engineering. Sources of uncertainty in this prediction include epistemic and aleatory uncertainty in the site ground motion hazard, the building response, the damage measures of each of the many building elements, and repair cost of each of the elements. These are interand cross-correlated random variables. Two desired results are the total uncertainty in annual losses, and the contribution of each uncertainty source to the total uncertainty. Monte Carlo simulation is a simple solution, but it can be computationally expensive. This study proposes an alternative approach using First-Order Second-Moment (FOSM) methods for all but the (dominant) ground motion intensity variable. Suggestions for characterization of correlations are presented. A procedure for applying FOSM methods in the calculation of total uncertainty is outlined. The proposed technique is very efficient, and easily used for sensitivity studies.

Research Article| July 01, 2003 OpenSHA: A Developing Community-modeling Environment for Seismic Hazard Analysis Edward H. Field; Edward H. Field U.S. Geological Survey 525 S. Wilson Avenue Pasadena, CA 91106 +1-626-583-7814 field@usgs.gov (E.H.F.) Search for other works by this author on: GSW Google Scholar Thomas H. Jordan; Thomas H. Jordan Search for other works by this author on: GSW Google Scholar C. Allin Cornell C. Allin Cornell Search for other works by this author on: GSW Google Scholar Seismological Research Letters (2003) 74 (4): 406–419. https://doi.org/10.1785/gssrl.74.4.406 Article history first online: 09 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation Edward H. Field, Thomas H. Jordan, C. Allin Cornell; OpenSHA: A Developing Community-modeling Environment for Seismic Hazard Analysis. Seismological Research Letters 2003;; 74 (4): 406–419. doi: https://doi.org/10.1785/gssrl.74.4.406 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietySeismological Research Letters Search Advanced Search Probabilistic seismic hazard analysis (PSHA) provides the conceptual framework for estimating the likelihood that something of concern related to earthquake shaking will occur over a specified time period. Based on more than thirty years of research and development (e.g., Cornell, 1968; Algermissen et al., 1982; SSHAC, 1997), PSHA has become a standard tool for combining information on earthquake occurrence, seismic radiation, and shaking response to produce hazard estimates, including the U.S. Geological Survey's national seismic hazard maps (Frankel et al., 1996, 1997). PSHA methods, while now mature, continue to evolve as scientists... You do not have access to this content, please speak to your institutional administrator if you feel you should have access.

A three-parameter distribution (TPD) is used to describe the record-to-record variability in displacement demand in the region of global dynamic instability. The incremental dynamic analysis (IDA) procedure is implemented as an analysis tool in order to obtain analytic parameter estimates for this three-parameter distribution, as functions of ground motion intensity measure. Demand and capacity factor design (DCFD) is a closed-form analytic format that can be used for making probability-based seismic assessments. The assumptions leading to the derivation of DCFD may not be valid when the displacement demand is in the region of global dynamic instability. In the context of DCFD format, factored demand is a definition that identifies the structural demand corresponding to a given allowable probability level. This definition is extended to a more general context in order to compare demand estimations based on the three-parameter distribution to those based on empirical distribution. A transverse frame in the Holiday Inn Hotel, Van Nuys, CA, which is an older reinforced concrete frame, is used as the model structure with degrading behavior in shear and flexure in the non-linear range.

We propose a building-specific methodology to estimate the annual frequency of fatalities due to earthquakes. The proposed procedure uses nonlinear dynamic analyses to characterize the damage state of the building, and couples these results with information on the expected spatial locations of the occupants and the ground motion site hazard curve of the site, to obtain a full probability distribution of the annual number of fatalities due to structural damage.

This paper presents and explores estimating design loads on wind turbines using the environmental contour method. Contours promise to provide both practical reliability estimation and valuable information about the combination of joint environmental variable values, e.g. wind speed and turbulence, most critical to each specific wind turbine. We present the background of the development of environmental contours as applied to wind energy systems, and apply this theory, in three examples, to develop contours based either (1) on design code description of environmental conditions, or (2) on measured data for a site-specific application. The site-specific case is used for both stall and pitch controlled turbine examples. From these contours, and a functional description of the short-term response of the turbine, implicit FORM estimates are made for the turbine response; these estimates are compared with results obtained from numerical integration of the short-term response of the turbine over the joint distribution of wind speed and turbulence. We find that the environmental contour method provides reasonable estimates of the expected extreme load, compared with the full integration method.

This paper presents a formal probabilistic framework for seismic design and assessment of structures and its application to steel moment-resisting frame buildings. This is the probabilistic basis for the 2000 SAC Federal Emergency Management Agency (FEMA) steel moment frame guidelines. The framework is based on realizing a performance objective expressed as the probability of exceeding a specified performance level. Performance levels are quantified as expressions relating generic structural variables "demand" and "capacity" that are described by nonlinear, dynamic displacements of the structure. Common probabilistic analysis tools are used to convolve both the randomness and uncertainty characteristics of ground motion intensity, structural "demand," and structural system "capacity" in order to derive an expression for the probability of achieving the specified performance level. Stemming from this probabilistic framework, a safety-checking for-mat of the conventional "load and resistance factor" kind is developed with load and resistance terms being replaced by the more generic terms "demand" and "capacity," respectively. This framework also allows for a peformance objective being met. This format has been format based on quantitative confidence statements regarding the likelihood of the performance objective being met. This format has been adopted in the SAC/FEMA guidelines.