Danny Arroyo

On the Forecasting of Ground-Motion Parameters for Probabilistic Seismic Hazard Analysis

It is well understood that the range of application for an empirical ground-motion prediction model is constrained by the range of predictor variables covered in the data used in the analysis. However, in probabilistic seismic hazard analysis (PSHA), the limits in the application of ground-motion prediction models (GMPMs) are often ignored, and the empirical relationships are extrapolated. In this paper, we show that this extrapolation leads to a quantifiable increment in the uncertainty of a GMPM when it is used to forecast a future value of a given intensity parameter. This increment, which is clearly of epistemic nature, depends on the adopted functional form, on the covariance matrix of the regression coefficients, on the used regression technique, and on the quality of the data set. In addition, through some examples using the database of the Next Generation of Ground-Motion Attenuation Models project and some currently favored functional forms we study the increment in the seismic hazard produced by the extrapolation of GMPMs.

Hysteretic Energy Demands for SDOF Systems Subjected to Narrow Band Earthquake Ground Motions. Applications to the Lake Bed Zone of Mexico City

This study proposes a way to estimate the hysteretic energy demands for oscillators subjected to narrow-band earthquake ground motions using an equivalent sinusoidal pulse. The parameters required to define the equivalent pulse are: the peak ground acceleration, the maximum of the Fourier amplitude spectrum, and the predominant period of the site. The equivalent pulse is utilized to compute the hysteretic energy demands associated to the design elastic pseudoacceleration spectra prescribed by the Mexico City Building Code and to construct damage index maps for systems designed according to this code and subjected to a seismic event with M = 8 and focal distance of 300 km.

Multivariate Bayesian Regression Analysis Applied to Ground-Motion Prediction Equations, Part 1: Theory and Synthetic Example

An application of a linear multivariate Bayesian regression model to compute pseudoacceleration (SA) ground-motion prediction equations (GMPEs )i s presented. The model is able to include the correlation between observations for a given earthquake, the correlation between SA ordinates at different periods, and the correlation between regression coefficients of the ground-motion prediction model. We evaluate the advantages of the Bayesian approach over the traditional regression methods, and we discuss the differences between univariate and multivariate analyses. Because the application of the Bayesian method is in general complex and implies an increase in the numerical effort with respect to the traditional methods, our computer code to perform linear Bayesian analyses is freely available on request.

Multivariate Bayesian Regression Analysis Applied to Ground-Motion Prediction Equations, Part 2: Numerical Example with Actual Data

Abstract An application of a linear multivariate Bayesian regression model, described in a companion article, to obtain a ground-motion prediction equation (GMPE) using a set of actual ground-motion records and a realistic functional form is presented. Based on seismological grounds and on an adopted functional form, we include a sound discussion about how the prior information required for the model can be defined. For the regression analyses we use two subsets of ground-motion records from the Next Generation of Ground-Motion Attenuation Models (NGA) database. We compare the results obtained with the Bayesian model with those obtained through the one-stage maximum-likelihood and the constrained maximum-likelihood methods. The advantages of the Bayesian approach over traditional regression techniques are discussed.

Seismic Loss Estimation and Environmental Issues

The consideration of environmental losses in seismic design is discussed within the framework of cost optimization analysis. Within this context, the equivalent carbon emissions (CO2-e) are used as a proxy for the environmental cost related to seismic damage, and a model to assess the environmental cost in seismic loss estimation is introduced. The use of the model is illustrated through its application to the analysis of simple earthquake-resistant structural systems. It is concluded that under certain circumstances, the consideration of environmental issues in seismic design may be important, especially as the planning time horizon of the facility increases.

On the Selection of Ground‐Motion Prediction Equations for Probabilistic Seismic‐Hazard Analysis

Abstract In current practice of probabilistic seismic‐hazard analysis (PSHA), the difference between ground‐motion prediction equations (GMPEs), which are in principle equally valid related to their quality and applicability, is attributed to epistemic uncertainty. The standard practice is to include this uncertainty through logic trees. Based on probability concepts, we present a method to assist during the selection and weighting of GMPEs to be included in different branches of a logic tree. We find that in regions with abundant recorded data, only those models with large likelihood should be considered. Although the presented method is not the only option to define the weighting of GMPEs for PSHA, it offers an ordered way to combine different sources of knowledge, such as recorded data and prior information.

On Uncertainties in Probabilistic Seismic Hazard Analysis

Probabilistic seismic hazard analysis (PSHA) is, in essence, a method to deal with uncertainty, the importance of which justifies the use of a formal and rigorous background for its study. Therefore, the purpose of this paper is to contribute to the reflections on how to correctly handle uncertainty in PSHA. We start by studying the simplest case, a Poisson process in which only “aleatory” uncertainty exists; then, we remove the Poisson hypothesis and find expressions for the occurrence probabilities of earthquakes in given time frames for general non-Poisson processes. Later, we include a simple variety of epistemic uncertainty and show that the resulting process is not Poissonian anymore, so computation of probabilities has to be made taking into account this fact. Next, we give a rigorous rule to combine uncertainties of aleatory and epistemic origin, which gives reasonable criteria to decide whether the epistemic uncertainty is large or not. Also, we propose unambiguous guidelines to decide whether a particular class of uncertainty has to be included in the hazard calculations as epistemic or as aleatory. Finally, we discuss the problem of how our estimates could differ if we wrongly considered that our epistemic uncertainty is of aleatory nature, or vice versa.

Evaluation of the Intensity Measure Approach in Performance‐Based Earthquake Engineering with Simulated Ground Motions

Abstract Within the framework of performance‐based earthquake engineering, the intensity‐measure approach (IMA) has become the standard option for the characterization of engineering‐demand parameters (EDPs) for systems undergoing significant inelastic behavior. Within this approach, the rates of exceedance of the EDPs are computed from a hazard curve corresponding to an intensity measure (IM; usually the spectral acceleration at the first mode period S A ( T 1 )) and the conditional probability density function (CPDF) of the EDP given the IM. In view of the lack of strong ground motion records associated with large values of currently used IMs, the parameters required to establish a CPDF are obtained from an incremental dynamic analysis that considers the S A ( T 1 ) linear scaling of motions recorded during seismic events of moderate intensity. However, from a seismological perspective, the linearly scaling method is too simple and may lead to unrealistic ground‐motion records that may affect the accuracy of the IMA. The dynamic response of single‐degree‐of‐freedom systems subjected to simulated ground motions is analyzed in order to assess the limitations of the S A ( T 1 ) linearly scaling method. These simulated ground motions were obtained via a stochastic simulation technique that has a solid seismological basis. The results presented herein are useful to numerically understand the limitations of the S A ( T 1 ) linearly scaling method and to identify situations in which a more sophisticated analysis is warranted.

Use of Corrected Sinusoidal Pulses to Estimate Inelastic Demands of Elasto-Perfectly Plastic Oscillators Subjected to Narrow-Band Motions

Expressions to estimate the maximum displacement of elasto-perfectly plastic oscillators undergoing inelastic response subjected to narrow-band earthquake ground motions are proposed. The ground motions are characterized by sinusoidal pulses, corrected in order to have realistic representations of ground motions due to earthquakes. Based on the results obtained from the corrected pulses, it is shown that, for the type of earthquake ground motions considered, the maximum inelastic demands tend to be independent of ground motion duration, while maximum elastic demands do depend on duration. It is also shown that ground motion duration has a strong influence on strength-reduction factors for narrow-band earthquake ground motions. In view of this fact, caution is warranted when using empirical equations developed with data that have very different durations than the accelerograms expected. Comparisons are made between our analytical solution and results obtained from purely empirical expressions and it is shown that the accuracy of the solution presented is comparable to that of the empirical formulations. The advantage of the expression proposed over expressions obtained from statistical analysis is that it is independent of the elastic strength and displacement spectra.

Inelastic-Strength Spectra in Probabilistic Seismic-Hazard Analysis

Abstract A comparison between two methods to compute uniform-hazard inelastic-strength spectra for single-degree-of-freedom systems subjected to earthquake ground motions is presented. In the first method the inelastic spectra are obtained by reducing uniform-hazard elastic pseudoacceleration (SA) spectra with deterministic strength-reduction factors, while in the second method inelastic-strength spectra are computed with a probabilistic seismic-hazard analysis that accounts for the variability in the strength-reduction factor. It is demonstrated that the first method yields similar results to the probabilistic analysis if the product of the slope of the hazard curve of SA and the standard deviation of the logarithm of the strength-reduction factor is small.