Vector Intensity Measures Research Articles

Conditional spectrum bidirectional record selection for risk assessment of 3D structures using scalar and vector IMs

SummarySeveral proposals are explored for the hazard and intensity measure (IM) consistent selection of bidirectional ground motions to assess the performance of 3D structural models. Recent studies have shown the necessity of selecting records that thoroughly represent the seismicity at the site of interest, as well as the usefulness of efficient IMs capable of estimating the response of buildings with low scatter. However, the advances realized are mostly geared towards the structural analysis of 2D models. Few are the combined record, and IM selection approaches suggested expressly for nonlinear dynamic analysis of 3D structural models, especially when plan asymmetry and torsion sensitivity come into play. Conditional spectrum selection is leveraged and expanded here to offer a suite of approaches based on both scalar and vector IMs that convey information from two orthogonal horizontal components of the ground motion. Applications on multiple 3D building models highlight the importance of (a) employing the same IM for both record selection and response assessment and (b) maintaining hazard consistency in both horizontal components, when using either a scalar or a vector IM. All tested approaches that respect these conditions can be viable, yet the one based on the geometric mean of multiple spectral ordinates from both components over a period range seems to hold the most promise for general use.

A vector intensity measure to reliably predict maximum drift in low- to mid-rise buildings

An optimal intensity measure (IM) should be able to predict the structural response with minimum dispersion, which is called efficiency, and also independently of other ground motion characteristics, such as earthquake magnitude (M) and source-to-site distance (R), which is called sufficiency. Using an optimal IM can play an important role in reliable seismic performance assessment of structures. The present study is aimed at investigating the efficiency and sufficiency of vector-valued IMs for predicting maximum inter-storey drift ratio (MIDR). The IMs considered in this study include response spectral acceleration at the fundamental period of the structure, Sa(T1), as a common scalar IM, the vectors (Sa(T1), εSa) and (Sa(T1), NP) as well-known vector-valued IMs, and ten other vector-valued IMs. These ten IMs consist of two components, with Sa(T1) as the first component and different parameters that are ratios of scalar IMs as the second component. By investigating the desirable features of an optimal IM, (Sa(T1), Sa(T1)/PGV) is proposed as an optimal vector-valued IM for the prediction of MIDR demand on low- to mid-rise reinforced concrete moment-resisting frame structures. To make the proposed IM predictable, a ground motion prediction equation (GMPE) is determined for Sa(T1)/PGV by using the existing GMPEs.

Multivariate Fragility Functions for Seismic Landslide Hazard Assessment

ABSTRACT This paper represents multivariate fragility functions (MFFs) based on sliding displacement of soil slopes for landslide hazard assessment. The MFFs correlate the sliding displacement probability of slopes to earthquake intensity measures (IMs). Conditional distributions are employed to develop MFFs for failure probability analysis of slopes by considering scalar and vector IMs in the absence of any predetermined predictive model for sliding displacement of slopes. Three sliding displacement-based damage states are defined herein as the low, moderate, and high levels of landslide hazard. The results demonstrate that the probability of exceedance from a given damage state strongly depends on the type and the number of IMs chosen for the fragility analysis whereas the predicted failure probabilities resulted from the scalar and multivariate analyses can vary up to three times. Results of this study indicates that the multivariate fragility analyses can lead to landslide damage estimation in more reliable manner, compared with the scalar-valued fragility curves which are commonly used to predict the seismic hazard of earth slopes.

Seismic intensity measures for above‐ground liquid storage tanks

SummaryA series of scalar and vector intensity measures is examined to determine their suitability within the seismic risk assessment of liquid storage tanks. Using a surrogate modelling approach on a squat tank that is examined under both anchored and unanchored support conditions, incremental dynamic analysis is adopted to generate the distributions of response parameters conditioned on each of the candidate intensity measures. Efficiency and sufficiency metrics are used in order to perform the intensity measure evaluation for individual failure modes, while a comparison in terms of mean annual frequency of exceedance is performed with respect to a damage state that is mutually governed by the impulsive and convective modes of the tank. The results reveal combinations of spectral acceleration ordinates as adequate predictors, among which the average spectral acceleration is singled out as the optimal solution. The sole exception is found for the sloshing‐controlled modes of failure, where mainly the convective period spectral acceleration is deemed adequate to represent the associated response due to their underlying linear relationship. A computationally efficient method in terms of site hazard analysis is finally proposed to serve in place of the vector‐valued intensity measures, providing a good match for the unanchored tank considered and a more conservative one for the corresponding anchored system.

Quantification of model uncertainty and variability in Newmark displacement analysis

Newmark displacement model has been extensively used to evaluate earthquake-induced displacement in earth systems. In this paper, model uncertainty and variability associated with the Newmark displacement analysis are systematically studied. Fourteen Newmark displacement models using scalar or vector intensity measures (IMs) as predictors are compared in this study. In general, model uncertainty for the vector-IM models is found smaller than that of the scalar-IM models, and remains consistent over different earthquake magnitude, distance and site conditions. Yet, the model uncertainty of these Newmark displacement models is still much larger than that of the ground-motion prediction equations (GMPEs) for IMs, indicating further development of the models is much needed. Considering the variabilities contributed from both GMPEs and Newmark displacement models, the total variability of the predicted Newmark displacements is rather consistent among the scalar- and vector-IM displacement models, due to extra sources of variability introduced by incorporating additional IMs. Finally, a logic tree scheme is implemented in the fully probabilistic Newmark displacement analysis to account for the model uncertainty and variability. Sensitivity analysis shows that specific weights would not significantly influence the displacement hazard curves as the results may be dominated by outlier models. Instead, selecting appropriate GMPEs and Newmark displacement models is more important in using the logic-tree framework.

Prediction of seismic demand model for pulse-like ground motions using artificial neural networks

A probabilistic seismic demand model that relates ground motion intensity measures (IMs) to the structural demand measures is a useful tool for reliability analysis of structures. It is common to utilize the scalar seismic parameters or a vector of a few seismic parameters to reveal ground motion uncertainty. However, for the qualification of an IM for representing the ground motion uncertainty, a larger vector of greater seismic component is required. This study aims to use more parameters as vector IMs in the demand model to achieve better estimation of the ground motion uncertainty. In this study, three-layer feed forward neural network was used to predict the seismic demand model of the mid-rise reinforced concrete buildings for pulse-like ground motions. The results indicate that due to the complexity of the relationship between seismic response of structures and seismic intensity parameters, using artificial neural networks method is more suitable than numerical methods to show uncertainties.

Implications of Intensity Measure Selection for Seismic Loss Assessment of 3-D Buildings

Present building-specific loss assessment state-of-art involves the convolution of seismic hazard and building seismic demands. The latter is conditioned on spectral acceleration, Sa( T1), at the building's first mode as the ground motion intensity measure (IM) and is typically estimated by carrying out nonlinear dynamic analyses on a two-dimensional (2-D) model. By new proposals on the use of improved IMs that can introduce higher fidelity, the accuracy in loss estimation becomes an open question. In reply, we offer a uniform basis for comparing the loss estimates for a set of eight different scalar and vector IMs whose hazard can be predicted with existing GMPEs. Despite all eight being legitimate IMs, and despite the consistent use of conditional spectrum record selection, we find large differences in the estimated loss hazard. This points to the large uncertainty still lingering when connecting hazard to loss. Among the IMs considered here, the vector IMs and at least a scalar average of spectral accelerations showed a remarkable stability in their predictions for the three-dimensional (3-D) buildings, pointing to a potential for reliable applications.

Vector and Scalar IMs in Structural Response Estimation, Part I: Hazard Analysis

A realistic assessment of building economic losses and collapse induced by earthquakes requires the monitoring of several response measures, both story-specific and global. The prediction of such response measures benefits from using multiple ground motion intensity measures (IMs) that are, in general, correlated. To allow the inclusion of multiple IMs in the risk assessment process, it is necessary to have a practical tool that computes the vector-valued hazard of all such IMs at the building site. In this paper, vector-valued probabilistic seismic hazard analysis (VPSHA) is implemented here as a post-processor to scalar PSHA results. A group of candidate scalar and vector IMs based on spectral acceleration values, ratios of spectral acceleration values, and spectral accelerations averaged over a period range are defined and their hazard evaluated. These IMs are used as structural response predictors of three-dimensional (3-D) models of reinforced concrete buildings described in a companion paper ( Kohrangi et al. 2016 ).

Vector and Scalar IMs in Structural Response Estimation, Part II: Building Demand Assessment

The advantages and disadvantages of using scalar and vector ground motion intensity measures (IMs) are discussed for the local, story-level seismic response assessment of three-dimensional (3-D) buildings. Candidate IMs are spectral accelerations, at a single period ( Sa) or averaged over a period range ( Sa avg). Consistent scalar and vector probabilistic seismic hazard analysis results were derived for each IM, as described in the companion paper in this issue ( Kohrangi et al. 2016 ). The response hazard curves were computed for three buildings with reinforced concrete infilled frames using the different IMs as predictors. Among the scalar IMs, Sa avg tends to be the best predictor of both floor accelerations and inter story drift ratios at practically any floor. However, there is an improvement in response estimation efficiency when employing vector IMs, specifically for 3-D buildings subjected to both horizontal components of ground motion. This improvement is shown to be most significant for a tall plan-asymmetric building.

Characterizing Ground Motions that Collapse Steel Special Moment-Resisting Frames or Make Them Unrepairable

This work applies 64,765 simulated seismic ground motions to four models each of 6- or 20-story, steel special moment-resisting frame buildings. We consider two vector intensity measures and categorize the building response as “collapsed,” “unrepairable,” or “repairable.” We then propose regression models to predict the building responses from the intensity measures. The best models for “collapse” or “unrepairable” use peak ground displacement and velocity as intensity measures, and the best models predicting peak interstory drift ratio, given that the frame model is “repairable,” use spectral acceleration and epsilon ( ∊) as intensity measures. The more flexible frame is always more likely than the stiffer frame to “collapse” or be “unrepairable.” A frame with fracture-prone welds is substantially more susceptible to “collapse” or “unrepairable” damage than the equivalent frame with sound welds. The 20-story frames with fracture-prone welds are more vulnerable to P-delta instability and have a much higher probability of collapse than do any of the 6-story frames.

Predictive relationships for seismically induced slope displacements using numerical analysis results

The aim of the paper is threefold: first, to evaluate earthquake-induced slope displacements using numerical dynamic analysis considering different real acceleration time histories as input motion and varying the resistance and the compliance of the sliding mass; then, to assess the reliability of the numerical approach by comparing the numerically calculated seismically induced slope displacements with predictions using available empirical models and finally, based on the numerical analysis results, to propose new displacement predictive models applicable in earthquake engineering practice, which relate the co-seismic slope displacement with the best correlated intensity parameters. Linear regression analyses are performed to correlate the computed displacements with various intensity measures (IMs). Optimal scalar and vector IMs are identified in a rigorous way based on proficiency (i.e. a composite measure of efficiency and practicality) and sufficiency criteria. The correlation coefficient between the IMs is also considered for the selection of appropriate vector IMs. Both scalar and vector regression analytical predictive expressions are proposed appropriate for probabilistic or deterministic evaluation of the co-seismic permanent slope displacements in regional and local scale. A generic example proves the reliability of the proposed analytical expressions.

Preliminary ranking of alternative scalar and vector intensity measures of ground shaking

In Performance-Based Earthquake Engineering, seismic demand in structures is predicted by building probabilistic seismic demand models that link measures of earthquake intensity (IMs) to measures of structural demand. Investigations are carried out herein for evaluating the predictive capability of a wide range of commonly-used scalar and vector-valued IMs for different peak-related demand parameters. To accomplish this goal, both efficiency and sufficiency of the candidate IMs are taken into account. The latter is evaluated with the recently-proposed “relative sufficiency measure”. This measure, which is derived based on information theory concepts, quantifies the amount of information gained (on average) by an IM relative to another about the demand parameter of interest. Evaluation of the IMs, herein, uses two sets of ground motions consisting of ordinary and pulse-like near-fault records. Two-dimensional RC frame structures, both fixed and isolated at the base, are selected. The most suitable IMs for predicting the considered different demand parameters and types of structure are identified in terms of both efficiency and sufficiency. The use of these most informative IMs is suggested to build improved probabilistic demand models.

Vector-intensity measure based seismic vulnerability analysis of bridge structures

This paper presents a method for seismic vulnerability analysis of bridge structures based on vector-valued intensity measure (vIM), which predicts the limit-state capacities efficiently with multi-intensity measures of seismic event. Accounting for the uncertainties of the bridge model, ten single-bent overpass bridge structures are taken as samples statistically using Latin hypercube sampling approach. 200 earthquake records are chosen randomly for the uncertainties of ground motions according to the site condition of the bridges. The uncertainties of structural capacity and seismic demand are evaluated with the ratios of demand to capacity in different damage state. By comparing the relative importance of different intensity measures, Sa(T1) and Sa(T2) are chosen as vIM. Then, the vector-valued fragility functions of different bridge components are developed. Finally, the system-level vulnerability of the bridge based on vIM is studied with Dunnett-Sobel class correlation matrix which can consider the correlation effects of different bridge components. The study indicates that an increment IMs from a scalar IM to vIM results in a significant reduction in the dispersion of fragility functions and in the uncertainties in evaluating earthquake risk. The feasibility and validity of the proposed vulnerability analysis method is validated and the bridge is more vulnerable than any components.

Spatial Cross-Correlation Models for Vector Intensity Measures (PGA, Ia, PGV, and SAs) Considering Regional Site Conditions

Abstract This study investigates spatial cross‐correlation models for two sets of vector intensity measures (IMs) considering the influence of regional site conditions. The first set of the vector IM consists of the peak ground acceleration, Arias intensity, and the peak ground velocity; the second set is for spectral accelerations at multiple periods. Geostatistics analyses are performed using 2686 strong‐motion data from 11 recent earthquakes that occurred in California, Japan, Taiwan, and Mexico. The results indicate that the spatial cross correlations of the vector IMs are strongly influenced by the spatial distribution of regional site conditions, which can be quantified using R V S 30 , the correlation range of shear‐wave velocity in the top 30 m. The linear model of coregionalization is proposed to construct a permissible spatial correlation model, and the short‐range and long‐range coregionalization matrices is specified to vary linearly with R V S 30 . The proposed model demonstrated excellent performance in quantifying the influence of regional site conditions on the spatial cross correlations for the vector IMs, meanwhile the model guarantees a positive‐definite covariance matrix for any reasonable value of R V S 30 , a mathematical condition required for stochastic generation of the spatially correlated random fields. The spatial cross‐correlation models proposed in this study can be conveniently used in regional‐specific seismic risk analysis and loss estimation of spatially distributed infrastructure using vector IMs.

Fully probabilistic seismic displacement analysis of spatially distributed slopes using spatially correlated vector intensity measures

SUMMARYEarthquake‐induced slope displacement is an important parameter for safety evaluation and earthquake design of slope systems. Traditional probabilistic seismic hazard analysis usually focuses on evaluating slope displacement at a particular location, and it is not suitable for spatially distributed slopes over a large region. This study proposes a computationally efficient framework for fully probabilistic seismic displacement analysis of spatially distributed slope systems using spatially correlated vector intensity measures (IMs). First, a spatial cross‐correlation model for three key ground motion IMs, that is, peak ground acceleration (PGA), Arias intensity, and peak ground velocity, is developed using 2686 ground motion recordings from 11 recent earthquakes. To reduce the computational cost, Monte Carlo simulation and data reduction techniques are utilized to generate spatially correlated random fields for the vector IMs. The slope displacement hazards over the region are further quantified using empirical predictive equations. Finally, an illustrative example is presented to highlight the importance of the spatial correlation and the advantage of using spatially correlated vector IMs in seismic hazard analysis of spatially distributed slopes. Copyright © 2013 John Wiley & Sons, Ltd.

Efficiency of scalar and vector intensity measures for seismic slope displacements

Ground motion intensity measures are usually used to predict the earthquake-induced displacements in earth dams, soil slopes and soil structures. In this study, the efficiency of various single ground motion intensity measures (scalar IMs) or a combination of them (vector IMs) are investigated using the PEER-NGA strong motion database and an equivalent-linear sliding-mass model. Although no single intensity measure is efficient enough for all slope conditions, the spectral acceleration at 1.5 times of the initial slope period and Arias intensity of the input motion are found to be the most efficient scalar IMs for flexible slopes and stiff slopes respectively. Vector IMs can incorporate different characteristics of the ground motion and thus significantly improve the efficiency over a wide range of slope conditions. Among various vector IMs considered, the spectral accelerations at multiple spectral periods achieve high efficiency for a wide range of slope conditions. This study provides useful guidance to the development of more efficient empirical prediction models as well as the ground motion selection criteria for time domain analysis of seismic slope displacements.

Analyzing the Sufficiency of Alternative Scalar and Vector Intensity Measures of Ground Shaking Based on Information Theory

The seismic risk assessment of a structure in performance-based design (PBD) may be significantly affected by the representation of ground motion uncertainty. In PBD, the uncertainty in the ground motion is often represented by a probabilistic description of a scalar parameter, or low-dimensional vector of parameters, known as the intensity measure (IM), rather than a full probabilistic description of the ground motion time history in terms of a stochastic model. In this work, a new procedure employing relative sufficiency measure is introduced on the basis of information theory concepts to quantify the suitability of one IM relative to another in the representation of ground motion uncertainty. On the basis of this relative sufficiency measure, several alternative scalar- and vector-valued IMs are compared in terms of the expected difference in information they provide about a predicted structural response parameter, namely, the seismically induced drift in an existing reinforced-concrete frame structure. It is concluded that the most informative of the eight considered IMs for predicting the nonlinear drift response are two scalar IMs and a vector IM that depend only on the spectral ordinates at the periods of the first two (small-amplitude) modes of vibration.

Vector-valued Intensity Measures Incorporating Spectral Shape For Prediction of Structural Response

Vector-valued ground motion intensity measures (IMs) are developed and considered for efficiently predicting structural response. The primary IM considered consists of spectral acceleration at the first-mode structural period along with a measure of spectral shape which indicates the spectral acceleration value at a second period. For the IM to effectively predict response, this second period must be selected intelligently in order to capture the most relevant spectral shape properties. Two methods for identifying effective periods are proposed and used to investigate IMs for example structures, and an improvement in the efficiency of structural response predictions is shown. A method is presented for predicting the probability distribution of structural response using a vector IM while accounting for the effect of collapses. The ground motion parameter ϵ is also considered as part of a three-parameter vector. It is seen that although the spectral shape parameter increases the efficiency of response predictions, it does not fully account for the effect of ϵ. Thus, ϵ should still be accounted for in response prediction, either through informed record selection or by including ϵ in the vector of IM parameters.

Increased Accuracy of Vector-IM-Based Seismic Risk Assessment?

The vector-valued ground motion intensity measure (IM) consisting of spectral acceleration at two different periods is considered for seismic risk assessment of structures. The first component of the IM is the spectral acceleration at the first-mode structural period T 1. The second period is selected to increase efficiency in the estimation of seismic risk (i.e., minimizing dispersion). A method to assess vector structural fragility using a scalar global measure of structural performance is proposed. With reference to an example RC frame structure, the accuracy of prediction of the seismic risk using the considered vector IM vs. a conventional scalar IM is presented. In both cases, probabilistic seismic hazard analysis (scalar and vector) is carried out by means of a subset simulation approach that employs a stochastic model of ground motion. Results show that an effective choice of the second period T2 leads to an estimate of the seismic risk close to that obtained employing the scalar IM consisting of Sa(T1) only, while reducing the associated dispersion in the estimate. For the examined example structure, however, the reduction is negligible in light of the effort required for switching from a scalar to a vector IM.

Vector-valued intensity measures for pulse-like near-fault ground motions

A vector-valued intensity measure (IM) is shown to account for the effects of pulse-like near-fault ground motions. This class of ground motions, which are indicated by the presence of a velocity pulse, can cause large responses in structures and their effects are not well described by traditional intensity measures such as spectral acceleration at the structure’s first-mode period, S a ( T 1 ) . It is seen that the period of the velocity pulse is an important parameter affecting structural response, and a vector intensity measure which combines S a ( T 1 ) with a measure of spectral shape is much more effective at accounting for the effects of this pulse period. By performing probabilistic seismic hazard analysis for this IM and combining the results with predictions of structural response as a function of the IM, it is possible to account for near-fault effects when assessing the reliability of structures located at sites where pulse-like ground motions may occur.