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This paper examines the question of which sources of uncertainty most strongly affect the repair cost of a building in a future earthquake. Uncertainties examined here include spectral acceleration, ground-motion details, mass, damping, structural force-deformation behavior, building-component fragility, contractor costs, and the contractor's overhead and profit. We measure the variation (or swing) of the repair cost when each basic input variable except one is taken at its median value, and the remaining variable is taken at its 10th and at its 90th percentile. We perform this study using a 1960s highrise nonductile reinforced-concrete moment-frame building. Repair costs are estimated using the assembly-based vulnerability (ABV) method. We find that the top three contributors to uncertainty are assembly capacity (the structural response at which a component exceeds some damage state), shaking intensity (measured here in terms of damped elastic spectral acceleration, Sa), and details of the ground motion with a given Sa.

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... Rayleigh damping model was used in dynamic analysis. In the aspect of structural uncertainties, the randomness of structural damping ratio ξ [41,42], yield strength s f , and initial elastic modulus s E were considered. The probability distribution, mean, and coefficient of variation (CoV) of the structural parameters are listed in Table 2. ...

... The probability distribution, mean, and coefficient of variation (CoV) of the structural parameters are listed in Table 2. In the aspect of structural uncertainties, the randomness of structural damping ratio ξ [41,42], yield strength s f , and initial elastic modulus s E were considered. The probability distribution, mean, and coefficient of variation (CoV) of the structural parameters are listed in Table 2. ...

... The probability distribution, mean, and coefficient of variation (CoV) of the structural parameters are listed in Table 2. In the aspect of structural uncertainties, the randomness of structural damping ratio ξ [41,42], yield strength f s , and initial elastic modulus E s were considered. The probability distribution, mean, and coefficient of variation (CoV) of the structural parameters are listed in Table 2. ...

Seismic fragility analysis of a mega-frame with vibration control substructure (MFVCS) considering structural uncertainties is computationally expensive. Dual surrogate model (DSM) can be used to improve computational efficiency, whereas the proper selection of design of experiments (DoE) is a difficult work in the DSM-based seismic fragility analysis (DSM-SFA) method. To efficiently assess the seismic fragility with sufficient accuracy, this paper proposes an improved DSM-SFA method based on active learning (AL). In this method, the Kriging model is employed for surrogate modeling to obtain the predicted error of approximation. An AL sampling strategy is presented to update the DoE adaptively, and the refinement of the surrogate models can reduce the error of the probability result computed by the Monte Carlo (MC) simulation. A numerical example was studied to verify the effectiveness and feasibility of the improved procedure. This method was applied to the fragility analysis of an MFVCS and a mega-frame structure (MFS). The finite element models were established using OpenSeesPy and SAP2000 software, respectively, and the correctness of the MFVCS model was verified. The results show that MFVCS is less vulnerable than MFS and has better seismic performance.

... Recent studies have proposed diverse yet independent or isolated methodologies for the seismic Vulnerability or Fragility (V/F) assessment of representative buildings (Dolšek and Fajfar 2005;Dolšek 2012;Abo-El-ezz et al. 2013;D'Ayala et al. 2015;Del Gaudio et al. 2015;Hosseinpour and Abdelnaby 2017;Yamin et al. 2017;Cremen and Baker 2019). Approaches may consider empirical, expert opinion-based, analytical or hybrid methods to derive vulnerability or fragility functions (Porter et al. 2002;D'Ayala et al. 2015;Silva et al. 2018). The analytical vulnerability approach allows for an unbiased and consistent assessment that has proven to be applicable worldwide, independently of historical seismic damage data and local expertise on specific building performance (Silva et al. 2018). ...

... With the resulting EDPs, the final step is the derivation of vulnerability functions. It is important to note that the development of functions should consider a wide range of uncertainties that depend on the quality of the available information and the types of models and analyses used in each assessment (Porter et al. 2002;Wen et al. 2003;D'Ayala et al. 2015;Silva 2019). In seismic vulnerability assessment, the uncertainty is associated to seismic input, numerical modeling, material properties, damage states, costs modeling and others ). ...

... Finally, the analysis type is also considered since it can have an important influence on the results. These analysis are done independently following the One Factor at a Time (OFT) method (Porter et al. 2002). ...

Several earthquakes have affected school infrastructure, compromising the safety of students and all the educational community. These damages are not caused solely by the
action of earthquakes, but also by the lack of adequate seismic design, deficient construction practices, and lack of regulations and normative to ensure an appropriate quality for infrastructure. Therefore, to analyze how is the expected infrastructure behavior in earthquakes, this study presents a simplified methodology for the seismic vulnerability assessment of school buildings. The methodology includes several components: data collection, the characterization of Index Buildings, hazard definition, nonlinear numerical modeling of the structural response, seismic performance assessment and the vulnerability integration using a component-based approach. The novelty of the proposed methodology resides in the fact of its simplicity and robustness obtained by combining a simplified non-linear incremental static analysis together with a component-based vulnerability derivation methodology to assess the behavior of school buildings. This methodology is applied to a set of 11 Reinforced Concrete school building types representing common structural systems and seismic design levels. A number of sensitivity analyses are also carried out, varying the geometry, the foundation-soil flexibility, the mechanical properties of infill masonry walls, the non-structural elements and the analysis type, showing the versatility and reliability of the proposed methodology.

... Samples of the parameters are generated by Monte Carlo methods for simulating thousands of realizations of the model [7] . Sensitivity analyses provide a straightforward method for interpreting the effects of modeling uncertainties on response quantities of interest (Liel et al (2009) [8] , Porter et al (2002) [9] , Lee and Mosalam (2005) [10] , Ibarra and Krawinkler (2005) [11] , Aslani (2005) [12] , and Esteva and Ruiz (1989) [13] ). The effect of each random variable (RV) on the structural response is first evaluated by varying each modeling parameter, one-at-a-time, and recording the corresponding structural response. ...

... Samples of the parameters are generated by Monte Carlo methods for simulating thousands of realizations of the model [7] . Sensitivity analyses provide a straightforward method for interpreting the effects of modeling uncertainties on response quantities of interest (Liel et al (2009) [8] , Porter et al (2002) [9] , Lee and Mosalam (2005) [10] , Ibarra and Krawinkler (2005) [11] , Aslani (2005) [12] , and Esteva and Ruiz (1989) [13] ). The effect of each random variable (RV) on the structural response is first evaluated by varying each modeling parameter, one-at-a-time, and recording the corresponding structural response. ...

... The equivalent damping ratio () has been usually selected to be 5%, but may vary for the same structure between ground motions of different or equal intensity, depending on the hysteretic energy dissipated by the components. According to a study conducted by Porter [9] , the variability for this parameter can be fit through a Normal PDF with a COV in the range of 0.3 to 0.4. In this study the lower bound is select, e.g. ...

Reinforced concrete (RC) walls are commonly used for buildings in regions of high seismicity to conform partly or totally their lateral load-resisting system. Among the features that influence the seismic response of RC walls are their geometry (e.g., I-, L-or C-shaped cross-section, cross-sectional aspect ratio), material properties, steel reinforcement detailing, confinement provisions, axial load ratio and shear span ratio. Several analytical models for nonlinear analysis of RC walls are available for research and design, programed based on different assumptions of material and/or element formulations (e.g. fiber-or strut-and-tie-based approaches, displacement-or force-based formulations with and without inelastic shear-flexure interaction). Studies have been conducted on the capability of these diverse approaches to simulate adequately the nonlinear behavior of RC walls with known experimental results, demonstrating their suitability for a wide range of engineering problems. However, other blind-prediction contests have also demonstrated that predicting accurately the actual response of a specimen under dynamic shaking is difficult, and the recorded dispersion in the results among team of experts is considerable; even when the geometric and material properties are well described, and the ground acceleration history is previously known. To determine the response sensitivity to variations in parameters of macroscopic models, sensitivity analysis based on Monte Carlo simulation is used through generation of plausible realizations in the Simcenter platform. RC wall specimen previously tested in the laboratory were used to validate two modeling approaches: (i) fiber forced-based model (FIBER), and (ii) the Nonlinear Truss model (NLT). For the NLT and the FIBER model, varied parameters for the formulations included material constitutive behavior of concrete and steel, axial load, mass, and damping ratio. The article quantifies the impact of modeling parameters in structural response, isolating in part, the record-to-record variability. Nevertheless, results indicate that the latter is the most important source of structural response variance.

... This method has been applied in the seismic sensitivity analysis of structures in many previous studies, e.g. (Porter et al., 2002;Barbato et al., 2010;Kim et al., 2011). ...

... More discussion about these methods can be found elsewhere (e.g. Porter et al., 2002). In the current study, the variation of plastic hinge property is obtained by scaling every force and deformation value on the force-deformation relationship by multiplying a single, random variable (random strength, constant stiffness). ...

After large economic losses followed Northridge earthquake, the need for simple and realistic quantitative seismic risk-analysis tool becomes obvious. The present study contributes to satisfy this need by developing a simple methodology for seismic life-cycle cost (LCC) estimation. This methodology accounts for accuracy of LCC modeling as well as simplicity of application. Accuracy is achieved through incorporating the effect of aleatory and epistemic uncertainty in the LCC estimation framework. Simplicity is achieved, firstly, by considering equivalent single-degree-of-freedom (ESDOF) system instead of the full multi-degree-of-freedom (MDOF) structure. Further simplification is achieved by reducing the computational cost significantly through eliminating the full construction of fragility curves and incremental dynamic analysis curves. Instead of the latter curves, an approximate fragility curve (AFC) and localized incremental dynamic analysis (LIDA) curve are used. Moreover, a probabilistic simple closed-form solution for loss estimation is used. This solution considers the randomness and the uncertainty in seismic demand and structural capacity.
A steel jacket offshore platform is used as a case study. The soil-pile-structure interaction (SPSI) is considered in developing the numerical model of the offshore platform with actual soil-in-situ characteristics. In order to investigate the importance of the seismic design method on LCC estimation, different design philosophies are used for the seismic design of the offshore platform, such as force-based and performance-based designs. In order to examine the effect of high ductile structure system on LCC, numerical models are developed using buckling-restrained braces (BRB) system and compared with the conventional bracing in the as-built platform structure.
As an application on the proposed LCC methodology, a comparative assessment study based on deterministic sensitivity analysis is conducted to investigate the relative importance of different uncertain variables on the LCC estimation. This sensitivity analysis is conducted using different methods such as tornado diagram analysis (TDA), first-order second-moment (FOSM) and Latin hypercube sampling (LHS). The considered uncertain parameters are categorized with regard to different sources such as, structural capacity, seismic hazard, soil-pile-structure interaction, loss estimation, and LCC formulation.
This study introduced a new relative stiffness index, which relates the stiffness of the sub-structure and super-structure. Based on this index, the results have shown the significant effect of SPSI on the seismic performance and consequently on the seismic LCC estimation of the platform models. However, it is found that for system designed with large ductility, i.e. large response modification factor, R, simplified SPSI modeling can be used to reduce the computational cost especially for the preliminary design stage.
In order to have an insight into the expected LCC estimation through structural seismic behavior, a seismic performance evaluation is conducted on the platform models. From the seismic LCC standpoint, using systems designed with large R factor, such as BRB models, provide more economical alternative, even though the initial cost is higher, compared to models designed with small R factor, such as conventional bracing. The displacement-based design (DBD) method shows that increasing the structure elements cross sections, to fulfill the required drift limit, may increase the initial cost of the structure; however, it decreases the total LCC when compared to the performance plastic-design method. On the other hand, the force-based design shows higher LCC estimations compared to the performance-based design.
The sensitivity analysis results show that loss estimation and seismic hazard uncertain variables have a more dominant influence on the LCC variability compared to the other variables. The LCC is found to be particularly sensitive to the drift-intensity regression coefficient “b” and seismic hazard slope “k”. Among the structural uncertain parameters, the variability in plastic hinge strength and modal damping ratio have the most significant impact on the LCC. Soil-pile friction variable proves to be the most important uncertain variables among the soil-pile modeling parameters. The initial cost has the most influential effect among the different cost items of LCC estimation. The variability in parameters such as yield strength, Young’s modulus, pile driving factors, maintenance cost,…etc, turned out to have insignificant impact on the LCC variation.

... In the OAT method, each uncertain parameter is perturbed individually and its effect on response is tracked to provide insight into only the local significance of behavior. However, this method has been used by many researchers [31,[44][45] to initial study of uncertain parameters due to some of its significant advantages: 1) comparability of results with respect to one central point in the input space where all parameters are kept on their central or median values; 2) unambiguously assigning change in response to perturbed input parameter. Porter et al. [44] used the OAT method to analyze the loss sensitivity of an RC building to the variety of uncertain parameters in the PBEE methodology. ...

... However, this method has been used by many researchers [31,[44][45] to initial study of uncertain parameters due to some of its significant advantages: 1) comparability of results with respect to one central point in the input space where all parameters are kept on their central or median values; 2) unambiguously assigning change in response to perturbed input parameter. Porter et al. [44] used the OAT method to analyze the loss sensitivity of an RC building to the variety of uncertain parameters in the PBEE methodology. They showed that repair cost is more sensitive to the damage of structural components and ground motion intensity than modeling parameters at a pre-collapse intensity level. ...

Uncertainty in parameters that define the behavior of yielding components in structures has been shown to affect the validity of predicted near-collapse behavior. After a large-magnitude seismic event, the effect of uncertainties on predicted seismic demands can be intensified by upcoming aftershocks. On the other hand, cumulated damage through seismic sequences should be quantified by demand parameters that are able to properly present the capacity loss of damaged buildings. Residual drifts, an important measure of inelastic deformations, have a significant role in post-mainshock assessment of structures, and of interest in this study is to quantify changes in the sensitivity of residual drifts to the uncertainty of modeling parameters during sequential seismic events. In addition, the relationship between residual drifts and peak transient drifts is investigated. The study is based on two prototype 3- and 9-story steel moment resisting frames subjected to two levels of mainshock intensities that are followed by aftershocks. 20 as-recorded seismic sequences recorded at far-field accelerographic stations are considered. Sensitivity analysis is performed using the one-at-a-time (OAT) method. It was found that seismic demands are more sensitive to strength modeling parameters and beam ductility modeling parameters, and these sensitivities increase by an average of 20% during aftershocks. As-recorded aftershocks increase residual drift demands up to 19 and 15% at risk-targeted maximum considered earthquake MCER level for the 3- and 9-story frames, respectively, while aftershocks increase the dispersion of peak drift demands considerably.

... Lamprou et al. 10 estimated the effect of uncertain parameters associated with seismic hazard and component-level damage on expected life-cycle seismic repair costs for a four-story concrete moment frame building. Finally, Porter et al. 11 evaluated the relative contribution of various ground motion, building, and economic parameters to overall seismic performance (i.e. repair cost) uncertainty for a 1960's high-rise nonductile moment-frame building. ...

... Building Loss Ratio). While the physical dimensions of the building examined in Porter et al. 11 are roughly equivalent to the 7story building investigated in this study and the underlying seismic performance methodology examined is very similar, the type of sensitivity analysis conducted here is fundamentally different. Porter et al. carried out a deterministic sensitivity analysis 14 , which used tornado diagrams to demonstrate the effects of changing different input variables one-at-a-time to various discrete values, while keeping all others constant in a baseline model. ...

Earthquake loss assessment procedures for individual buildings can be a useful tool for various stakeholders, including building owners, insurers, and lenders. However, it is often not possible to provide complete information for the required inputs to these procedures, since there is substantial cost and effort associated with gathering necessary data. It is therefore important to understand how different inputs to these procedures (building information/ground shaking intensity) impact the loss predictions. This can be done via sensitivity analyses. We conduct variance-based sensitivity analyses for the FEMA P-58 methodology, a building-specific seismic performance assessment procedure that is making its way into seismic design and risk analysis practice. We determine how variations in different input variables of the methodology affect predictions of Building Loss Ratio and Re-occupancy Time, and benchmark calculated sensitivities using the HAZUS earthquake loss estimation methodology. We also quantify additional uncertainty in consequence predictions caused by uncertainty in input variables. We use an example site in downtown Los Angeles and consider a 7-story and a 14-story building. Of the six inputs considered in the analyses, Building Loss Ratio predictions are most sensitive to shaking intensity and building age, while Re-occupancy Time predictions are most sensitive to shaking intensity and the type of lateral system/building period. The largest additional uncertainties in Building Loss Ratio predictions are caused by the building's lateral system or age (or both) being unknown. The results of this study provide an enhanced understanding of the interaction between inputs and consequence predictions of the P-58 methodology.

... In the probabilistic seismic demand analysis (PSDA) of bridge structures, it is necessary to investigate the effects of various uncertain parameters on some typical bridge EDPs (as presented in Table 3) of the case-study bridge, and based on a series of previous studies (Porter et al 2002;Celik and Ellingwood 2010;Zhong et al. 2018;Wu et al. 2018), the sensitivity analyses of seismic responses for different bridge components to the modeling related uncertain parameters are performed herein through the tornado diagram technique. According to the work done by Celik andEllingwood 2010, Zhong et al. (2018), and Wu et al. (2018), the sensitivity analysis with the tornado diagram technique can be carried out as follows. ...

... Pseudo-acceleration spectra Median spectra E1 level earthquake spectra T 1 =1.33 sec Pseudo-acceleration spectra Median spectra E2 level earthquake spectra T 1 =1.33 sec Fig. 3 Response spectra of ground motions for sensitivity analysis: a E1 level and b E2 level (Porter et al 2002;Celik and Ellingwood 2010;Zhong et al 2018). For example, Figs. 4, 5, 6 ,7 and 8 illustrate the tornado diagram for the seismic responses, Φ L , δ LRB_L , δ PTEB_L , Δ Abut_active , and Δ Abut_passive , under E1 and E2 designed levels of ground motions. ...

This paper proposes an alternative time-dependent seismic fragility assessment framework considering the variable correlation of structural random parameters for aging highway bridges subject to non-uniform chloride-induced corrosion attacks. The proposed systematic framework is implemented to perform a probabilistic time-dependent seismic fragility assessment for a typical multi-span reinforced concrete continuous girder (MSRCCG) bridge. Effects of non-uniform chloride-induced deterioration on the time-evolving seismic capacity, seismic demand of reinforced concrete (RC) columns and the time-dependent seismic fragility of the case-study bridge are investigated using nonlinear sectional moment-curvature and nonlinear time history analysis. Furthermore, this paper performs comparative studies to investigate the influence of variable correlation of structural random parameters on the time-variant seismic capacity, seismic demand of RC columns and time-dependent seismic fragility of the case study bridge. The results indicate the following conclusions: (1) Non-uniform chloride-induced corrosion may change the vulnerable position and the damage mechanisms of RC columns; (2) Due to non-uniform chloride-induced deterioration, the flexural capacity and curvature ductility of RC columns may exhibit a nonlinear reduction, while there is a nonlinear accelerated growth of time-dependent seismic fragility for aging highway bridges along their service lives; (3) The time-variant seismic capacity (i.e., the flexural capacity and curvature ductility) and seismic demand of RC columns tends to have a certain reduction and increase by ignoring the variable correlation of structural random parameters, respectively; and (4) The time-dependent seismic vulnerabilities of aging highway bridges may be overestimated by ignoring the variable correlation of structural random parameters.

... Seismic loss assessment methodologies have received a growing interest over the past 20 years as a method to manage the consequences of earthquakes on structures and infrastructures (e.g. see (Porter et al. 2002), (Aslani and Miranda 2005), (Ramirez and Miranda 2012), (Günay and Mosalam 2013), (Hasik et al. 2018), among others). Modern Performance Based Earthquake Engineering (PBEE) concepts were first developed following high-impact earthquakes that occurred in the mid-1990s and the first generation of PBEE procedures (SEAOC 1995) established a framework that was able to integrate the performance of structures and infrastructures at several seismic hazard levels. ...

... It is important to note herein that a comparison of the obtained results in absolute terms should only be performed with buildings located in Europe and with studies using European fragility and loss assembly functions. Since the loss assembly functions have been found to significantly affect the overall losses (Porter et al. 2002), comparing these results with those of studies that involve data from other sources was considered to be inadequate. Nevertheless, results from such studies can be used to analyse and compare the relative value of different loss components to extract relevant trends. ...

The proposed study examines the propagation of uncertainty associated with the angle of seismic incidence of a group of ground motions, as well as to that of the ground motion group size, to the expected seismic loss estimates of reinforced concrete buildings. Six buildings with infilled frame systems are studied, representative of non-seismically designed structures typical of southern European practice. Their monetary losses are computed using a performance-based earthquake engineering framework, which integrates the site-specific seismic hazard, structural response, damage to building components and contents, and the resulting costs (repair, demolition, reconstruction). To estimate monetary losses, an inventory of the structural and non-structural elements is compiled and existing damage and cost data/functions are employed. Seismic loss estimates account for both the probability of collapse and the probability of demolition as a result of excessive residual storey drifts. Multiple stripe analysis is performed for this purpose using numerical models capable of simulating the relevant limit states up to collapse. Results are presented in terms of expected losses conditional on the ground motion intensity and expected annual losses, which are determined by integrating the former with the seismic hazard curve of the site. Results show that the comparative effect of the ground motion group size in the expected annual losses is much more important when compared to that of the angle of seismic incidence, whose influence is shown to be less significant and mostly concentrated on the variability of the results.

... In these works, output is commonly computed first with all input variables set to their medians, and then setting one input variable at a time to a lower or upper fractile (typically 16% and 84%): the resulting variations are represented with tornado diagrams. Along the same lines, Porter et al. (2002) [27] used the OAT approach to carry out a deterministic sensitivity analysis of building loss estimates to major uncertain variables, which include spectral acceleration, mass, damping and structural force-deformation behaviour. Tornado diagrams were also used by Pourreza et al. (2020) [28] to eliminate the least influential modelling variables on the collapse capacity of a five-storey steel special moment resisting frame (SMRF). ...

... In these works, output is commonly computed first with all input variables set to their medians, and then setting one input variable at a time to a lower or upper fractile (typically 16% and 84%): the resulting variations are represented with tornado diagrams. Along the same lines, Porter et al. (2002) [27] used the OAT approach to carry out a deterministic sensitivity analysis of building loss estimates to major uncertain variables, which include spectral acceleration, mass, damping and structural force-deformation behaviour. Tornado diagrams were also used by Pourreza et al. (2020) [28] to eliminate the least influential modelling variables on the collapse capacity of a five-storey steel special moment resisting frame (SMRF). ...

Modern society's very existence is tied to the proper and reliable functioning of its Critical Infrastructure (CI) systems. In the seismic risk assessment of an infrastructure, taking into account all the relevant uncertainties affecting the problem is crucial. While both aleatory and epistemic uncertainties affect the estimate of seismic risk to an infrastructure and should be considered, the focus herein is on the latter. After providing an up-to-date literature review about the treatment of and sensitivity to epistemic uncertainty, this paper presents a comprehensive framework for seismic risk assessment of interdependent spatially distributed infrastructure systems that accounts for both aleatory and epistemic uncertainties and provides confidence in the estimate, as well as sensitivity of uncertainty in the output to the components of epistemic uncertainty in the input. The logic tree approach is used for the treatment of epistemic uncertainty and for the sensitivity analysis, whose results are presented through tornado diagrams. Sensitivity is also evaluated by elaborating the logic tree results through weighted ANOVA. The formulation is general and can be applied to risk assessment problems involving not only infrastructural but also structural systems. The presented methodology was implemented into an open-source software, OOFIMS, and applied to a synthetic city composed of buildings and a gas network and subjected to seismic hazard. The gas system's performance is assessed through a flow-based analysis. The seismic hazard, the vulnerability assessment and the evaluation of the gas system's operational state are addressed with a simulation-based approach. The presence of two systems (buildings and gas network) proves the capability to handle system interdependencies and highlights that uncertainty in models/parameters related to one system can affect uncertainty in the output related to dependent systems.

... It is necessary to investigate the effects of various uncertain parameters on some typical EDPs (as presented in Table 2) of the case-study bridge, and based on a series of previous studies (Porter et al 2002;Celik and Ellingwood 2010;Zhong et al. 2018;Wu et al. 2018), sensitivity analyses of seismic responses for different bridge components to the modeling related uncertain parameters are performed herein using the tornado diagram technique. According to the work done by Celik and Ellingwood (2010), Zhong et al. (2018), and Wu et al. (2018), sensitivity analysis with the tornado diagram technique can be performed as following. ...

... Then, this procedure is carried out repeatedly for each of the 22 modeling related uncertain parameters, in turn, varying only one at a time and setting each parameter to its lower bound (5 th percentile) and upper bound (95 th percentile) while holding the remaining parameters at their median values. Furthermore, after a series of NLTHAs are performed, the variation in median values of the seismic responses with each modeling uncertain parameter can be displayed through a tornado diagram (Porter et al 2002;Celik and Ellingwood 2010;Zhong et al 2018). For example, Figs. 4, 5, 6, 7 and 8 illustrate the tornado diagrams for the seismic responses, Φ L , δ LRB_L , δ PTEB_L , Δ Abut_active , and Δ Abut_passive , under E1 and E2 designed levels of ground motions. ...

The stability assessment of a soil embankment in the flooding season has attracted increasing attention in recent years. The current study performs a coupled hydraulic-mechanical analysis of an embankment subjected to water level fluctuation. The coefficient of permeability of embankment soils is represented by a uniform random field with upper and lower bounds. The random finite element method is incorporated for the solution of such coupled analysis. The results indicate that the horizontal correlation length of the permeability field has significant effects on the seepage patterns, leading to a greater variability in the total flow rate, since water flows more easily along the regions of higher permeability. In addition, the failure mechanism resulted from the coupled analysis shows that a rise of water level plays a predominant role in the instability of the embankment, compared with the generated irregular seepage force. The factor of safety of the embankment decreases with the increase of upstream water level, and the corresponding failure mode also changes significantly. The findings from this study can serve as a guidance for the design or reinforcement of a soil embankment and provide a new insight into the solution of green life cycle and sustainable development of embankment engineering.

... Several studies (e.g. D'Ayala and Meslem 2013; Porter et al. 2002, Lee et al., 2005 observed that capacity uncertainty has a low effect on the slight and moderate damage level. Instead, higher impact, comparable to that one related to demand uncertainty, can be found for the collapse state (Ibarra and Krawinkler 2003). ...

Within the 2019–2021 research agreement between the Civil Protection Department (DPC) and the Network of University Laboratories for Earthquake Engineering (ReLUIS), the work package WP4 “Seismic Risk Maps—MARS” is specifically devoted to update the 2018 release of the Italian National Seismic Risk Assessment. To this end, the previously considered models of hazard, exposure and vulnerability will be critically reviewed and updated by taking advantage also from the results deriving from other WPs of the DPC-ReLUIS research project. In the present paper some of the most relevant aspects that are being introduced in the development of the new Italian risk maps have been described and shortly analysed. First, a significant upgrade of the vulnerability model implemented in the new version of the platform used for risk calculation (IRMA) is proposed, where reference to the six EMS-98 classes is made also considering regional vulnerability features. Further, empirical data from observed real damage are integrated with results from numerical simulations (mechanical approach), in particular for reinforced concrete buildings. Finally, some special construction types such as schools, churches and bridges are included in order to provide a more comprehensive view of the national risk.

... For example, in earthquake engineering, the description of time-histories through stochastic ground motion models dependent on seismological parameters (Bijelić et al., 2018;Vlachos et al., 2018); in coastal risk estimation surge modeling numerical tools are dependent on atmospheric storm characteristics (Resio et al., 2007). Beyond the hazard variability, uncertainties related to parameters of the structural model or generalized system model (for applications not examining directly structural risk) and to the characteristics for describing performance are also recognized as important for inclusion in risk estimation (Porter et al., 2002). The term "system" will be used herein to describe the application of interest; e.g., this may pertain to a building model, to an infrastructure network, or to a soil-structure interaction system configuration. ...

https://simcenter.designsafe-ci.org/media/filer_public/a8/e5/a8e56717-6c92-444e-8aa3-296c23a8e210/nheri_simcenter_state_of_the_art_report_2nd_edition_2021.pdf

... The COV for the mass is based on [65]. However, there are other references that specify a higher COV, e.g., [83]. ...

The impact of a disaster is spread over a region and thus the corresponding risks can be managed effectively by carefully considering the community impact. Since structural design codes regulate the safety levels of structures, it is appropriate to consider a community-level objective in the determination of the safety levels stipulated in the structural design codes. However, evaluating community disaster impact requires consideration of loss interdependency among different buildings, which could be a complex task. Furthermore, implementing a community-level objective to design safety level determination requires the establishment of feasible methods to calculate it in a reasonable time. This paper develops a simple and viable framework for community-level objective-based design safety target optimization for multiple building classes subjected to seismic hazard. To reduce the computation cost, the framework employs an efficient procedure of using an artificial neural network to approximate the seismic response of buildings with common characteristics (occupancy use, and type and size of lateral resisting system). The methodology is illustrated for optimizing the target reliability indices of office and hospital building classes exposed to seismic hazard, with minimizing regional economic cost as objective. Simple loss and interdependency models are used for this illustration due to lack of available complex models, which can be replaced by more recent and complex models to improve accuracy of the analysis once they become available.

... To circumvent problems associated with unidentifiability of model parameters, various methods for quantifying and visualizing sensitivity have been developed. Tornado diagrams, which sort parameters based on the sensitivity of measured response to a designated variation in their value, were selected for the current study [52]. This is a simple, single-variate, sensitivity analysis in which each unknown model parameter is individually perturbed around its true value by ±5% with other parameters being fixed. ...

A novel approach to deal with nonlinear system identification of civil structures subjected to unmeasured excitations is presented. Using only sparse global dynamic structural response, mechanics-based nonlinear finite element (FE) model parameters and unmeasured inputs are estimated. Unmeasured inputs are represented by a time-varying autoregressive (TAR) model. Unknown FE model parameters and TAR model parameters are jointly estimated using an unscented Kalman filter. The proposed method is validated using numerically simulated data from a 3D steel frame subjected to seismic base excitation. Six material parameters and one component of the base excitation are considered as unknowns. Excellent input and model parameter estimations are obtained, even for low order TAR models.

... For example, in earthquake engineering, the description of time-histories through stochastic ground motion models dependent on seismological parameters (Bijelić et al., 2018;Vlachos et al., 2018); in coastal risk estimation surge modeling numerical tools are dependent on atmospheric storm characteristics (Resio et al., 2007). Beyond the hazard variability, uncertainties related to parameters of the structural model or generalized system model (for applications not examining directly structural risk) and to the characteristics for describing performance are also recognized as important for inclusion in risk estimation (Porter et al., 2002). The term "system" will be used herein to describe the application of interest; e.g., this may pertain to a building model, to an infrastructure network, or to a soil-structure interaction system configuration. ...

This report is a product of the NHERI SimCenter under the auspices of the U.S. National Science Foundation (NSF). It provides an overview and review of simulation requirements and software tools for natural hazards engineering (NHE) of the built environment. The simulations discussed in this report are an essential component of research to address the three grand challenge areas and associated research questions outlined in the NHERI Science Plan. These grand challenges entail: (1) identifying and quantifying the characteristics of natural hazards that are damaging to civil infrastructure and disruptive to communities; (2) evaluating the physical vulnerability of civil infrastructure and the social vulnerability of populations in at-risk communities; and (3) creation of technologies and tools to design, retrofit, and operate a resilient and sustainable infrastructure for the Nation. Accordingly, required simulation technologies encompass a broad range of phenomena and considerations, from characterization and simulation of natural hazards and their damaging effects on buildings and civil infrastructure, to quantifying the resulting economic losses, disruption, and other consequences on society. Ultimately, the goal is to enable high-fidelity and high-resolution models in regional simulations that can support technological, economic, and policy solutions to mitigate the threat of natural hazards.
The natural hazards addressed in this report include earthquakes, tsunami, storm and tornado winds, and storm surge. While not an exhaustive list of all possible natural hazards, these are the hazards addressed under NSF's NHERI research program. The first chapter of the report provides an introduction to the SimCenter and its goals, including an overview of the plans and status for software tool development. The subsequent chapters of the report are organized into five parts in a sequential fashion, including: (1) simulation methods to characterize the natural hazards; (2) response simulation of structural and geotechnical systems and localized wind and water flows; (3) quantifying the resulting damage and its effects on the performance of buildings, transportation systems, and utility infrastructure systems; (4) strategies and emerging tools to model recovery from natural disasters; and (5) the cross-cutting applications of uncertainty quantification methods and artificial intelligence to NHE.
Owing to the broad scope of the simulation topics, this review of the state of the art is presented with the goal of educating and informing researchers---including both simulation tool developers and users---on key requirements and capabilities within each simulation topic. The report is also a guide to the on-going development of simulation capabilities by the NSF NHERI SimCenter. Each chapter of the report begins with a brief overview of the purpose of the simulation component, including a discussion of the goals of the analysis (what is being calculated), the underlying physics or principles involved in the simulation, common modeling assumptions and simplifications, and typical input and output of the simulations.
With the aim of taking stock of computational simulation capabilities, informing the NHERI community of research advances to date, and positioning the work of the NHERI SimCenter as it relates to computational simulation, the summaries identify and review commonly used simulation software that is widely known and used for research in academia and industry. Particular emphasis is placed on open-source or other software that is hosted on DesignSafe or is otherwise easily accessible to researchers. Summary tables of the simulation software tools is provided as an appendix to the report. In addition to summarizing the state of the art in the various topic areas, each chapter of the report identifies major research gaps and needs, with the intent that these could motivate research proposals to NSF or other agencies that will lead to future advancements.
This report is an update to a State of Art Report that the SimCenter first published in February 2019. This update reflects comments and suggestions that were solicited from leading researchers in NHE. It includes new chapters on disaster recovery modeling and applications of artificial intelligence technologies to NHE. Readers are encouraged to contribute feedback regarding this report and the SimCenter simulation tool development through the online SimCenter Forum at http://simcenter-messageboard.designsafe-ci.org/smf/ .

... The first refers to model parameter uncertainty, i.e., the variability induced by uncertainties in the model parameters (strength, stiffness, mass, dimensions, etc.), and the second to model type uncertainty, or the variability that results from different modelling choices (e.g., 3D versus 2D model assumptions, type of finite element or damping model, the modeling or not of foundations and soil, etc.). Up until now, several studies (O'Reilly and Sullivan 2018; Kazantzi et al. 2014;Ibarra and Krawinkler 2011;Jalayer et al. 2010;Vamvatsikos and Fragiadakis 2010;Dolsek 2009;Liel et al. 2009;Kwon and Elnashai 2006;Wen et al. 2003;Porter et al. 2002;Yun et al. 2002) have investigated mainly model parameter uncertainty, finding small to moderate effects in most cases, especially for modern structures. Contrarily, on the subject of model type uncertainty, due to the practically unbounded range of options available, few comprehensive studies exist (e.g., Lignos et al. 2013;Chi et al. 1998). ...

Finite-element models of varying sophistication may be employed to determine a building’s seismic response with increasing complexity, potentially offering a higher fidelity at the cost of the computational load. To account for this effect on the reliability of performance assessment, model-type uncertainty needs to be incorporated as distinct to the uncertainty related to a given model’s parameters. At present, only placeholder values are available in seismic guidelines. Instead, we attempt to quantify them accurately for a modern 20-story steel moment-resisting frame. Different types of three-dimensional (3D), two-dimensional (2D) multibay, and 2D single-bay multidegree-of-freedom models are investigated, together with their equivalent single-degree-of-freedom ones, to evaluate the model dependency of the response both within each broad model category, as well as among different categories. In conclusion, ensemble values are recommended for the uncertainty in each model category showing that for the perfectly-symmetric perimeter-frame P-Δ sensitive building under investigation, the uncertainty stemming from 3D versus 2D or distributed versus lumped plasticity models is lower than the governing record-to-record variability.

... been used by many researchers investigating various aspects of sensitivity analyses(Porter et al. 2002;Lee and Mosalam 2005;Na et al. 2008;Fellin et al. 2010;Shin and Kim 2014) ...

This chapter proposes nonlinear multiple degree-of-freedom (MDOF) models for city-scale nonlinear time-history analyses in an attempt to predict seismic damage to buildings in large urban areas. The computational models and the corresponding parameter determination methods are developed for multi-story masonry buildings, reinforced concrete and steel frames and tall buildings. The parameter uncertainties of the MDOF models and their impacts on the simulation results are also discussed. A numerical coupling scheme for city-scale nonlinear time-history analyses considering the interaction of densely distributed buildings in a city and the site (i.e., site-city interaction, or SCI for short) is also proposed. Finally, to take full consideration of the diversity of the structural types, available data, and simulation scenarios in a real application of the seismic-damage simulation to urban buildings, a multiple level-of-detail (LOD) simulation framework is established.

... The tornado diagram, commonly used in decision analysis, is an effective way of representing uncertainties. It has been used in sensitivity analysis in earthquake engineering (e.g., Porter et al. [2002]) and probabilistic seismic evaluation of structural components and systems (e.g., Lee and Mosalam [2005]). The tornado diagram consists of a set of horizontal bars, referred to as swings, one for each source of uncertainty (random variable). ...

Over the past decade, several long-duration subduction earthquakes took place in different locations around the world, e.g., Chile in 2010, Japan in 2011, China in 2008, and Indonesia in 2004. Recent research has revealed that long-duration, large-magnitude earthquakes may occur along the Cascadia subduction zone of the Pacific Northwest Coast of the U.S. The duration of an earthquake often affects the response of structures. Current seismic design specifications mostly use response spectra to identify the hazard and do not consider duration effects. Thus, a comprehensive understanding of the effect of the duration of the ground motion on structural performance and its design implications is an important issue.
The goal of this study was to investigate how the duration of an earthquake affects the
structural response of special concentric braced frames (SCBFs). A comprehensive
experimental program and detailed analytical investigations were conducted to understand and quantify the effect of duration on collapse capacity of SCBFs, with the goal of improving seismic design provisions by incorporating these effects. The experimental program included large-scale shake table tests, and the analytical program consisted of pre-test and post-test phases. The pre-test analysis phase performed a sensitivity analysis that used OpenSees models preliminarily calibrated against previous experimental results for different configuration of SCBFs. A tornado-diagram framework was used to rank the influence of the different modeling parameters, e.g., low-cycle fatigue, on the seismic response of SCBFs under short- and long-duration ground motions. Based on the results obtained from the experimental program, these models were revisited for further calibration and validation in the post-test analysis.
The experimental program included three large-scale shake-table tests of identical single-story single-bay SCBF with a chevron-brace configuration tested under different ground
motions. Two specimens were tested under a set of spectrally-matched short and long-duration ground motions. The third specimen was tested under another long-duration ground motion. All tests started with a 100% scale of the selected ground motions; testing continued with an everincreasing ground-motion scale until failure occurred, e.g., until both braces ruptured. The shake table tests showed that the duration of the earthquake may lead to premature seismic failure or lower capacities, supporting the initiative to consider duration effects as part of the seismic design provisions. Identical frames failed at different displacements demands because of the damage accumulation associated with the earthquake duration, with about 40% reduction in the displacement capacity of the two specimens tested under long-duration earthquakes versus the
short-duration one.
Post-test analysis focused first on calibrating an OpenSees model to capture the
experimental behavior of the test specimens. The calibration started by matching the initial stiffness and overall global response. Next, the low-cycle fatigue parameters were fine-tuned to properly capture the experimental local behavior, i.e., brace buckling and rupture. The post-test analysis showed that the input for the low-cycle fatigue models currently available in the literature does not reflect the observed experimental results. New values for the fatigue parameters are suggested herein based on the results of the three shake-table tests.
The calibrated model was then used to conduct incremental dynamic analysis (IDA)
using 44 pairs of spectrally-matched short- and long-duration ground motions. To compare the effect of the duration of ground motion, this analysis aimed at incorporating ground-motion variability for more generalized observations and developing collapse fragility curves using different intensity measures (IMs). The difference in the median fragility was found to be 45% in the drift capacity at failure and about 10% in the spectral acceleration (Sa). Using regression analysis, the obtained drift capacity from analysis was found to be reduced by about 8% on average for every additional 10 sec in the duration of the ground motion.
The last stage of this study extended the calibrated model to SCBF archetype buildings to
study the effect of the duration of ground motion on full-sized structures. Two buildings were studied: a three-story and nine-story build that resembled the original SAC buildings but were modified with SCBFs as lateral support system instead of moment resisting frames. Two planer frames were adopted from the two buildings and used for the analysis. The same 44 spectrally-matched pairs previously used in post-test analysis were used to conduct nonlinear time history analysis and study the effect of duration. All the ground motions were scaled to two hazard levels for the deterministic time history analysis: 10% exceedance in 50 years and 2% exceedance in 50 years. All analysis results were interpreted in a comparative way to isolate the effect of duration, which was the main variable in the ground-motion pairs. In general, the results showed that the analyzed SCBFs experienced higher drift values under the long-duration suite of ground motions, and, in turn, a larger percentage of fractured braces under long-duration cases. The archetype SCBFs analysis provided similar conclusions on duration effects as the experimental and numerical results on the single-story single-bay frame.

... Tornado charts are common in decision analysis [2] , and are suitable for depicting sensitivity analysis results. Several research studies adopted using tornado charts in different domains, like retrofitting of concrete columns [3] , earthquake engineering [4] , and nonlinear finite element analysis of buckling restrained braces [5] . A typical tornado chart consists of horizontal bars called swings. ...

This article provides a wide range of circular columns strength values under different loading conditions. The provided strength values are dependent on various parameters including the longitudinal and transverse reinforcement ratios. Results for GFRP, steel and hybrid reinforcement configurations are provided. The results were collected from analysis output files of more than 60,000 columns, and tabulated in a form that is suitable for generating analytical strength curves. The provided data format allows the generation of strength curves for a wide range of slenderness ratios and the applied load eccentricities. Inspecting the analytical strength curves could provide insights on the slenderness limits for maintaining specific strength thresholds. Also, further investigations of data could provide a group of recommendations to avoid longitudinal and transverse reinforcement underutilization. Additional data processing could provide axial load-bending moment interaction diagrams for different columns` configurations taking into consideration the slenderness effects. The use of interaction diagrams in inspecting slender columns behavior is a ubiquitous subject that has been utilized in many recent research papers. Moreover, the results of a sensitivity analysis are provided within the article.

... In the probabilistic seismic demand analysis (PSDA) of bridge structures, it is necessary to investigate the effects of various uncertain parameters on some typical bridge EDPs (as presented in Table 3) of the case-study bridge, and based on a series of previous studies (Porter et al 2002;Celik and Ellingwood 2010;Zhong et al. 2018;Wu et al. 2018), the sensitivity analyses of seismic responses for different bridge components to the modeling related uncertain parameters are performed herein through the tornado diagram technique. According to the work done by Celik andEllingwood 2010, Zhong et al. (2018), and Wu et al. (2018), the sensitivity analysis with the tornado diagram technique can be carried out as follows. ...

This paper proposes an alternative time-dependent seismic fragility assessment framework for aging highway bridges considering the non-uniform chloride-induced corrosion and various modeling uncertainty parameters. Firstly, sensitivity analysis with the tornado diagram technique is performed to determine the sensitivity of some typical bridge engineering demand parameters (EDPs) to 22 modeling related uncertain parameters, and then 10 critical parameters are identified. Subsequently, based on a series of nonlinear time history analyses (NLTHAs) on the sample models generated by using the Latin hypercube sampling (LHS) method, comparative studies for the time-invariant and time-evolving seismic response, as well as the time-dependent seismic fragility estimates incorporating different levels of uncertainty are performed, respectively. It is concluded that (1) the uncertainty of the modeling related uncertain parameters may lead to the difference in the trajectory of seismic hysteretic response for a given bridge member, whereas the variation of the peak value of seismic response may result from the couple contributions of the uncertainty of ground motions and modeling related parameters; (2) the inclusion of only ground motion uncertainty is inadequate and inappropriate, and the proper way is to incorporate the uncertainty of the identified critical modeling parameters and ground motions into the time-evolving seismic response and the time-dependent seismic fragility assessment of the deteriorating highway bridges.

... Different from the static pushover analysis method, the MSA method can consider the effects of both the hysteresis characteristics of structural components and higher modal properties of structures. Porter et al. (2002) In the process of fragility analysis herein, the MSA method is employed due to the lower amount of calculation. However, the MSA method can only obtain the fractions exceeding the limit states at some intensity levels; thus, as the parameter estimation method for the MSA method, the maximum likelihood estimation method is widely used (Shinozuka et al. 2000;Baker 2015). ...

Based on the first-order second-moment method, a comparative study on seismic fragility analysis with consideration of modeling uncertainty is carried out for a 12-story reinforced concrete frame structure under excitation with far-field and pulse-like near-field ground motions by using the multiple stripes analysis method. The sensitivity of the median fragility capacity of the building to fourteen parameters in the cases of three limit states (i.e., immediate occupancy, life safety, and collapse prevention) is analysed, and the effect of the selection of ground motion intensity measures on the determination of modeling uncertainty is investigated. Finally, the annual probabilities of exceeding each limit state with different confidence levels are calculated, and two methods, the mean estimates approach and the confidence interval method, are used to incorporate uncertainties. The results show that the characteristics of ground motions affect the sensitivity of the median capacity to the disturbance of structural parameters. The modeling uncertainty estimated in the near-field records is meaningfully less than that in the far-field records. Judging from this limited case study, the modeling uncertainty estimated may be underestimated by using an inefficient IM. The influence of the modeling uncertainty in the fragility analysis for each limit state cannot be ignored when using the confidence interval method.

... It has been used in sensitivity analysis in earthquake engineering (e.g. Porter et al. 2002) and probabilistic seismic evaluation of structural components and systems (e.g. Lee and Mosalam 2005). The tornado diagram consists of a set of horizontal bars, referred to as swings, one for each source of uncertainty (random variable). ...

Over the past decade, several long duration subduction earthquakes took place in different locations around the world such as Chile in 2010, Japan in 2011, China in 2008, and Indonesia in 2004. Long-duration and large-magnitude earthquakes are also possible to occur in the Cascadia subduction zone along the Pacific Northwest Coast of the United States. The duration of an earthquake is expected to affect the response of structures. However, current seismic design specifications mostly use response spectra to identify the hazard and do not consider duration effects. Thus, a comprehensive understanding of the effect of the ground motion duration on structural performance and its design implications is an important issue.The goal of this study was to investigate the influence of earthquake duration on the structural response of Special Concentric Braced Frames (SCBFs). A comprehensive experimental program and detailed analytical investigations were conducted to understand and quantify the effect of duration on collapse capacity of SCBFs to possibly incorporate these effects in improved seismic design provisions. The experimental program included large-scale shake table tests and the analytical program consisted of pre-test and post-test phases. The pre-test analysis phase used OpenSEES models that were preliminarily calibrated against previous experimental results for different configuration of SCBFs to conduct a sensitivity analysis. A tornado diagram framework was used to rank the influence of the different modeling parameters, e.g. low-cycle fatigue, on the seismic response of SCBFs under short and long duration ground motions. These models were revisited for further calibration and validation in the post-test analysis using the experimental program.The experimental program included three large-scale shake table tests of identical single-story single-bay SCBF with chevron brace configuration tested under different ground motions. Two specimens were tested under a set of spectrally-matched short and long duration ground motions. The third specimen was tested under another long duration ground motion. All tests started with a 100% scale of the selected ground motions then testing continued with increasing ground motion scale until failure, i.e. until both braces ruptured. The conducted shake table tests showed that earthquake duration effects can lead to premature seismic failures or lower capacities, which provides more confidence for future initiatives to consider duration effects as part of the seismic design provisions. Identical frames failed at different displacements demands because of the damage accumulation associated with the earthquake duration with about 40% reduction in the displacement capacity of the two specimens tested under long duration earthquakes versus the short duration one.Using tests results, the post-test analysis phase focused first on calibrating an OpenSEES model for the test specimens to capture the experimental behavior. The calibration started by matching the initial stiffness and overall global response, then the low-cycle fatigue parameters were fine-tuned to properly capture the experimental local behavior, i.e. brace buckling and rupture. The post-test analysis showed that the input for the low-cycle fatigue models available in the literature cannot capture the observed experimental results. Hence, new values for the fatigue parameters were suggested in this study based on the three shake-table tests. The calibrated model for the test specimens was used to conduct incremental dynamic analysis using 44 pairs of spectrally-matched short and long duration ground motions. This analysis aimed at incorporating ground motions variability for better generalized observations and developing collapse fragility curves using different intensity measures to compare the effect of ground motion duration. The difference in the median fragility was found to be 45% in the drift capacity at failure and about 10% in the spectral acceleration. Using regression analysis, the obtained drift capacity from analysis was found to be reduced by about 8% on average for every additional 10 seconds in ground motions significant duration. The last stage of this study extended the calibrated model to full SCBF archetype buildings to study the effect of ground motion duration on full structures. Two buildings, three-story and nine-story, that resembled original SAC buildings but modified to have SCBFs as lateral support system instead of moment resisting frames, were used. Two planer frames were adopted from the two buildings and used for the analysis. The same 44 spectrally-matched pairs previously used in post-test analysis were used to conduct nonlinear time history analysis and study the effect of duration. All the ground motions were scaled to two hazard levels for the deterministic time history analysis: 10% exceedance in 50 years and 2% exceedance in 50 years. All analysis results were interpreted in a comparative way to isolate the ground motions duration effects, which was the main variable in the ground motion pairs. In general, the results showed that the analyzed SCBFs experienced higher drift values under the long duration suite of ground motions, and in turn, larger percentage of fractured braces was observed under long duration cases. The archetype SCBFs analysis provided similar conclusion on duration effects as the experimental and numerical results on the single-story single-bay frame.

... The vulnerability-class definition, therefore, links the hazard intensities to the expected damage based on a clear understanding of the building's structural and non-structural characteristics (e.g., Calvi et al. 2006). Porter et al. (2002) showed that the influence of uncertainties in ground shaking on the overall uncertainty in the seismic performance of individual buildings (repair cost) is similar to the influence of uncertainty in the capacity of a building to resist the damage. However, for large-scale seismic risk, it has been conventionally assumed that the relative uncertainty associated with the definition of building classes and their relative proportions contributes much less to the final loss estimates than the aleatory components of the risk processing chain (i.e., ground motion variability in seismic hazard). ...

In seismic risk assessment, the sources of uncertainty associated with building exposure modelling have not received as much attention as other components related to hazard and vulnerability. Conventional practices such as assuming absolute portfolio compositions (i.e., proportions per building class) from expert-based assumptions over aggregated data crudely disregard the contribution of uncertainty of the exposure upon earthquake loss models. In this work, we introduce the concept that the degree of knowledge of a building stock can be described within a Bayesian probabilistic approach that integrates both expert-based prior distributions and data collection on individual buildings. We investigate the impact of the epistemic uncertainty in the portfolio composition on scenario-based earthquake loss models through an exposure-oriented logic tree arrangement based on synthetic building portfolios. For illustrative purposes, we consider the residential building stock of Valparaíso (Chile) subjected to seismic ground-shaking from one subduction earthquake. We have found that building class reconnaissance, either from prior assumptions by desktop studies with aggregated data (top–down approach), or from building-by-building data collection (bottom–up approach), plays a fundamental role in the statistical modelling of exposure. To model the vulnerability of such a heterogeneous building stock, we require that their associated set of structural fragility functions handle multiple spectral periods. Thereby, we also discuss the relevance and specific uncertainty upon generating either uncorrelated or spatially cross-correlated ground motion fields within this framework. We successively show how various epistemic uncertainties embedded within these probabilistic exposure models are differently propagated throughout the computed direct financial losses. This work calls for further efforts to redesign desktop exposure studies, while also highlighting the importance of exposure data collection with standardized and iterative approaches.

... Quantifying uncertainty in seismic response due to material variability is important for advancing PBEE because it provides a means to better characterize the probabilistic structural response, enables thorough risk evaluation, and improves insight about potential bias in deterministic analytical models. Evaluation of uncertainty in structural seismic performance evaluations has been discussed in publications [3][4][5][6][7][8] and seismic assessment frameworks. [9][10][11] However, the impact of material variability has not been examined as a separate source of statistical uncertainty through a comprehensive evaluation of the material properties that affect the nonlinear seismic response of reinforced concrete structures. ...

... The performance-based earthquake engineering (PBEE) framework proposed by the Pacific Earthquake Research Center (PEER) has offered a feasible pathway to conduct the design and optimization of seismic protective devices in a fully probabilistic manner (Cornell and Krawinkler 2000). PBEE stands on the premise that seismic risk can be predicted and evaluated with quantifiable confidence of all pertinent uncertainties that propagate from earthquake occurrence modeling to the assessment of earthquake consequences, such as casualties, dollar losses, and downtime (Park et al. 2004;Porter et al. 2002). The PBEE has also fostered related studies on highway bridges. ...

Base isolators and fluid viscous dampers are viable protective devices that have been commonly considered in the seismic protection of civil engineering structures. However, the optimal design of these devices remains a tedious and iterative undertaking due to the uncertainty of ground motions, the nonlinear behavior of the structure, and its change of dynamic characteristics (i.e., effective stiffness and damping ratio) under each new design. The optimal design problem becomes more challenging concerning a multiresponse bridge system where conflicting damage potential is often expected among multiple bridge components (e.g., column, bearing, shear key, deck unseating, foundation). In this respect, this study develops a risk-based optimization strategy that directly links the expected annual repair cost ratio (ARCR) of the bridge to the design parameters of base isolators and fluid dampers. This strategy is achieved by devising a multistep workflow that integrates a seismic hazard model, a design of experiment for bearings and dampers, a logistic regression towards parameterized component-level fragility models, and a bridge system-level seismic loss assessment. The developed ARCR is parameterized as a convex function of the influential parameters of seismic protective devices. As such, optimal bearing and damper designs can be pinpointed by directly visualizing the global minimum of the parameterized ARCR surface. The optimal design is carried out against a typical reinforced concrete highway bridge in California that is installed with the fluid dampers and three types of widely-used isolation bearings-the elasto-meric bearing, lead-rubber bearing, and friction pendulum system. It is shown that optimal design parameters can be obtained to significantly reduce the expected ARCR of the bridge, whereas combining optimally designed bearings and dampers can provide the minimum seismic risk.

... e accuracy and efficiency of the proposed method are verified by comparing it with the MC method because the MC method is usually considered the precise solution. e results are also compared with the Tornado graphic method, which is a LSA method [27]. ...

Seismic demand analysis of structures plays an important role in the structural seismic calculation; however, studies on the importance analysis of seismic demand are limited. A new method based on a support vector machine (SVM) is proposed to analyze the importance of structural seismic demand and study the influence of random variables on structural seismic demand in this study, where the linear kernel function, Gauss kernel function, and polynomial kernel function are used in SVM. The time history analysis of the steel-reinforced concrete (SRC) frame structures has been carried out by the finite element software OpenSees under the action of different seismic records. Four kinds of seismic demand of the SRC frame structure are analyzed in this study, which are top displacement, maximum floor acceleration, base shear, and maximum interstory drift angle, respectively. Importance indexes of the four kinds of structural seismic demand are in good agreement with those of the Monte Carlo (MC) numerical simulation method and Tornado graphic method, which verify the accuracy of the proposed method. Moreover, the sample size of the proposed method is greatly smaller than that of the MC method. Therefore, the computation efficiency has been improved significantly by the proposed method.

... spectrum (Lin et al. 2013a)). Finally, there is the structural modelling and evaluation of the dynamic response of the building at many IM levels through different techniques such as incremental dynamic analysis (IDA) (Vamvatsikos and Cornell 2002) or multiple stripe analysis (MSA) (Jalayer 2003), while also accounting for the structural response and modelling uncertainties Porter et al. 2002). In this study, we apply the latest and most recent tools in the field developed to evaluate the λ(EDP) of the case study buildings. ...

Recent seismic design approaches developed under the umbrella of performance-based
earthquake engineering (PBEE) pursue pre-defined performance objectives in terms
of structural response, economic losses, or casualties. The earlier PBEE methods were
mainly concerned with the deterministic evaluation of performance at a single ground
motion intensity level. This premise, however, provides little insight into the long-term
risk-based performance of a structure, and limits the ability to make informed design decisions. Given the inherent sources of uncertainty in all aspects of seismic design, probability theory needs to be employed to enable reliable design solutions. However, applying a risk-oriented design approach is not currently feasible for most practitioners, making it essential to understand how the current deterministic applications of these intensity-based PBEE approaches perform in terms of risk. Specifically, the aim is to investigate the capability of the direct displacement-based design (DDBD) method in producing reliable, risk consistent designs. A probabilistic PBEE assessment framework is applied as the benchmark to determine the risk of exceeding performance objectives for multiple DDBD-based reinforced-concrete-wall and dual reinforced-concrete-wall/steel-frame buildings located at three different sites. The significant variation in the achieved risk estimates related to the limit states of damage limitation, life safety and global collapse for the buildings considered, questions the ability of DDBD—or any other intensity-based design method that does not account for uncertainty—to offer risk consistency.

... In this approach, the importance of each parameter is computed based on the difference between values of the engineering demand parameter at its lower and upper bounds. Further, tornado diagram analysis tool is utilised to visualise the uncertainties in the input parameters [1][2]. The outcome of his tool is a bar diagram that depicts the estimated effect of each uncertain parameter based on the chosen engineering demand parameter that resembles a tornado in shape. ...

Inherent uncertainties in input parameters significantly impact the seismic performance characteristics of Reinforced Concrete (RC) frame structures. Hence, it is imperative to study the sensitivity of input parameters before resorting to any analysis or design. Therefore, the present investigation primarily focusses on identifying the most uncertain input parameters from the material properties considered,
that has utmost influence on the structural capacity and its behaviour. This is determined by carrying out a deterministic sensitivity analysis, by performing nonlinear analysis on the RC moment resisting frames using SAP2000 software. Further, tornado diagram analysis is utilised to understand the relative importance of each parameter. The influence of sensitivity of input parameters on performance of RC structure is determined by developing fragility curves. It can be observed from the present investigation that the sensitivity of material properties viz., compressive strength of concrete,yield strength of steel has substantial influence on the seismic performance

... The different levels of damage states, like intact, light, moderate, and extensive, are classified as learned damage patterns in this research. Uncertainty of different modeling parameters such as mass, damping, and material strength has been evaluated in seismic performance predictions [62,63]. This study utilizes CCD as a sampling method within the criteria of the DOEs methodologies for evaluating the effects of modeling uncertainty. ...

This paper presents a hybrid deep learning methodology for seismic structural monitoring, damage detection, and localization of instrumented buildings. The proposed methodology develops mechanics-based structural models to generate sample response datasets by accounting for the uncertainty of model parameters that can highly affect the estimation of baseline model nonlinear responses. The uncertainty of model parameters is evaluated through the design of experiments methodology by employing the central composite design for sampling. The generated sample response dataset is utilized for training a hybrid data-driven model that combines a convolutional neural network and wavelet packet transform modules for feature extraction. The global story-level noise-contaminated response measurements are used as input for the data-driven model to perform damage detection and localization in a manner consistent with performance-based design criteria. The performance of the proposed methodology is studied in the context of numerical and experimental case studies developed based on the shake table testing of a concentrically braced frame subject to various input ground motion intensities at the E-Defense facility in Miki, Japan.

... In this study, we adopt a screening method which aims to preliminarily and qualitatively analyze the most important input parameter. In particular, we develop a modified version of the Morris method (Morris, 1991), which solves some drawbacks of the "tornado diagram" (Porter et al., 2002) used in Mignan et al. (2015). A tornado diagram is a type of sensitivity analysis based on a graphical representation of the independent contribution of each input variable to the variability in the selected QoI. ...

The rapid increase in energy demand in the city of Reykjavik has posed the need for an additional supply of deep geothermal energy. The deep-hydraulic (re-)stimulation of well RV-43 on the peninsula of Geldinganes (north of Reykjavik) is an essential component of the plan implemented by Reykjavik Energy to meet this energy target. Hydraulic stimulation is often associated with fluid-induced seismicity, most of which is not felt on the surface but which, in rare cases, can be a nuisance to the population and even damage the nearby building stock. This study presents a first-of-its-kind pre-drilling probabilistic induced seismic hazard and risk analysis for the site of interest. Specifically, we provide probabilistic estimates of peak ground acceleration, European macroseismicity intensity, probability of light damage (damage risk), and individual risk. The results of the risk assessment indicate that the individual risk within a radius of 2 km around the injection point is below 0.1 micromorts, and damage risk is below 10−2, for the total duration of the project. However, these results are affected by several orders of magnitude of variability due to the deep uncertainties present at all levels of the analysis, indicating a critical need in updating this risk assessment with in situ data collected during the stimulation. Therefore, it is important to stress that this a priori study represents a baseline model and starting point to be updated and refined after the start of the project.

... It is noted that the ground motion intensity measure S a is the most sensitive parameter for the maximum story drift of the archetypes. This observation agrees with earlier findings [55][56][57][58]. Referring to Fig. 9, the RC beam modeling parameters related to deformation capacity (θ p ) and post-peak softening response (θ pc ) of the component are considerably more sensitive for predicting the maximum story drifts, compared to the column counterparts. ...

Robust seismic vulnerability assessment for a building under expected earthquake ground motions necessitates explicit consideration of all-important sources of uncertainty in structural model idealization. This paper presents a machine learning-based methodology for reliably predicting the seismic response and structural collapse classification of ductile reinforced concrete frame buildings under future earthquake events by accounting for component- and system-level modeling uncertainties. The proposed methodology uses two different types of machine learning methods—regression-based and classification-based methods—to achieve the goal of this study. Machine learning techniques with boosting algorithms (i.e., adaptive boosting and extreme gradient boosting) are the best methods for both response prediction and collapse status classification of modern code-compliant reinforced concrete frame buildings. Finally, the effect of uncertain modeling parameters on the response and collapse identification is examined. The reinforced concrete beam modeling-related parameters (i.e., plastic deformation properties) of ductile, low-to mid-rise frame buildings are significant predictors of seismic response due to capacity design principles.

Deterioration parameters that are commonly used to simulate nonlinear behavior of steel components were mainly calibrated based on the results from experiments on steel beams. Recently, the state of knowledge for deterioration behavior of steel columns has been improved by experimental and analytical studies on the wide-flange steel columns. These deteriorating characteristics are introduced as regression relationships in which the associated uncertainties are represented by the coefficient of variation (COV). Accounting for these uncertainties in estimating collapse fragility curves through the incremental dynamic analysis (IDA) and simulation-based reliability methods is impractical due to the large amount of required computational effort. In this study, two main goals are pursued. The first goal is comprehensive evaluation of the main, interaction, and quadratic effects of the modeling random variables on the collapse capacity of steel structures. The second goal is to propose an efficient approach to create response surface (RS), which in combination with the Monte Carlo (MC) sampling method will be used to incorporate modeling uncertainties into the collapse fragility. This efficiency will be achieved by employing screening design techniques to reduce the amount of analysis required to create a quadratic RS and also endurance time (ET) analysis as an efficient alternative nonlinear dynamic analysis method with less computational time to estimate the structural responses. In order to develop a reliable probabilistic model, the Bayesian model inference approach is applied to account for the uncertainties in the created model. The proposed procedure is performed with both IDA and ET methods on a prototype 5-story steel frame. Results indicate that collapse capacity is highly influenced by the strength modeling variables of beam as well as the ultimate rotation capacity of column components. In addition, ET method by a considerable reduction in the computational costs provides comparable responses with IDA in a probabilistic framework.

Accurate and computationally efficient building energy models are critical to the development of online or pseudo-online control strategies and other building management activities. However, such models need to overcome the large uncertainty involved with continuously changing occupant activities and building status. The present study uses unscented Kalman filtering (UKF) in the model parameter estimation for simple yet accurate resistor-capacitor (RC) models to develop reliable building energy models. The estimation procedure, mathematical operations, and other estimation enhancing techniques are presented in detail. Synthetic and measured data were used to validate and evaluate the methodology. The obtained model shows better performance when compared with a model that was calibrated using genetic algorithms in a previous study. This remarkable model performance shows that UKF can enable timely online model update and improve the model predictability.

The paper presents a computationally efficient algorithm to integrate a probabilistic, non‐Gaussian parameter estimation approach for nonlinear finite element models with the performance‐based earthquake engineering (PBEE) framework for accurate performance evaluations of instrumented civil infrastructures. The algorithm first utilizes a minimum variance framework to fuse predictions from a numerical model of a civil infrastructure with its measured behavior during a past earthquake to update the parameters of the numerical model that is, then, used for performance prediction of the civil infrastructure during future earthquakes. A nonproduct quadrature rule, based on the conjugate unscented transformation, forms an enabling tool to drive the computationally efficient model prediction, model‐data fusion, and performance evaluation. The algorithm is illustrated and validated on Meloland Road overpass, a heavily instrumented highway bridge in El Centro, CA, which experienced three moderate earthquake events in the past. The benefits of integrating measurement data into the PBEE framework are highlighted by comparing damage fragilities of and annual probabilities of damages to the bridge estimated using the presented algorithm with that estimated using the conventional PBEE approach.

In this study, the reliability assessment of the system of structure-MR damper in controlling seismic responses of the structure via semi-active control is studied. In this regard, numerical results are presented for two different examples including three and ten-storey shear structures. The limit state functions are defined based on the control responses obtained from the use of MR dampers in the structure stories. By defining several uncertainties in parameters of the structure-MR damper system, probability of failure of structure is obtained using weighted uniform simulation (WUS) method and compared with the results of traditional Monte Carlo Simulation (MCS). Moreover, the most probable point of failure, which cannot be calculated by MCS, is determined for each uncertain event. Graphs of system reliability are derived and interpreted. The results show satisfactory performance of the WUS method in the reliability analysis of smart structures. The results also indicate that reliability of the system is highly dependent on the mass uncertainty of the structure. Moreover, the highest probability of failure takes place when all parameters are considered to be simultaneously uncertain.

This study complements and extends a recent work on the development of a rigorous framework for risk‐targeted performance‐based seismic design/assessment of ordinary standard bridges (OSBs) in California. Rooted in the formulation of this framework is an updated fully probabilistic performance‐based earthquake engineering (PBEE) assessment methodology wherein metrics of structural performance are formulated in terms of the mean return periods of exceedances for several strain‐based limit‐states (LSs). The originally proposed framework explicitly considering: (1) the uncertainty in the seismic input, and (2) the uncertainty in the capacity of the various LSs, is extended in this study to account for the following additional pertinent sources of uncertainty: (i) the aleatory uncertainty associated with finite element (FE) model parameters, and (ii) the epistemic parameter estimation uncertainty associated with using finite datasets to estimate the parameters of the probability distributions characterizing the FE model parameters and LS fragilities. These additional sources of uncertainty are commonly omitted or neglected in PBEE often by invoking that the earthquake ground motion uncertainty is the predominant source of uncertainty. However, their inclusion and consistent propagation in seismic performance‐based assessment of OSBs is imperative to obtain a more complete picture of seismic performance, thereby leading to a more comprehensive, transparent, and reliable design of these simple, yet essential bridges which represent an integral part of lifeline infrastructure systems especially in earthquake‐prone regions. The analytical and computational framework previously assembled is extended via modular incorporation of these additional sources of uncertainty. Four OSB testbeds and their risk‐targeted re‐designed versions are analyzed with and without these additional sources of uncertainty to evaluate their significance.

The promising seismic response emerged by the concept of base isolation leads to increasing practical applications into buildings located at low-to-moderate seismicity regions. However, it is questionable that their collapse capacities can be ensured with reasonable reliability, although they would be designed according to a current seismic design code. This paper aims to investigate the collapse capacities of isolated buildings governed by the prescribed design criteria on the displacement and strength capacities of the employed isolation systems. In order to evaluate their collapse capacity under maximum considered earthquakes (MCEs), simplified numerical models are constructed for a larger number of nonlinear incremental dynamic analyses. The influential factors on the collapse probabilities of the prototype buildings are found out to specifically suggest the potential modifications of the design requirements. Although the MCE collapse probabilities of all isolated buildings are smaller than those expected for typical non-isolated buildings, these values are significantly different according to the degree of seismicity. The MCE collapse probabilities are dependent upon the governing collapse mechanism and the total system uncertainty. For the prototype buildings located at low-to-moderate seismicity regions, this study proposed the acceptable uncertainty to achieve a similar collapse performance to the corresponding buildings built at high seismicity regions.

This paper presents a comprehensive economic seismic loss assessment of emerging steel frames incorporating different types of self-centering braces. Particular focus is on failure mechanism of the braces and accurate modelling of the possible failure modes, especially fracture of the PT tendons and failure of energy dissipation devices. Moreover, the damage state, component fragility, and repair cost of the considered braces are developed in a more rigorous manner, aided by professional judgment and market research with reduced subjective decision. System-level analysis shows that tendon fracture indeed happens in the braces with FRP tendons under the maximum considered earthquake (MCE), which compromises the self-centering capability of the structures. Shape memory alloy (SMA)-viscoelastic hybrid braces are shown to effectively reduce the deformation and floor acceleration demands, and leads to the lowest probability of collapse. By examining the vulnerability functions and expected losses of the structures, a single-core SCB configuration with FRP tendons leads to the worst economic performance due to the limited brace ductility. A dual-core configuration can significantly improve the brace ductility and hence reduce the economic loss. The SMA-viscoelastic hybrid brace results in the best economic performance with the lowest expected loss. A subsequent sensitivity analysis shows that the vulnerability curves of the structures exhibit mild sensitivity to the residual inter-story drift threshold, but the modelling assumption has a more remarkable influence on the economic loss estimation results. Employing idealized numerical models without considering brace failure in the analysis could underestimate the seismic loss of self-centering braced frames by more than 30%.

There has been ongoing deliberation to arrive at promising retrofit strategies for pre-seismic code reinforced concrete (RC) structures. Against this backdrop, the research reported in this study puts forth solutions by focusing on advanced retrofit approaches for improving the seismic performance of substandard RC buildings with structural systems common to medium seismicity regions. High-performance reinforced concrete (HPRC) jacket application and self-centering energy dissipative (SCED) braces are the contemporary retrofit alternatives prioritized in this study to upgrade RC structural systems deficient in stiffness, strength and/or ductility. While these retrofit techniques were previously investigated at the member level, this study focuses on implementing thin-HPRC jacket applications, innovative outrigger-belt truss SCED bracing systems, and hybrid approaches on three-dimensional (3D) fiber-based numerical models representing substandard RC structures with different heights. Inelastic pushover analyses and multi-record dynamic response simulations are conducted to assess the retrofit alternatives by monitoring several local damage indices (LDIs) and the related global damage measure (GDM). The study confirms the effectiveness of retrofit measures for a moment-resisting frame building (MRF) deficient in lateral capacity and a high-rise shear wall (SW) building with insufficient global ductility. The presented systematic methodology accounts for the redistribution of seismic demands after retrofitting critical elements and enables selecting effective seismic retrofit solutions, namely SCED bracing system for MRF structure and hybrid retrofit for the high-rise SW building, using probabilistic seismic performance assessment along with cost and practical considerations.

Structural fragility assessment is a fundamental component of modern performance-based earthquake design and assessment processes. Major advances in fragility functions development and implementation have occurred over the past three decades.

This paper proposes an alternative seismic assessment framework considering various modeling uncertainty parameters, and investigates their effects on the seismic response and seismic fragility estimates of a case-study bridge. Firstly, sensitivity analyses with the tornado diagram technique are performed to determine the sensitivity of some typical bridge engineering demand parameters (EDPs) to twenty-two modeling related uncertain parameters, and the results indicate that the variability in ten identified critical parameters has significant effects on the bridge EDPs. Subsequently, based on a series of nonlinear time history analyses (NLTHAs) on the sample models generated by using Latin hypercube sampling (LHS) method, comparative studies for the seismic responses of some typical bridge members and the seismic fragility estimates both at bridge component and system levels incorporating different levels of uncertainty are performed, respectively. It is concluded that (1) the uncertainty of the modeling related parameters may lead to the difference in the trajectory of seismic response for a given bridge member, whereas the variation of the peak value of such seismic response may due to the joint actions of the uncertainty of ground motions and modeling parameters; (2) the inclusion of only ground motion uncertainty is inadequate and inappropriate, and the proper way is incorporating the uncertainty in those identified significant modeling parameters and ground motions into the seismic response and seismic fragility assessment of highway bridges.

The study presented in this paper focused on developing accurate computational finite element (FE) model of electrical substations ceramic (porcelain) post insulators. The objective is to investigate the structural behavior and seismic response of these critical equipment through detailed numerical simulations that can replace or minimize experimental qualification tests and optimize future design of electrical equipment. Detailed three-dimensional solid FE modeling was used to capture the complex geometry of post insulators and the brittle nature of ceramics. Dedicated material characterization tests were utilized to define the porcelain nonlinear material model parameters. The developed model was verified using previously conducted experiments and used to perform linear and nonlinear static and dynamic analyses. A sensitivity parametric study was conducted first to calibrate the model and rank the sources of uncertainties in porcelain insulator modeling using the so-called tornado diagram analysis. The calibrated model was further utilized to carry out nonlinear time history analysis under earthquake excitation and capture the dynamic mode of failure, which is not always feasible to achieve using experimental tests. The study concluded with identification of which modeling parameters significantly affect the simulated structural behavior of post insulators, and compared the inelastic response at failure under static and dynamic loading.

Buildings are among the major contributors to environmental impacts, in terms of non-renewable resource depletion, energy and material consumption, and greenhouse gas (GHG) emissions. For this reason, modern societies are pushing towards the refurbishment of existing buildings aiming at the reduction of their operational energy consumption and at a major use of renewable energy and low-carbon materials. At the same time, buildings are expected to provide population with safe living and working conditions, even when hit by different kinds of hazards during their service life, such as earthquakes. Until recently, life cycle assessment (LCA) procedures tended not to include the effects of natural hazards. However, if considered in a building LCA, earthquake-induced environmental impacts would constitute a very informative performance metric to decision-makers, in addition to the more customarily used monetary losses or downtime indicators. Within this context, therefore, a comprehensive review of the existing literature is presented, with comparisons between available methodologies being carried out in terms of their employed seismic loss estimation method, environmental impact assessment procedure, damage-to-impact conversion, impact-to-cost conversion, and selected decision variable. Further, an illustrative case-study application is also included.

People's cognitive limitations and the unpredictability of structures introduce uncertainties into seismic performance analyses of structures in which transmission tower-line systems are essential components that may exhibit highly uncertain behavior. Nevertheless, it is important to have a clear understanding of the procedure required to manage the uncertainties surrounding structural seismic demand estimations. A practical method used to solve uncertainty problems is sensitivity and uncertainty analysis based on randomness and probability. To propagate all pertinent sources in aleatory uncertainty (input loading) in conjunction with epistemic randomness (modeling assumption errors) to actual structural seismic response and failure quantitative analysis, an uncertainty analysis method developed especially for transmission tower-line systems under seismic excitation is constructed based on sensitivity analysis and the Latin hypercube sampling method combined with incremental dynamic analysis. Sensitivity analysis reveals the relative importance of each parameter independently, while uncertainty analysis indicates the variation in the structural seismic performance under the combined actions of different uncertainty parameters. The final results demonstrate the need to consider the effects of both ground motion and structural modeling parameter uncertainties in seismic performance analyses of transmission tower-line systems.

Over recent decades, regarding the spread of unusual events such as fires, explosions, and vehicle collisions, the study of the behavior of structures subjected to abnormal loadings has been taken into account by the researchers and structural engineers. In this study, 2 and 5-story steel moment-resisting frame structures have been considered under the heavy vehicle collision impact. They are modeled in OpenSees software two-dimensionally with regarding to uncertainty in materials and applied loads and the sensitivity based reliability analysis of the studied random parameters is performed in Matlab software. Then, the effect of each of the variables is investigated using simulation-based methods according to limit state functions based on the maximum permitted beam rotation of damaged bay of frames. The results of this study presented that the random variables such as mass and velocity of vehicle and yield strength of material were the most influential parameters in calculating the failure probability in representative structures. Also, the control variates-based subset simulation (CSS) method compared to Monte Carlo Simulation (MCS) approach estimated the failure probability with permissible error rate, less sample number and the minimum computer processing time duration. Furthermore, the results of this research indicated that by increasing the number of stories of the building, the probability of its failure due to vehicle collision increased. According to the results of this study, the value of beam rotation of damaged bay parameter of the 5-story frame compared to 2-story one has increased by 55, 18 and 33% under the LSF1, LSF2 and LSF3 functions, respectively

Effective disaster risk management (DRM) and disaster risk reduction (DRR) require modeling potential and post-event impacts using building exposure data. The data used to develop building exposure databases will influence the accuracy of risk assessments and the appropriateness of subsequent decisions. This article proposes a framework for classifying approaches of developing building exposure databases into levels. To examine the uncertainty introduced through using various approaches to exposure development, a probabilistic seismic risk assessment was run with the exposure data corresponding to each proposed level using the County of Los Angeles as the study area. A factor of ∼2.5 was observed in the final loss estimates. The variance was less dependent on the spatial scale of data than on key values, most notably estimates of building size and replacement cost.

This study examined the effect of earthquake frequency on the seismic response of a typical modern container crane. A time-history analysis was carried out on the crane using 93 real ground motion records to investigate its behavior. Also, an eigenvalue and a nonlinear pushover analysis were conducted to obtain the dynamic properties and assess the structural performance of the crane, respectively. Three earthquake suites categorized as low-frequency earthquake suite (LFES), intermediate frequency earthquake suite (IFES), and high-frequency earthquake suite (HFES) were considered in this study. The earthquakes were categorized into the three frequency suites based on their peak ground acceleration-to-peak ground velocity ratio (PGA/PGV). By applying the three earthquake suites in the time-history analysis of the crane, drift ratio, internal forces, stresses, and strain were captured to examine its critical seismic response. The results demonstrated the effect of the frequency content on the seismic response of the crane. The LFES was found to cause drift responses averaging 114% and 480% and stress responses averaging 82% and 261%, which were higher than those of IFES and HFES. LFES, IFES, and HFES were found to exact inelastic demands on the crane above the PGA thresholds of 0.34 g, 0.80 g, and 1.99 g, respectively. The LFES was found to cause an uplift response that averaged 468% higher than that of IFES. The uplift caused by the HFES was observed to be inconsequential. Furthermore, it was found that the ground motions with low PGA/PGV ratio values had a larger damage potential on the container crane.

The effectiveness of six seismic retrofitting intervention schemes on an existing jumbo-size container crane is investigated. They include the use of conventional steel braces and buckling-restrained braces, fluid viscous dampers and friction dampers, lead rubber bearing isolators, and natural rubber bearing isolators with viscous dampers. The six schemes can be grouped under three main strategies, i.e., the use of different types of bracings, dampers, and isolation systems. Nonlinear response history analyses, using eight spectrally matched ground motions, were conducted on 3D models of the crane, with and without any upgrading, using SAP 2000. The results showed that with the exception of the conventionally braced crane, which produced inconclusive responses, the other two retrofitting strategies of using different types of dampers and isolation systems significantly reduced the critical seismic responses of the crane. At a target drift of one-third the original, the damping systems caused on average reduction of approximately 32%, 36%, and 98% in the base shear, stress, and uplift responses, respectively. Moreover, a significant reduction of about 65% in the stress and base shear responses and a condition of no uplift were recorded when the isolation systems were applied. The results of this study show that the isolation systems produce the best performance and therefore can be considered as the most effective seismic retrofitting technique.

The structural damping ratio, structural quality, yield strength, and elastic modulus of section steel, compressive strength, elastic modulus of concrete, yield strength, and elastic modulus of steel bars play important roles in the stability of the steel-reinforced concrete (SRC) frame structure, which are usually uncertain. However, their importance influence on the different seismic demands of SRC is rarely investigated simultaneously. In order to investigate the effects of the above parameters on four seismic demands (i.e., the top displacement, the maximum floor acceleration, the base shear force, and the maximum interstory displacement angle) of SRC frame structures, the orthogonal polynomial estimation method is first applied to the importance analysis of structural seismic demand based on the moment-independent method. Two engineering examples are performed to verify the accuracy and efficiency of the proposed method. The results have the characteristics of fast convergence and are in good agreement with those obtained by the moment-independent method based on kernel density estimation. The variance importance index based on Monte Carlo (MC) method is also calculated for comparison. The influence of each random variable on the four structural seismic demands is basically the same. Therefore, the accuracy and efficiency of the proposed method are proved sufficiently.

A thirteen storey, two bay, reinforced concrete framed structure is subjected to a series of non-linear, dynamic analyses in an attempt to find some correlation between the damaging potential of various digitised earthquakes and their relative strengths which have been computed in a variety of ways. Much of the previous work in this field has been with respect to simple one degree of freedom systems and these do not appear to give any indication of the correlation that could be expected for a non-linear multi-degree of freedom structure. The results show the effects of the different scalings of the various earthquakes and compare these with those obtained for the familiar North-South component of the May 18, 1940 El Centro earthquake. These results highlight the difficulty of trying to relate the use of such a dynamic earthquake analysis to the present pseudo-static code requirements. Further, the results of the analyses show also the great difference between the present assumption of the plastic hinge distributions, used in the ultimate seismic design method, and those observed during the earthquake excitation with the consequences on the lower-floor column axial loads.

Through analysis of recorded earthquake response and by forced vibration and shake-table
testing, a database of dynamic characteristics of woodframe buildings was developed. Modal
identification was performed on eight sets of strong-motion records obtained from five
buildings, and forced vibration tests were performed on five other buildings. The periods
identified were sensitive to the amplitude of shaking, due to the reduction in lateral stiffness at
stronger shaking levels. Data obtained from the UC San Diego and UC Berkeley full-scale
shake-table tests illustrate the shift in periods due to increasing shaking amplitude. A
regression analysis was performed on the data to obtain a simple but reasonably accurate
period formula for woodframe buildings at low drift levels (less than 0.1%). The equivalent
viscous dampings were usually more than 10% of critical during earthquake shaking.

This paper evaluates the performance of a seven-story reinforced concrete frame building that was severely damaged during the 1994 Northridge, California, earthquake. The building was designed and constructed in the 1960s and contains details that are typical of that construction era in the western United States. The building sustained severe damage that included column shear failures. The building was analyzed independently by three research teams using analysis methodologies that were similar in concept but different in details. An objective of each analysis was to correlate observed and calculated performance. The different analyses were successful to varying degrees. The results provide a test case of the effectiveness of various seismic performance assessment methodologies.

Rupture directivity effects cause spatial variations in ground motion amplitude and duration around faults and cause differences
between the strike-normal and strike-parallel components of horizontal ground motion amplitudes, which also have spatial variation
around the fault. These variations become significant at a period of 0.6 second and generally grow in size with increasing
period. We have developed modifications to empirical strong ground motion attenuation relations to account for the effects
of rupture directivity on strong motion amplitudes and durations. The modifications are based on an empirical analysis of
near-fault data. The ground motion parameters that are modified include the average horizontal response spectral acceleration,
the duration of the acceleration time history, and the ratio of strike-normal to strike-parallel spectral acceleration. The
parameters upon which the adjustments to average horizontal amplitude and duration depend are the fraction of the fault rupture
that occurs on the part of the fault that lies between the hypocenter and the site, and the angle between the fault plane
and the path from the hypocenter to the site. Since both of these parameters can be derived from the hypocenter location and
the fault geometry, the model of rupture directivity effects on ground motions that we have developed can be directly included
in probabilistic seismic hazard calculations. The spectral acceleration is larger for periods longer than 0.6 second, and
the duration is smaller, when rupture propagates toward a site. For sites located close to faults, the strike-normal spectral
acceleration is larger than the strike-parallel spectral acceleration at periods longer than 0.6 second in a manner that depends
on magnitude, distance, and angle. To facilitate the selection of time histories that represent near-fault ground motion conditions
in an appropriate manner, we provide a list of near-fault records indicating the rupture directivity parameters that each
contains.

A method to evaluate the seismic collapse performance of frame structures is presented, considering uncertainties in both the ground motion hazard and inelastic structural response to extreme input ground motions. The procedure includes a new seismic-intensity scaling index that accounts for period softening and thereby reduces the large record-to-record variability typically observed in inelastic time-history analyses. Equations are developed to combine results from inelastic time history analyses and a site-specific hazard curve to calculate the mean annual probability of a structure exceeding its collapse limit state.

Assembly-based vulnerability (ABV) is a framework for evaluating the seismic vulnerability and performance of buildings on a building-specific basis. It utilizes the damage to individual building components and accounts for the building's seismic setting, structural and nonstructural design and use. A simulation approach to implementing ABV first applies a ground motion time history to a structural model to determine structural response. The response is applied to assembly fragility functions to simulate damage to each structural and nonstructural element in the building, and to its contents. Probabilistic construction cost estimation and scheduling are used to estimate repair cost and loss-of-use duration as random variables. It also provides a framework for accumulating post-earthquake damage observations in a statistically systematic and consistent manner. The framework and simulation approach are novel in that they are fully probabilistic, address damage at a highly detailed and building-specific level, and do not rely extensively on expert opinion. ABV is illustrated using an example pre-Northridge welded-steel-moment-frame office building.

This report describes the results of a project titled Decision Support Tools f or Earthquake
Recovery of Businesses funded under Years 2 and 3 of Phase ill of the CUREe-Kajima Joint
Research Program. CUREe (California Universities for Research in Earthquake Engineering) is a
non-profit organization founded in 1988 by eight California universities to collaborate on
scientific research and applications that advance our understanding of how earthquakes affect the
built environment-structures, bridges, roads and other infrastructure. Kajima Corporation is a
prominent international engineering and construction firm based in Japan. Two CUREe
members, California Institute of Technology and Stanford University, partnered with Kajima to
develop the concept and methodologies for a decision-support system (DSS) to assist business
managers in determining how to mitigate or to recover from earthquake damage to company
facilities.

The U. S. Geological Survey (USGS) has completed new probabilistic seismic hazard maps for the United States. The maps depict peak horizontal ground acceleration, and 0.2, 0.3, and 1.0 sec response spectral acceleration values for 10%, 5%, and 2% probabilities of exceedance in 50 years (corresponding to approximate return times of 500, 1000, and 2500 years, respectively). The maps for the 0.2 sec and 1.0 sec response spectral acceleration with a 2% probability exceedance in 50 years, modified by engineering judgement, are the basis for seismic design maps developed for the 1997 NEHRP Recommended Provisions for Seismic Regulations for New Buildings. The USGS team preparing the new maps made a concentrated effort to make as much of the data used available via our Internet Website. This includes documentation, input data, output data, and computer code used to calculate the maps. In addition two CDROMs have been prepared - one for the probabilistic maps and one for the seismic design maps. Paper maps are also available.

The extensive damage and economic losses that occurred during the 1994 Northridge and other recent moderate earthquakes have stimulated structural engineers to consider how to protect economic investment besides meeting life safety requirements of buildings. The equivalent lateral force procedure for seismic design is based on implicit consideration of inelastic response of structures in earthquakes. Experience with past earthquakes has indicated that this procedure is inadequate in controlling damage in buildings. The objective of this study is to demonstrate the capability of nonlinear dynamic analyses to predict performance of reinforced concrete structures subjected to earthquake ground motions. An instrumented building damaged during the 1994 Northridge earthquake was analyzed using DRAIN-2D, and the results were compared with recorded response data. Both nonlinear dynamic time history and nonlinear static push-over analyses were performed, and correlations between these two nonlinear analysis methods were studied. A simplified shear failure model was proposed in the study.

Introduced in this paper are several alternative ground-motion intensity measures (IMs) that are intended for use in assessing the seismic performance of a structure at a site susceptible to near-source and/or ordinary ground motions. A comparison of such IMs is facilitated by defining the "efficiency" and "sufficiency" of an IM, both of which are criteria necessary for ensuring the accuracy of the structural performance assessment. The efficiency and sufficiency of each alternative IM, which are quantified via (i) nonlinear dynamic analyses of the structure under a suite of earthquake records and (ii) linear regression analysis, are demonstrated for the drift response of three different moderate- to long-period buildings subjected to suites of ordinary and of near-source earthquake records. One of the alternative IMs in particular is found to be relatively efficient and sufficient for the range of buildings considered and for both the near-source and ordinary ground motions.

A nonlinear model and an analytical procedure for calculating the cyclic response of nonductile reinforced concrete columns are presented. The main characteristics of the model include the ability to represent flexure or shear failure under monotonically increasing or reversed cyclic loading. Stiffness degradation with cyclic loading can also be represented. The model was implemented in a multipurpose analysis program and was used to calculate the response of selected columns representative of older construction. A comparison of the calculated response with experimental results shows that the strength, failure mode and general characteristics of the measured cyclic response can be well represented by the model.

Areal differences in damage caused by shaking from earthquakes commonly can be related to variations in near-surface geologic materials. For the Los Angeles region, a technique is presented for differentiating Quaternary sedimentary deposits that it is hoped will be transferrable to other areas. On the basis of a two-dimensional model of sedimentation pattern, the authors present a series of regional maps grouping the surficial deposits according to distinctive ranges in shear-wave velocity; these maps provide an approximate characterization of relative shaking response. Refs.

The response of a seven-story reinforced concrete building recorded during the Northridge earthquake is analysed in this paper. The building was designed in 1965 to the lateral force requirements of 1964 Los Angeles City Building Code. Non-ductile concrete moment frames and interior slab-column frames form the lateral resisting system of the building. The building suffered severe damage during the Northridge earthquake and was ‘red tagged’. This building was instrumented by as many as 16 sensors during the earthquake. These accelerogram records were analysed using system identification techniques to obtain important building response information. This also provided the opportunity to see if certain analytical techniques that are commonly used by practising engineers and/or researchers and many of which are currently being incorporated in various upcoming documents dealing with seismic evaluation of existing buildings could have predicted the observed performance of the building.

The object of the study was to attempt to simplify the nonlinear seismic analysis of reinforced concrete structures. The work consisted of two independent parts. One was to study the influence of calculated responses to hysteresis models used in the analysis, and to determine if satisfactory results can be obtained using less complicated models. For this part, a multi-degree analytical model was developed to work with three hysteresis systems previously proposed in addition to two systems introduced in this report. The results of experiment on a small-scale ten-story reinforced concrete frame were compared with the analytical results using different hysteresis systems. In the other part of the study, an economical simple "single-degree" model was introduced to calculate nonlinear displacement-response histories of structures (Q-Model). National Science Foundation Research Grant PFR 78-16318

This report presents a methodology for establishing the uncertain net asset value, NAV, of a real-estate investment opportunity considering both market risk and seismic risk for the property. It also presents a decision-making procedure to assist in making real-estate investment choices under conditions of uncertainty and risk-aversion. It is shown that that market risk, as measured by the coefficient of variation of NAV, is at least 0.2 and may exceed 1.0. In a situation of such high uncertainty, where potential gains and losses are large relative to a decision-maker's risk tolerance, it is appropriate to adopt a decision-analysis approach to real-estate investment decision-making. A simple equation for doing so is presented. The decision-analysis approach uses the certainty equivalent, CE, as opposed to NAV as the basis for investment decision-making. That is, when faced with multiple investment alternatives, one should choose the alternative that maximizes CE. It is shown that CE is less than the expected value of NAV by an amount proportional to the variance of NAV and the inverse of the decision-maker's risk tolerance, [rho].
The procedure for establishing NAV and CE is illustrated in parallel demonstrations by CUREE and Kajima research teams. The CUREE demonstration is performed using a real 1960s-era hotel building in Van Nuys, California. The building, a 7-story non-ductile reinforced-concrete moment-frame building, is analyzed using the assembly-based vulnerability (ABV) method, developed in Phase III of the CUREE-Kajima Joint Research Program. The building is analyzed three ways: in its condition prior to the 1994 Northridge Earthquake, with a hypothetical shearwall upgrade, and with earthquake insurance. This is the first application of ABV to a real building, and the first time ABV has incorporated stochastic structural analyses that consider uncertainties in the mass, damping, and force-deformation behavior of the structure, along with uncertainties in ground motion, component damageability, and repair costs. New fragility functions are developed for the reinforced concrete flexural members using published laboratory test data, and new unit repair costs for these components are developed by a professional construction cost estimator. Four investment alternatives are considered: do not buy; buy; buy and retrofit; and buy and insure. It is found that the best alternative for most reasonable values of discount rate, risk tolerance, and market risk is to buy and leave the building as-is. However, risk tolerance and market risk (variability of income) both materially affect the decision. That is, for certain ranges of each parameter, the best investment alternative changes. This indicates that expected-value decision-making is inappropriate for some decision-makers and investment opportunities. It is also found that the majority of the economic seismic risk results from shaking of S[subscript a] < 0.3g, i.e., shaking with return periods on the order of 50 to 100 yr that cause primarily architectural damage, rather than from the strong, rare events of which common probable maximum loss (PML) measurements are indicative.
The Kajima demonstration is performed using three Tokyo buildings. A nine-story, steel-reinforced-concrete building built in 1961 is analyzed as two designs: as-is, and with a steel-braced-frame structural upgrade. The third building is 29-story, 1999 steel-frame structure. The three buildings are intended to meet collapse-prevention, life-safety, and operational performance levels, respectively, in shaking with 10%exceedance probability in 50 years. The buildings are assessed using levels 2 and 3 of Kajima's three-level analysis methodology. These are semi-assembly based approaches, which subdivide a building into categories of components, estimate the loss of these component categories for given ground motions, and combine the losses for the entire building. The two methods are used to estimate annualized losses and to create curves that relate loss to exceedance probability. The results are incorporated in the input to a sophisticated program developed by the Kajima Corporation, called Kajima D, which forecasts cash flows for office, retail, and residential projects for purposes of property screening, due diligence, negotiation, financial structuring, and strategic planning. The result is an estimate of NAV for each building. A parametric study of CE for each building is presented, along with a simplified model for calculating CE as a function of mean NAV and coefficient of variation of NAV. The equation agrees with that developed in parallel by the CUREE team.
Both the CUREE and Kajima teams collaborated with a number of real-estate investors to understand their seismic risk-management practices, and to formulate and to assess the viability of the proposed decision-making methodologies. Investors were interviewed to elicit their risk-tolerance, r, using scripts developed and presented here in English and Japanese. Results of 10 such interviews are presented, which show that a strong relationship exists between a decision-maker's annual revenue, R, and his or her risk tolerance, [rho is approximately equal to] 0.0075R[superscript 1.34]. The interviews show that earthquake risk is a marginal consideration in current investment practice. Probable maximum loss (PML) is the only earthquake risk parameter these investors consider, and they typically do not use seismic risk at all in their financial analysis of an investment opportunity. For competitive reasons, a public investor interviewed here would not wish to account for seismic risk in his financial analysis unless rating agencies required him to do so or such consideration otherwise became standard practice. However, in cases where seismic risk is high enough to significantly reduce return, a private investor expressed the desire to account for seismic risk via expected annualized loss (EAL) if it were inexpensive to do so, i.e., if the cost of calculating the EAL were not substantially greater than that of PML alone.
The study results point to a number of interesting opportunities for future research, namely: improve the market-risk stochastic model, including comparison of actual long-term income with initial income projections; improve the risk-attitude interview; account for uncertainties in repair method and in the relationship between repair cost and loss; relate the damage state of structural elements with points on the force-deformation relationship; examine simpler dynamic analysis as a means to estimate vulnerability; examine the relationship between simplified engineering demand parameters and performance; enhance category-based vulnerability functions by compiling a library of building-specific ones; and work with lenders and real-estate industry analysts to determine the conditions under which seismic risk should be reflected in investors' financial analyses.

Because of its consequences, the San Fernando earthquake was a major earthquake from the engineering point of view, even though it was only a moderate shock in seismological terms. As a result of the many effects of the earthquake, a large number of detailed studies and reports will be forthcoming from a wide variety of sources, and the papers collected in this volume are only preliminary studies of some of the more important and interesting engineering features of the earthquake. The papers were prepared by staff and students working in earthquake engineering within the Division of Engineering and Applied Science at the California Institute of Technology.
The timely financial support of the Engineering Division of the National Science Foundation and the Earthquake Research Affiliates of the California Institute of Technology in conducting the research and preparing this report is gratefully acknowledged.

The usefulness of simple linear mathematical models for representing the behaviour of tall buildings during earthquake response is investigated for a variety of structures over a range of motions including the onset of structural damage. The linear models which best reproduce the measured response of the structures are determined from the recorded earthquake motions. In order to improve upon unsatisfactory results obtained by methods using transfer functions, a systematic frequency domain identification technique is developed to determine the optimal models. The periods, dampings and participation factors are estimated for the structural modes which are dominant in the measured response.
The identification is performed by finding the values of the modal parameters which produce a least-squares match over a specified frequency range between the unsmoothed, complex-valued, finite Fourier transform of the acceleration response recorded in the structure and that calculated for the model. It is possible to identify a single linear model appropriate for the entire response, or to approximate the nonlinear behavior exhibited by some structures with a series of models optimal for different segments of the response.
The investigation considered the earthquake records obtained in ten structures ranging in height from seven to forty-two stories. Most of the records were from the San Fernando earthquake. For two of these structures, smaller-amplitude records from more distant earthquakes were also analyzed. The maximum response amplitudes ranged from approximately 0.025 g to 0.40g.
The very small amplitude responses were reproduced well by linear models with fundamental periods similar to those measured in vibration tests. Most of the San Fernando responses in which no structural damage occurred (typically 0.2g-0.3g maximum accelerations) were also matched closely by linear models. However, the effective fundamental periods in these responses were characteristically 50 percent longer than in vibration tests. The average first mode damping identified from these records was about 5 percent of critical. Only those motions which produced structural damage could not be represented satisfactorily by time-invariant linear models. Segment-by-segment analysis of these records revealed effective periods of two to three times the vibration test values with fundamental mode dampings of 15 to 20 percent.
The systematic identification technique generally achieves better matches of the recorded responses than those produced by models derived by trial-and-error methods, and consequently more reliable estimates of the modal parameters. The close reproductions of the measured motions confirm the accuracy of linear models with only a few modes for representing the behaviour during earthquake response of tall buildings in which no structural damage occurs.

System identification applied to strong motion records from structures, Earthquake Ground Motion and its Effects on Structures

- J L Beck

Beck, J. L., 1982. System identification applied to strong motion records from structures,
Earthquake Ground Motion and its Effects on Structures, S. K. Datta, ed., American Society
of Mechanical Engineers, New York, 109-134.

Critical review of the state-of-the-art analytical tools and acceptance criterion in light of observed response of an instrumented nonductile concrete frame building

- M S Islam
- M Gupta
- S Kunnath

Islam, M. S., Gupta, M., and Kunnath, S., 1998. Critical review of the state-of-the-art analytical
tools and acceptance criterion in light of observed response of an instrumented nonductile
concrete frame building, Proceedings, Sixth U.S. National Conference on Earthquake Engineering, Seattle, Washington, May 31-June 4, 1998, Earthquake Engineering Research Institute, Oakland, CA, 11 pp.

Earthquake Damage Evaluation Data for Califor-nia, ATC-13, Redwood City, System identification applied to strong motion records from structures, Earthquake Ground Motion and its Effects on Structures

- Ca Beck

Applied Technology Council (ATC), 1985. Earthquake Damage Evaluation Data for Califor-nia, ATC-13, Redwood City, CA. Beck, J. L., 1982. System identification applied to strong motion records from structures, Earthquake Ground Motion and its Effects on Structures, S. K. Datta, ed., American Society of Mechanical Engineers, New York, 109–134.

Engineering Features of the San Fernando Earthquake of February 9 Report EERL 71-02, California Institute of Technology Nonlinear analyses of an instrumented structure damaged in the 1994 Northridge earthquake

- P C Jennings
- Y R Li

Jennings, P. C., 1971. Engineering Features of the San Fernando Earthquake of February 9, 1971, Report EERL 71-02, California Institute of Technology, Pasadena, CA. Li, Y. R., and Jirsa, J. O., 1998, Nonlinear analyses of an instrumented structure damaged in the 1994 Northridge earthquake, Earthquake Spectra 14 (2), 245–264.

Development of Ground Mo-tion Time Histories for Phase 2 of the FEMA Structural Engineers Association of California Recommended Lateral Force Require-ments and Commentary

- P Somerville
- N Smith
- S Punyamurthula
- S Sun

Somerville, P., Smith, N., Punyamurthula, S., and Sun, S., 1997. Development of Ground Mo-tion Time Histories for Phase 2 of the FEMA/SAC Steel Project, SAC Joint Venture, Back-ground Document Report No. SAC/BD-97/04. Structural Engineers Association of California, 1999. Recommended Lateral Force Require-ments and Commentary, 7 th Edition, Sacramento, CA, 440 pp.

Decision Support Tools for Earthquake Recovery of Businesses, Final Report, CUREe-Kajima Joint Research Program Phase III, Consortium of Universities for Earthquake Engineering Research Impact of Seismic Risk on Lifetime Property Values, Final Report, CUREE-Kajima Joint Re-search Program Phase IV

- J L Beck
- A Kiremidjian
- S Wilkie
- A Mason
- T Salmon
- J Goltz
- R Olson
- J Workman
- A Irfanoglu
- K Porter
- J L Beck
- K A Porter
- R Shaikhutdinov
- T Moroi
- Y Tsukada
- M Masuda

Beck, J. L., Kiremidjian, A., Wilkie, S., Mason, A., Salmon, T., Goltz, J., Olson, R., Workman, J., Irfanoglu, A., and Porter, K., 1999. Decision Support Tools for Earthquake Recovery of Businesses, Final Report, CUREe-Kajima Joint Research Program Phase III, Consortium of Universities for Earthquake Engineering Research, Richmond, CA. Beck, J. L., Porter, K. A., Shaikhutdinov, R., Moroi, T., Tsukada, Y., and Masuda, M., 2002. Impact of Seismic Risk on Lifetime Property Values, Final Report, CUREE-Kajima Joint Re-search Program Phase IV, Consortium of Universities for Earthquake Engineering Research, Richmond, CA. Browning, J., Li, Y., Lynn, A., and Moehle, J. P., 2000, Performance assessment for a reinforced concrete frame building, Earthquake Spectra 16 (3), 541–555.

Development of a Probability-Based Load Criterion for American National Standard A58, National Bureau of Standards

- B Ellingwood
- T V Galambos
- J G Macgregor
- C A Cornell

Ellingwood, B., Galambos, T. V., MacGregor, J. G., and Cornell, C. A., 1980. Development of a Probability-Based Load Criterion for American National Standard A58, National Bureau of Standards, Washington, DC, 222 pp. Federal Emergency Management Agency (FEMA), 2000. FEMA-356, Prestandard and Com-mentary for the Seismic Rehabilitation of Buildings, Washington, DC.

Damping measurements of tall structures

- G T Taoko

Taoko, G. T., 1981. Damping measurements of tall structures, Proc. Second Specialty Conference on Dynamic Response of Structures: Experimentation, Observation, Prediction, and
Control, January 15-16, 1981, Atlanta, GA, American Society of Civil Engineers, New York,
NY, 308-322.

Development of a two-parameter seismic intensity measure and probabilistic assessment procedure, 2nd U.S.Japan Workshop on Performance-Based Earthquake Engineering for Reinforced Concrete Building Structures 11

- P P Cordova
- G G Deierlein
- S S F Mehanny

Cordova, P. P., Deierlein, G. G., Mehanny, S. S. F., and Cornell, C. A., 2001. Development of a
two-parameter seismic intensity measure and probabilistic assessment procedure, 2nd U.S.Japan Workshop on Performance-Based Earthquake Engineering for Reinforced Concrete
Building Structures 11-13 September 2000 in Sapporo, Japan, Pacific Earthquake Engineering Research Center, Richmond, CA.

Seismic Damage Assessment for High-Rise Buildings

- R E Scholl
- O Kustu
- C L Perry
- J M Zanetti

Scholl, R. E., Kustu, O., Perry, C. L., and Zanetti, J. M., 1982. Seismic Damage Assessment for
High-Rise Buildings, URS/JAB 8020, URS/John A. Blume & Associates, Engineers, San
Francisco, CA, 321 pp.

Assembly-Based Vulnerability and Its Uses in Seismic Performance Evaluation and Risk-Management Decision-Making

- K A Porter
- A S Kiremidjian

Porter, K. A., and Kiremidjian, A. S., 2001. Assembly-Based Vulnerability and Its Uses in Seismic Performance Evaluation and Risk-Management Decision-Making, John A. Blume Earthquake Engineering Center, Stanford, CA, 214 pp.

Means Assemblies Cost Data

- Rs Means

RS Means Corp., 1997. Means Assemblies Cost Data, Kingston, MA.

Earthquake Damage Evaluation Data for California, ATC-13

Applied Technology Council (ATC), 1985. Earthquake Damage Evaluation Data for California, ATC-13, Redwood City, CA.

Holiday Inn Van Nuys Structural Drawings

- Rissman Rissman
- Associates

Rissman and Rissman Associates, 1965. Holiday Inn Van Nuys Structural Drawings, Pacific
Palisades, CA.

International Building Code

- Code International
- Council

International Code Council, 2000. International Building Code 2000, International Conference
of Building Officials, Whittier, CA, 756 pp.

Foundation Soils Investigation, Existing Holiday Inn Building

- California Geosystems

California Geosystems, 1994. Foundation Soils Investigation, Existing Holiday Inn Building,
Roscoe Blvd and Orion Ave, Van Nuys, CA, Glendale, CA, 26 pp.

Analysis of the response of an instrumented 7-story nonductile concrete frame building damaged during the Northridge Earthquake

- M S Islam

Islam, M. S., 1996a. Analysis of the response of an instrumented 7-story nonductile concrete
frame building damaged during the Northridge Earthquake, Proceedings of the 1996 Annual
Meeting of the Los Angeles Tall Buildings Structural Council, May 10, 1996, Los Angeles,
CA.

E1557-96 Standard classification for building elements and related sitework-UNIFORMAT II

American Society for Testing and Materials (ASTM), 1996. E1557-96 Standard classification
for building elements and related sitework-UNIFORMAT II, 1997 Annual Book of ASTM
Standards, Section 4, Construction, Volume 04.11 Building Constructions, West Conshohocken, PA, 630-639.

Mapping Quaternary sedimentary deposits for areal variations in shaking response, Evaluating Earthquake Hazards in the Los Angeles Region-An Earth-Science Perspective, U.S. Geological Survey Professional Paper 1360

- J C Tinsley
- T E Fumal

Tinsley, J. C., and Fumal, T. E., 1985. Mapping Quaternary sedimentary deposits for areal
variations in shaking response, Evaluating Earthquake Hazards in the Los Angeles
Region-An Earth-Science Perspective, U.S. Geological Survey Professional Paper 1360,
U.S. Government Printing Office, Washington DC, 101-126.

Holiday Inn, 1994 Northridge Earthquake Buildings Case Study Project Proposition 122: Product 3.2, Seismic Safety Commission

- M S Islam

Islam, M. S., 1996b. Holiday Inn, 1994 Northridge Earthquake Buildings Case Study Project
Proposition 122: Product 3.2, Seismic Safety Commission, Sacramento, CA, 189-233.

Development of a Probability-Based Load Criterion for American National Standard A58

- B Ellingwood
- T V Galambos
- J G Macgregor

Ellingwood, B., Galambos, T. V., MacGregor, J. G., and Cornell, C. A., 1980. Development of a
Probability-Based Load Criterion for American National Standard A58, National Bureau of
Standards, Washington, DC, 222 pp.
Federal Emergency Management Agency (FEMA), 2000. FEMA-356, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Washington, DC.

Dynamic Characteristics of Woodframe Structures, Consortium of Universities for Research in Earthquake Engineering

- V S Camelo
- J L Beck
- J F Hall

Camelo, V. S., Beck, J. L., and Hall, J. F., 2001. Dynamic Characteristics of Woodframe Structures, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA,
68 pp.

System identification applied to strong motion records from structures

- J L S K Beck
- Datta