Sensitivity analysis of the seismic demands of RC moment resisting frames to different aspects of ground motions

A weight vector representing the relative importance of various characteristics of ground motions (GMs) and a conditioning intensity measure (IM) are required to be able to use the generalized conditional IM framework for the purpose of GM selection. An inappropriate weight vector may result in the biased distributions of some important characteristics of GMs and, consequently, the bias in the structural responses. This article aims to provide the analyst with the understanding of which properties of GMs are important in capturing the accurate structural responses, to specifically assign a suitable weight to them and to select an appropriate conditioning IM as well. To this end, 4 reinforced concrete buildings, located at the site in which the seismic hazard is dominated by shallow crustal earthquakes, are considered. The findings reveal that the appropriate weight vectors depend on the characteristics of the employed structural systems. In addition, the role played by each IM in capturing the true structural responses changes over different earthquake intensity levels implying that different weight vectors are required over different earthquake levels. Furthermore, this study shows that, even in case of shorter‐duration GMs from shallow events, GM duration should be incorporated in GM selection as it has effects on the peak‐based structural responses in the earthquake levels beyond the level of 2%‐in‐50‐years. Specifically, the findings reveal that in case of shallow events, unlike large magnitude earthquakes, the shorter the duration of GM the more rapid release of energy and, consequently, the larger the peak‐based structural responses.     

Effect of ground motion selection methods on seismic collapse fragility of RC frame buildings

Variation in the seismic collapse fragility of reinforced concrete frame buildings predicted using different ground motion (GM) selection methods is investigated in this paper. To simulate the structural collapse, a fiber‐element modelling approach with path‐dependent cyclic nonlinear material models that account for concrete confinement and crushing, reinforcement buckling as well as low cycle fatigue is used. The adopted fiber analysis approach has been found to reliably predict the loss in vertical load carrying capacity of structural components in addition to the sidesway mode of collapse due to destabilizing P–Δ moments at large inelastic deflections. Multiple stripe analysis is performed by conducting response history analyses at various hazard levels to generate the collapse fragility curves. To select GMs at various hazard levels, two alternatives of uniform hazard spectrum (UHS), conditional mean spectrum (CMS) and generalized conditional intensity measure (GCIM) are used. Collapse analyses are repeated based on structural periods corresponding to initial un‐cracked stiffness and cracked stiffness of the frame members. A return period‐based intensity measure is then introduced and applied in estimating collapse fragility of frame buildings. In line with the results of previous research, it is shown that the choice of structural period significantly affects the collapse fragility predictions. Among the GM selection methods used in this study, GCIM and CMS methods predict similar collapse fragilities for the case study building investigated herein, and UHS provides the most conservative prediction of the collapse capacity, with approximately 40% smaller median collapse capacity compared to the CMS method. The results confirm that collapse probability prediction of buildings using UHS offers a higher level of conservatism in comparison to the other selection methods. Copyright © 2017 John Wiley & Sons, Ltd.     

From regional- to local-scale seismic hazard assessment: examples from Southern Spain

An approach that relates results from a regional seismic hazard assessment study with local-scale site-effect characterizations in an area of low-to-moderate seismic activity such as Andalusia (southern Spain), is presented. Results of a previous probabilistic seismic hazard analysis of Andalusia on rock conditions are disaggregated to infer hazard controlling earthquakes for different target motions. A collection of controlling magnitude-distance pairs and the corresponding site-specific response spectra at main capital cities of the region are obtained. These spectra are first-order approximations to expected seismic actions required in local earthquake risk assessments. In addition, results of independent, local-scale studies developed in Almeria City (SE Andalusia) are used to derive an updated seismic zonation of the city. These include predominant soil period estimates and shear-wave velocity profiles at different locations. If a local seismic risk assessment study or an earthquake-resistant structural design is to be developed, it may be recommended the use of different seismic actions on sites characterized by distinct response to seismic shaking (as derived from the seismic zonation). The seismic action related to worst-case scenarios may be modeled through a hazard-consistent response spectrum, obtained by hazard disaggregation at the spectral acceleration with period matching the prevailing resonant period of the target site or structure.     

Practice‐oriented estimation of the seismic demand hazard using ground motions at few intensity levels

This paper examines the calculation of the seismic demand hazard in a practice‐oriented manner via the use of seismic response analyses at few intensity levels. The seismic demand hazard is a more robust measure for quantifying seismic performance, when seismic hazard is represented in a probabilistic format, than intensity‐based assessments, which remain prevalent in seismic design codes. It is illustrated that, for a relatively complex bridge–foundation–soil system case study, the seismic demand hazard can be estimated with sufficient accuracy using as little as three intensity measure levels that have exceedance probabilities of 50%, 10% and 2% in 50 years which are already of interest in multi‐objective performance‐based design. Compared with the conventional use of the mean demand from an intensity‐based assessment(s), it is illustrated that, for the same number of seismic response analyses, a practice‐oriented ‘approximate’ seismic demand hazard is a more accurate and precise estimate of the ‘exact’ seismic demand hazard. Direct estimation of the seismic demand hazard also provides information of seismic performance at multiple exceedance rates. Thus, it is advocated that if seismic hazard is considered in a probabilistic format, then seismic performance assessment, and acceptance criteria, should be in terms of the seismic demand hazard and not intensity‐based assessments. Copyright © 2013 John Wiley & Sons, Ltd.     

Probabilistic seismic demand model for nonstructural components

Past earthquakes have shown the importance for critical facilities to remain functional during seismic events. In the performance assessment of these facilities, it is therefore essential to accurately evaluate the seismic demand of nonstructural components. Evaluation of these components is also important when estimation of nonstructural repair costs is a concern. In this paper, the use of a multivariate demand model for nonstructural components is proposed, in which demand is expressed in terms of both interstory drifts and floor acceleration spectra. A model is built using statistics of the demand vector derived from the results of a limited number of inelastic response history analyses of a structure. The model is then used to simulate any number of additional realizations of the demand vector required for an accurate estimation of the probability of functionality loss. A new proposal for a predictive equation to generate approximate realizations of floor response spectra is presented. A reinforced concrete frame is selected as an illustrative example to show the implementation of the probabilistic seismic demand model and to evaluate the proposed predictive equation for the floor response spectra. The results of the case study are used to demonstrate the importance of accounting for the correlation among the demand parameters when realizations of the seismic demand of nonstructural components are simulated. Copyright © 2015 John Wiley & Sons, Ltd.     

Probabilistic evaluation of soil–foundation–structure interaction effects on seismic structural response

Complex seismic behaviour of soil–foundation–structure (SFS) systems together with uncertainties in system parameters and variability in earthquake ground motions result in a significant debate over the effects of soil–foundation–structure interaction (SFSI) on structural response. The aim of this study is to evaluate the influence of foundation flexibility on the structural seismic response by considering the variability in the system and uncertainties in the ground motion characteristics through comprehensive numerical simulations. An established rheological soil‐shallow foundation–structure model with equivalent linear soil behaviour and nonlinear behaviour of the superstructure has been used. A large number of models incorporating wide range of soil, foundation and structural parameters were generated using a robust Monte‐Carlo simulation. In total, 4.08 million time‐history analyses were performed over the adopted models using an ensemble of 40 earthquake ground motions as seismic input. The results of the analyses are used to rigorously quantify the effects of foundation flexibility on the structural distortion and total displacement of the superstructure through comparisons between the responses of SFS models and corresponding fixed‐base (FB) models. The effects of predominant period of the FB system, linear vs nonlinear modelling of the superstructure, type of nonlinear model used and key system parameters are quantified in terms of different probability levels for SFSI effects to cause an increase in the structural response and the level of amplification of the response in such cases. The results clearly illustrate the risk of underestimating the structural response associated with simplified approaches in which SFSI and nonlinear effects are ignored. Copyright © 2010 John Wiley & Sons, Ltd.     

A comparison of intensity‐based demand distributions and the seismic demand hazard for seismic performance assessment

This paper compares the seismic demands obtained from an intensity‐based assessment, as conventionally considered in seismic design guidelines, with the seismic demand hazard. Intensity‐based assessments utilize the distribution of seismic demand from ground motions that have a specific value of some conditioning intensity measure, and the mean of this distribution is conventionally used in design verification. The seismic demand hazard provides the rate of exceedance of various seismic demand values and is obtained by integrating the distribution of seismic demand at multiple intensity levels with the seismic hazard curve. The seismic demand hazard is a more robust metric for quantifying seismic performance, because seismic demands from an intensity‐based assessment: (i) are not unique, with different values obtained using different conditioning intensity measures; and (ii) do not consider the possibility that demand values could be exceeded from different intensity ground motions. Empirical results, for a bridge‐foundation‐soil system, illustrate that the mean seismic demand from an intensity‐based assessment almost always underestimates the demand hazard value for the exceedance rate considered, on average by 17% and with a large variability. Furthermore, modification factors based on approximate theory are found to be unreliable. Adopting the maximum of the mean values from multiple intensity‐based assessments, with different conditional intensity measures, provides a less biased prediction of the seismic demand hazard value, but with still a large variability, and a proportional increase the required number of analyses. For an equivalent number of analyses, direct computation of the seismic demand hazard is a more logical choice and provides additional performance insight. Copyright © 2013 John Wiley & Sons, Ltd.     

Estimation of seismic drift demands for frame structures

A process is outlined and evaluated for the estimation of seismic roof and storey drift demands for frame structures from the spectral displacement demand at the first mode period of the structure. The spectral displacement demand is related to the roof drift demand for the multi‐degree‐of‐freedom (MDOF) structure using three modification factors, accounting for MDOF effects, inelasticity effects, and P‐delta effects. Median values and measures of dispersion for the factors are obtained from elastic and inelastic time history analyses of nine steel moment resisting frame structures subjected to sets of ground motions representative of different hazard levels. The roof drift demand is related to the storey drift demands, with the results being strongly dependent on the number of stories and the ground motion characteristics. The relationships proposed in this paper should prove useful in the conceptual design phase, in estimating deformation demands for performance assessment, and in improving basic understanding of seismic behaviour. Copyright © 2000 John Wiley & Sons, Ltd.     

Derivation of new SAC/FEMA performance evaluation solutions with second‐order hazard approximation

A novel set of SAC/FEMA‐style closed‐form expressions is presented to accurately assess structural safety under seismic action. Such solutions allow the practical evaluation of the risk integral convolving seismic hazard and structural response by using a number of idealizations to achieve a simple analytical form. The most heavily criticized approximation of the SAC/FEMA formats is the first‐order power‐law fit of the hazard curve. It results to unacceptable errors whenever the curvature of the hazard function becomes significant. Adopting a second‐order fit, instead, allows capturing the hazard curvature at the cost of necessitating new analytic forms. The new set of equations is a complete replacement of the original, enabling (a) accurate estimation of the mean annual frequency of limit‐state exceedance and (b) safety checking for specified performance objectives in a code‐compatible format. More importantly, the flexibility of higher‐order fitting guarantees a wider‐range validity of the local hazard approximation. Thus, it enables the inversion of the formulas for practically estimating the allowable demand or the required capacity to fulfill any design objective. Copyright © 2012 John Wiley & Sons, Ltd.     

Pre- and post-earthquake regional loss assessment using deep learning

As urban systems become more highly sophisticated and interdependent, their vulnerability to earthquake events exhibits a significant level of uncertainties. Thus, community-level seismic risk assessments are indispensable to facilitate decision making for effective hazard mitigation and disaster responses. To this end, new frameworks for pre- and post-earthquake regional loss assessments are proposed using deep learning methods. First, to improve the accuracy of the response prediction of individual structures during the pre-earthquake loss assessment, a widely used nonlinear static procedure is replaced by the recently developed probabilistic deep neural network model. The variabilities of the nonlinear responses of a structural system given the seismic intensity can be quantified during the loss assessment process. Second, to facilitate near-real-time post-earthquake loss assessments, an adaptive algorithm, which identifies the optimal number and locations of sensors in a given urban area, is proposed. Using a deep neural network that estimates area-wide structural damage given the spatial distribution of the seismic intensity levels as a surrogate model, the algorithm adaptively places additional sensors at property lots at which errors from surrogate estimations of the structural damage are the greatest. Note that the surrogate model is constructed before earthquake events using simulated datasets. To test and demonstrate the proposed frameworks, the paper introduces thorough numerical investigations of two hypothetical urban communities. The proposed frameworks using the deep learning methods are expected to make critical advances in pre- and post-earthquake regional loss assessments.     

A probabilistic approach for estimating the seismic response of elasto‐plastic SDOF systems

The seismic response of elasto‐plastic structures to both recorded and generated accelerograms is characterized by a large scattering of the results, even for accelerograms with similar peak ground acceleration values and frequency content. According to current code recommendations a design value of the seismic response of an elasto‐plastic structure can be computed as the mean of the responses to a certain number of spectrum‐fitting generated accelerograms. A more effective probabilistic approach is presented herein. It allows the analyst to calculate a design value of the seismic response characterized by a predefined non‐exceedance probability using a limited number of generated accelerograms. The results of the performed analyses are presented in diagrams that can be used for structural design applications. The applicability of the proposed method is demonstrated in the case of an elasto‐plastic structural system and the results are compared with those obtained applying current code recommendations. Copyright © 2005 John Wiley & Sons, Ltd.     

Ground motion selection for simulation‐based seismic hazard and structural reliability assessment

This paper examines four methods by which ground motions can be selected for dynamic seismic response analyses of engineered systems when the underlying seismic hazard is quantified via ground motion simulation rather than empirical ground motion prediction equations. Even with simulation‐based seismic hazard, a ground motion selection process is still required in order to extract a small number of time series from the much larger set developed as part of the hazard calculation. Four specific methods are presented for ground motion selection from simulation‐based seismic hazard analyses, and pros and cons of each are discussed via a simple and reproducible illustrative example. One of the four methods (method 1 ‘direct analysis’) provides a ‘benchmark’ result (i.e., using all simulated ground motions), enabling the consistency of the other three more efficient selection methods to be addressed. Method 2 (‘stratified sampling’) is a relatively simple way to achieve a significant reduction in the number of ground motions required through selecting subsets of ground motions binned based on an intensity measure, IM. Method 3 (‘simple multiple stripes’) has the benefit of being consistent with conventional seismic assessment practice using as‐recorded ground motions, but both methods 2 and 3 are strongly dependent on the efficiency of the conditioning IM to predict the seismic responses of interest. Method 4 (‘generalized conditional intensity measure‐based selection’) is consistent with ‘advanced’ selection methods used for as‐recorded ground motions and selects subsets of ground motions based on multiple IMs, thus overcoming this limitation in methods 2 and 3. Copyright © 2015 John Wiley & Sons, Ltd.     

Analytical investigations of seismic responses for reinforced concrete bridge columns subjected to strong near-fault ground motion

Strong near-fault ground motion, usually caused by the fault-rupture and characterized by a pulse-like velocity- wave form, often causes dramatic instantaneous seismic energy (Jadhav and Jangid 2006). Some reinforced concrete (RC) bridge columns, even those built according to ductile design principles, were damaged in the 1999 Chi-Chi earthquake. Thus, it is very important to evaluate the seismic response of a RC bridge column to improve its seismic design and prevent future damage. Nonlinear time history analysis using step-by-step integration is capable of tracing the dynamic response of a structure during the entire vibration period and is able to accommodate the pulsing wave form. However, the accuracy of the numerical results is very sensitive to the modeling of the nonlinear load-deformation relationship of the structural member. FEMA 273 and ATC-40 provide the modeling parameters for structural nonlinear analyses of RC beams and RC columns. They use three parameters to define the plastic rotation angles and a residual strength ratio to describe the nonlinear load- deformation relationship of an RC member. Structural nonlinear analyses are performed based on these parameters. This method provides a convenient way to obtain the nonlinear seismic responses of RC structures. However, the accuracy of the numerical solutions might be further improved. For this purpose, results from a previous study on modeling of the static pushover analyses for RC bridge columns (Sung et al. 2005) is adopted for the nonlinear time history analysis presented herein to evaluate the structural responses excited by a near-fault ground motion. To ensure the reliability of this approach, the numerical results were compared to experimental results. The results confirm that the proposed approach is valid.     

Improved performance‐based seismic assessment of buildings by utilizing Bayesian statistics

This paper addresses two important issues of concern to practicing engineers and researchers alike in application of performance‐based seismic assessment (PBSA) methodology on buildings: (i) the number of ground motion records required to exercise PBSA—current practice (FEMA P‐58‐1) requires eleven or more pairs of motions for this purpose, and (ii) the time and effort associated with performing the number of nonlinear response history analyses required to exercise PBSA. We present a method for exercising of PBSA that employs classical linear modal analysis to develop a first estimate (i.e., a priori) of probability distribution of loss, followed by utilizing Bayesian statistics to update this estimate using estimates of loss obtained by utilizing a small number of nonlinear response history analyses of a detailed model of the building (i.e., posterior). The proposed technique is used to assess the distribution of monetary loss of two case studies, a 4‐story reinforced concrete moment‐resisting frame building and a 20‐story steel moment‐resisting frame building, both located in Los Angeles, for a ground motion hazard with 10% probability of exceedance in 50 years. The efficiency of the proposed PBSA method is demonstrated by showing the similarity between the distribution of monetary loss at each story of case study buildings obtained from the traditional/sophisticated PBSA methodology and the proposed PBSA method in this study. Copyright © 2015 John Wiley & Sons, Ltd.     

Interbuilding interpolation of peak seismic response using spatially correlated demand parameters

Seismic structural responses recorded in instrumented buildings during an earthquake are used to provide insights into the demands placed on neighboring, noninstrumented buildings, using a framework to interpolate structural response demands across buildings. The interbuilding interpolation model relies on the spatial and structural correlations of responses in coregionally located buildings subjected to a seismic event. A dataset of response demands for a portfolio of reinforced concrete moment frame buildings is generated by performing nonlinear response history analyses on structural models using ground motions recorded from historical scenario earthquakes. The dataset is used to characterize the correlation between seismic demands across different buildings. Semivariograms are used to model spatial and structural correlations and then incorporated into a kriging algorithm, which forms the basis of the interpolation models. The effect of several model and dataset attributes and assumptions, for example, using intensity‐measure‐based versus engineering demand parameter‐based semivariograms, and size of training dataset relative to portfolio, on the overall performance are evaluated along with the limitations of the proposed model.     

Effectiveness of nonlinear static procedures for slender masonry towers

This paper investigates the accuracy of pushover-based methods in predicting the seismic response of slender masonry towers, through comparison with the results from a large number of nonlinear time-history dynamic analyses. In particular, conventional pushover analyses, in both their force- and displacement-based variants, are considered, and seismic assessment through the well-established N2 method is also addressed. The study is conducted by applying a simple non-linear elastic model recently developed and implemented in the computational code MADY to represent slender masonry structures. The model enables both pushover analyses and non-linear dynamic analyses to be performed with a minimum of effort. A multi-record incremental dynamic analysis carried out for a quite large number of structural cases, each of which is subjected to a comprehensive set of dynamic nonlinear analyses, is used to evaluate the accuracy of pushover methods in predicting the global structural response, as represented by the usual capacity curve together with a damage curve, both of which are compared with dynamic envelopes. Local responses, in terms of lateral displacements and the distribution of damage along the tower height are also compared. The results reveal that the key issue in the accuracy of pushover methods is the nature of the lateral load applied, that is, whether it is a force or a displacement. Different ranges of expected deformation are suggested for adopting each type of lateral load to better represent the actual behaviour of masonry towers and their damage under seismic events through pushover methods.     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Sensitivity of site response analysis on the number of ground motion records and implications for PSHA

This paper investigates issues related to the number of ground-motion records required for the performance of site response analysis and the inclusion of the site-specific amplification function within probabilistic seismic hazard calculations (PSHA). It explores the minimum number of records required for a robust estimation of the median and standard deviation of the site amplification function, as well as the impact of the selected ground-motion suites on the results of PSHA. Site response analyses are performed using both equivalent linear and nonlinear methodologies. Although the median amplification was observed to be relatively easy to capture, the standard deviation was seen to fluctuate considerably, especially when suites of few records were used. It was observed that in the case of the nonlinear site response analysis 10 records provide relatively stable estimates of the hazard curves for the majority of periods, while in the case of the equivalent linear analysis 20 records or more are required to achieve a similar level of accuracy.     

基于地脉动和地铁振动的钢筋混凝土建筑结构响应分析

在北京城区的一栋钢筋混凝土建筑(Reinforced Concrete building,简称RC)中,进行历时两天的地脉动和地铁振动观测.介绍了利用地脉动和地铁振动信号研究RC建筑结构响应的观测方法、仪器设备、数据采集和数据处理方法.对观测数据进行两种分析:(1)对连续的地脉动背景噪声,采用H/V谱比法;(2)对经过...     

Peak earthquake response of structures under multi-component excitations

Accurate estimation of the peak seismic responses of structures is important in earthquake resistant design. The internal force distributions and the seismic responses of structures are quite complex, since ground motions are multi- directional. One key issue is the uncertainty of the incident angle between the directions of ground motion and the reference axes of the structure. Different assumed seismic incidences can result in different peak values within the scope of design spectrum analysis for a given structure and earthquake ground motion record combination. Using time history analysis to determine the maximum structural responses excited by a given earthquake record requires repetitive calculations to determine the critical incident angle. This paper presents a transformation approach for relatively accurate and rapid determination of the maximum peak responses of a linear structure subjected to three-dimensional excitations within all possible seismic incident angles. The responses can be deformations, internal forces, strains and so on. An irregular building structure model is established using SAP2000 program. Several typical earthquake records and an artifi cial white noise are applied to the structure model to illustrate the variation of the maximum structural responses for different incident angles. Numerical results show that for many structural parameters, the variation can be greater than 100%. This method can be directly applied to time history analysis of structures using existing computer software to determine the peak responses without carrying out the analyses for all possible incident angles. It can also be used to verify and/or modify aseismic designs by using response spectrum analysis.