Introduction of conditional mean spectrum and conditional spectrum in the practice of seismic safety evaluation in China

This paper aims at implementing and introducing the use of conditional mean spectrum (CMS) and conditional spectrum (CS) as the main input parameters in the practice of seismic safety evaluation (SSE) in China, instead of the currently used uniform hazard spectrum (UHS). For this purpose, a procedure for M-R-epsilon seismic hazard deaggregation in China was first developed. For illustration purposes, two different typical sites in China, with one to two dominant seismic zones, were considered as examples to carry out seismic hazard deaggregation and illustrate the construction of CMS/CS. Two types of correlation coefficients were used to generate CMS and the results were compared over a vibration period range of interest. Ground motion records were selected from the NSMONS (2007–2015) and PEER NGA-West2 databases to correspond to the target CMS and CS. Hazard consistency of the spectral accelerations of the selected ground motion records was evaluated and validated by computing the annual exceedance probability rate of the response spectra and comparing the results to the hazard curve corresponding to each site of concern at different periods. The tools developed in this work and their illustrative application to specific case studies in China are a first step towards the adoption of CMS and CS into the practice of seismic safety evaluation in this country.     

Incremental dynamic analysis of wood-frame houses in Canada: Effects of dominant earthquake scenarios on seismic fragility

Seismic fragility can be assessed by conducting incremental dynamic analysis (IDA). This study extends the current conditional mean spectrum (CMS)-based record selection approach for IDA by taking into account detailed seismic hazard information. The proposed method is applied to conventional wood-frame houses in Canada, across which dominant earthquake scenarios and associated hazard levels vary significantly. Effects due to different seismic environments, site conditions, CMS-based record selection methods, and house models are investigated by comparing various seismic fragility models. Moreover, relative impact of the key characteristics is evaluated in terms of seismic loss curve for a group of wood-frame houses. Importantly, a close examination of regional seismic hazard characteristics using seismic hazard curve and seismic deaggregation facilitates the deeper understanding of the impact of ground motion characteristics on seismic fragility. A comprehensive and systematic assessment of key uncertainties associated with seismic fragility is provided.     

Occurrence of negative epsilon in seismic hazard analysis deaggregation,and its impact on target spectra computation

This paper investigates circumstances behind the occurrence of negative ε (the normalized difference between the spectral acceleration of a recorded ground motion and the median response predicted by a ground motion prediction equation) in probabilistic seismic hazard deaggregation. Negative ε values are of engineering interest because of their impact on the conditional mean spectrum (CMS), which is a proposed alternative to the uniform hazard spectrum (UHS) as a target spectrum for ground motion selection. In the case where target ε values from deaggregation are positive, the CMS calculation produces relatively lower response spectra than the UHS. Positive target ε values occur almost universally in active seismic regions at long return periods of engineering interest, but the possibility of negative target ε values is important because in the case of negative target ε, some relationships between the CMS and UHS would reverse. This paper describes the calculation of target ε, performs parametric studies to determine when negative ε values occur in deaggregation, and investigates the potential impact on target spectrum calculation and ground motion selection. The case studies indicate that special seismicity models and certain ground motion prediction equations have the most significant effect on ε values and a combination of these characteristics in Eastern North America creates the most likely situation for negative target ε to occur. CMS results are nonintuitive when the target ε is negative, but it is not clear that this is a common practical concern because negative target ε occurs only in well‐constrained areas. Copyright © 2011 John Wiley & Sons, Ltd.     

Probabilistic versus deterministic seismic hazard analysis: an integrated approach for siting problems

A methodology is proposed to determine design earthquakes for site-specific studies such as the siting of critical structures (power plants, waste disposals, large dams, etc.), strategic structures (fire stations, military commands, hospitals, etc.), or for seismic microzoning studies, matching the results of probabilistic seismic hazard analyses. This goal is achieved by calculating the source contribution to hazard and the magnitude–distance deaggregation, showing that, varying the selected frequency and the level of hazard, the reference earthquakes are changed as a result. A procedure is then adopted to minimize the residuals between the uniform hazard spectrum (target motion) and the design earthquake spectrum, to provide a specific earthquake scenario encompassing all the frequencies of the target motion. Finally, some considerations on the use and the influence exerted by ground motion uncertainty (σ) on hazard deaggregation are outlined.     

The effect of causal parameter bounds in PSHA‐based ground motion selection

In this paper the effect of causal parameter bounds (e.g. magnitude, source‐to‐site distance, and site condition) on ground motion selection, based on probabilistic seismic hazard analysis (PSHA) results, is investigated. Despite the prevalent application of causal parameter bounds in ground motion selection, present literature on the topic is cast in the context of a scenario earthquake of interest, and thus specific bounds for use in ground motion selection based on PSHA, and the implications of such bounds, is yet to be examined. Thirty‐six PSHA cases, which cover a wide range of causal rupture deaggregation distributions and site conditions, are considered to empirically investigate the effects of various causal parameter bounds on the characteristics of selected ground motions based on the generalized conditional intensity measure (GCIM) approach. It is demonstrated that the application of relatively ‘wide’ bounds on causal parameters effectively removes ground motions with drastically different characteristics with respect to the target seismic hazard and results in an improved representation of the target causal parameters. In contrast, the use of excessively ‘narrow’ bounds can lead to ground motion ensembles with a poor representation of the target intensity measure distributions, typically as a result of an insufficient number of prospective ground motions. Quantitative criteria for specifying bounds for general PSHA cases are provided, which are expected to be sufficient in the majority of problems encountered in ground motion selection for seismic demand analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

A site‐consistent method to quantify sufficiency of alternative IMs in relation to PSDA

In probabilistic seismic demand analysis, evaluation of the sufficiency of an intensity measure (IM) is an important criterion to avoid biased assessment of the demand hazard. However, there exists no metric to quantify the degree of sufficiency as per the criterion of Luco and Cornell (2007). This paper proposes a site‐specific unified measure for degree of sufficiency from all seismological parameters under consideration using a total information gain metric. This unified metric for sufficiency supports not only comparison of the performance of different IMs given a response quantity but also assessment of the performance of a particular IM across different response quantities. The proposed sufficiency metric was evaluated for a 4‐story steel moment frame building, and the influence of ground motion selection on the degree of sufficiency was investigated. It was observed that ground motion selection can have a significant impact on IM sufficiency. Because computing the total information gain requires continuous deaggregation across the IM space, an approximate deaggregation technique that allows for a more practical estimation of marginal deaggregation probabilities is proposed. It is expected that the total information gain metric proposed in this paper will aid in understanding the efficiency‐sufficiency relation, thus enabling the selection of a proper scalar IM for a given site and application in probabilistic seismic demand analysis.     

Conditional spectrum‐based ground motion selection. Part I: Hazard consistency for risk‐based assessments

The conditional spectrum (CS, with mean and variability) is a target response spectrum that links nonlinear dynamic analysis back to probabilistic seismic hazard analysis for ground motion selection. The CS is computed on the basis of a specified conditioning period, whereas structures under consideration may be sensitive to response spectral amplitudes at multiple periods of excitation. Questions remain regarding the appropriate choice of conditioning period when utilizing the CS as the target spectrum. This paper focuses on risk‐based assessments, which estimate the annual rate of exceeding a specified structural response amplitude. Seismic hazard analysis, ground motion selection, and nonlinear dynamic analysis are performed, using the conditional spectra with varying conditioning periods, to assess the performance of a 20‐story reinforced concrete frame structure. It is shown here that risk‐based assessments are relatively insensitive to the choice of conditioning period when the ground motions are carefully selected to ensure hazard consistency. This observed insensitivity to the conditioning period comes from the fact that, when CS‐based ground motion selection is used, the distributions of response spectra of the selected ground motions are consistent with the site ground motion hazard curves at all relevant periods; this consistency with the site hazard curves is independent of the conditioning period. The importance of an exact CS (which incorporates multiple causal earthquakes and ground motion prediction models) to achieve the appropriate spectral variability at periods away from the conditioning period is also highlighted. The findings of this paper are expected theoretically but have not been empirically demonstrated previously. Copyright © 2013 John Wiley & Sons, Ltd.     

Hazard-consistent response spectra in the Region of Murcia (Southeast Spain): comparison to earthquake-resistant provisions

Hazard-consistent ground-motion characterisations of three representative sites located in the Region of Murcia (southeast Spain) are presented. This is the area where the last three damaging events in Spain occurred and there is a significant amount of data for comparing them with seismic hazard estimates and earthquake-resistant provisions. Results of a probabilistic seismic hazard analysis are used to derive uniform hazard spectra (UHS) for the 475-year return period, on rock and soil conditions. Hazard deaggregation shows that the largest hazard contributions are due to small, local events for short-period target motions and to moderate, more distant events for long-period target motions. For each target motion and site considered, the associated specific response spectra (SRS) are obtained. It is shown that the combination of two SRS, for short- and long-period ground motions respectively, provides a good approximation to the UHS at each site. The UHS are compared to design response spectra contained in current Spanish and European seismic codes for the 475-year return period. For the three sites analysed, only the Eurocode 8 (EC8) type 2 spectrum captures the basic shape of the UHS (and not the EC8 type 1, as could be expected a priori). An alternative response spectrum, anchored at short- and long-period accelerations, is tested, providing a close match to the UHS spectra at the three sites. Results underline the important contribution of the frequent, low-to-moderate earthquakes that characterize the seismicity of this area to seismic hazard (at the 475-year return period).     

Response spectrum analysis of structures subjected to spatially varying motions

An important aspect of earthquake loads exerted on extended structures, or structures founded on several foundations, is the spatial variability of the seismic motion. Hence, a rigorous earthquake resistant design of lifeline structures should account for the spatial character of the seismic input, at least in an approximate way. A procedure is proposed which enables addressing the problem of multiply supported structures, subjected to imperfectly correlated seismic excitations, by means of an extension to the response spectrum method. A modified response spectrum model is developed for the design of extended facilities subjected to single and multicomponent ground motion. The modification procedure is based on adjusting each spectral value of the given design response spectrum by means of a correction factor, which depends on the structural properties and on the characteristics of the wave propagation phenomenon. Finally, the theoretical model is validated through digital simulation of seismic ground motion, whereby model predictions are found to be in good agreement with exact results.     

Wavelet-based response spectrum compatible synthesis of accelerograms—Eurocode application (EC8)

An integrated approach for addressing the problem of synthesizing artificial seismic accelerograms compatible with a given displacement design/target spectrum is presented in conjunction with aseismic design applications. Initially, a stochastic dynamics solution is used to obtain a family of simulated non-stationary earthquake records whose response spectrum is on the average in good agreement with the target spectrum. The degree of the agreement depends significantly on the adoption of an appropriate parametric evolutionary power spectral form, which is related to the target spectrum in an approximate manner. The performance of two commonly used spectral forms along with a newly proposed one is assessed with respect to the elastic displacement design spectrum defined by the European code regulations (EC8). Subsequently, the computational versatility of the family of harmonic wavelets is employed to modify iteratively the simulated records to satisfy the compatibility criteria for artificial accelerograms prescribed by EC8. In the process, baseline correction steps, ordinarily taken to ensure that the obtained accelerograms are characterized by physically meaningful velocity and displacement traces, are elucidated. Obviously, the presented approach can be used not only in the case of the EC8, for which extensive numerical results/examples are included, but also for any code provisions mandated by regulatory agencies. In any case, the presented numerical results can be quite useful in any aseismic design process dominated by the EC8 specifications.     

Scaling of response spectrum and duration for aftershocks

Aftershocks have the potential to cause collapse of a structure that has been already damaged by the preceding main shock. Seismic safety of a structure should therefore be ascertained through a damage analysis using the anticipated main shock and few larger-aftershock motions. Simulation of aftershock motions needs characterization of the seismic hazard due to aftershocks, and therefore it will be useful to develop a conditional scaling model that can predict the response spectrum of an anticipated aftershock motion consistent with the design spectrum of the main shock motion anticipated at the same station. In this study an attempt is made to develop a conditional scaling model for the pseudo spectral velocity spectrum via linear regression analysis on the aftershock and main shock recordings for the 1999 Chi–Chi earthquake. It is shown that it may be possible to obtain a simpler and approximate version of the conditional model from an unconditional model. Damage-causing potential of a ground motion also depends on its strong motion duration (SMD) and therefore a conditional scaling model is developed for SMD of the aftershock motion in several narrow frequency-bands. The model is developed for the larger-aftershock motions and it is shown that a reasonable replacement of such a model may be obtainable directly from an unconditional model. Finally, a simple weighted averaging scheme is proposed to obtain the composite SMD from the SMDs for different frequency bands by using the pseudo spectral acceleration spectrum of the motion.     

Evaluation of the exact conditional spectrum and generalized conditional intensity measure methods for ground motion selection

Two existing, contemporary ground motion selection and modification procedures – (i) exact conditional spectrum (CS‐exact) and (ii) generalized conditional intensity measure (GCIM) – are evaluated in their ability to accurately estimate seismic demand hazard curves (SDHCs) of a given structure at a specified site. The amount of effort involved in implementing these procedures to compute a single SDHC is studied, and a case study is chosen where rigorous benchmark SDHCs can be determined for evaluation purposes. By comparing estimates from ground motion selection and modification procedures with the benchmark, we conclude that estimates from CS‐exact are unbiased in many of the cases considered. The estimates from GCIM are even more accurate, as they are unbiased for most – but not all – of the cases where estimates from CS‐exact are biased. We find that it is possible to obtain biased SDHCs from GCIM, even after employing a very diverse collection of intensity measures to select ground motions and implementing its bias‐checking feature, because it is usually difficult to identify intensity measures that are truly ‘sufficient’ for the response of a complex, multi‐degree‐of‐freedom system. Copyright © 2015 John Wiley & Sons, Ltd.     

ATI介质中四次时差系数解析近似

非双曲（远偏移距）时差为各向异性介质中正、反演研究,特别是各向异性参数估计提供了重要信息.本文在任意空间取向TI（ATI）介质水平界面同类反射波四次时差系数(A4)精确解的基础上,进一步讨论我们推导得出的ATI介质中四次时差系数解析近似解,比较随CMP测线方位变化的近似解与精确解之间的差别,为利用近似解来解析研究ATI介质中非双曲时距以及参数反演提供有价值的信息．结合实际岩性资料的数值研究表明,ATI条件下四次时差系数近似解与精确解之间存在差别,不仅表现在A4数的大小及符号特征上,更突出地表现在A4系数随方位的变化特征上;在强各向异性条件下,近似解相比精确解存在较大误差．但在各向异性参数满足0ε-δδ｜<0.20的情况下,对于TI对称轴的特殊倾角范围(75°～80°),近似解与精确解的差别很小,可用近似解进行各向异性观测解释及参数反演．     

Introducing new design spectra derived from Italian recorded ground motions 1972 to 2017

The shape of design spectra, traditionally based on regions characterized by constant displacement, constant velocity, and constant acceleration, has been discussed from a conceptual point of view by Calvi (2018). In the same study, a formulation for the definition of the design spectra relying on four parameters was proposed. Predictive models are proposed herein to calculate these four parameters, conditional on magnitude and distance. These models were developed using a large number of recorded ground motions in Italy, and they allow defining combined spectral acceleration versus spectral displacement plots. Such design spectra are shown to reasonably interpolate the experimental data, resulting in acceleration and displacement demand that approximate the response spectra resulting from +1σ results obtained from recorded ground motions. While it is recognized that numerous additional parameter should be considered (eg, focal depth and fault distance, site amplification), it is also concluded that this approach to define the seismic demand is promising toward a rationalization of seismic design. A thorough application of the approach developed and preliminary tested in this work may result in a re‐visitation of seismic design approaches and, ultimately, in a more efficient use of the available resources.     

An alternative approach for computing seismic response with accidental eccentricity

Accidental eccentricity is a non-standard assumption for seismic design of tall buildings. Taking it into consideration requires reanalysis of seismic resistance, which requires either time consuming computation of natural vibration of eccentric structures or finding a static displacement solution by applying an approximated equivalent torsional moment for each eccentric case. This study proposes an alternative modal response spectrum analysis(MRSA) approach to calculate seismic responses with accidental eccentricity. The proposed approach, called the Rayleigh Ritz Projection-MRSA(RRP-MRSA), is developed based on MRSA and two strategies:(a) a RRP method to obtain a fast calculation of approximate modes of eccentric structures; and(b) an approach to assemble mass matrices of eccentric structures. The efficiency of RRP-MRSA is tested via engineering examples and compared with the standard MRSA(ST-MRSA) and one approximate method, i.e., the equivalent torsional moment hybrid MRSA(ETM-MRSA). Numerical results show that RRP-MRSA not only achieves almost the same precision as ST-MRSA, and is much better than ETM-MRSA, but is also more economical. Thus, RRP-MRSA can be in place of current accidental eccentricity computations in seismic design.     

A generalized conditional intensity measure approach and holistic ground‐motion selection

A generalized conditional intensity measure (GCIM) approach is proposed for use in the holistic selection of ground motions for any form of seismic response analysis. The essence of the method is the construction of the multivariate distribution of any set of ground‐motion intensity measures conditioned on the occurrence of a specific ground‐motion intensity measure (commonly obtained from probabilistic seismic hazard analysis). The approach therefore allows any number of ground‐motion intensity measures identified as important in a particular seismic response problem to be considered. A holistic method of ground‐motion selection is also proposed based on the statistical comparison, for each intensity measure, of the empirical distribution of the ground‐motion suite with the ‘target’ GCIM distribution. A simple procedure to estimate the magnitude of potential bias in the results of seismic response analyses when the ground‐motion suite does not conform to the GCIM distribution is also demonstrated. The combination of these three features of the approach make it entirely holistic in that: any level of complexity in ground‐motion selection for any seismic response analysis can be exercised; users explicitly understand the simplifications made in the selected suite of ground motions; and an approximate estimate of any bias associated with such simplifications is obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Conditional spectrum‐based ground motion selection. Part II: Intensity‐based assessments and evaluation of alternative target spectra

In a companion paper, an overview and problem definition was presented for ground motion selection on the basis of the conditional spectrum (CS), to perform risk‐based assessments (which estimate the annual rate of exceeding a specified structural response amplitude) for a 20‐story reinforced concrete frame structure. Here, the methodology is repeated for intensity‐based assessments (which estimate structural response for ground motions with a specified intensity level) to determine the effect of conditioning period. Additionally, intensity‐based and risk‐based assessments are evaluated for two other possible target spectra, specifically the uniform hazard spectrum (UHS) and the conditional mean spectrum (CMS, without variability).It is demonstrated for the structure considered that the choice of conditioning period in the CS can substantially impact structural response estimates in an intensity‐based assessment. When used for intensity‐based assessments, the UHS typically results in equal or higher median estimates of structural response than the CS; the CMS results in similar median estimates of structural response compared with the CS but exhibits lower dispersion because of the omission of variability. The choice of target spectrum is then evaluated for risk‐based assessments, showing that the UHS results in overestimation of structural response hazard, whereas the CMS results in underestimation. Additional analyses are completed for other structures to confirm the generality of the conclusions here. These findings have potentially important implications both for the intensity‐based seismic assessments using the CS in future building codes and the risk‐based seismic assessments typically used in performance‐based earthquake engineering applications. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic hazard assessment of Tehran,Iran with emphasis on near-fault rupture directivity effects

Many destructive earthquakes happened in Tehran, Iran in the last centuries. The existence of active faults like the North Tehran is the main cause of seismicity in this city. According to past investigations, it is estimated that in the scenario of activation of the North Tehran fault, many structures in Tehran will collapse. Therefore, it is necessary to incorporate the near field rupture directivity effects of this fault into the seismic hazard assessment of important sites in Tehran. In this study, using calculations coded in MATLAB,Probabilistic Seismic Hazard Analysis(PSHA) is conducted for an important site in Tehran. Following that, deaggregation technique is performed on PSHA and the contribution of seismic scenarios to hazard is obtained in the range of distance and magnitude. After identifying the North Tehran fault as the most hazardous source affecting the site in 10000-year return period, rupture directivity effects of this fault is incorporated into the seismic hazard assessment using Somerville et al.(1997) model with broadband approach and Shahi and Baker(2011) model with narrowband approach. The results show that the narrowband approach caused a 27% increase in the peak of response spectrum in 10000-year return period compared with the conventional PSHA. Therefore, it is necessary to incorporate the near fault rupture directivity effects into the higher levels of seismic hazard assessment attributed to important sites.     

A multidirectional conditional spectrum

This paper presents a procedure to generate multidirectional conditional spectra (MDCS) that allow for the characterisation of seismic demands at different angles of incidence. Being conditional on a particular period and its direction of maximum response, it is considered to be a natural evolution of the conditional spectrum to account for the effects of directionality, that is, the variation of seismic demands as a function of the angle of incidence of ground motions, which can have a significant effect on the performance of different kinds of structures. The three main components needed for the generation of MDCS are explained in detail. Monte Carlo simulations are conducted using different sampling methods to assess the effects of incorporating the correlation between demands at different orientations for the same oscillator period, and a novel correlation model is proposed for this purpose. The statistical characteristics of MDCS, their relation with the conditional spectrum, the advantages of the MDCS over previous definitions of orientation‐specific spectra, and prospective future developments are discussed.     

P-SV波展平变换的精确求解--以地震面波为例

以地震面波问题为例,提出P——SV波展平变换的精确求解方法并以此为基础讨论了近似求解方法的适用性及适用范围. 结果表明,展平变换指数m对最终结果没有显著影响,因此可选取任意值;在短波近似条件下,展平变换的近似解法是适当且合理的;展平变换的近似解法比精确解法的效率高一倍. 对于频率较低的问题,应采用精确的求解方法.