Intensity measures for the assessment of the seismic response of buried steel pipelines

To estimate the demand of structures, investigating the correlation between engineering demand parameters and intensity measures (IMs) is of prime importance in performance-based earthquake engineering. In the present paper, the efficiency and sufficiency of some IMs for evaluating the seismic response of buried steel pipelines are investigated. Six buried pipe models with different diameter to thickness and burial depth to diameter ratios, and different soil properties are subjected to an ensemble of 30 far-field earthquake ground motion records. The records are scaled to several intensity levels and a number of incremental dynamic analyses are performed. The approach used in the analyses is finite element modeling. Pipes are modeled using shell elements while equivalent springs and dashpots are used for modeling the soil. Several ground motion intensity measures are used to investigate their efficiency and sufficiency in assessing the seismic demand and capacity of the buried steel pipelines in terms of engineering demand parameter measured by the peak axial compressive strain at the critical section of the pipe. Using the regression analysis, efficient and sufficient IMs are proposed for two groups of buried pipelines separately. The first one is a group of pipes buried in soils with low stiffness and the second one is those buried in soils with higher stiffness. It is concluded that for the first group of pipes, \(\sqrt {{\text{VSI}}[\upomega_{1} ({\text{PGD}} + {\text{RMS}}_{\text{d}} )]}\) followed by root mean square of displacement (RMS_d) are the optimal IMs based on both efficiency and sufficiency; and for the second group, the only optimal IM is PGD²/RMS_d.     

Structural performance assessment under near‐source pulse‐like ground motions using advanced ground motion intensity measures

This paper demonstrates the effectiveness of utilizing advanced ground motion intensity measures (IMs) to evaluate the seismic performance of a structure subject to near‐source ground motions. Ordinary records are, in addition, utilized to demonstrate the robustness of the advanced IM with respect to record selection and scaling. To perform nonlinear dynamic analyses (NDAs), ground motions need to be selected; as a result, choosing records that are not representative of the site hazard can alter the seismic performance of structures. The median collapse capacity (in terms of IM), for example, can be systematically dictated by including a few aggressive or benign pulse‐like records into the record set used for analyses. In this paper, the elastic‐based IM such as the pseudo‐spectral acceleration (S_a) or a vector of S_a and epsilon has been demonstrated to be deficient to assess the structural responses subject to pulse‐like motions. Using advanced IMs can be, however, more accurate in terms of probabilistic response prediction. Scaling earthquake records using advanced IMs (e.g. inelastic spectral displacement, S_di, and IM _1I&2E; the latter is for the significant higher‐mode contribution structures) subject to ordinary and/or pulse‐like records is efficient, sufficient, and robust relative to record selection and scaling. As a result, detailed record selection is not necessary, and records with virtually any magnitude, distance, epsilon and pulse period can be selected for NDAs. Copyright © 2008 John Wiley & Sons, Ltd.     

A spectral-velocity-based combination-type earthquake intensity measure for super high-rise buildings

A spectral-velocity-based combination-type ground motion intensity measure (IM), which is inspired by the superior sensitivity of spectral velocity to structural response compared with other two spectral quantities, is proposed for super high-rise building structures with the consideration of the characteristics of ground motions and structures themselves. Two super high-rise buildings with typical frame/core-tube/outrigger lateral resisting system and a wide range of structural height (H = 258 m~660 m) are deliberately selected to identify the correlation between the maximum inter-story drift ratio and nineteen IMs developed in recent decade together with the proposed IM, with sixty chosen far-field and near-field pulse-like ground motions. With the suggested optimal number of lower vibration modes and corresponding combination factors, the efficiency, sufficiency and the scaling robustness of the proposed IM is further demonstrated. In addition, the relative sufficiency measures of other IMs with respect to the proposed IM are investigated. The results from the study indicate that, the proposed IM is believed, from the standpoint of efficiency, sufficiency, relative sufficiency measure and scaling robustness, to be a more specialized and desirable tool for super high-rise buildings, either for far-field or near-field ground motions.     

Spectral shape proxies and nonlinear structural response

In this paper, spectral-shape-based intensity measures (IMs) are discussed with respect to ordinary, pulse-like and narrow-band records. First, the analyses address the ability of these IMs to capture the peak and cumulative damage potentials of ground motions. Second, a new vector-valued ground motion IM based on the spectral acceleration at the first mode of the structure, Sa(T₁), and a parameter proxy for the spectral shape, namely N_p, is introduced. The vector 〈Sa,N_p〉 is compared to other state-of-the-art IMs in terms of estimation of the seismic response of nonlinear single degree of freedom systems, reinforced concrete and steel moment resisting frames. Results show that 〈Sa,N_p〉 may be especially useful to represent the ground motion potential in the case of records with peculiar spectral shape. Further, it is shown that 〈Sa,N_p〉 has the properties of efficiency, sufficiency and scaling robustness. Finally, a scalar ground motion IM based on Sa(T₁) and N_p is also discussed, and the possibility to compute the seismic hazard analysis for it is illustrated.     

A ground motion selection algorithm based on the generalized conditional intensity measure approach

An algorithm is presented for the selection of ground motions for use in seismic response analysis. The algorithm is based on the use of random realizations from the conditional multivariate distribution of ground motion intensity measures, IM|IM_j, obtained from the generalized conditional intensity measure (GCIM) approach. The algorithm can be applied to the selection of both as-recorded amplitude-scaled and synthetic/simulated ground motions. A key feature is that the generality of the GCIM methodology allows for ground motion selection based on only explicit measures of the ground motions themselves, as represented by the various IM’s considered, rather than implicit causal parameters (e.g., source magnitude, source-to-site distance) which are presently used in other contemporary ground motion selection procedures. Several examples are used to illustrate the salient features of the algorithm, including: the effect of intensity measures considered; and the properties of ground motions selected for multiple exceedance probabilities. The flexibility of the proposed algorithm coupled with the GCIM methodology allows for objective and consistent ground motion selection as a natural extension of seismic hazard analysis.     

The effect of amplitude scaling limits on conditional spectrum-based ground motion selection

Amplitude scaling is commonly used to select ground motions matching a target response spectrum. In this paper, the effect of scaling limits on ground motion selection, based on the conditional spectrum framework, is investigated. Target spectra are computed for four probabilistic seismic hazard cases in Western United States, and 16 ground motion suites are selected using different scaling limits (ie, 2, 5, 10, and 15). Comparison of spectral acceleration distributions of the selected ground motion suites demonstrates that the use of a scaling limit of 2 yields a relatively poor representation of the target spectra, because of the small limit leading to an insufficient number of available ground motions. It is also shown that increasing scaling limit results in selected ground motions with generally increased distributions of Arias intensity and significant duration Ds_5-75, implying that scaling limit consideration can significantly influence the cumulative and duration characteristics of selected ground motions. The ground motion suites selected are then used as input for slope displacement and structural dynamic analyses. Comparative results demonstrate that the consideration of scaling limits in ground motion selection has a notable influence on the distribution of the engineering demand parameters calculated (ie, slope displacement and interstory drift ratio). Finally, based on extensive analyses, a scaling limit range of 3 to 5 is recommended for general use when selecting ground motion records from the NGA-West2 database.     

Evaluation of ground motion selection and modification procedures using synthetic ground motions

This study presents a novel approach for evaluating ground motion selection and modification (GMSM) procedures in the context of probabilistic seismic demand analysis. In essence, synthetic ground motions are employed to derive the benchmark seismic demand hazard curve (SDHC), for any structure and response quantity of interest, and to establish the causal relationship between a GMSM procedure and the bias in its resulting estimate of the SDHC. An example is presented to illustrate how GMSM procedures may be evaluated using synthetic motions. To demonstrate the robustness of the proposed approach, two significantly different stochastic models for simulating ground motions are considered. By quantifying the bias in any estimate of the SDHC, the proposed approach enables the analyst to rank GMSM procedures in their ability to accurately estimate the SDHC, examine the sufficiency of intensity measures employed in ground motion selection, and assess the significance of the conditioning intensity measure in probabilistic seismic demand analysis. Copyright © 2015 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.     

Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses

Practical methods for the probability‐based seismic assessment of structures make use of estimates of demands produced by earthquakes of different intensities. The uncertainties associated with these estimates are highly dependent on the variable adopted as the intensity measure (IM, e.g., PGA, spectral acceleration, etc.). This generates the need to compare the efficiency of an originally adopted IMwith that of a new candidate. This implies comparing the dispersion of the demand measure (DM, e.g., maximum interstorey drift ratio, ductility demand, etc.) conditional to each of the two IMs. In order to obtain the demand estimates in a conventional way, a full set of dynamic response analyses should be performed for each IM under scrutiny, i.e., multiple records scaled at several fixed values of each IM. The procedure developed here serves to accelerate this comparison avoiding the effort required to evaluate the dynamic responses of the structure for all the ground motion time histories considered every time that a new IM is adopted. For this purpose, use is made of available results of analyses performed for a different (i.e., the original) IM. Two methods are proposed: the direct method involves performing a regression of the results obtained from the original analyses, taking the candidate IM as the independent variable. The indirect method involves rebuilding the probability density function of the DM given a defined value of the candidate IM by means of the total probability theorem, using the results of the original analyses and certain data relating the two IMs. The proposed methods have been tested by application to several SDOF systems with different periods and different cyclic‐response backbone curves. The conditions affecting their approximation are explored, and some criteria to improve them are identified. The procedure can also be used to determine the optimum value of a parameter to be used in a parameter‐based IM. Copyright © 2004 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.     

Intensity measures for probabilistic assessment of non‐structural components acceleration demand

A fundamental issue in the framework of seismic probabilistic risk analysis is the choice of ground motion intensity measures (IMs). Based on the floor response spectrum method, the present contribution focuses on the ability of IMs to predict non‐structural components (NSCs) horizontal acceleration demand. A large panel of IMs is examined and a new IM, namely equipment relative average spectral acceleration (E‐ASA_R), is proposed for the purpose of NSCs acceleration demand prediction. The IMs efficiency and sufficiency comparisons are based on (i) the use of a large dataset of recorded earthquake ground motions; (ii) numerical analyses performed on three‐dimensional numerical models, representing actual structural wall and frame buildings; and (iii) systematic statistical analysis of the results. From the comparative study, the herein introduced E‐ASA_R shows high efficiency with respect to the estimation of maximum floor response spectra ordinates. Such efficiency is particularly remarkable in the case of structural wall buildings. Besides, the sufficiency and the simple formulation allowing the use of existing ground motion prediction models make the E‐ASA_R a promising IMs for seismic probabilistic risk assessment. Copyright © 2015 John Wiley & Sons, Ltd.     

A new energy-based ground motion selection and modification method limiting the dynamic response dispersion and preserving the median demand

A novel ground motion selection and modifications method to perform response history analysis of structures is presented in this paper. Currently, the accessibility of ground motion information permits the analysis of structures using real ground motion data. Predicting the dynamic behavior of structures is a primary objective; therefore, the selection of a set of ground motions that shows a reduction in the variability of the structural response and accuracy in preserving the median demand is a challenging task. The new selection and scaling procedure emerges from comparing a set of horizontal ground motions at various ranges of frequency. In this study, the conditional mean spectrum and the design response spectrum are used as target spectra, and the records that give an applicable and compelling contribution to the hazard are considered. It is possible to obtain a set of ground motions with similar seismic severity by matching the target spectrum at the period of interest T _ref , where the scaled spectrum should have an equivalent Housner intensity in the period range 0.2T _ref –2T _ref . The horizontal components for every band of frequency is obtained using a specific index that depends on the energy-frequency trend’s shape as well as on its scattering degree around the mean value. This allows obtaining a set of spectrum-compatible records with almost identical severity and low dispersion of the structural response parameters. The methodology has been tested showing a significant effectiveness in terms of low variability of parameters and accuracy in preserving the median demand for a given hazard scenario.     

A method for computing interstory drift spectra with consideration of gravity effects

Vertical loads such as gravity may have an important influence on the seismic response of buildings. In this paper, the continuous shear-beam model is extended to study the seismic demand of shear buildings with consideration of the gravity load effect under near-field ground motions. An analytical solution of the free motion equation of as gravity shear beam model is provided in terms of a Bessel series. A method for computing interstory drift spectra is proposed. The interstory drift spectra for two near-field records with distinct pulses are presented to illustrate the effects of gravity and the damping ratio. The interstory drift spectra are also used to analyze the spectral characteristics of near fault ground motion during the 2008 Wenchuan earthquake. The effects of the gravity load ratio, damping ratio and higher modes are investigated and discussed.     

Ground motion scaling methods for different site conditions and structure characteristics

Non‐linear dynamic time‐history analyses conducted as part of a performance‐based seismic design approach often require that the ground motion records are scaled to a specified level of seismic intensity. Recent research has demonstrated that certain ground motion scaling methods can introduce a large scatter in the estimated seismic demands. The resulting demand estimates may be biased, leading to designs with significant uncertainty and unknown margins of safety, unless a relatively large ensemble of ground motion records is used. This paper investigates the effectiveness of seven ground motion scaling methods in reducing the scatter in estimated peak lateral displacement demands. Non‐linear single‐degree‐of‐freedom systems and non‐linear multi‐degree‐of‐freedom systems are considered with different site conditions (site soil profile and epicentral distance) and structural characteristics (yield strength, period, and hysteretic behavior). It is shown that scaling methods that work well for ground motions representative of stiff soil and far‐field conditions lose their effectiveness for soft soil and near‐field conditions for a wide range of structural characteristics. Copyright © 2003 John Wiley & Sons, Ltd.     

Prediction of spatially distributed seismic demands in specific structures: Structural response to loss estimation

A companion paper has investigated the effects of intensity measure (IM) selection in the prediction of spatially distributed response in a multi‐degree‐of‐freedom structure. This paper extends from structural response prediction to performance assessment metrics such as probability of structural collapse; probability of exceeding a specified level of demand or direct repair cost; and the distribution of direct repair loss for a given level of ground motion. In addition, a method is proposed to account for the effect of varying seismological properties of ground motions on seismic demand that does not require different ground motion records to be used for each intensity level. Results illustrate that the conventional IM, spectral displacement at the first mode, S_de(T₁), produces higher risk estimates than alternative velocity‐based IM's, namely spectrum intensity, SI, and peak ground velocity, PGV, because of its high uncertainty in ground motion prediction and poor efficiency in predicting peak acceleration demands. Copyright © 2009 John Wiley & Sons, Ltd.     

Generation of probabilistic displacement response spectra for displacement-based design

Displacement response spectrum (DRS), as the input, is of great significance to the displacement-based design just like the acceleration response spectrum to the traditional force-based design. Although the procedure of performance-based, in particular the displacement-based design has achieved considerable development, there is not a general DRS covering an enough long period range for common seismic design yet. This paper develops a systematic ground motion data processing procedure for the purpose of correcting the noise in the earthquake records and generating consistent DRS for seismic design. An adaptive algorithm is proposed to determine the cutoff frequency of the high-pass digital filter. The DRS of more than 500 recorded earthquake ground motions are generated and they are classified into three groups according to the ratio of the peak ground acceleration to the peak ground velocity (A/V) and/or the ratio of the peak ground velocity to the peak ground displacement (V/D). In each group, all the ground motions are normalized with respect to a selected scaling factor. Their corresponding DRS are obtained and then averaged to get the mean and standard deviation DRS, which can be used for both deterministic and probabilistic displacement-based design.     

Ductility‐dependent intensity measure that accounts for ground‐motion spectral shape and duration

The calculated nonlinear structural responses of a building can vary greatly, even if recorded ground motions are scaled to the same spectral acceleration at a building's fundamental period. To reduce the variation in structural response at a particular ground‐motion intensity, this paper proposes an intensity measure (IM_comb) that accounts for the combined effects of spectral acceleration, ground‐motion duration, and response spectrum shape. The intensity measure includes a new measure of spectral shape that integrates the spectrum over a period range that depends on the structure's ductility. The new IM is efficient, sufficient, scalable, transparent, and versatile. These features make it suitable for evaluating the intensities of measured and simulated ground motions. The efficiency and sufficiency of the new IM is demonstrated for the following: (i) elastic‐perfectly plastic single‐degree‐of‐freedom (SDOF) oscillators with a variety of ductility demands and periods; (ii) ductile and brittle deteriorating SDOF systems with a variety of periods; and (iii) collapse analysis for 30 previously designed frames. The efficiency is attributable to the inclusion of duration and to the ductility dependence of the spectral shape measure. For each of these systems, the transparency of the intensity measure made it possible to identify the sensitivity of structural response to the various characteristics of the ground motion. Spectral shape affected all structures, but in particular, ductile structures. Duration only affected structures with cyclic deterioration. Copyright © 2015 John Wiley & Sons, Ltd.     

基于实测记录分析场地因素对海底地震动特性影响

目前基于海底实测记录的分析发现海底与陆地地震动特性存在明显差异,但难以进一步确定海底地震动特性的影响因素。在以往研究的基础上对比同次地震中相邻海底台站间地震动特性的差异,并分析造成差异的原因。以日本K-NET地震台网中6个海底强震台站及其相邻不同场地条件陆地台站监测的8次强震记录为研究对象,通过分析强震记录的峰值加速度、水平放大系数谱、竖向与水平反应谱的比谱等,对比分析不同海底台站地震动的特性,以及海底台站与相邻不同场地条件陆地台站地震动特性的差别。研究发现：（1）海底与陆地竖向地震动存在明显差异;（2）不同海底台站间地震动特性亦存在较大差异和明显的规律性,海底场地条件、地形等场地因素对海底地震动特性的影响较大;（3）海底水平向地震动反应谱的特征周期较大,谱特性介于陆地中硬土与软土场地间。     

Estimating ground motion incoherence through finite source simulation: a case study of the 1980 El-Asnam Earthquake

Spatial variability of ground motions has significant influence on dynamic response of extended structures such as bridges and tunnels. In this study, the widely used finite-source ground motion simulation approach, the so-called Empirical Green’s Function (EGF) method, is extended to synthesize seismic motions across an array of stations located at bedrock in the epicentral region of the 1980 El-Asnam region (North-West Algeria). The target event being simulated is the October 10 1980 \( M_{s} = 7.2 \) Earthquake, and the EGF is obtained from the ground motion recorded at Sogedia Factory station during the 8 November 1980 \( M_{L} = 5.6 \) aftershock. Coherency functions are then estimated from the simulated ground accelerations. A parametric study investigating the influence of shear wave velocity, earthquake magnitude, and epicentral distance is conducted by simulating ground acceleration for different scenarios using the Hybrid Green’s Function method. The main finding of the study is that finite source effects can cause significant loss in coherency at bedrock in the near-field. In the far-field, the source effect alone does not seem to produce incoherent motion, which implies that scattering and local site effects could be dominating there. Furthermore, coherency functions are found to be more sensitive to inter-station separation in the near-field than in the far-field. Increasing shear wave velocity seems to increase coherency functions, and larger earthquakes seem to produce more incoherent motion than smaller ones. The simulation method presented here produces incoherent motion mainly due to the finite source effect, while path effects are partially accounted for through the EGF, and local site effects are not considered. In this sense, the estimated coherency functions represent that of plane waves. A parametric model of plane wave coherency is calibrated and presented based on the simulation results. The results indicate that the parametric model can be used as a first approximation, and at least an upper bound of lagged coherency in the near-field region of the El-Asnam Earthquake scenario. This model could be useful in random vibration analysis or generation of spatially variable ground motion for time history analysis of lifeline structures in the study area.