Relative displacement response spectra with pounding effect

To avoid unseating of a deck, an adequate seat width must be provided. The seat width is basically determined from maximum relative displacement between two bridge segments. Under a strong ground excitation, pounding between two decks may occur at a joint. The pounding will affect the response of two bridge segments. This research is conducted to investigate the effect of pounding on the relative displacement between two adjacent bridge segments. A simplified analytical model of two linear single‐degree‐of‐freedom systems is employed. To take into account the pounding, the laws of conservation of momentum and energy are applied. The analytical results are represented in the form of relative displacement response spectra with pounding effect. It is found that due to the pounding the relative displacement can be amplified, resulting in the requirement of a longer seat width to support a deck. The formulation of normalized relative displacement response spectra is presented together with an application example. It is found that the seat width determined from the relative displacement response spectra with pounding effect becomes close to the value specified in the Japanese design specifications for structures with large difference of natural periods. Copyright © 2001 John Wiley & Sons, Ltd.     

Conditional spectrum‐based ground motion record selection using average spectral acceleration

The use of a seismic intensity measure (IM) is paramount in decoupling seismic hazard and structural response estimation when assessing the performance of structures. For this to be valid, the IM needs to be sufficient;that is, the engineering demand parameter (EDP) response should be independent of other ground motion characteristics when conditioned on the IM. Whenever non‐trivial dependence is found, such as in the case of the IM being the first‐mode spectral acceleration, ground motion selection must be employed to generate sets of ground motion records that are consistent vis‐à‐vis the hazard conditioned on the IM. Conditional spectrum record selection is such a method for choosing records that are consistent with the site‐dependent spectral shape conditioned on the first‐mode spectral acceleration. Based on a single structural period, however the result may be suboptimal, or insufficient, for EDPs influenced by different period values, for example, peak interstory drifts or peak floor accelerations at different floors, potentially requiring different record suites for each. Recently, the log‐average spectral acceleration over a period range, AvgSA, has emerged as an improved scalar IM for building response estimation whose hazard can be evaluated using existing ground motion prediction equations. Herein, we present a recasting of conditional spectrum record selection that is based on AvgSA over a period range as the conditioning IM. This procedure ensures increased efficiency and sufficiency in simultaneously estimating multiple EDPs by means of a single IM. Copyright © 2017 John Wiley & Sons, Ltd.     

On the treatment of uncertainties in the development of fragility functions for earthquake loss estimation of building portfolios

State‐of‐the‐art methods for the assessment of building fragility consider the structural capacity and seismic demand variability in the estimation of the probability of exceeding different damage states. However, questions remain regarding the appropriate treatment of such sources of uncertainty from a statistical significance perspective. In this study, material, geometrical and mechanical properties of a number of building classes are simulated by means of a Monte Carlo sampling process in which the statistical distribution of the aforementioned parameters is taken into consideration. Record selection is performed in accordance with hazard‐consistent distributions of a comprehensive set of intensity measures, and issues related with sufficiency, efficiency, predictability and scaling robustness are addressed. Based on the appraised minimum number of ground motion records required to achieve statistically meaningful estimates of response variability conditioned on different levels of seismic intensity, the concept of conditional fragility functions is presented. These functions translate the probability of exceeding a set of damage states as a function of a secondary sufficient intensity measure, when records are selected and scaled for a particular level of primary seismic intensity parameter. It is demonstrated that this process allows a hazard‐consistent and statistically meaningful representation of uncertainty and correlation in the estimation of intensity‐dependent damage exceedance probabilities. Copyright © 2016 John Wiley & Sons, Ltd.     

Probabilistic seismic demand model for pounding risk assessment

Earthquake‐induced pounding of adjacent structures can cause severe structural damage, and advanced probabilistic approaches are needed to obtain a reliable estimate of the risk of impact. This study aims to develop an efficient and accurate probabilistic seismic demand model (PSDM) for pounding risk assessment between adjacent buildings, which is suitable for use within modern performance‐based engineering frameworks. In developing a PSDM, different choices can be made regarding the intensity measures (IMs) to be used, the record selection, the analysis technique applied for estimating the system response at increasing IM levels, and the model to be employed for describing the response statistics given the IM. In the present paper, some of these choices are analyzed and evaluated first by performing an extensive parametric study for the adjacent buildings modeled as linear single‐degree‐of‐freedom systems, and successively by considering more complex nonlinear multi‐degree‐of‐freedom building models. An efficient and accurate PSDM is defined using advanced intensity measures and a bilinear regression model for the response samples obtained by cloud analysis. The results of the study demonstrate that the proposed PSDM allows accurate estimates of the risk of pounding to be obtained while limiting the number of simulations required. Copyright © 2016 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.     

On the treatment of uncertainty in seismic vulnerability and portfolio risk assessment

In a related study developed by the authors, building fragility is represented by intensity‐specific distributions of damage exceedance probability of various damage states. The contribution of the latter has been demonstrated in the context of loss estimation of building portfolios, where it is shown that the proposed concept of conditional fragility functions provides the link between seismic intensity and the uncertainty in damage exceedance probabilities. In the present study, this methodology is extended to the definition of building vulnerability, whereby vulnerability functions are characterized by hazard‐consistent distributions of damage ratio per level of primary seismic intensity parameter—Sa(T₁). The latter is further included in a loss assessment framework, in which the impact of variability and spatial correlation of damage ratio in the probabilistic evaluation of seismic loss is accounted for, using test‐bed portfolios of 2, 5, and 8‐story precode reinforced concrete buildings located in the district of Lisbon, Portugal. This methodology is evaluated in comparison with current state‐of‐the‐art methods of vulnerability and loss calculation, highlighting the discrepancies that can arise in loss estimates when the variability and spatial distributions of damage ratio, influenced by ground motion properties other than the considered primary intensity measure, are not taken into account.     

Seismic analysis of a curved bridge considering deck‐abutment pounding interaction: an analytical investigation on the post‐impact response

Horizontal curved bridges are very common at intersections and at the changing angle of bridge alignment. Almost in every previous earthquake report, it can be seen that the columns of a curved segment experience torsional damage, and the curved decks are unseated from the abutment support. The main reason behind that phenomenon is the in‐plane deck rotation which results because of the complex dynamic coupling between two longitudinal directional vibrations. The curved decks are susceptible to deck rotation because in a curved segment, the centre of mass and the centre of stiffness generally lie outside the bridge deck and are not located at the same point. The pounding with the abutment often increases the rotational tendency of the deck. In this paper, a classical mechanics‐based approach is adopted to analytically estimate the deck rotation potential of curved bridge considering the deck‐abutment pounding interaction. The deck‐abutment pounding is modelled using non‐smooth techniques considering the Newton's impact law in the normal and Coulomb's friction in the tangential direction. Within the scope of this paper, a parametric study is performed to get the ideal combination of the column and bent arrangement and the gap distance. Copyright © 2016 John Wiley & Sons, Ltd.     

Average spectral acceleration as an intensity measure for collapse risk assessment

This paper investigates the performance of spectral acceleration averaged over a period range (Sa_avg) as an intensity measure (IM) for estimating the collapse risk of structures subjected to earthquake loading. The performance of Sa_avg is evaluated using the following criteria: efficiency, sufficiency, the availability or ease of developing probabilistic seismic hazard information in terms of the IM and the variability of collapse risk estimates produced by the IM. Comparisons are also made between Sa_avg and the more traditional IM: spectral acceleration at the first‐mode period of the structure (Sa(T₁)). Though most previous studies have evaluated IMs using a relatively limited set of structures, this paper considers nearly 700 moment‐resisting frame and shear wall structures of various heights to compare the efficiency and sufficiency of the IMs. The collapse risk estimates produced by Sa_avg and Sa(T₁) are also compared, and the variability of the risk estimates is evaluated when different ground motion sets are used to assess the structural response. The results of this paper suggest that Sa_avg, when computed using an appropriate period range, is generally more efficient, more likely to be sufficient and provides more stable collapse risk estimates than Sa(T₁). Copyright © 2015 John Wiley & Sons, Ltd.     

Developing efficient scalar and vector intensity measures for IDA capacity estimation by incorporating elastic spectral shape information

Scalar and vector intensity measures are developed for the efficient estimation of limit‐state capacities through incremental dynamic analysis (IDA) by exploiting the elastic spectral shape of individual records. IDA is a powerful analysis method that involves subjecting a structural model to several ground motion records, each scaled to multiple levels of intensity (measured by the intensity measure or IM), thus producing curves of structural response parameterized by the IM on top of which limit‐states can be defined and corresponding capacities can be calculated. When traditional IMs are used, such as the peak ground acceleration or the first‐mode spectral acceleration, the IM‐values of the capacities can display large record‐to‐record variability, forcing the use of many records to achieve reliable results. By using single optimal spectral values as well as vectors and scalar combinations of them on three multistorey buildings significant dispersion reductions are realized. Furthermore, IDA is extended to vector IMs, resulting in intricate fractile IDA surfaces. The results reveal the most influential spectral regions/periods for each limit‐state and building, illustrating the evolution of such periods as the seismic intensity and the structural response increase towards global collapse. The ordinates of the elastic spectrum and the spectral shape of each individual record are found to significantly influence the seismic performance and they are shown to provide promising candidates for highly efficient IMs. Copyright © 2005 John Wiley & Sons, Ltd.     

Analytical expression between the impact damping ratio and the coefficient of restitution in the non‐linear viscoelastic model of structural pounding

Earthquake‐induced structural pounding has been recently intensively studied with the help of different models of impact force. It has been verified through comparisons, that the non‐linear viscoelastic model may be considered somewhat the most accurate one among them. The aim of this short paper is to derive an approximating formula relating the impact damping ratio, as a parameter of the model mentioned, with a more widely used coefficient of restitution. The accuracy of the derived analytical formulation has been confirmed through the comparison with the results of numerical simulations. Copyright © 2005 John Wiley & Sons, Ltd.     

Implications of seismic pounding on the longitudinal response of multi-span bridges-an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach, Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is essential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

适用于全周期结构的速度脉冲型地震动强度表征参数研究

鉴于传统的地震动强度表征参数（IM）不能有效地反映速度脉冲型地震动的破坏特征,需要研究能够在全周期段内表征速度脉冲型地震动强度的参数。本文首先从NGA-West2强震数据库中选取了236条速度脉冲记录,分析了42种地震动参数之间的相似性和相关性,初步给出了速度脉冲型地震动强度的表征参数;其次,利用单自由度体系动力时程分析方法,研究了不同延性μ条件下速度脉冲型地震动强度表征参数与最大非线性位移u_m之间的相关性系数随周期T的变化特征,并通过线性回归和离差分析方法确定了初步给出的速度脉冲型地震动强度表征参数的有效性及其应用范围;最后,将速度脉冲对加速度反应谱的放大系数A_f作为速度脉冲型地震动强度表征参数,并验证其有效性。结果表明:① 当0＜T＜1 s时,S_a（T）作为速度脉冲型地震动强度表征参数的有效性较好;② 当1＜T＜3 s时,S_a,avg,S_v,avg,PPV,I_f和PGV作为速度脉冲型地震动强度表征参数的有效性较好;③ 当3＜T＜6 s时,S_a,avg,S_v,avg,PPV,I_f,PGV和S_a（T）不宜作为速度脉冲型地震动强度表征参数;④ 当0＜T＜6 s时,A_f作为速度脉冲型地震动强度表征参数的有效性较好,而且,当结构自振周期小于速度脉冲周期时,A_f作为速度脉冲型地震动强度表征参数时u_m的离散性最小。      

The implications of regional variations in rainfall for reconstructing rainfall patterns using tree rings

In Australia, multidecadal periods of floods and droughts have major economic consequences. Due to the short duration of Australian instrumental precipitation records, it is difficult to determine the patterns of these multidecadal periods. Proxy records can be used to create long‐term rainfall reconstructions for regions that are lacking instrumental data. However, the spatial extent over which single‐site proxy records can be applied is poorly understood. Southeast Queensland (SEQ) is an area where tree rings can be used to reconstruct long‐term rainfall patterns, but their regional representation is unknown. In this study, the spatial variability in rainfall across SEQ is investigated from 1908 to 2007 using 140 instrumental rainfall stations. Pearson correlation analysis between stations is used to create groups at the r = 0.80, 0.85, and 0.90 correlation levels, and then annual deviations from the mean are determined. These patterns indicate that rainfall is not uniform across SEQ but can be broken into 2 main spatially consistent groups. Each of these groups is broken down into several subgroups with higher correlation levels. Long‐term streamflow records are found to be correlated to rainfall patterns local to the streamflow stations, indicating that analysis of extreme events should consider spatial precipitation variability. Finally, the only currently available proxy rainfall reconstruction for the region, a 140‐year Toona ciliata tree ring width record from Lamington National Park, is compared to rainfall groups at different correlation levels across all of SEQ. The correlation between the reconstruction and the rainfall station groupings is best for the groups within which the tree‐ring record is spatially located, and this correlation improves as rainfall group correlation increases. Correlation is nearly nonexistent for groupings located at a distance from the tree‐ring site. These results demonstrate the importance of assessing the spatial variability of precipitation so that the spatial applicability of proxy records can be assessed.     

Modelling three‐dimensional non‐linear seismic performance of elevated bridges with emphasis on pounding of girders

Unseating of bridge girders/decks during earthquakes is very harmful to the safety and serviceability of bridges. Evidence from recent severe earthquakes indicates that in addition to damage along longitudinal direction, lateral displacement and rotation of bridge girders caused by pounding to adjacent girders can also lead to unseating. To simulate this effect, 3D modelling of the dynamic performance of whole bridge structures, including pounding, is needed strongly. This paper presents a 3D model that is practically suitable to precisely analyse pounding between bridge girders. Experiments have been conducted to verify the proposed pounding model. The 3D non‐linear modelling of steel elevated bridges is also discussed. A general‐purpose dynamic analysis program for bridges, namely dynamic analysis of bridge systems (DABS) has been developed. Seismic analyses on a chosen three‐span steel bridge are conducted for several cases including pounding as a case study. The applicability of the proposed pounding model is illustrated by the computations. The effects of poundings on the response of bridge girders are discussed and the computation results are given. Copyright © 2002 John Wiley & Sons, Ltd.     

论确定地震震源深度的地震宏观方法及其解答

作者基于在近场震源不能视作点源的认识,分析导出了相当于线、面源幅射场的深度公式,进而对源的类型不予作假定,将源指标的几何扩散率n作为待定参数,导出了一个物理意义明确且普遍化的震源深度公式。该公式的诸种解法中,以计算方法较准确,精度高;作图求解有较直观的优点,但准确性差,精度低;图算法仅作为获取粗略值和考察数据的均匀性用。用该公式对我国发生的一些不同震级的地震的震源深度进行了计算,经对比,效果很好。利用计算所得震源类型,初步研究了这些地震的震源几何学,并且首次给出了宏观地震震源深度测定值的标准误差。     

Performance of base‐isolated reinforced concrete buildings under bidirectional seismic excitation considering pounding with retaining walls including friction effects

Seismic pounding of base‐isolated buildings has been mostly studied in the past assuming unidirectional excitation. Therefore, in this study, the effects of seismic pounding on the response of base‐isolated reinforced concrete buildings under bidirectional excitation are investigated. For this purpose, a three‐dimensional finite element model of a code‐compliant four‐story building is considered, where a newly developed contact element that accounts for friction and is capable of simulating pounding with retaining walls at the base, is used. Nonlinear behavior of the superstructure as well as the isolation system is considered. The performance of the building is evaluated separately for far‐fault non‐pulse‐like ground motions and near‐fault pulse‐like ground motions, which are weighted scaled to represent two levels of shaking viz. the design earthquake (DE) level and the risk‐targeted maximum considered earthquake (MCE_R) level. Nonlinear time‐history analyses are carried out considering lower bound as well as upper bound properties of isolators. The influence of separation distance between the building and the retaining walls at the base is also investigated. It is found that if pounding is avoided, the performance of the building is satisfactory in terms of limiting structural and nonstructural damage, under DE‐level motions and MCE_R‐level far‐fault motions, whereas unacceptably large demands are imposed by MCE_R‐level near‐fault motions. In the case of seismic pounding, MCE_R‐level near‐fault motions are found to be detrimental, where the effect of pounding is mostly concentrated at the first story. In addition, it is determined that considering unidirectional excitation instead of bidirectional excitation for MCE_R‐level near‐fault motions provides highly unconservative estimates of superstructure demands. Copyright © 2014 John Wiley & Sons, Ltd.     

Near‐fault effects on residual displacements of RC structures

Residual displacements of single‐degree‐of‐freedom systems due to ground motions with velocity pulses or fling step displacements are presented as a function of period T and of its ratio to the pulse period T_p. Four hysteretic behaviors are considered: bilinear elastoplastic, stiffness‐degrading with cycling, stiffness‐cum‐strength degrading, with or without pinching. When expressed in terms of T/T_p, peak inelastic and residual displacements due to motions with a pulse or fling appear similar to those due to far‐fault motions, if the response to far‐field records are expressed in terms of the ratio of T to the record's characteristic period. However, as the latter is usually much shorter than the pulse period of motions with fling, the range of periods of interest for common structures becomes a short‐period range under fling motions and exhibits very large amplification of residual and peak inelastic displacements. Similar, but less acute, are the effects of motions with a velocity pulse. Wavelets of different complexity are studied as approximations to near‐fault records. Simple two‐parameter wavelets for fling motions overestimate peak inelastic displacements; those for pulse‐type motions overestimate residual displacements. A more complex four‐parameter wavelet for motions with a velocity pulse predicts overall well residual and peak displacements due to either pulse‐ or fling‐type motions; a hard‐to‐identify parameter of the wavelet impacts little computed residual displacements; another significantly affects them and should be carefully estimated from the record. Even this most successful of wavelets overpredicts residual displacements for the periods of engineering interest. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Interrill erosion on cultivated Greek soils: modelling sediment delivery

For interrill erosion, raindrop‐induced detachment and transport of sediment by rainfall‐disturbed sheet flow are the predominant processes, while detachment by sheet flow and transport by raindrop impact are negligible. In general, interrill subprocesses are inter‐actively affected by rainfall, soil and surface properties. The objective of this work was to study the relationships among interrill runoff and sediment loss and some selected para‐meters, for cultivated soils in central Greece, and also the development of a formula for predicting single storm sediment delivery. Runoff and soil loss measurement field experiments have been conducted for a 3·5‐year period, under natural storms. The soils studied were developed on Tertiary calcareous materials and Quaternary alluvial deposits and were textured from sandy loam to clay. The second group of soils showed greater susceptibility to sealing and erosion than the first group. Single storm sediment loss was mainly affected by rain and runoff erosivity, being significantly correlated with rain kinetic energy (r = 0·64***), its maximum 30‐minute intensity (r = 0·64***) and runoff amount (r = 0·56***). Runoff had the greatest correlation with rain kinetic energy (r = 0·64***). A complementary effect on soil loss was detected between rain kinetic energy and its maximum 30‐minute intensity. The same was true for rain kinetic energy and topsoil aggregate instability, on surface seal formation and thus on infiltration characteristics and overland flow rate. Empirical analysis showed that the following formula can be used for the successful prediction of sediment delivery (D_i): D_i = 0·638βEI₃₀tan(θ) (R² = 0·893***), where β is a topsoil aggregate instability index, E the rain kinetic energy, I₃₀ the maximum 30‐minute rain intensity and θ the slope angle. It describes soil erodibility using a topsoil aggregate instability index, which can be determined easily by a simple laboratory technique, and runoff through the product of this index and rain kinetic energy. Copyright © 2006 John Wiley & Sons, Ltd.     

Spectral shape,epsilon and record selection

Selection of earthquake ground motions is considered with the goal of accurately estimating the response of a structure at a specified ground motion intensity, as measured by spectral acceleration at the first‐mode period of the structure, Sa(T₁). Consideration is given to the magnitude, distance and epsilon (ε) values of ground motions. First, it is seen that selecting records based on their ε values is more effective than selecting records based on magnitude and distance. Second, a method is discussed for finding the conditional response spectrum of a ground motion, given a level of Sa(T₁) and its associated mean (disaggregation‐based) causal magnitude, distance and ε value. Records can then be selected to match the mean of this target spectrum, and the same benefits are achieved as when records are selected based on ε. This mean target spectrum differs from a Uniform Hazard Spectrum, and it is argued that this new spectrum is a more appropriate target for record selection. When properly selecting records based on either spectral shape or ε, the reductions in bias and variance of resulting structural response estimates are comparable to the reductions achieved by using a vector‐valued measure of earthquake intensity. Copyright © 2006 John Wiley & Sons, Ltd.