ALBERT

Description: Response Spectrum Analysis (RSA), one of the most popular methods to carry out the seismic design of multi-degree-offreedom (MDOF) structures, is based on the concept of modal superposition, by which the uncoupled equations of motion that represent each mode of vibration of the system can be solved independently and the resulting responses superimposed by assuming linear elastic behaviour. Each mode is represented by a single-degree-of-freedom (SDOF) system, whose peak response is retrieved from response spectra deemed suitable for design. However, while modal superposition allows for the total response of a MDOF system to be determined by simple addition of the individual modal responses at each time step, combination of spectral values needs to take into account the fact that peak modal responses do not necessarily occur at the same time or along the same horizontal directions. These considerations give rise to the use of modal and spatial combination rules that aim to calculate the likely peak response of a MDOF system instead of conservatively carrying out an algebraic sum of maxima. Current design codes prescribe methodologies that were defined in the 1970s and 1980s, such as the Complete Quadratic Combination (CQC) [1], its three-dimensional extension CQC3 [2], the Square Root of the Sum of the Squares (SRSS) [3], or the 30% rules [4], based mostly on random vibration theory. However, access to large numbers of ground motion records at the present time allow us to revisit these approaches from a data-driven perspective, and investigate the relationship across the peaks of SDOF responses to seismic excitation at different orientations and at different points in time, with the ultimate goal of characterising this relationship in a fully probabilistic way. This paper presents results of a study of SDOF demands obtained considering 1,218 accelerograms from the RESORCE database [5], whose two horizontal perpendicular components were rotated around all non-redundant angles every 2° and applied to SDOF systems with periods of vibration of 0.2, 1.0 and 3.0 seconds, and sets of secondary systems with periods ranging from 0.5 through 0.95 times the three aforementioned periods. The concept of peak response was extended to include all peaks with amplitudes above two alternative thresholds of 80% and 95% of the maximum absolute response. Two main kinds of parameters were studied and are presented: (i) time differences between peaks of the same component and across perpendicular components, and (ii) ratios of instantaneous displacement demands between perpendicular components and the same component for different oscillator periods, as one of the components reaches a peak in the oscillator’s response. While results for the latter resemble the idea of the 0.3 coefficient from the 30% rule in average terms, the dispersion associated with all these parameters is large and should not be neglected.

Description: The relation between the response of an elastic single degree of freedom oscillator subject to seismic shaking and the seismological characteristics of the input waveforms represented in terms of the Fourier amplitude spectrum (FAS) has become a topic of growing interest in the engineering seismological community in recent years. As simulations of ground motions assume a greater prominence in engineering design and databases of both strong and weak motion records expand exponentially, the need to reconcile the influence of the controlling seismological properties of the motions with their potential impacts on structural response is becoming ever more important. Prediction of ground motion in the Fourier amplitude domain has several key advantages when compared to that of the response spectrum, namely a closer relationship to the physical seismological properties of the source, path and site that can be inferred from more abundant small magnitude and weak motion data, as well as maintained linearity of site response at all frequencies. Recognising this, new empirical ground motion models have been developed in terms of FAS [1, 2], in addition to an inter-frequency correlation model that can facilitate the definition of conditional spectrum compatible empirical and simulated ground motion records for design [3]. In spite of these advantages, the usage of FAS in seismic hazard and risk analysis remains limited to the scaling of simulated ground motions in the development of median ground motion models using random vibration theory (RVT). One major factor behind this is that translation from FAS to response spectra via RVT requires joint characterization not only of ground motions across a range of frequencies but also of strong motion duration. However, this limitation could potentially be overcome if fragility functions were to be derived directly in terms of FAS. It is for this purpose that a comparison is made in this paper between the efficiency of intensity measures based on the FAS and those based on conventional response spectra for a set of simple building fragility models of the type commonly used in seismic risk analysis. The feasibility of achieving end-to-end loss estimation exclusively in the Fourier amplitude domain is subsequently explored. While its full range of benefits and limitations will require further study, the potential for embedding seismological theory and data more deeply into engineering applications is appealing for the future practice of seismic design and risk analysis.

Description: Interest in small-to-medium magnitude earthquakes and their potential consequences has increased significantly in recent years, mostly due to the occurrence of some unusually damaging small events, the development of seismic risk assessment methodologies for existing building stock, and the recognition of the potential risk of induced seismicity. As part of a clear ongoing effort of the earthquake engineering community to develop knowledge on the risk posed by smaller events, a global database of earthquakes with moment magnitudes in the range from 4.0 to 5.5 for which damage and/or casualties have been reported has been compiled and is made publicly available. The two main purposes were to facilitate studies on the potential for earthquakes in this magnitude range to cause material damage and to carry out a statistical study to characterise the frequency with which earthquakes of this size cause damage and/or casualties (published separately). The present paper describes the data sources and process followed for the compilation of the database, while providing critical discussions on the challenges encountered and decisions made, which are of relevance for its interpretation and use. The geographic, temporal, and magnitude distributions of the 1958 earthquakes that make up the database are presented alongside the general statistics on damage and casualties, noting that these stem from a variety of sources of differing reliability. Despite its inherent limitations, we believe it is an important contribution to the understanding of the extent of the consequences that may arise from earthquakes in the magnitude range of study.

Description: The spatial resolution of exposure data has a substantial impact on the accuracy and reliability of seismic risk estimates. While several studies have investigated the influence of the geographical detail of urban exposure data in earthquake loss models, there is also a need to understand its implications at the regional scale. This study investigates the effects of exposure resolution on the European loss model and its influence on the resulting loss estimates by simulating dozens of exposure and site models (630 models) representing a wide range of assumptions related to the geo-resolution of the exposed asset locations and the associated site conditions. Losses are examined in terms of portfolio average annual loss (AAL) and return period losses at national and sub-national levels. The results indicate that neglecting the uncertainty related to asset locations and their associated site conditions within an exposure model can introduce significant bias to the risk results. The results also demonstrate that disaggregating exposure to a grid or weighting/relocating exposure locations and site properties using a density map of the built areas can improve the accuracy of the estimated losses.

Description: Major earthquakes, such as the Canterbury and Kaikoura events recorded in New Zealand in 2010-2011 and 2016 respectively, highlighted that floor systems can be heavily damaged. Quasi-static cyclic experimental tests of structural sub-assemblies can help to establish the seismic performance of structural systems. However, the experimental performance obtained with such tests is likely to be dependent on the loading protocol adopted. This paper provides an overview of the loading protocols which have been assumed in previous experimental activities, with emphasis on those adopted for testing floor systems. The paper also describes the procedure used to define the loading protocol applied in the testing of a large precast concrete floor diaphragm as part of the ReCast floor project jointly conducted by the University of Canterbury, the University of Auckland and BRANZ. Subsequently the limitations of current loading protocols for bi-directional testing are discussed. The relevance of local seismicity on bidirectional demand is demonstrated by examining a large dataset of records from the RESORCE database. It is concluded that bi-directional experimental testing be undertaken using at least two loading protocols that impose different ratios of demand in orthogonal directions.

Description: For the seismic design of a structure, horizontal ground shaking is usually considered in two perpendicular directions, even though real horizontal ground motions are complex two‐dimensional phenomena that impose different demands at different orientations. While the issue of ground motion dependence on the orientation of the recording devices has been the focus of many significant developments during the last decade, the effects of directionality on the characteristics of the structure have received less attention. This work presents a proposal to calculate the probability of exceedance of elastic spectral displacements accounting for structural typology and illustrates its relevance by means of its application to two case‐study buildings. In order to ease its implementation in seismic design codes, a simplification is developed by means of a detailed statistical analysis of the results obtained using four sets of real hazard curves. The framework presented herein is considered to represent an important contribution to the field of performance‐based earthquake engineering, permitting improved treatment of directionality effects within seismic risk design and assessment.

Description: While quite extensive research has been undertaken during the last decades to extend the direct displacement-based design (DDBD) method to a wide range of structural types and materials, it is recognized that there are still some areas requiring further study and development. Steel structures and, more specifically, steel moment resisting frames with setbacks are one of these and, therefore, this work aims to investigate the seismic response of such structures designed according to the DDBD procedure currently prescribed for regular frames and to elaborate specific recommendations based on the results obtained. The main aspects to be considered are the adequacy of the displacement profile and higher mode reduction factor to be used, as well as the suitable strength distribution required. In a trial application of the current DDBD procedure, two two-dimensional 12-storey frames with setbacks are designed, and the solutions obtained are used to develop models of the structures, which are then subject to a series of non-linear time-history analyses at increasing levels of intensity, using spectrum-compatible scaled accelerograms. The results obtained are contrasted with those of Karavasilis et al. (J Constr Steel Res 64:644–654, 2008), which were developed for steel frames designed via code methods. It is recognized that the DDBD method can benefit from the expressions developed by these authors, and recommendations for the adjustment of the DDBD higher mode reduction factors are subsequently proposed. The efficacy of the latter is evaluated by the design and verification at a range of diverse intensities of a set of two-dimensional frames of 6, 9 and 12 storeys, and satisfactory outcomes are obtained. These results have been fundamental in revealing the need for future research regarding the influence of the design spectral shapes, ductility demand and P-Delta instability in the dynamic amplification of drifts due to higher mode effects.

Description: The Lower Rhine Embayment in western Germany is one of the most important areas of earthquake recurrence north of the Alps, facing a moderate level of seismic hazard in the European context but a significant level of risk. This study deals with the impact of a scenario earthquake with a moment magnitude of 6.5 occurring along the Erft fault system south-west to the city of Cologne, the fourth largest German city with more than one million inhabitants and accommodating important industrial facilities. Since the city is located on thick layers of Quarternary sediments, the geological discontinuities at depth will have a significant influence on the duration and the amplification of ground-motion. Based on a new, harmonized and spatially highly resolved, model of the sedimentary cover, the sensitivity of spectral intensity measures to the site response analysis method is assessed employing random vibration theory approaches. Corresponding damage calculations are conducted in terms of European Macroseismic Scale (EMS-98) damage grades. Residential buildings and buildings with mixed residential and commercial occupancy are included in the corresponding calculations only, in line with most seismic risk assessment studies which have traditionally focused on residential typologies. Results from the damage calculations are presented in terms of number of buildings exposed to bands of EMS-98 intensity levels and probabilities of EMS-98 damage grades for residential buildings and buildings with mixed residential and commercial occupancy. Casualties in the city and the neighboring districts are estimated by means of the PAGER empirical method using population counts at the quartier (“Stadtviertel”) level in Cologne, the “Bezirk” level in Bonn and Aachen and at the municipality (“Gemeinde”) level for the surrounding areas, all of these comprised within the district (“Regierungsbezirk”) of Cologne.

Description: Despite their much smaller individual contribution to the global counts of casualties and damage than their larger counterparts, earthquakes with moment magnitudes Mw in the range 4.0–5.5 may dominate seismic hazard and risk in areas of low overall seismicity, a statement that is particularly true for regions where anthropogenically-induced earthquakes are predominant. With the risk posed by these earthquakes causing increasing alarm in certain areas of the globe, it is of interest to determine what proportion of earthquakes in this magnitude range that occur sufficiently close to population or the built environment do actually result in damage and/or casualties. For this purpose, a global catalogue of potentially damaging events—that is, earthquakes deemed as potentially capable of causing damage or casualties based on a series of pre-defined criteria—has been generated and contrasted against a database of reportedly damaging small-to-medium earthquakes compiled in parallel to this work. This paper discusses the criteria and methodology followed to define such a set of potentially damaging events, from the issues inherent to earthquake catalogue compilation to the definition of criteria to establish how much potential exposure is sufficient to consider each earthquake a threat. The resulting statistics show that, on average, around 2% of all potentially-damaging shocks were actually reported as damaging, though the proportion varies significantly in time as a consequence of the impact of accessibility to data on damage and seismicity in general. Inspection of the years believed to be more complete suggests that a value of around 4–5% might be a more realistic figure.