Terms Of Spectral Acceleration Research Articles

Estimation of Uniform Risk Spectra Suitable for the Seismic Design of Structures

The aim of this paper is to present a performance-based method to estimate uniform risk spectra (URS) for the seismic design and assessment of structures. These spectra, computed with the proposed methodology, provide the lateral capacity (in terms of spectral acceleration) that should be given to a structure, characterized by a reference single degree of freedom system, to achieve a predetermined exceedance rate of economic loss. This procedure involves the seismic hazard assessment necessary to define a seismic design level consistent with the accepted loss value, using a large enough number of synthetic seismic records of several magnitudes, which were obtained by means of an improved empirical Green function method. The statistics of the expected losses of a reference single degree of freedom system are obtained using Monte Carlo simulation, considering the seismic demand and the lateral strength of the structure as random variables. The method is divided into two main stages: (1) definition of the seismic hazard at the site of interest and (2) the probabilistic analysis of the seismic performance in terms of an economical loss ratio of nonlinear SDOF. To illustrate the proposed methodology and, subsequently, to validate it, a URS was computed for a site located in the Mexico City lake-bed zone, and its use in the design of three reinforced concrete frames is shown. The results show that the proposed spectra provide a sufficient approximation between the seismic risk level considered in the seismic design and that of the designed structure. It is concluded that the proposed procedure is a significant improvement over others considered in the literature and a useful research tool for the further development of risk-based earthquake engineering.

A Logic-Tree Approach for Probabilistic Seismic Hazard Assessment in the Administrative Region of Attica (Greece)

Probabilistic Seismic Hazard Assessment (PSHA) was carried out for the administrative region of Attica (Greece). Peak Ground Acceleration (PGA) and Peak Ground Velocity (PGV) values were calculated for return periods of 475 and 950 years for five sub-areas covering the entire region. PGA hazard curves and Uniform Hazard Spectra (UHS) in terms of spectral acceleration (Sa) values were generated for Athens, Methana, and the capitals of each island of Attica (Salamina, Aegina, Poros, Hydra, Spetses, Kythira, and Antikythira). Area sources were adopted from the Euro-Mediterranean Seismic Hazard Model 2013 (ESHM13) and its update, ESHM20, taking into account both crustal and slab tectonic environments. Ground Motion Prediction Equations (GMPEs) proposed for the Greek territory were ranked for PGA and PGV. Each GMPE was reconstructed as a weighted model, accounting for normal and non-normal focal mechanisms for each area source. PGA, PGV, and Sa values were computed using a logic tree, integrating the seismotectonic models as major branches and sub-logic trees, comprised of multiple ranked GMPEs for each area source, as minor branches. The results showed higher seismic hazard values in sub-areas near the Gulf of Corinth and the slab interface, which could indicate a need to revise the active building code in Attica.

Broadband Strong Ground Motion Modeling Using Planar Dynamic Rupture With Fractal Parameters

AbstractDynamic rupture modeling represents a promising physics‐based approach to strong ground motion simulations. However, its application in a broad frequency range (0–10 Hz), interesting for engineering studies, is challenging. The main reason is that widely used and relatively simple planar fault models with smooth distributions of initial stress and frictional parameters, or even self‐similar initial stress, result in ground motions depleted in high‐frequency content. Here we propose an efficient approach for the linear slip‐weakening friction model on a planar fault based on the Ide and Aochi (2005, https://doi.org/10.1029/2004jb003591) multiscale model with a small‐scale random fractal distribution of the slip‐weakening distance Dc. We propose a way to combine these variations with a large‐scale deterministic dynamic model. We illustrate the approach on an elliptical model and a smooth model of the 2016 Mw 6.2 Amatrice, Italy, earthquake from low‐frequency dynamic rupture inversion. To intensify the incoherence of the rupture propagation, we also include a variation of the strength and initial stress, both correlated with Dc. These additions result in sustained high‐frequency radiation during the whole rupture propagation and omega‐square source time functions. The new model of the Amatrice earthquake generates synthetics that agree with the local ground motion model up to 5 Hz in terms of spectral accelerations while preserving the average and integral dynamic rupture parameters (e.g., stress drop, fracture and radiated energy). The fractal dynamic model can be easily implemented in any dynamic rupture propagation code and is thus readily applicable in broadband physics‐based ground motion predictions for earthquake scenarios in seismic hazard assessment.

Probabilistic and Scenario-Based Seismic Hazard Assessment on the Western Gulf of Corinth (Central Greece)

The Gulf of Corinth (Central Greece) is one of the most rapidly extending rifts worldwide, with its western part being the most seismically active, hosting numerous strong (M ≥ 6.0) earthquakes that have caused significant damage. The main objective of this study was the evaluation of seismic hazard through a probabilistic and stochastic methodology. The implementation of three seismotectonic models in the form of area source zones via a logic tree framework revealed the expected level of peak ground acceleration and velocity for return periods of 475 and 950 years. Moreover, PGA values were obtained through the stochastic simulation of strong ground motion by adopting worst-case seismic scenarios of potential earthquake occurrences for known active faults in the area. Site-specific analysis of the most populated urban areas (Patras, Aigion, Nafpaktos) was performed by constructing uniform hazard spectra in terms of spectral acceleration. The relative contribution of each selected fault segment to the seismic hazard characterizing each site was evaluated through response spectra obtained for the adopted scenarios. Almost all parts of the study area were found to exceed the reference value proposed by the current Greek National Building Code; however, the three urban areas are covered by the Eurocode 8 regulations.

Amplification analysis at Nador city and surrounding area (NE of Morocco)

This study presents a ground response assessment performed at Nador city (Morocco) and surrounding areas. We carried out the one-dimensional equivalent linear approach using the known geotechnical parameters to derive amplification analysis at studied sites, using the shear wave velocity (VS(30)) derived from boreholes. Seismic hazard assessment is performed using two gridded seismicity models and four ground motions attenuation equations, in order to address the epistemic uncertainty in a logic-tree framework. Seismic hazard maps depicting the mean estimated hazard values and including the uncertainty are presented in terms of spectral acceleration at 0.0, 0.1 and 0.2 s, with 10% and 5% probabilities of exceedance in 50 years, and for B, B/C and C soil conditions, as defined by the National Earthquake Hazards Reduction Program classification and for local site conditions as well. Typical values of Peak Ground Acceleration (PGA) equal to 0.18g±0.03 and 0.26g±0.05 are obtained at the Nador city for 475 and 975 return period respectively and for B/C soil conditions. The deaggregation analysis for both returns periods (475 and 975 years) in terms of magnitude-distance (named 2D deaggregation) and in azimuth (longitude and latitude named 3D deaggregation) allows us to derive the contribution of the different couple of magnitude-distance (M,D) and the different sources, the controlling earthquake are also determined at the five considered cities, for both return periods. From the site-specific seismic hazard analysis performed at five main cities located in the studied area, the seismic hazard curves and the uniform hazard spectra (UHS) are obtained with their uncertainties for the considered return periods and soil conditions, as well as the design spectra proposed by Malhotra (2005). Real accelerogram time-history is used to generate compatible acceleration time-history with the design spectra proposed by Malhotra (2005) and the EC-8 type 2 (Eurocode 8.2004), for both return periods and for B/C soil conditions. The lower root mean square error value (RMSE) is archived by using the Malhotra design spectra for the considered return periods. The results display a clear amplification in silty and clayey soils, greater than in silt-gravely soils, as well as no significant amplification in volcanic soils. Moreover, the resulting fundamental frequency is in the range of 1.4–2.8 Hz, and the maximum amplification factor observed in Nador is about 3.5. These values are consistent with the results derived from ambient noise, seismic records using HVSR technique and with the values given by Moroccan Seismic Code in the 2000 and 2011 regulations.

Evaluation of seismicity of Karachi city in the context of modern building codes

Spectral acceleration is representative of seismic hazard in modern building codes as well as an important parameter used in seismic design these days. Karachi, an economic artery of Pakistan, is located in the vicinity of an active tectonic setting, i.e., triple junction, with uncertain seismicity. Keeping in view the modern seismic design practices, efforts are required to evaluate the seismic hazard of Karachi city in terms of spectral acceleration. This study is focused on the estimation of seismic hazard for the metropolitan city of Karachi in the context of modern building codes. The seismic potential of around 800–900-km circle was considered a threat for the city, and 13 seismic zones (A-1 to A-13) were identified as seismic sources. A seismicity model based on Gutenberg-Richter law was developed, identifying A-1 and A-11 as zones of high seismicity. The ground attenuation model recommended for the Middle East region proposed by Akkar and Bommer was utilized for the computation of different ground motion scenarios. Short-period, SS, and 1-s, S1, spectral acceleration values for considered region were calculated as 1.37 m/s2 and 0.41 m/s2, respectively. In addition, peak ground acceleration (PGA) values for Karachi city were observed to be in a range of 0.7–0.77 m/s2. The results of this study provide bases for the preparation of seismic risk maps, the estimation of earthquake insurance premiums, seismic zonation for region lying on Arabian and Indian plates, and the preliminary site evaluation of critical facilities.

Probabilistic seismic hazard assessment for Iraq

Probabilistic seismic hazard assessments (PSHA) form the basis for calculating seismic loads in most contemporary seismic provisions in building codes around the world. The current building code of Iraq, which was published in 1997, is currently undergoing a significant engineering update. This study was undertaken in order to support the building code update and to satisfy the need in Iraq for a contemporary assessment of seismic hazard in terms of spectral accelerations. Seismic source characterization largely relies on a newly compiled earthquake catalog since sufficiently detailed information is not available on active faulting in the country even though there are numerous known active faults. There is also a lack of locally recorded strong-motion data. As a result, we make use of attenuation tomography studies in the region to compare local attenuation characteristics with that in other parts of the world where ground-motion prediction equations are available for use in PSHA. For most of the country, the attenuation of 1HzLg waves indicates an attenuation rate that is slower than active tectonic regions but faster than stable continental regions. Hence, we use ground-motion prediction equations from active tectonic and stable continental regions, weighted equally. The PSHA results are presented for a 2% chance of being exceeded in 50 years and on a reference ground condition of the National Earthquake Hazards Reduction Program (NEHRP) site class B. The probability level and reference ground conditions were selected to be consistent with the update of Iraq’s building code. The largest hazard, and consequently the design ground motions, is in the northern cities of Sulaymaniyah and Erbil, consistent with the fact that they are the two urban areas closest to major tectonic features to the north and east of Iraq. Additionally, the Badra–Amarah fault zone is a significant contributor to seismic hazard in the country; therefore, urban areas near it exhibit high seismic hazard.

Influence of Epistemic Uncertainty in Shear Wave Velocity on Seismic Ground Response Analyses

This study aims to evaluate the influence of epistemic uncertainties in shear wave velocity ( VS) on seismic ground response analyses (GRAs). A number of alternative VSprofiles obtained from both invasive (i.e., borehole) and noninvasive (i.e., surface waves) testing methods are available for two blind study sites. These profiles are used to estimate epistemic uncertainties in VS, which are then propagated through equivalent linear-elastic GRAs, allowing for the quantification of intramethod uncertainty and intermethod variability in terms of spectral accelerations, amplification functions, and damage parameters (i.e., Arias and Housner intensities). This study demonstrates that nonlinearity of soil response plays a fundamental role in increasing the propagated uncertainty in GRA. Additionally, GRAs were also performed by means of VSupper/lower-range profiles developed from assumptions commonly used to account for epistemic uncertainties. These VSprofiles were found to yield unrealistic site response estimates for both low strain (i.e., linear-elastic) and high strain (i.e., nonlinear) levels.

Improving the Structural Reliability of Steel Frames Using Posttensioned Connections

In this paper, various moment‐resisting steel frames (MRSFs) are subjected to 30 narrow‐band motions scaled at different ground motion intensity levels in terms of spectral acceleration at first mode of vibration Sa(T1) in order to perform incremental dynamic analysis for peak and residual interstory drift demands. The results are used to compute the structural reliability of the steel frames by means of hazard curves for peak and residual drifts. It is observed that the structures exceed the threshold residual drift of 0.5%, which is perceptible to human occupants, and it could lead to human discomfort according to recent investigations. For this reason, posttensioned connections (PTCs) are incorporated into the steel frames in order to improve the structural reliability. The results suggest that the annual rate of exceedance of peak and residual interstory drift demands are reduced with the use of PTC. Thus, the structural reliability of the steel frames with PTC is superior to that of the MRSFs. In particular, the residual drift demands tend to be smaller when PTCs are incorporated in the steel structures.

Quantification of the amplitude variability of the ground motion in Argostoli, Greece. Variability of linear and non-linear structural response of a single degree of freedom system.

The term “spatial variability of seismic ground motions” denotes the differences in the amplitude and phase content of seismic motions. The effect of such spatial variability on the structural response is still an open issue. In-situ experiments may be helpful in order to answer the questions regarding both the quantification of the spatial variability of the ground motion within the dimensions of a structure as well as the effect on its dynamic response. The goal of the present study is to quantify the variability of the seismic ground motion accelerations in the shallow sedimentary basin of Argostoli, Greece, and thereafter to identify its effect on the linear and non-linear elasto-plastic response of a single degree of freedom system in terms of spectral displacements. Around 400 earthquakes are used, recorded by the 21-element very dense seismological array deployed in Argostoli with inter-station spacing ranging from 5 to 160 meters. The seismic motion variability, evaluated in terms of spectral accelerations, is found to be significant and to increase with inter-station distance and frequency. Thereafter, the amplitude variability in terms of spectral displacements, which is indeed the linear response of a single degree of freedom (SDOF) system with various fundamental periods, is compared with the amplitude variability of a SDOF with non-linear elasto-plastic response. The variability of the maximum top displacement of the linear single degree of freedom system is estimated to be on average 12% with larger variabilities to be observed within two narrow frequency ranges (between 1.5 and 1.7 Hz and between 3 and 4 Hz). Such high variabilities are caused by locally edge-generated diffracted surface waves. The non-linear perfectly elasto-platic structural response of the SDOF system shows that although the variability has the same trends as in the case of linear response, it is almost constantly increased by 5%.

Estimating fragility curves of pre-70 RC frame buildings considering different performance limit states

In seismic risk assessment, fragility (or vulnerability) curves are commonly used to express the likelihood that constructions (e.g. buildings) will sustain different degrees of loss over a range of earthquake ground motion intensities. In the paper, fragility curves for typical older residential RC buildings, realized in Italy and other southern Europe countries from the 50s to the early 70s, are derived following a hybrid approach. Fragility curves are expressed in terms of spectral acceleration. Median values for each damage state (or performance limit state) are estimated based on the results of comprehensive loss assessment analysis and the definition of a suitable loss index. Dispersions are evaluated based on the results of accurate inelastic dynamic analyses carried out for a number of archetype buildings at increasing levels of seismic intensity. A detailed discussion on the parameters that influence most the fragility curves, such as the number of storeys of the building, is provided.

A LiDAR-aided urban-scale assessment of soil-structure interaction effects: the case of Kalochori residential area (N. Greece)

We present a methodology for a large-scale assessment of soil-structure interaction (SSI) effects on the vibrational characteristics and the seismic loading of structures in a real urban fabric by combining airborne monitoring techniques, field surveys and simple calculations in the realm of structural and geotechnical dynamics. The proposed procedure combines geometrical features of a building stock acquired from a LiDAR-based 3D city model, material and typology data of structures from in situ inspections in representative building blocks, geotechnical data from field surveys and strong ground motion data from seismic hazard and site effects analyses. The integrated data are employed to compute at a first stage the fundamental period of each building in the urban area by means of code-defined formulas for both fixed- and flexible-base foundation conditions, thus treating soil-structure interaction effects in a simplified manner. The seismic action in terms of spectral acceleration at the fundamental period of structures is then computed, following a series of 1D site-specific analyses of soil response under different seismic scenarios. Spatially distributed ratios of structural fundamental periods and spectral accelerations, corresponding to flexible- over fixed-base foundation conditions, are mapped in GIS environment as an index of SSI effects at large-scale. The methodology is implemented in the urban area of Kalochori located west of Thessaloniki in Greece. The examined case study showed that SSI may be significant even for low-amplitude motions and may lead to higher seismic forces compared to the fixed-base case, depending on the dynamic characteristics of the structures, the soil conditions and the shape of the response spectrum. The above may be of importance in microzonation and seismic vulnerability studies at urban-scale when a building-by-building assessment is not feasible and SSI effects are too important to be ignored.

Probabilistic seismic hazard assessment in the Constantine region, Northeast of Algeria

This paper presents a seismic hazard evaluation and develops an earthquake catalogue for the Constantine region over the period from 1357 to 2014. The study contributes to the improvement of seismic risk management by evaluating the seismic hazards in Northeast Algeria. A regional seismicity analysis was conducted based on reliable earthquake data obtained from various agencies (CRAAG, IGN, USGS and ISC). All magnitudes (M l, m b) and intensities (I 0, I MM, I MSK and I EMS) were converted to M s magnitudes using the appropriate relationships. Earthquake hazard maps were created for the Constantine region. These maps were estimated in terms of spectral acceleration (SA) at periods of 0.1, 0.2, 0.5, 0.7, 0.9, 1.0, 1.5 and 2.0 s. Five seismogenic zones are proposed. This new method differs from the conventional method because it incorporates earthquake magnitude uncertainty and mixed datasets containing large historical events and recent data. The method can be used to estimate the b value of the Gutenberg-Richter relationship, annual activity rate λ(M) of an event and maximum possible magnitude M max using incomplete and heterogeneous data files. In addition, an earthquake is considered a Poisson with an annual activity rate λ and with a doubly truncated exponential earthquake magnitude distribution. Map of seismic hazard and an earthquake catalogue, graphs and maps were created using geographic information systems (GIS), the Z-map code version 6 and Crisis software 2012.

Seismic Vulnerability of RC Buildings under the Effect of Aging

The present study aims at the assessment of the seismic vulnerability of reinforced concrete (RC) buildings considering performance degradation over time due to aging effects. Chloride induced corrosion is taken into account based on probabilistic modeling of corrosion initiation time and corrosion rate. Two-dimensional incremental dynamic analysis (IDA) is performed to assess the seismic performance of the initial uncorroded (t=0 years) and corroded (t= 25, 50, 75 years) RC fixed base frame structures designed based on different seismic code levels. The time-dependent fragility functions are derived at the various time periods in terms of spectral acceleration corresponding to the fundamental mode of the structure Sa(T1,5%) for the immediate occupancy (IO) and collapse prevention (CP) limit states. Results show an overall increase in seismic vulnerability over time due to corrosion indicating the significant effect of deterioration due to aging effects on structural behavior.

Probabilistic Earthquake–Tsunami Multi-Hazard Analysis: Application to the Tohoku Region, Japan

This study develops a novel simulation-based procedure for the estimation of the likelihood that seismic intensity (in terms of spectral acceleration) and tsunami inundation (in terms of wave height), at a particular location, will exceed given hazard levels. The procedure accounts for a common physical rupture process for shaking and tsunami. Numerous realizations of stochastic slip distributions of earthquakes having different magnitudes are generated using scaling relationships of source parameters for subduction zones and then using a stochastic synthesis method of earthquake slip distribution. Probabilistic characterization of earthquake and tsunami intensity parameters is carried out by evaluating spatially correlated strong motion intensity through the adoption of ground motion prediction equations as a function of magnitude and shortest distance from the rupture plane and by solving nonlinear shallow water equations for tsunami wave propagation and inundation. The minimum number of simulations required to obtain stable estimates of seismic and tsunami intensity measures is investigated through a statistical bootstrap analysis. The main output of the proposed procedure is the earthquake-tsunami hazard curves representing, for each mean annual rate of occurrence, the corresponding seismic and inundation tsunami intensity measures. This simulation-based procedure facilitates the earthquake-tsunami hazard deaggregation with respect to magnitude and distance. Results are particularly useful for multi-hazard mapping purposes and the developed framework can be further extended to probabilistic earthquake-tsunami risk assessment.

Preliminary Analysis of Strong Ground Motions in the Heavily Damaged Zone in Mashiki Town, Kumamoto, Japan, during the Mainshock of the 2016 Kumamoto Earthquake (Mw 7.0) Observed by a Dense Seismic Array

ABSTRACT In this article, the authors make a brief report on the strong ground motions observed in the midst of the heavily damaged zone during the 16 April M w 7.0 mainshock of the 2016 Kumamoto, Japan, earthquake. The observation was accidentally made by a dense seismic array that was deployed by the authors with the intention of observing aftershocks of the 14 April M w 6.2 event, which later turned into the foreshock of the M w 7.0 event. The observed ground motions are characterized by a large‐amplitude pulse with an approximate period of 1 s that is predominant in the east–west (EW) components, which is comparable in shape to those observed during the 1994 Northridge and the 1995 Kobe earthquakes. In particular, the observed ground motions exceed the largest observed ground motions during the 1995 Kobe earthquake in terms of spectral accelerations in the 0.5–1.2 s period range. The importance of these records is that this was observed in the midst of a heavily damaged zone, where the ratio of totally collapsed wooden houses, due either to the foreshock or the mainshock, reportedly reached as high as 50% causing significant loss of life. Therefore, the records should be used in future research to reveal how the buildings were damaged, to develop appropriate measures, and to mitigate damages attributed to future large earthquakes.

Eurocode 8-compatible synthetic time-series as input to dynamic analysis

Nonlinear dynamic analysis of existing or planned structures often requires the use of accelerograms that match a target design spectrum. Here, our main concern is to generate a set of motions with a good level of fit to the Eurocode 8 design spectra for France. Synthetic time series are generated by means of a non-stationary stochastic method. To calibrate the input parameters in the stochastic approach, we select a reference set of accelerograms for a Eurocode 8 type B site category from the PEER Ground-Motion Database, which are then adjusted to the target spectrum through wavelet addition. Then, we compute nonlinear seismic responses of a soil column, including pore pressure effects, and brittle and ductile structures to the stochastic time-series, the natural accelerograms and time-series generated using stationary stochastic approaches. The results of these calculations reveal considerable variability in response despite the similarities in terms of spectral acceleration.

Effect of the Seismic Input on Non-Linear Response of R/C Building Structures

The effects of the variability of seismic input on system structural response are investigated. Non linear time history analyses are performed using as input sets of accelerograms satisfying the compatibility criteria with an elastic design spectrum according to the Eurocode 8. The response of elastic SDOF systems, in terms of spectral acceleration, is analyzed; the same parameter, for corresponding non linear SDOF systems as well as ductility demand and strength reduction factors, is also discussed. The analyses are extended to a r/c multi-storey space frame, which is designed according to Eurocode provisions. The main conclusion of the paper is that, when the input is selected according to the Eurocode 8 provisions as recorded accelerograms, a “natural” mean CoV of spectra ordinates is expected; it proportionally conditions the CoV of the parameters characterising the non linear response of structures.

Retrofit Yield Spectra-a practical device in seismic rehabilitation

The Retrofit Yield Spectrum (RYS) is a new spectrum-based device that relates seismic demand of a retrofitted structure with the fundamental design parameters of the retrofit. This is obtained from superposition of Yield Point Spectra with design charts that summarize in pertinent spectrum-compatible coordinates the attributes of a number of alternative retrofit scenarios. Therefore, once the requirements for upgrading a given structure have been determined, the RYS enable direct insight of the sensitivity of the seismic response of the upgraded structure to the preliminary design decisions made while establishing the retrofit plan. By virtue of their spectrum-based origin, RYS are derived with reference to a single mode of structural vibration; a primary objective is to control the contribution of this mode in the retrofit design so as to produce a desirable distribution of damage at the ultimate limit state by removing soft storey formations and engaging the maximum number of structural members in deformation, in response to the input motion. Calculations are performed with reference to the yield-point, where secant stiffness is proportional to the flexural strength of reinforced concrete members. Derivation and use of the Retrofit Yield Spectra (RYS) refers to the seismic demand expressed either in terms of spectral acceleration, spectral displacement or interstory drift, at yield of the first storey. A reinforced concrete building that has been tested in full scale to a sequence of simulated earthquake excitations is used in the paper as a demonstration case study to examine the effectiveness of the proposed methodology.

Response spectra for the deep sediment-filled Rhône Valley in the Swiss Alps

We present numerical modeling of earthquake ground motion for various profiles across the Swiss Rhône Valley and characterize the seismic response in terms of spectral acceleration. First, we evaluate the relative amplification of 2D with respect to 1D response. Then, we show how the selected bedrock spectrum influences the response spectra of the valley sites. Particular attention is paid to how the internal sediment structure and the often weakly constrained Q-factor shape the seismic response. Results obtained for the different profiles are compared with reference spectra (Swiss building code and Eurocode 8) and for one profile with recorded data as well. From this comparison, we infer that the surficial layer strongly influences spectral acceleration values between 0.1 and 1 s. The total thickness of sediments significantly affects the seismic response at longer periods around the fundamental period of the studied valley sections between 1.8 and 3.6 s.