Average Response Spectra Research Articles

Performing Dynamic Analysis of the Conceret Structures using Genetic Algorithm and Determining the Optimal Range during a Natural Hazard Crisis (Tempe, Arizona, USA)

The approach employs a binary genetic algorithm alongside natural numbers. Given the differences between accelerometers and scale coefficients, the genetic algorithm introduced herein is a hybrid, featuring two chromosomes. A key factor influencing the accuracy and effectiveness of these programs is the precise estimation of their parameters. When these parameters are determined accurately, the gap between the average response spectrum and the design spectrum is significantly minimized. This program operates with two genetics that run concurrently, yielding results that closely approximate the optimal solution. The program itself is capable of offering users a range of desired coefficients, as well as values for the covariance and mutation of each chromosome. The algorithm detailed in this article can generate a new generation of individuals from an infinite array of ground motion records, utilizing processes such as natural selection, mating, and mutation, and continue this cycle until an individual meets the desired characteristics. This paper presents a novel method for optimally selecting accelerometers and scaling them for dynamic time history analysis, aiming for an average response spectrum that closely aligns with the target spectrum, reflecting the expected seismic activity for the structure in Tempe district in Arizona State. Given the relatively high number of parameters involved, reliance on trial-and-error methods is significantly influenced by the user’s skill set; thus, the hybrid genetic algorithm presented here addresses this limitation.

Site-Specific Seismic Hazard Analysis for Shallow Tunnel in Nepal

Abstract Several seismic codes are implemented for the design and construction of superstructures in Nepal but there is no seismic guideline for shallow tunnels which are often constructed using conventional engineering approaches. The uniform hazard spectrum was obtained after performing a Probabilistic Seismic Hazard Analysis at Dhulikhel and the target spectrum was estimated by comparing it with the spectrum recommended by the seismic code of Nepal Building Code NBC 105:2020 and Indian standard IS 1893:2016. The average response spectrum from ten recorded earthquake ground motions was selected from a peer ground motion database with the known shear wave velocity obtained from geophysical survey. The comparative analysis revealed that the design spectra for identical soil classes, as determined by this study are slightly higher than those prescribed by the present seismic code provisions. This finding emphasizes the necessity for developing more specific guidelines tailored to the design of shallow tunnels in Nepal to ensure their structural resilience in the event of an earthquake.

Seismic fragility analysis of human perception in high‐rise buildings subjected to far‐field long‐period earthquake ground motions: A case study for Shanghai tower

AbstractHuman perception in high‐rise buildings during far‐field long‐period earthquake ground motions often induces psychological discomfort, including fear and anxiety. A comprehensive understanding on human perception of seismic events is vital for city planning and emergency management, facilitating effective evacuation plans and minimizing stampede risks. This study addresses a gap by employing the seismic fragility analysis method to delineate how human perception in high‐rise buildings is affected during far‐field long‐period ground motions. The methodology involves several key steps. First, the far‐field long‐period earthquake ground motion was identified by detecting the later‐arriving surface waves, and a series of records were selected from the next generation attenuation (NGA) West‐2 ground motion database of the Pacific Earthquake Engineering Research center. Then, a high‐rise building in Shanghai, China was modeled using ETABS 20. Through the linear‐elastic time history analysis, the structural seismic response at each floor was computed. Furthermore, human perception thresholds to vibration were introduced to assess the degree of human perception at each floor, illustrating the difference of human perception to seismic tremor at different floors. Finally, a novel earthquake intensity measure (IM), namely average response spectrum intensity (ARSI) within the vibration period ranging from 0.1 s to 10 s was introduced to generate seismic fragility curves for human perception. According to the investigation, it was found that the corner frequency and the associated energy ratio are useful indicators to identify the far‐field long‐period earthquake ground motions. The ARSI is an effective parameter to assess human perception to seismic tremor compared to the spectral acceleration at a given fundamental period. The generated seismic fragility analysis can provide a complete and thorough understanding on the probability of people that should be evacuated under different earthquake intensity levels. The probability of human perception at different floors varies along the building height, demonstrating the difficulty to make crowd evacuation plan in practice. This insight is vital for understanding and mitigating seismic concerns in high‐rise buildings, particularly in low‐to‐moderate seismicity regions.

Composite Source Model for Broadband Ground-Motion Simulations: 2021 Mw 7.4 Maduo, China, Earthquake Case Study

Abstract On 22 May 2021, at 2:40 a.m. (local time), an earthquake with a moment magnitude of 7.4 was reported to have occurred in Maduo County (34.59° N, 98.34° E), China. The focal depth was 17 km. After the earthquake, many scholars inverted the slip distribution of the Maduo earthquake based on ground-motion recordings, and the Global Positioning System and the Interferometric Synthetic Aperture Radar data. To verify the reliability of the fast estimation source model method adopted in this study, the hybrid slip model of the 2011 Mw 7.4 Maduo earthquake, in Qinghai Province, China, is synthetized based on the stochastic finite-fault model and the semiempirical relation between the earthquake magnitude (Mw) and source parameters. The truncated normal distribution and regional crustal structure are used to generate 30 sets of global source parameters, which describes that the deterministic characteristics of the source mainly include the size of the rupture fault, and the average slip, and the local source parameters. The local parameters include asperity and k2 model parameters. Finally, stochastic finite-fault modeling is adopted to synthetic the acceleration response spectra at four selected sites meeting different geological conditions and orientations, and the minimum residual principle is used to select the final slip model for the Maduo earthquake with the minimum residual of the average response spectra. The research results show that the width, maximum slip, and asperity body position of the source model estimated in this study are consistent with those of the inversion slip model, which verifies the reliability and applicability of this method. This work provides technical and theoretical support for rapid prediction of the source model of earthquakes with specific magnitudes.

Simulation of the 2022 Mw 6.6 Luding, China, earthquake by a stochastic finite-fault model with a nonstationary phase

We adopted stochastic finite-fault simulations considering the nonstationary frequency characteristics for the 2022 Mw 6.6 Luding, China, earthquake at 16 strong-motion stations using the stochastic finite-fault model based on a dynamic corner frequency (EXSIM) code. The average simulated response spectra of earthquake ground motions were obtained and then compared with response spectra of 5% damped single degree of freedom system under recorded ground motion excitation to verify whether the finite-fault model that considers the nonstationary frequency characteristics can reproduce the critical characteristics of ground motions and improve the simulation accuracy. The high-frequency spectral decay is calculated by the real recordings and the stress drop is determined by the trial-and-error method. In addition, the local site amplifications are estimated from the horizontal-vertical spectral ratio (H/V). An improved EXSIM that considers the slip-related corner frequency is also used in this study. The results indicate that the nonstationary phase can significantly improve the simulation accuracy of EXSIM in the short period and has little effect on the long-period simulation results. However, the effect of the nonstationary phase on the simulation results obtained from the improved EXSIM is not significant. Regarding the peak ground acceleration (PGA), the nonstationary phase can produce waveform characteristics that are more similar to the real waveform, and the synthetic PGA is closer to the observed ones.

A STUDY ON SEISMIC GROUND MOTION INTENSITY TO ESTIMATE THE DAMAGE RATES OF LOW- AND MIDDLE-RISE REINFORCED CONCRETE BUILDINGS IN THE SHIKOKU REGION

This study investigated seismic ground motion intensity to estimate the damage rates of low- and middle-rise RC buildings due to various earthquakes. It calculated the vulnerability functions of analytical models of RC buildings for earthquake motions with different spectral characteristics and evaluated the effects of earthquake motions with different spectral characteristics on vulnerability functions. The results confirmed that the average acceleration response spectrum of the periodic band corresponding to the primary natural period of the building can usually estimate the damage rates of low- and middle-rise RC buildings due to various earthquakes.

Site specific seismic hazard analysis of monumental site Dharahara, Kathmandu, Nepal

This study was carried out to estimate the seismic requirement for analyzing and designing the monumental structure, Dharahara, in Kathmandu, Nepal. A probabilistic seismic hazard analysis of the study region was performed to develop the elastic response spectrum for the bedrock site. The obtained spectrum was compared with the existing seismic codes, NBC 105:2020 and IS 1893:2016, to estimate the target response spectrum. One-dimensional equivalent linear (EQL) and non-linear (NL) ground response analyses were performed using DEEPSOIL v7, incorporating a suite of ground motions. The three borehole logs exhibited very soft soil in the region. Due to the presence of soft soil strata in the region under study, strength-corrected modulus reduction and damping curves were adopted in the current study to overcome the effect of larger shear strain. The average response spectra from EQL analyses predicted higher values than NL analyses. Finally, a comparison of the proposed design response spectrum with the code spectra was performed. Comparisons revealed that the mean EQL and NL outputs fall in between the design spectra of similar soil classes in NBC 105:2020 and IS 1893:2016 seismic codes.

Estimating the response of concrete moment frames subjected to individual ground motions using Endurance Time excitation functions fitted to average acceleration response spectra

Endurance Time (ET) method is a time history-based analysis procedure that applies special intensifying acceleration functions for estimating the seismic performance of structures at different excitation levels in every single analysis, and therefore, remarkably reduces the computational time, effort, and cost. For some structures with complicated models, such as dams, performing multiple seismic analyses are impractical. In such cases, it is recommended that researchers pay conscious attention to choose appropriate and compatible Endurance Time excitation functions (ETEF) considering the basic properties of their structure. However, in this study, it is observed that selecting and using various ETEFs for analyzing an intermediate concrete moment frame structure subjected to individual earthquake ground motions will lead us to obtain false and unreliable responses. In other words, different ETEF series have significantly different accuracies (over 26 percent error) in predicting the responses of the mentioned structure subjected to individual earthquake ground motions. This problem mainly arises due to the turbulent nature of the spectrum of a single ground motion which is in contrast to the smoothed shape of spectra of the ETEFs. One solution to avoid this problem might be to produce a specific ETEF.

Design Response Spectra and Site Coefficients for Various Seismic Site Classes of Guwahati, India, Based on Extensive Ground Response Analyses

Seismicity of northeast India and its surroundings is governed by complex tectonic setting. Guwahati, the largest city of northeast India, had suffered minor to major damages during past earthquakes (EQs). Known seismic source information also suggests that Guwahati is susceptible for future EQs both from nearby as well as distance source. Taking into account the subsoil information of Guwahati, present work attempts to understand the role of Guwahati soil during probable seismic excitation. In the absence of regional ground motion records, covering a possible variation in ground motion characteristics, which can occur during potential future EQ, 30 globally recorded ground motions are used as input motions in this work. Each input motion is applied to each of the 225 boreholes resulting in 225 × 30 = 6750 ground response analyses using equivalent linear approach. Based on the response of subsoil to each input motion, site coefficients as well as average response spectra for various seismic site classes are proposed. It has to be mentioned here that in comparison to previous works which attempted to understand the subsoil of Guwahati based on specific location-based subsoil information and specific scenario EQ, present work provides a broader picture of soil response which can be applied to any level of ground shaking. Further, based on predominant period, suggestion of maximum building storeys are suggested for Guwahati. In addition, based on the work, characteristics of EQ scenario, which can trigger maximum response from local soil of Guwahati, are assessed. Based on the present analyses, design response spectra of Guwahati are also proposed. Keeping in mind Government of India’s policy towards the development of northeast India and further to develop Guwahati as “Smart city”, the present findings will be very useful in city planning, estimation of induced effects as well as for seismic design of probable infrastructure in Guwahati.

Damping reduction equation for the equivalent linear analysis of seismic isolated structures subjected to near fault ground motions

In this study, a new damping reduction equation is proposed to obtain reasonable estimates of the actual nonlinear responses of seismic isolated structures (SIS) subjected to near fault ground motions (NFGM) with forward-rupture-directivity effect, using equivalent linear analysis (ELA) procedure. For this purpose, first, a set of 29 NFGM are selected and grouped according to their site soil classification. Then, the average response spectra of the NFGM are plotted and a smoothed design response spectrum for each set of ground motions are obtained. Next, nonlinear time history analysis (NLTHA) and ELA of SIS are performed for the selected ground motions. Subsequently, the average of the isolator displacements calculated from the NLTHA are obtained for each set of NFGM considered in the analyses. Then, the damping reduction factor required to obtain an isolator displacement equal to the average isolator displacements obtained from the NLTHA of SIS is back calculated via the ELA procedure. Next, the variation of the damping reduction factor is plotted as a function of various combinations of the parameters considered in this research in dimensionless form and nonlinear regression analyses are performed to formulate the damping reduction equation. The isolator characteristic strength, post elastic period, the corner period of the response spectrum and peak ground acceleration are found to affect the damping reduction factor and hence, the displacements obtained from ELA. The proposed damping reduction equation is found to yield more reasonable estimates of the actual nonlinear responses compared to those available in the literature and design codes.

Seismic effect assessment of the southern slope of Greater Caucasus (Azerbaijan) based on the earthquake scenarios: ground parameters and acceleration models

In this paper, earthquake scenarios parameters were assessed for deterministic seis-mic hazard of the southern slope of Greater Caucasus (Azerbaijan). Historically, there occurred strong earthquakes in the studied region. Series of soft and strong earthquakes occurred for the recent years on the southern slope of Greater Caucasus in Azerbaijan in Balakan (14.10.2012, M = 5,6; 29.06.2014, M = 5,3); Zagatala (07.05.2012, M = 5,7; 18.05.2012, M = 5,0; 05.06.2018, M = 5,5); Sheki (earthquake swarm 05.02.2004, M = 3,2 ¸ 4.6); Sheki-Oguz (04.09.2015, M = 5,9); Gabala 04.10.2014, M = 5,0); Ismailli (05.02.2019, M = 5,2) demonstrates the increase of seismic activity in the given region and proves once aga-in the necessity and actuality of continuation of the seismic hazard assessment resear-ches. For earthquake scenarios of various distances, average response spectrum (5 % attenuation) of surface ground fluctuation was plotted, peak ground acceleration were assessed at the maximum magnitude, series of peak ground acceleration models were simulated at respective MSK-64 intensity, and also amplification factor distribution map. The comparative analysis allows presuming that amplification occurs due to the resonance processes, that is, softer soils produce seismic wave amplitude amplification as a result of impedance differences of those layers and harder rocks. Seismic intensity increase is observed in the sites with soft-cemented sand-clayey soils, although with sands-tones, limestone and sandy marlstone of various thicknesses. It is demonstrated that ground displacements are various and not obviously oriented towards seismic source.

Stochastic seismic performance assessment of high CFRDs based on generalized probability density evolution method

Determining the failure probabilities of high concrete-faced rockfill dams (CFRDs) is an important component of seismic performance assessment, considering the randomness of earthquake ground motions. In this paper, a new efficient methodology that couples the recently developed generalized probability density evolution method (GPDEM) with the spectral representation-random function method is proposed to evaluate the seismic performance of high CFRDs from a stochastic perspective. A set of representative acceleration time histories of non-stationary earthquake ground motions with complete probability are generated based on an evolutionary power spectral density model through an iterative correction to produce a good fit between the average response spectrum and the code spectrum in China’s hydraulic structure seismic code. Then, a series of deterministic dynamic calculations for a 200-m CFRD based on a generalized plasticity model modified for rockfills and a generalized plasticity interface model are performed to solve the GPDEM equation. A new face-slab damage index that considers double physical parameters (demand capacity ratio and cumulative overstress duration based on stress) is presented and its probabilityinformation is determined by constructing a virtual random process. Finally, probability density functions and cumulative distribution functions are obtained under two seismic levels by considering three performance indices corresponding to deformation, stability of dam slope and safety of face-slabs. The failure probability of different failure grades demonstrates that this new method has a good applicability to seismic performance assessment of high CFRDs.

Overview of Ground-Motion Issues for Cascadia Megathrust Events: Simulation of Ground-Motions and Earthquake Site Response

Ground motions for earthquakes of M7.5 to 9.0 on the Cascadia subduction interface are simulated based on a stochastic finite-fault model, and used to estimate average response spectra for reference firm soil conditions. The simulations are first validated by modeling the wealth of ground-motion data from the the 2011 M9.0 Tohoku earthquake of Japan. Adjustments to the calibrated model are then made to consider average source, attenuation and site parameters for the Cascadia region. This includes an evaluation of the likely variability in stress drop for large interface earthquakes, and an assessment of regional attenuation and site effects. We perform best-estimate simulations for a preferred set of input parameters. Typical results suggest mean values of 5%-damped pseudo-acceleration in the range from about 100 to 200 cm/s2, at frequencies from 1 to 4 Hz, for firm-ground conditions in Vancouver. Uncertainty in most-likely value of the parameter representing stress drop causes variability in simulated response spectra of about ±50%. Uncertainties in the attenuation model produce even larger variability in response spectral amplitudes – a factor of about two at a closest distance to the rupture plane (Rcd) of 100 km, becoming even larger at greater distances. It is thus important to establish the regional attenuation model for ground-motion simulations, and to bound the source properties controlling radiation of ground motion. We calculate theoretical 1D spectral amplification estimates for four selected Fraser River Delta sites to show how the presence of softer sediments in the region may alter the predicted ground motions. The amplification functions are largely consistent with observed spectral amplification at Fraser River delta sites, suggesting amplification by factors of 2.5 to 5 at the peak frequency of the site; we note that deep sites in the delta have a low peak frequency, ~0.3 Hz. This work will aid in seismic hazard assessment and mitigation efforts in the active Cascadia region of southwestern B.C. An important consideration is that the uncertainties are large and present a dominant unknown when assessing seismic risk. We find that variability in the expected motions exceeds a factor of two even on rock-like sites, with uncertainty

Methodology for estimating human perception to tremors in high-rise buildings

Human perception to tremors during earthquakes in high-rise buildings is usually associated with psychological discomfort such as fear and anxiety. This paper presents a methodology for estimating the level of perception to tremors for occupants living in high-rise buildings subjected to ground motion excitations. Unlike other approaches based on empirical or historical data, the proposed methodology performs a regression analysis using the analytical results of two generic models of 15 and 30 stories. The recorded ground motions in Singapore are collected and modified for structural response analyses. Simple predictive models are then developed to estimate the perception level to tremors based on a proposed ground motion intensity parameter—the average response spectrum intensity in the period range between 0.1 and 2.0 s. These models can be used to predict the percentage of occupants in high-rise buildings who may perceive the tremors at a given ground motion intensity. Furthermore, the models are validated with two recent tremor events reportedly felt in Singapore. It is found that the estimated results match reasonably well with the reports in the local newspapers and from the authorities. The proposed methodology is applicable to urban regions where people living in high-rise buildings might feel tremors during earthquakes.

An effective method for substance detection using the broad spectrum THz signal with a "terahertz nose".

We propose an effective method for the detection and identification of dangerous substances by using the broadband THz pulse. This pulse excites, for example, many vibrational or rotational energy levels of molecules simultaneously. By analyzing the time-dependent spectrum of the THz pulse transmitted through or reflected from a substance, we follow the average response spectrum dynamics. Comparing the absorption and emission spectrum dynamics of a substance under analysis with the corresponding data for a standard substance, one can detect and identify the substance under real conditions taking into account the influence of packing material, water vapor and substance surface. For quality assessment of the standard substance detection in the signal under analysis, we propose time-dependent integral correlation criteria. Restrictions of usually used detection and identification methods, based on a comparison between the absorption frequencies of a substance under analysis and a standard substance, are demonstrated using a physical experiment with paper napkins.

A Suggestion to the Vertical Earthquake Action Stipulated in Seismic Design Specification

In order to further regulate the vertical earthquake action in seismic design specification, to overcome the unreasonable and inconvenient flaws in certain conditions by using vertical to horizontal spectra ratio function, the feasibility of stipulating vertical design response spectrum with the same way of horizontal one is deal with in this paper. 1513 sets of three component records during 64 earthquakes from NGA-west1 database are selected and grouped by magnitude, distance and site conditions. Average acceleration response spectrum of each group is generalized to get the corresponding mean maximum amplitude and effective peak acceleration EPA. Furthermore, some groups with EPA in an interval are merged into one. Once again, the parameters, such as maximum amplitude and characteristic periods of each final grouping are acquired by the same way. The former is divided by the corresponding horizontal value for site category, to obtain the site coefficient for vertical action. Finally a preliminary suggestion of vertical site coefficient and characteristic period are presented. Comparison of observed data with results from the new suggestion and those from spectral ratio shows that the improvement of this study is obvious.

Stochastic Finite-Fault Simulations of the 2011 Tohoku, Japan, Earthquake

We performed stochastic finite‐fault simulations for the moment magnitude ( M ) 9.0 11 March 2011 Tohoku earthquake at KiK‐net sites using the EXSIM algorithm (Motazedian and Atkinson, 2005; Atkinson et al. , 2009; Boore, 2009). The average response spectra of the simulated ground motions were calculated and compared with observed ground motions to determine whether stochastic finite‐fault modeling can reproduce key features of the recorded motions. To account for variations in source characteristics, we examined three rupture‐process models: a single‐event model with random slip distribution, a single‐event model with prescribed slip distribution (Yagi, 2011; see [Data and Resources][1]), and a multiple‐event model with five strong‐motion generation areas (Kurahashi and Irikura, 2011). The analysis results indicate that the single‐event models can model the high‐frequency response spectra values well but result in significant model bias in the low‐frequency range. By contrast, the multiple‐event model produces ground motions that are in good agreement with the observations in both high‐ and low‐frequency ranges. Furthermore, the multiple‐event model can capture temporal characteristics of observed ground motions, including multiphase arrivals of major seismic‐wave groups. Importantly, the calibrated EXSIM model for the 2011 Tohoku earthquake can be used to produce predicted ground motions in other regions, such as the Cascadia subduction region of North America, by suitable modifications of regional attenuation and site parameters. The suitability of the simple stochastic simulation method to prediction of motions for future events, the details of which are poorly known, makes its calibration to Tohoku a useful exercise. [1]: #sec-14

Acceleration response spectra for the earthquakes of the southwestern flank of the Baikal Rift Zone

The acceleration response spectra of earthquakes with M = 4–6.5 in the southwestern part of the Baikal Rift Zone have been studied. The absorption properties of the medium and the attenuation of seismic signals in the study area were determined. Average acceleration response spectra were obtained for regional earthquakes. A comparative analysis of the acceleration response spectra was made for earthquake focal mechanisms with different senses of motion: reverse fault, reverse slip, strike slip, and oblique slip. The effect of the sense of fault motion in the seismic source on acceleration response spectra was determined.

Support vector regression for estimating earthquake response spectra

This study uses support vector regression (SVR), a supervised machine learning algorithm, to model the average horizontal response spectrum as a nonparametric function of a set of predictor ground motion variables. Traditional ground motion prediction equations (GMPEs) are derived using parametric regression, where a fixed functional form is selected, and the model coefficients are determined by minimizing the errors on the training set. The SVR model is nonparametric; there is no need to assume a fixed functional form. Using nonlinear basis functions, the data points are mapped into a high dimensional feature space, where nonlinear input-output relationships can be expressed as a linear combination of nonlinear functions, using a subset of the data points. The combination weights are determined by minimizing the generalization error, using a formal mechanism to characterize the trade-off between the model complexity and the quality of fit to the data. Minimization of the generalization error instead of the fitting error leads to better generation to unseen data, and thus reduces the risk of over-fitting for a given number of data points. The SVR model is not based on a specific probability distribution, and is readily applicable to non-Gaussian data. An example application is presented for vertical strike-slip earthquakes, and the predictions from the SVR model are compared to the recently developed GMPEs. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion prediction models.

Refined harmony search for optimal scaling and selection of accelerograms

Time history analyses of structures typically require some accelerograms of strong ground motion expected at the site. They should be scaled, avoiding the average response spectrum, to fall below the target design spectrum given by the employed seismic-code procedure within a given period range. In this paper, a harmony search, as a recently developed meta-heuristic, is utilized and adapted to solve the problem of the optimal selection and scaling of such recorded accelerograms. Treating a number of ground motion records, close agreement between the scaled-average spectra and the design target were achieved, identifying the proposed algorithm as an acceptable and efficient technique to generate a spectrum compatible set of records for further dynamic structural analyses.