Ground Motion Response Spectra Research Articles

Variability of response spectra of single-path ground-motion record pairs

To improve the accuracy of seismic hazard analysis, understanding the uncertainty of the prediction of the ground-motion amplitude for a specific site owing to a specific source is important. In this study, the variability of the acceleration response spectra of single-path ground motion was evaluated using record pairs obtained from two earthquakes at the same site with the same magnitude, location, and focal mechanism, recorded by high-density strong-motion observation networks in Japan. The natural log standard deviations of the single-path ground motions varied with the period and were distributed in the range of approximately 0.3–0.5. Even if an empirical ground-motion prediction model that accurately models the characteristics of single-path ground motions could be developed, avoiding this variability in the prediction is difficult. The standard deviation of the within-event residuals was smaller at larger distances, and the period of the maximum standard deviation tended to increase as the earthquake magnitude increased. These features may be attributed to differences in the source characteristics of each earthquake. These findings will be useful for the development of advanced empirical ground-motion models and for improving the accuracy of seismic hazard analysis.

Pulse-like ground motion observed during the 6 February 2023 MW7.8 Pazarcık Earthquake (Kahramanmaraş, SE Türkiye)

In this study, we analyzed 100 three-component strong ground motion records observed within 200 km of the causative fault of the 6 February 2023 MW7.8 Pazarcık (Kahramanmaraş) Earthquake in SE Türkiye. The wavelet method was utilized to identify and analyze the characteristics of pulse-like ground motions in the near-fault region, while considering the uncertainty of the pulse orientation during the analysis. Our investigation focused on the effects of the focal mechanism and rupture process on the spatial distribution, pulse orientation, and maximum pulse direction of the observed pulse-like ground motion. We also analyzed the amplitude and period of the observed ground pulses and the effect of long-period amplification on the ground motion response spectra. Our results indicated the following: (1) A total of 21 typical ground velocity pulses were observed during this earthquake, exhibiting complex characteristics due to the influence of the strike-slip mechanism and rupture directivity. Most ground pulses (17 out of 21) were recorded within 20 km of the fault, in a wide range of orientations, including normal and parallel to the fault direction. The waveforms exhibited unidirectional features, indicating the effects of left-lateral fault slip. Distinct pulses observed more than 20 km from the fault were mainly oriented normal to the fault. The waveforms were bidirectional with double- or multi-round trips as a result of rupture directivity. (2) The amplitudes of the observed pulses ranged from 30.5 to 220.0 cm/s, with the largest peak velocity of 220.0 cm/s observed at Station 3138. The pulse periods ranged from 2.3 to 14.5 s, with the longest pulse period of 14.5 s observed at Station 3116. The amplitude and period of the pulses observed during this earthquake were comparable to those of similar-magnitude global earthquakes. The amplitude of the pulses decreased significantly with increasing fault distance, whereas the pulse period was not significantly affected by the fault distance. (3) Compared with non-pulse records, the velocity pulse records had a pronounced amplification effect on the acceleration response spectra near the pulse period, with factors ranging from 2.1 to 5.8. The larger velocity pulses also significantly amplified the velocity response spectra, particularly over the long periods. This significant amplification effect of the pulses on the response spectra leads to empirical models underestimating the long-period earthquake ground motion.

Influence of seawater depth on offshore ground motion characteristics and seismic responses of sea-crossing cable-stayed bridges

This paper studies the effect of seawater depth on offshore earthquake motion characteristics and seismic response of bridges. By analyzing the offshore seismic data recorded by the K-NET during 2006–2021, the horizontal amplification coefficient spectrum and V/H spectral ratio of offshore ground motions were compared for various offshore stations at different seawater depths. Moreover, a numerical model simulating the propagation process of seismic waves in the seabed was developed to investigate the effects of seawater depth and site conditions on offshore ground motions. Finally, a site-seawater-pile foundation-cable-stayed bridge coupling model was created to study the influence of seawater depth on the seismic responses of sea-crossing cable-stayed bridges. The results reveal that the vertical response spectrum of offshore ground motion in deeper seawater is lower for periods longer than 0.3 s. The numerical models reveal that seawater has a suppression effect on the P wave near the resonance frequency of the seawater layer. Due to the hydrodynamic effect, the longitudinal bridge seismic response is significantly amplified. The amplification effect becomes more obvious with an increase in seawater depth. Therefore, it is important to consider the influence of the seawater layer in the seismic design of sea-crossing bridges.

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.

Effects of response spectrum of pulse-like ground motion on stochastic seismic response of tunnel

It is widely accepted that near-fault pulse-like ground motions potentially cause more severe damage to structures than ordinary ground motions. However, the effects of stochastic pulse-like ground motions on underground structures are not effectively considered. The impacts of response spectra of pulse-like ground motions on seismic response are also unclear. Hence, this study utilizes an underground tunnel to investigate the effects of response spectra of pulse-like ground motions on the stochastic seismic response by combining a pulse-like ground motion simulation method and a finite element method. The combination procedure enables stochastic seismic response analysis under spectrum-compatible pulse-like/ordinary ground motions. The finite element model considers the nonlinear dynamic properties of soil and soil–structure interaction. Monte Carlo simulations are carried out to quantify uncertainties of stochastic tunnel response. Results show that pulse-like ground motions cause larger bending moments for tunnel lining even when they match the same target spectrum of ordinary ground motions. Furthermore, the bending moment of tunnel lining is significantly amplified when the spectral acceleration of pulse-like ground motion contains bulges or multiple peaks in the ranges of 1 s–6 s. Therefore, the seismic risk of tunnels may be significantly underestimated in the near-fault regions without considering pulse-like ground motions and their spectral acceleration characteristics.

Determination of damage potential of seismic ground motion to underground structures at soft sites through experimental approach

The selection of a ground motion intensity measure (IM) is an essential criterion for judging the expected intensity level of ground motion in the vulnerability analysis of underground structures, and it is also part and parcel of the resilience-based seismic design of underground structures. Most of the current studies are based on a statistical analysis of numerical simulation results to obtain a specific IM measuring the damage potential of ground motions for an underground structure, and there is a lack of mechanistic studies based on experimental ways. In view of this, a series of large-scale shaking-table tests of an underground structure in soft soils were carried out in this paper to explore the appropriate IMs for measuring the damage potential of ground motions. It is found that the response characteristics of the tested soil-structure interaction (SSI) system gradually become similar to the long-period system as the ground motion intensity increases. The transient fundamental frequency of the tested SSI system moves from the acceleration-sensitive band to the velocity-sensitive band in the ground motion response spectrum. This leads to a decrease in the correlation between the response indicators (RIs) of the system and acceleration-based IMs and an increase in the correlation between RIs and velocity-based IMs as well as displacement-based IMs. Based on the test results, the site fundamental period (Tg) and the boundary periods between the sensitive bands in the bedrock response spectrum (Tc and Td) are proposed as identification indexes for selecting the appropriate IM. One of the three measures, PBA, PBV, and PBD, or a composite measure consisting of two of the three, can be adopted as an appropriate IM for an actual underground structure in soft soils in different cases.

Seismic Evaluation Approaches for Spent Fuel Pool Structures in Nuclear Power Plants

The United States Nuclear Regulatory Commission issued requests for licensees to re-evaluate the seismic hazards at their sites after the accident at the Fukushima Daiichi Nuclear Power Plant in Japan on March 11 in 2011 and to identify and address any site-specific vulnerabilities associated with seismic hazards. The primary guidance for performing those evaluations is provided in the Electric Power Research Institute EPRI-1025287 report, which also provides guidance for evaluating spent fuel pool (SFP) integrity. In addition, the EPRI-3002009564 report also provides evaluation approaches regarding the effects of seismic ground motions on SFPs that supplement the guidance provided in EPRI-1025287. SFP integrity has become increasingly important for active and decommissioned nuclear power plants. According to EPRI-1025287, the SFP integrity evaluation emphasizes failure modes of the SFP that could result in “rapid drain-down.” The definition of “rapid drain-down” is a failure that could lead to the uncovering of irradiated fuel stored in the SFP within 72[Formula: see text]h of an earthquake. Possible failures can be classified into two categories: failures relevant to the SFP structure and failures relevant to non-structural elements. This paper aims to study the approaches of implementing seismic evaluation of an SFP structure. EPRI-3002009564 provides separate seismic evaluation approaches for plants with a ground motion response spectrum (GMRS) peak [Formula: see text][Formula: see text]g and for plants with a GMRS peak [Formula: see text][Formula: see text]g. Structural dynamic analysis is also a common approach for implementing seismic evaluation if a detailed finite element model is available. In this paper, a sample SFP structure was evaluated using the two approaches, structural dynamic analysis and structural analysis criteria. The results indicate that shear failure controlled the failure mode of the SFP structure for both approaches. This shows that the two approaches drew the same conclusion regarding the failure mode. Furthermore, a smaller seismic margin was obtained using the structural analysis criteria, which means this evaluative approach is more conservative.

Evaluation of random-vibration procedures to estimate response spectral ordinates on soft soil sites from fourier amplitude spectra

This study evaluates Random-Vibration Procedures (RVP) to estimate 5% damped response spectra of ground motions recorded on soft soil sites from Fourier Amplitude Spectra (FAS). The study makes use of 136 ground motions recorded in the soft soil Mexico City region during two recent large magnitude earthquakes. Seven different RVP are considered in this investigation consisting of four peak factor models, three strong ground motion duration models, and four non-stationary empirical correction factors. Spectral ordinates computed through conventional time integration were compared to approximate spectral ordinates computed using the FAS of the recorded acceleration time series in combination with RVP. A statistical error analysis was then conducted to determine how effective the various RVP were at estimating the exact pseudo-acceleration response spectra computed with response history analyses. It is found that most RVP commonly used today produce significant systematic overestimations of spectral ordinates at the fundamental mode of the soil deposit. Modifications to durations are proposed to be used in conjunction with various peak factors to reduce overestimations at the site period.

Site amplification prediction model of shallow bedrock sites based on machine learning models

Prediction of the site amplification is of primary importance for a site-specific seismic hazard assessment. A large suite of both empirical and simulation-based site amplification models has been proposed. Because they are conditioned on a few simplified site proxies including time-averaged shear wave velocity up to a depth of 30 m (VS30) and site period (TG), they only provide approximate estimates of the site amplification. In this study, site amplification prediction models are developed using two machine learning algorithms, which are random forest (RF) and deep neural network (DNN). A comprehensive database of site response analysis outputs obtained from simulations performed on shallow bedrock profiles is used. Instead of simplified site proxies and ground motion intensity measures, matrix data which include the response spectrum of the input ground motion and shear wave velocity profile. Both machine learning based models provide exceptional prediction accuracies of both the linear and nonlinear amplifications compared with the regression-based model, producing accurate predictions of both binned mean and standard deviation of the site amplification. Among two machine learning techniques, DNN-based model is revealed to produce better predictions.

Multi-pulse decomposition for nonlinear seismic analysis of structural systems

Large sympathetic, resonance-like, structural behaviour to earthquake excitations with analogous frequency content often plays a critical role in determining its maximum seismic response. Earthquake excitation typically contains a broad spectrum of non-stationary frequency content, wave packets, which are difficult to observe from the recorded time series. Therefore, identifying the root cause of large responses (which act sympathically with the input but do not achieve full-resonance) of a structure is problematic. Hence, this paper proposes a new multi-pulse decomposition method of ground motions, through which components of a ground motion within a specific period range are determined. In this method, a ground motion is approximated with a Gauss-Fourier wave packet series. The decomposed components, wave packets, contain information about its time-position, frequency, amplitude, pulse width and phase angle. Unlike the Ricker (Morlet) wavelet the Gauss-Fourier wave packet is not limited to symmetrical pulses. One ensemble of 40 near-fault ground motions and one ensemble of 44 far-fault ground motions are used to demonstrate the application and efficiency of the proposed method. The method is shown to be precise in reconstructing the original ground motion using its decomposed components. It is also concluded that the method is accurate in replication of elastic and inelastic response spectra of ground motions within a specific period range. It is demonstrated that for some structure/ground motion combinations, only a few Gauss-Fourier components are required to faithfully describe response behaviour. This highlights that, for these systems, most of the recorded earthquake time series acts like noise on a much simpler wave-packet signal.

Modeling response spectrum compatible pulse-like ground motion

The seismic response analysis of near-fault pulse-like ground motions is severely restricted due to the scarcity of pulse-like records. The requirement in regulations that the response spectra of artificial ground motions should be compatible with the target response spectrum makes the relevant studies more difficult. As a result, this study proposes a trigonometric series-based stochastic method to simulate pulse-like ground motions, with the advantage that the corresponding pseudo-spectral acceleration is compatible with the given target response spectrum. This goal is achieved by two parts. (1) The envelope function of pulse-like records obtained by the Hilbert transform is utilized as the amplitude modulation function to ensure that the simulated ground motion contains a pulse. (2) A novel iteration scheme based on random frequency parameters is proposed to guarantee the response spectrum compatibility. The velocity ground motion is first simulated since the pulse usually exists in velocity. The ground-motion acceleration subsequently obtained by differentiating the velocity is adopted to calculate the response spectrum. Two cases are implemented and verified the effectiveness of the proposed method in enriching existing pulse-like databases and generating pulse-like ground motion in areas that lack records. Moreover, the amplitude modulation function and target spectrum, as two key factors in the proposed method, determines the presence of a pulse and the pulse periods, respectively. This property makes the proposed method potentially universal applicability for stochastic pulse-like ground motion simulation in engineering.

A deep neural network framework for real‐time on‐site estimation of acceleration response spectra of seismic ground motions

AbstractVarious earthquake early warning (EEW) methodologies have been proposed globally for speedily estimating information (i.e., location, magnitude, ground‐shaking intensities, and/or potential consequences) about ongoing seismic events for real‐time/near real‐time earthquake risk management. Conventional EEW algorithms have often been based on the inferred physics of a fault rupture combined with simplified empirical models to estimate the source parameters and intensity measures of interest. Given the recent boost in computational resources, data‐driven methods/models are now widely accepted as effective alternatives for EEW. This study introduces a highly accurate deep‐learning‐based computational framework named ROSERS (i.e., Real‐time On‐Site Estimation of Response Spectra) to estimate the acceleration response spectrum (Sa(T)) of the expected on‐site ground‐motion waveforms using early non‐damage‐causing early p‐waves and site characteristics. The framework is trained using a carefully selected extensive database of recorded ground motions. Due to the well‐known correlation of Sa(T) with structures’ seismic response and resulting damage/losses, rapid and accurate knowledge of expected on‐site Sa(T) values is highly beneficial to various end‐users to make well‐informed real‐time and near‐real‐time decisions. The framework is thoroughly assessed and investigated through multiple statistical tests under three historical earthquake events. These analyses demonstrate that the overall framework leads to excellent prediction power and, on average, has an accuracy above 85% for hazard‐consistent early‐warning trigger classification.

Earthquake Early Warning for Estimating Floor Shaking Levels of Tall Buildings

ABSTRACTThis article investigates methods to improve earthquake early warning (EEW) predictions of shaking levels for residents of tall buildings. In the current U.S. Geological Survey ShakeAlert EEW system, regions far from an epicenter will not receive alerts due to low predicted ground-shaking intensities. However, residents of tall buildings in those areas may still experience significant shaking due to the acceleration amplification caused by tall buildings’ dynamic behavior, as recently experienced by residents of the 52-story building in downtown Los Angeles (DTLA) during the 2019 M 7.1 Ridgecrest earthquake. Using more than 400 recorded response data acquired from 77 instrumented buildings in California, here we compare the Federal Emergency Management Agency (FEMA) P-58 and American Society of Civil Engineers (ASCE) 7-16 simplified equations for peak floor acceleration (PFA), finding that the ASCE estimation is close to the median of data recorded in large and long-distance events, whereas the current FEMA estimation is not suitable. In the second part of this article, four instrumented tall buildings in DTLA are extensively studied, and the performance of the simplified and response spectrum (RS) methods giving both an estimation of the free-field horizontal peak ground acceleration (PGA) and pseudospectral acceleration is evaluated. The results show that the RS method is as accurate as the response history analysis as long as the ground-motion RS is accurate, whereas the ASCE 7-16 prediction is conservative. However, when ground-motion RS or PGA is estimated for DTLA using a ground-motion model (GMM), the performance of the RS method significantly degrades due to underestimation by the GMM at long periods. The results of this study imply that a nonergodic GMM, which may give more accurate prediction in Los Angeles, could improve the results for PFA when the building’s behavior is dominated by a few long-period fundamental modes, as is the case for the 52-story building in DTLA.

Factors Affecting Site-Specific Response Analysis

ABSTRACT The engineering purpose of a site-specific response analysis is to estimate the uniform hazard acceleration spectrum on the ground surface for a selected hazard level. One of the mandatory components for site response analyses is one or more representative acceleration time histories that need to be scaled with respect to the calculated seismic hazard level for the selected site. The selection and scaling procedures of earthquake acceleration records play an important role in this approach. The effects and differences in using two different scaling approaches are studied: scaling with respect to ground motion parameters and response spectrum scaling. A set of homogeneous ground motion prediction relationships are developed for peak ground acceleration, peak ground velocity, root-mean-square acceleration, Arias intensity, cumulative absolute velocity, maximum spectral acceleration, response spectrum intensity, and acceleration spectrum intensity based on a uniform set of acceleration records for ground motion parameter scaling. The uncertainties associated with site response analysis are considered as epistemic and aleatory uncertainties in source characteristics, soil profile, and soil properties. Aleatory variability is due to the intrinsic randomness of natural systems; it cannot be reduced with additional data (Passeri et al. 2020), however; its variability may be modeled by probability distribution functions. Thus, one possibility is to determine the probability distribution of the acceleration spectrum calculated on the ground surface for all possible input acceleration records, site profiles, and dynamic soil properties. The variability in the earthquake source and path effects are considered using a large number of acceleration records compatible with the site-dependent earthquake hazard in terms of fault mechanism, magnitude, and distance range recorded on stiff site conditions. Likewise, a large number of soil profiles may be considered to account for the site condition variability. The uncertainties related to dynamic soil properties may be considered as possible variability of maximum dynamic shear modulus in site response analyses. A methodology is proposed to estimate a uniform hazard acceleration spectrum on the ground surface based on the probabilistic assessment of the factors involved in site response analysis. The uniform hazard acceleration spectra obtained from a case study are compared with the spectra calculated by probabilistic models proposed in the literature.

Probabilistic site response analysis for nuclear facilities considering variability of soil properties and its effects on uniform hazard response spectra and ground motion response spectra

Because seismic waves are influenced by variability at local soil sites, their effects on the uniform hazard response spectra (UHRS) and ground motion response spectra (GMRS) of nuclear facilities at soil sites are studied by means of a probabilistic site response analysis based on the random vibration theory. Monte Carlo simulations are employed to take into consideration the effects of variability of the layer thickness, low-strain shear-wave velocity, and nonlinear dependence of the shear modulus and hysteretic damping on shear strain at soil sites. A new probabilistic model is proposed to simulate the variability of the layer thickness using an Erlang distribution. Random field models are considered for the nonlinear shear modulus reduction and damping curves. The probabilistic approach is applied to generic soil sites to evaluate their soil-amplification functions. The seismic hazard curves and the UHRS can be obtained using the amplification functions and the hazard curves of outcropping bedrock motions. Then, the seismic risk for structures installed at these types of sites is calculated and the resulting GMRS values for a seismic design are derived. It can be observed from the simulations that the variability in the layer thickness and the low-strain shear-wave velocity influences the soil-amplification functions and the resulting UHRS and GMRS values for the soil sites significantly. The effects increase with the variances of the considered random properties. Because the input motions for probabilistic earthquake response analyses of nuclear facilities are determined based on the UHRS/GMRS values, the effects of random soil sites must be carefully considered to ensure the seismic safety of these facilities.

Understanding the seismic response of electrical equipment subjected to high–frequency ground motions

Ground motion studies in Central and Eastern United States (CEUS) show that the ground motion response spectra exceeds design spectrum of nuclear power plants in high–frequency range. To ensure safe shutdown of nuclear power plants in events where design spectrum is exceeded, the safety–related digital control systems and electrical equipment such as relays must be seismically qualified for high–frequency ground motions. Conventionally, uncoupled linear analysis of building and electrical cabinet is conducted and then seismic demands on equipment are evaluated. The conventional analysis ignores effects of various factors such as geometric nonlinearities, mass interaction between primary (building) and secondary (electrical cabinet) systems, etc. Ignoring such factors leads to unnecessarily high seismic demands on equipment. In this study, the seismic demands on equipment are evaluated by conducting both coupled and uncoupled analysis of linear primary system and linear as well as nonlinear secondary system. Various cases are analyzed where at least one mode of primary system is tuned with one mode of secondary systems. Each case is subjected to both low–frequency and high–frequency ground motions to compare the difference in response to each ground motion. The seismic demands on equipment are compared for coupled and uncoupled analysis as well as for linear and nonlinear systems. The results show reduction in seismic demands on electrical equipment for various nonlinear coupled analysis cases. The high seismic demands evaluated from linear uncoupled analysis may lead to exclusion of some electrical equipment which can be avoided by conducting coupled nonlinear analysis of primary–secondary systems and obtaining the realistic seismic demands on equipment.

Effects of Soil Amplification on Ground Motion Response Spectra with High-Frequency Contents at Generic Soil Sites for Nuclear Facilities in Korea

Ground motion response spectra (GMRS) at rock/soil sites in regions where earthquake ground motions have dominant contents at high frequencies of 10 Hz or more are evaluated and the effects of soil amplification on the GMRS are studied. The seismic hazard levels at the soil sites are estimated from soil amplification functions and hazard curves for rock outcrop motions. The soil amplification functions are obtained using modified earthquake ground motions which match the uniform hazard response spectra (UHRS) for rock outcrop motions with various mean annual frequencies of exceedance in order to consider the effects of earthquake ground motions consistently in a site response analysis. UHRS at soil sites are determined from the calculated seismic hazard curves. Subsequently, design factors, which will be applied to UHRS, and the corresponding GMRS are evaluated such that the seismic risk for the structures, systems, and components of nuclear facilities would be equal to a target seismic risk. It can be observed from example applications that the UHRS and GMRS at soil sites have peaks at the natural frequencies of the soil, where the soil responses are amplified. Amplification at soil sites depends on the frequency contents of rock outcrop motions.

Site effect and microzonation of the Jizan coastal area, southwestern Saudi Arabia, for earthquake hazard assessment based on the geotechnical borehole data

Ninety-one geotechnical boreholes were drilled throughout Jizan City and the subsoil profiles were modeled. The SPT-N values were corrected to the N60 parameter. Then, the calculated shear wave velocity for 30 m depth (Vs30) varies between 196.086 and 589.931 m/s. Moreover, the site soil was classified into two of soil classes detected. Thereafter, the site response with SMSIM software is assigned at all borehole locations using Vs30, predominant frequency, and corresponding amplitude amplification factor. The estimated amplification factor varied between 1.6 and 18.2, reflecting the significant difference in the thicknesses of soil. The values of high amplification extend in a north–south strip to the west indicating very soft/loose sediments with a considerable thickness. Higher fundamental frequency values extend due north along the coast until the Ash-Shati and Ar-Rawabi districts verifying the compacted sediments. The peak ground acceleration (PGA) has been estimated for 91 borehole sites at bedrock level in the Jizan area using Mw 6.25 earthquake magnitude. This PGA was used to generate an ArcGIS contour map. The values of the PGA for the bedrock vary between 4.8 and 10.7 cm/s2. Moreover, PGA is computed at the ground surface level, where it varies between 7.7 and 32.0 cm/s2. Finally, the ground motion response spectra were also estimated with 5% critical damping for the locations of all of the boreholes. The pseudo-spectral acceleration (PSA) and its corresponding frequency/period were calculated for the 91 borehole locations. The values of the maximum PSA ranged between 17 and 103 cm/s2, covering the western zone of the Jizan study area. Furthermore, the PSAs were computed for 1.5, 3, 5, 8, and 10 Hz at 91 locations, and then contoured using the ArcGIS package. This frequency range from 1.5 to 10 Hz represents the range in the natural frequencies for tall to low-rise buildings.

Simulation of the MW = 7.9 Gulf of Alaska earthquake on January 23, 2018, by the stochastic finite fault model

On the premise of constraining the seismogenic fault structure of a future large earthquake, we proposed using empirical equations to determine the length, width, seismic moment and slip distribution of a large seismogenic fault plane and using the stochastic finite fault model to predict future large earthquakes. The ground motion time histories and response spectra recorded by 12 seismic stations on bedrock during the MW = 7.9 Gulf of Alaska earthquake on January 23, 2018, were simulated. The simulation error determined by the average ratio of the simulated spectrum amplitude to the recorded spectrum amplitude varied between 1.08 and 0.92 in the period range of 0–10 s, and the standard deviation of the simulation error at different frequencies did not exceed 1; the 95% confidence interval also did not change significantly with the period. The above analyses show that our simulation results reflect the mean ground motion. To further discuss the reliability of predicting future large earthquakes by the stochastic finite fault model, we redistributed the initial rupture point and slip distribution on the seismogenic fault plane by the quasi-random method, and the simulation errors and simulation results of the redistribution model were similar to those of the previous model. Further research confirmed that our method for obtaining the seismic source parameters is viable and that the stochastic finite fault model for the prediction of future large earthquakes is reliable, especially for large far-field earthquakes. The seismic stations that we used are all situated on bedrock on one side of the fault and do not involve rupture directivity, i.e., the seismic wave pathways may be similar, so the simulation results are ideal. However, if the rupture directivity, different site conditions, surface topography and basin effects are considered, it will be necessary to amend the proposed method.

Seismic response of electrical equipment subjected to high–frequency ground motions

Recent ground motion studies conducted at nuclear facilities indicate that in Central and Eastern United States, the ground motion response spectra exceed the safe–shutdown earthquake spectra at high frequencies. Even though high–frequency ground motions do not cause structural damage, high–frequency accelerations may propagate through the structure and interfere with the output of the safety–related equipment such as relays required to ensure safe shutdown of the plant during a seismic event. Hence, it is essential to seismically qualify electrical equipment subjected to high–frequency accelerations. The seismic qualification is conducted by comparing in–cabinet response spectra evaluated at the equipment locations with the capacities of equipment obtained from shake table tests. The in–cabinet response spectrum is obtained from analysis of nuclear power plant building and electrical cabinet in which the equipment are mounted. This study is based on the hypothesis that the high–frequency motions do not reach the equipment as the small displacements induced by such motions are filtered out by the geometric nonlinearities. The effect of two different types of nonlinearities are studied: (1) a gap in the connection between electrical cabinet and floor; (2) sliding friction between electrical cabinet’s base and the floor. The results from an analyses of various different cases show that the high–frequency motions do not reach the relays if the maximum displacement of building floor is less than the gap. Even if the displacement is larger than the gap, the in–cabinet spectral accelerations are not excessively high. On the contrary, results from a conventional linear analysis give excessively high unrealistic spectral accelerations.