Ground Motion Intensity Levels Research Articles

Fragility evaluation of nuclear containment structure subjected to earthquake and subsequent internal pressure

Strong earthquake may lead to the rupture of pipeline inside the nuclear containment structure, which leads to overpressure of the nuclear containment structure. Therefore, nuclear containment structure suffers from the risk of subjected to earthquake and internal pressure sequence. However, studies on the performance evaluation of the nuclear containment structure subjected to earthquake and subsequent internal pressure sequence is very rare. This study presents fragility evaluation of the nuclear containment structure subjected to earthquake and subsequent internal pressure sequence. Firstly, detailed nonlinear finite element model of the nuclear containment structure is developed with layered shell element and concrete damage plasticity model. Then, 20 far-fault ground motion records are selected and scaled to different intensity levels to simulate different damage states of the nuclear containment structure. Nonlinear response of maximum strain, displacement and fragility of the nuclear containment structure subjected to earthquake and subsequent internal pressure sequence is analyzed. Results reveal that distribution of maximum strain and displacement of the nuclear containment structure subjected to earthquake and subsequent internal pressure are significantly different. Maximum displacement distribution of the nuclear containment structure subjected to earthquake is related to the ground motion intensity level. The variation of the median pressure capacity and logarithmic standard deviation presents a quadratic form with the increase of ground motion intensity level.

Orientation and intensity of maximum response spectral ordinates during the December 20, 2022 Mw 6.4 Ferndale, California earthquake

The level of horizontal ground motion intensity can have large variations from one orientation to another. This study examines the orientation of the maximum response of 5%-damped linear oscillators and its geographical distribution for ground motions recorded during the December 20, 2022, Ferndale, CA earthquake. The orientation of the maximum intensity is found to generally occur close to the transverse orientation for epicentral distances greater than 30 km. At epicentral distances less than 30 km, the angular difference between the orientation of the maximum intensity and the transverse orientation does not show a clear predominant orientation. The angular difference with respect to the transverse orientation is found to be strongly correlated with the level of intensity. The ground motion intensity at the transverse orientation was, on average, between 85% and 95% of the maximum intensity and was 1.0–1.26 times greater than the RotD50 intensity (i.e., the median intensity from all horizontal orientations). The level of polarization increases with the period of the oscillator and ground motions remain fairly polarized up to 350 km from the epicenter. The results support a case for future incorporation of directionality effects, and in particular, the use of orientation relative to the transverse orientation, when estimating response spectral ordinates from strike-slip earthquakes.

Improving the Seismic Performance of Steel Frames under Mainshock–Aftershock Using Post-Tensioned Connections

In this study, the seismic responses of moment-resisting steel frames (MRSFs) with welded and post-tensioned connections under 28 artificial seismic sequences (mainshock–aftershock) are compared. For this aim, the mainshock are scaled at different ground motion intensity levels as a function of the spectral pseudo-acceleration corresponding to the fundamental period of vibration of the structure Sa(T1), whereas different intensity levels of the aftershocks are used for a percentage of the peak maximum acceleration of the mainshock. The seismic performance comparison of both structural systems is computed for the maximum, residual inter-story drift and hysteretic energy demands. The results show that post-tensioned frames significantly reduce the structural demands, especially in the case of residual inter-story drifts and hysteretic energy in comparison with moment-resisting steel frames with welded connections. The reductions in the structural response tend to be larger as the intensity of the aftershock tends to increase. Therefore, it is concluded that the use of post-tensioned connections is a great alternative to mitigate the seismic response of buildings subjected to seismic sequences.

Seismic fragility analysis of nuclear containment structure under chloride-induced reinforcing steel corrosion conditions

Chloride-induced corrosion of reinforcing steel is one of the critical degradation factors influence the life cycle performance of the containment structure. Therefore, it is of great significance to study the safety performance of containment structure under chloride-induced reinforcing steel corrosion condition. This study presents fragility evaluation of the containment structure under chloride-induced reinforcing steel corrosion condition. Nonlinear time history analysis of the containment structure under different reinforcing steel corrosion conditions is carried out considering various uncertainties including uncertainty in material strength, record to record uncertainty and uncertainty in corrosion parameters. Roof drift under different ground motion intensity levels and seismic fragility of the containment structure corresponding to different performance level with typical service life are analyzed. Results reveal that with the increase of the service life of the containment structure, the increasing rate for roof drift of the containment structure decreases, while the variability of roof drift of the containment structure changes slightly. Service life of the containment structure has different impacts on the fragility of the containment structure corresponding to different performance levels. With the increase of service life, the increasing rate for failure probability of containment structure increases.

Seismic Fragility Assessment of SMRFs Equipped with TMD Considering Cyclic Deterioration of Members and Nonlinear Geometry

This paper presents seismic fragility curves to assess the effect of far-field ground motions on the behavior of high-rise steel moment resisting frame (SMRF) structures equipped with Tuned Mass Damper, considering the cyclic deterioration of members and P-Delta effect in the nonlinear region. For this purpose, three 8-, 20-, and 30-story SMRF structures are selected, 44 earthquake record sets are extracted from the FEMA P-695, Incremental Dynamic Analysis (IDA) is operated, and four structural damage states are considered through the framework of HAZUS, including slight, moderate, extensive, and complete. Maximum structural inter-story drift and floor acceleration are employed to quantify the damage states, and spectral acceleration is used as the intensity measure. Results show that the Tuned Mass Damper can reduce the probability of damage under earthquake excitation in all damage states for both structural and non-structural elements. The decline varies from 4.0% to 20.0%, depending on the ground motion intensity level, based on engineering demand parameters. Moreover, it is clear that nonlinear properties and component deterioration under cyclic excitation can affect structural response in all damage states, which concerns the obtained curves.

Seismic fragility analysis of containment structure subjected to near fault ground motions

This study presents seismic fragility analysis of the containment structure subjected to near fault ground motion. Prior to perform seismic fragility analysis, 20 near fault ground motion records with pulse characteristics are selected PEER database. Nonlinear dynamic analysis of the containment structure is performed automatically using Matlab scripts and Batch files. To quantify the global damage behavior of the containment structure subjected to near fault ground motion, energy-based global damage index is proposed. The evolution of global damage behavior and tensile damage of the containment structure are analyzed in depth. Goodness of fit for two widely used fragility fitting methods is compared. To quantify the uncertainty in fragility function parameters, Bootstrap resampling procedure and analytical statistical inference method are adopted to estimate the confidence interval of the fragility function parameters. Results indicated that the bottom of containment structure suffered from severe tensile damage and it is most vulnerable location of the containment structure. With the increase of peak ground motion intensity level, tensile damage increases rapidly and extends to higher elevations of the containment structure. The relative error for fragility function parameter x˜m is not more than 4%, and the error of fragility function parameter β˜R is more than 12%. In general, analytical statistical method provides good estimation for the confidence interval of fragility function parameter x˜m, while overestimate the confidence interval of fragility function parameter β˜R.

Probabilistic seismic performance assessment of nuclear containment structure considering statistical uncertainty

Statistical uncertainty is inherently involved in probabilistic seismic performance assessment of containment structure due to heavy computational efforts of nonlinear dynamic analysis. Aiming at the statistical uncertainty involved in seismic fragility and seismic risk evaluation of containment structure, this study proposes a method for quantifying the statistical uncertainty in probabilistic seismic performance assessment of the containment structure. Taking a three story reinforced concrete frame as an example, effectiveness and efficiency of the proposed method for confidence interval estimation of seismic fragility curve is verified. Then, the proposed method is applied to fragility analysis and seismic risk evaluation of the containment structure. Roof drift of the containment structure under different ground motion intensity levels is discussed. Confidence interval for seismic fragility curve and seismic risk of the containment structure considering statistical uncertainty is quantified by the proposed method. The results highlighted the necessity for quantifying the impact of statistical uncertainty involved in probabilistic seismic performance evaluation of the containment structure.

Seismic retrofit of reinforced concrete frames by direct loss-based design

This paper introduces a procedure for the retrofit design of reinforced concrete (RC) frame buildings to achieve the desired target level of earthquake-induced loss for a given seismic hazard profile. The methodology is “direct” because the loss target is specified in the first step of the procedure, and, in principle, no design iterations are required. The target loss level is defined based on designer/client preferences and/or external constraints (e.g., foundation capacity). The proposed procedure relies on a simplified loss assessment enabled by a surrogate model defining the probability distribution of the seismic deformation demands of single degree of freedom (SDoF) systems given different ground-motion intensity levels. Combined with a hazard curve and a building-level damage-to-loss model, such a surrogate model is used to map candidate SDoF force-displacement curves to their earthquake-induced loss by assuming a given retrofit strategy. In this case, the considered retrofit strategy involves changing the frame's local hierarchy of strength to ensure a global plastic structure mechanism. Under such assumptions, a designer can select a design force-displacement curve among those that comply with the chosen loss target. The detailing of the retrofitted frame is carried out according to the direct displacement-based design principles and the Simplified Lateral Mechanism Analysis (SLaMA). The procedure is applied to an under-designed RC frame building retrofitted with concrete jacketing. A benchmark loss estimate is calculated using non-linear time-history analyses for loss assessment purposes. The proposed procedure shows satisfactory compliance with the benchmark loss, emphasising the procedure's effectiveness in practice.

Gaussian process regression-based surrogate modelling for direct loss-based seismic design of low-rise base-isolated structures

Seismic base isolation has gained popularity in the last decades. As a result, many structures are now equipped with base isolation systems to offer enhanced seismic performance and meet the needs of risk-aware stakeholders. However, a robust performance-based seismic design of these types of structures is generally not carried out due to the iterative nature of common design approaches and the time/computational resources required for such iterations, which are incompatible with the preliminary design phase. Indeed, seismic risk/loss is often just assessed at the end of the design process as a final verification step. This paper offers an overview of a simplified methodology for the seismic design of low-rise structures equipped with a base isolation system to achieve a predefined level of earthquake-induced economic loss while complying with a predefined minimum level of structural reliability. The main advantage of the proposed methodology is that it requires no design iterations. The procedure is enabled by Gaussian-process-regression-based surrogate probabilistic seismic demand modelling of equivalent single degree of freedom systems (i.e., the probability distribution of peak horizontal displacements and accelerations on top of the isolation layer conditional on different ground-motion intensity levels). Combined with simplified loss models for the base isolation system and the structural and non-structural components of the superstructure, this approach allows mapping a range of structural configurations to their resulting seismic loss. A designer can then select one of the identified combinations of the strength of the superstructure and properties of the isolation system conforming with the loss target, and reliability requirements, and consequently detail the superstructure and isolation system accordingly. This paper introduces the implemented surrogate probabilistic seismic demand models and provides an overview of a tentative Direct Loss-based Design procedure for low-rise base-isolated structures.

Component repair cost functions in Indian context for seismic loss estimation of reinforced concrete buildings

This study proposes component level repair cost functions for efficient estimation of financial losses expected to be incurred due to earthquake-induced damages to typical reinforced concrete (RC) buildings in the Indian context. The proposed repair cost functions account for the variability in the local construction practices and their associated financial implications. Repair cost functions for four drift sensitive building components, i.e., unreinforced masonry walls, reinforced concrete beams, reinforced concrete columns and reinforced concrete beam-column joints, are developed. A detailed case study is presented for three different building configurations commonly observed in the hilly region, i.e., 4-story stepback, 4-story split-foundation, and 4-story regular buildings. The variation in the floor-wise and component-wise repair cost ratio with varying levels of ground motion intensity is investigated. This study also proposes the expected repair cost ratio function for the considered building configurations corresponding to the four building components. It is observed that the expected repair cost ratio is least in 4-story regular building and maximum in 4-story split-foundation building.

Analysis of Seismic Isolation Performance of X-Shaped Rubber Bearings (XRBs)

A detailed analysis of the seismic safety performance of building structures using X-shaped rubber bearings (XRBs) under seismic action at different seismic levels of intensity were carried out in this study. The horizontal mechanical properties of XRB were studied by analytical methods. To reveal the failure prevention and control capability of XRBs under strong ground motions, a detailed comparative analysis was conducted of the seismic performances of three-story buildings using XRBs, typical rubber bearings (TRBs), and TRBs with retaining wall protection (RWP). A nonlinear dynamic finite element method was used to analyze the displacement, velocity, and acceleration responses of the seismically isolated structures at different ground motion intensity levels. The results show that the failure of the seismic isolation layer occurs in the building using TRBs under seismic intensity with a 1‱ probability of exceedance (PE) in one year. When the RWP is set around the seismic isolation layer, the superstructure will collide with the wall, which leads to a dramatic increase in superstructure acceleration, while the overall seismic isolation performance of the structure is affected. Nevertheless, XRBs can effectively prevent deformation failure of the seismic isolation layer of a building, reduce the seismic response of a superstructure, and can improve the seismic safety level of a building.

A risk-based evaluation of direct displacement-based design

Recent seismic design approaches developed under the umbrella of performance-based earthquake engineering (PBEE) pursue pre-defined performance objectives in terms of structural response, economic losses, or casualties. The earlier PBEE methods were mainly concerned with the deterministic evaluation of performance at a single ground motion intensity level. This premise, however, provides little insight into the long-term risk-based performance of a structure, and limits the ability to make informed design decisions. Given the inherent sources of uncertainty in all aspects of seismic design, probability theory needs to be employed to enable reliable design solutions. However, applying a risk-oriented design approach is not currently feasible for most practitioners, making it essential to understand how the current deterministic applications of these intensity-based PBEE approaches perform in terms of risk. Specifically, the aim is to investigate the capability of the direct displacement-based design (DDBD) method in producing reliable, risk-consistent designs. A probabilistic PBEE assessment framework is applied as the benchmark to determine the risk of exceeding performance objectives for multiple DDBD-based reinforced-concrete-wall and dual reinforced-concrete-wall/steel-frame buildings located at three different sites. The significant variation in the achieved risk estimates related to the limit states of damage limitation, life safety and global collapse for the buildings considered, questions the ability of DDBD—or any other intensity-based design method that does not account for uncertainty—to offer risk consistency.

Comparative nonlinear soil-structure interaction analyses using macro-element and soil-block modelling approaches

In dynamic soil-structure interaction problems, involving the coupling of structure, foundation and soil, the use of a nonlinear macro-element modelling approach may result particularly advantageous not only to consider nonlinear effects and thus avoid the introduction of possible bias in seismic risk assessment analyses, especially when ground motion intensity levels are high, but also to greatly reduce the heavy computational effort required by 3D finite element soil-block models. In this work, a footing macro-element that models the soil nonlinear behaviour at near-field, as well as the far-field dynamic impedance and energy dissipation through radiation damping, is verified against results obtained from the analysis with OpenSees of a 3D nonlinear soil-block model, itself verified through cross-checks and cross-modelling efforts with equivalent-linear analyses in STRATA and nonlinear analyses in DEEPSOIL. Considering two soil profiles of different complexity and two records of different intensity, one of which leads to extensive soil nonlinearity, the soil-block is verified first. Then, the macro-element model, available in SeismoStruct, is verified against the soil-block model in terms of structural response of a single-degree-of-freedom (SDOF) system as well as near-field soil-footing behaviour.

Probabilistic seismic performance evaluation of nuclear containment structure subjected to far-fault ground motions

This study presents probabilistic seismic performance evaluation of nuclear containment structure subjected to far-fault ground motions. To achieve this objective, refined finite element model of nuclear containment structure is established and incremental dynamic analysis (IDA) is performed automatically using pre-processing and post-processing scripts. Cracking status, roof drift, damage dissipated energy and floor acceleration of the nuclear containment structure is discussed. Furthermore, probabilistic seismic safety margin of nuclear containment structure is quantitatively evaluated by median value method and confidence interval method. Finally, a closed-form solution for the annual frequency of exceedance for the roof drift of the nuclear containment structure is derived, and the effectiveness of the closed-form solution is verified by the classical direct numerical integration method. Annual frequency of exceedance for the roof drift of the nuclear containment structure corresponding to different performance levels is analyzed. Results indicated that the bottom of nuclear containment structure is the most vulnerable location. In general, nuclear containment structure subjected to far-fault ground motions is dominated by shearing cracks. When the ground motion intensity level is less than 0.4 g, damage dissipated energy of the nuclear containment structure is very small. In general, with the increase of elevation, acceleration amplification factor of the nuclear containment structure increases rapidly. Probabilistic seismic safety margin of the nuclear containment structure evaluated by median value method tends to be conservative. Analytical and classical numerical integration method provides almost the same prediction of the annual frequency of exceedance for the roof drift of the nuclear containment structure, which indicates the effectiveness of the proposed closed-form solution.

Strong-Motions From Damaging Moderate Magnitude (5.9 ≥ Mw) Earthquakes in Japan Recorded by K-NET and KiK-net

Strong-motions from 79 moderate magnitude (5.9 ≥ Mw) earthquakes that caused various degrees of impact on humans and built-environment in Japan between 1996 and 2019, after the start of K-NET and KiK-net, are presented. As such, most of the earthquakes occurred beneath the land, and agencies had reported damages from events as small as Mw 4.1. Together, large peak ground accelerations exceeding 500 cm/s2were recorded during 15 earthquakes, reaching approximately 1128 cm/s2during one event. Similarly, large peak ground velocities exceeding 30 cm/s were recorded during ten earthquakes, reaching about 76 cm/s to the maximum. Most of the large values aforementioned were recorded within a hypocentral distance of approximately 30 km and on soil site conditions. Intermediate to long-period ground motions are of growing concerns in urban areas located on sedimentary basins with mid-rise and high-rise buildings. The threshold magnitude for the large ground motions at the periods of about 2–5 s is not well understood. In March 2013, the Japan Meteorological Agency introduced four levels of long-period ground motion intensity (LPGMI) based on absolute velocity response spectra (AVRS) between 1.6 and 7.8 s. In the present data set, LPGMI of level 3 (AVRS 50–100 cm/s) and level 4 (AVRS >100 cm/s) were observed each at a single site from shallow-focus earthquakes of Mw 5.8 and 5.9 at distances of approximately 12 and 15 km, respectively. However, the peak response periods were relatively short (1.6–1.8 s). The data showed that LPGM from moderate earthquakes is of lower concern regarding earthquake early warning at distances beyond 200 km. The 2018 Mw 5.5 North Osaka earthquake, despite the moderate magnitude, caused the loss of six human lives and brought significant damage to buildings and lifelines. Comparing the data with the ground motion prediction equations (GMPEs) and other events suggested that the North Osaka earthquake was probably a higher stress drop event. These moderate earthquakes’ observations hinted that the commonly used GMPEs in Japan may not sufficiently grasp these earthquakes' hazards.

Mathematical sustainability assessment framework of earthquake-induced steel building population

The ability to estimate the probability a building population under seismic events will be sustainable is timely, useful in appropriately allocating earthquake mitigation funds earmarked for repair, rehabilitation, and replacement. A building population is considered sustainable if actual cost incurred is less than a target cost at a given ground motion intensity level such as a certain level of spectral accelerations. The purpose of this study is to construct a mathematical framework coupled with Gompertz and power functions to determine the probability of sustainability of building population subjected to seismic events as a function of target repair-cost ratios. The framework accounts for the exceedence probability of certain earthquake occurrence in 50 years and the fragility data created by joint response surface metamodels (RSMs) and Monte Carlo Simulation (MCS). The fragility data for a population of L-shaped Steel Moment-Frame (LSMF) buildings located in the Central United States and the probability of spectral acceleration exceedence for the target region are used for this study. The probability of sustainability of the LSMF buildings built from pre-1970, between 1970 and 1990, and post-1990 are determined through the developed framework. The mathematical and graphical relationship between the probability of sustainability of the building population under a broad range of spectral accelerations and its target repair-cost ratio are determined. Key findings show that the buildings built in the post-1990 are more sustainable than those built from the pre-1970.

Evaluation of approximate methods for estimating residual drift demands in BRBFs

Nowadays, Buckling Restrained Braced Frame (BRBF) system is extensively used for the seismic design of new buildings. This system is composed of Buckling Restrained Braces (BRBs) that do not buckle under compression forces, and have high energy-dissipation capacity. However, low post-yield stiffness of the brace core in BRBs may cause large residual drifts after the occurrence of an earthquake. In this study, four approximate methods for estimating residual drift demands in BRBFs are evaluated. These methods include the FEMA P-58 method, the method proposed in this study, the method proposed by Erochko et al. and the coefficients method introduced by Ruiz-García and Chora, calibrated in this study for BRBFs. To evaluate the estimated residual drifts of BRBFs according to these approximate methods, 2-, 4-, 6-, 8-, 10- and 12-story BRBFs are designed. Nonlinear dynamic analyses are performed on the BRBFs using 78 ground motion records scaled to different ground motion intensity levels. The results show that the proposed method is more accurate than the FEMA P-58 and Erochko et al. methods that are conservative for estimating the median and mean residual drifts of BRBFs, respectively. Moreover, the coefficients method, which estimates the median of maximum residual drifts, is the most accurate method among the four methods considered. However, it does not provide information about the height-wise distribution of residual drifts.

Torsional irregularity indices for the seismic demand assessment of RC moment resisting frame buildings

Design standards across the world use different parameters to quantify degree of torsional irregularity of buildings. Popular among such descriptors are the normalized static eccentricity ratio, torsional radius to mass radius of gyration ratio, maximum to minimum (or average) elastic floor displacement ratio, etc. However prior research, particularly on idealized single storey systems have indicated that these parameters do not correlate well with the seismic demands at all stages of structural behaviour (i.e. elastic and inelastic). The present study aims to identify a robust torsional irregularity index that captures the susceptibility of a structure to torsional effects at all ground motion intensity levels. To this end, the correlation between the maximum interstorey drift demands and popular torsional irregularity descriptors is first examined under different intensities of ground shaking using an approach that integrates multiple stripe analysis and statistical regression analysis. The numerical study is based on the nonlinear seismic assessment of thirteen three-storey gravity designed RC moment frame buildings subjected to bidirectional seismic excitation. The results indicate that none of the scalar indices considered correlate well with the drift demands at all intensities of ground shaking. A vector comprising of the normalized static eccentricity ratio and the torsional radius to mass radius of gyration ratio is found to perform well at low shaking intensity levels, where the structure responds in an elastic manner. However, at high intensity levels where the structure undergoes significant excursions into the inelastic range of behaviour, the strength eccentricity is observed to be a better descriptor of torsional irregularity. A three-element vector comprising of the above indices is found to capture the maximum interstorey drifts accurately at all ground motion intensity levels. A seismic demand model for maximum interstorey drift, sensitive to the above torsional irregularity descriptors, is also defined.

Empirical fragility curves: The effect of uncertainty in ground motion intensity

Empirical fragility curves derived from large post-disaster databases with data aggregated at municipality-level, commonly make the assumption that the ground motion intensity level is known and is determined at the centroid of each municipality from a ground motion prediction equation. A flexible Bayesian framework is applied here to the 1980 Irpinia database to explore whether more complex statistical models that account for sources of uncertainty in the intensity can significantly change the shape of the fragility curves. Through this framework the effect of explicitly modelling the uncertainty in the intensity, the spatial correlation of its intra-event component and the uncertainty due to the scatter of the buildings in the municipality are investigated. The analyses showed that the results did not change substantively with increased model complexity or the choice of prior. Nonetheless, informed decisions should be based on the defensible modelling of the significant variability in the data between municipalities.

Mapping of ground motion amplifications for the Fraser River delta in Greater Vancouver, Canada

The Fraser River delta in Greater Vancouver, Canada consists of deep soft deposits of silts and clays, and it is well known that the deep soil deposits can amplify the low frequency contents of ground motions. This study aims to investigate the effects of deep soil deposits in the delta on ground motion amplifications by using thorough site response simulations that account for the full soil profiles and a suite of recorded ground motions that covers a wide range of intensity levels. Based on both equivalent-linear and nonlinear site response simulations, the effects of soil depth (represented by natural period of the soil, TS) on ground motion amplifications for various spectral periods are clearly demonstrated. The ground motion amplification maps for various spectral periods and rock ground motion intensity levels are also generated to be used in the regional seismic hazard assessment for infrastructure. It is found that ground motions for long periods are substantially amplified in the center of the delta, while those for short periods are de-amplified when input rock motions are large.