Structural Fundamental Period Research Articles

Average spectral acceleration (AvgSa) for high-confidence probabilistic seismic demand modeling of urban highway bridge portfolios: What period range and damping ratio shall we use?

The average spectral acceleration (AvgSa), i.e., the geometric mean of spectral accelerations over a period range, has attracted widespread recognition as one of the most promising intensity measures (IMs) for probabilistic seismic demand modeling of structures. As AvgSa is a structure-related spectral IM, a pivotal step in calculating AvgSa is to determine an appropriate period range and damping ratio. Whilst optimal AvgSa has been well documented for buildings, consensus on the period range and damping ratio of AvgSa for urban highway bridges is yet to be reached. To this end, a pool of AvgSa candidates with different combinations of lower and upper period bounds and damping ratios are assessed to identify the optimum combination(s) for straight and curved urban highway bridge portfolios against bidirectional seismic excitations, in terms of peak pier drift ratio, peak bearing displacement, and residual pier drift ratio. Results indicate that for the peak demand parameters, optimal AvgSa is characterized by a damping ratio of 0.2 and a period range of [Tf, 1.5Tf], where Tf is the structural fundamental period, for bridges with relatively short piers; and the optimal period range becomes [Tf, 2Tf] for medium to tall-pier bridges. Besides, the optimal period range for the conventional 5%-damped AvgSa is also detected, where [0.5Tf, 1.5Tf] is the optimal range for bridges with relatively short piers, while [0.5Tf, 2Tf] is recommended for medium to tall-pier bridges. Regarding the residual pier drift ratio, averaging spectral accelerations over any examined period ranges does not outperform traditional spectral accelerations at specific periods.

Seismic resilience assessment of extended pile shaft supported coastal bridges considering scour and uniform corrosion effects

The resilience-informed assessment for coastal highway bridges exposed to multiple hazards plays a crucial role in the decision-making process for their operation, maintenance, and management during the bridge’s long-term service period. This study performs a seismic resilience assessment for a coastal reinforced concrete (RC) bridge under the combined effects of scour and uniform corrosion. Toward this goal, an extended pile shaft supported coastal RC bridge is taken as the benchmark and fifteen scenarios are generated to cover three regular scour conditions and five different corrosion levels. To inform the bridge management, the probabilistic distribution of the bridge service time corresponding to different corrosion levels is developed. Subsequently, the finite element model (FEM) for each scenario of the benchmark coastal highway RC bridge is developed, involving the soil-pile interaction and considering the uncertainty of structural and geotechnical parameters, as well as earthquake ground motions. The failure mode of the corroded extended pile shaft is identified as a flexural failure by comparing their flexural and shear capacities. Finally, a resilience loss ratio is proposed in this study for the first time to quantify the impacts of corrosion level and scour depth changes on seismic resilience across different ground motion intensities. Results indicate that both the seismic fragility and resilience decrease as the corrosion intensifies over time. Specifically, at a given intensity measure (IM) level, the resilience loss ratio increases as the corrosion level intensifies. For the studied benchmark bridge, the scour significantly increases the structural fundamental period, consequently reducing the curvature demand on the pile shaft. As a result, the scour generally decreases the failure probability and the earthquake-induced functionality loss for the extended pile shaft. As scour depth increases, the resilience loss of the bridge at a given corrosion level decreases.

Nonlinear time-domain soil-structure interaction analysis of a mid-rise building benchmarked against earthquake recordings: A case study of the BRI's annex building

Performing soil-structure interaction (SSI) analysis under strong shaking scenarios using the direct method is becoming more prevalent in engineering practice. However, given the pronounced nonlinearity in soil, structure, and foundation response, the robustness of current methodologies is open to question, and benchmarking these methodologies against instrumented case histories is needed to identify the strengths and weaknesses in the approach. In this study, a three-dimensional (3D) Nonlinear (NL) Soil-Structure Interaction (SSI) analysis methodology in the time-domain code LS-DYNA is benchmarked against the actual recordings for a mid-rise building. The well-instrumented Building Research Institute (BRI) Annex Building (ANX) in Tsukuba City northeast of Tokyo, Japan, which features an adjacent free-field geotechnical downhole array, is used for this case study. A Finite Element (FE) three-dimensional 3D SSI model of the site, including the BRI ANX building, that considers both material and geometric nonlinearities is first developed. Two events are applied to the model: the 2011 Tohoku-Oki earthquake main shock (Mw9.1), referred to as the Great East Japan Earthquake (GEJE), and the 2002 Southern Ibaraki Prefecture earthquake (Mw4.9), selected from the BRI strong motion network due to the relatively wide amplitudes recorded at the site. The former event induced maximum shear strains in the soil of 1.6%, while the latter event induced maximum shear strains of 0.08%. For both horizontal and vertical components of shakings, the predicted response of the structure and adjacent free-field downhole array are compared with the corresponding recordings. The results show that the structural response is significantly affected by the accuracy of the predicted free-field ground surface response, especially at the structural fundamental period as opposed to the site period. In addition, results indicate that the fixed-base and flexible-base structural models’ responses are substantially different, mainly attributed to the SSI effects that cannot be captured in the fixed-base model. Finally, a comprehensive discussion on the minimum amount of data required to adequately capture nonlinear structural response using the proposed SSI methodology is provided in this case study.

Simplified Life Cycle Cost Estimation of Low-Rise Steel Buildings Using Fundamental Period

In the current study, a simplified seismic life cycle cost (LCC) estimation procedure is proposed utilizing the mean values of the structure’s main input variables. The main input variables of the building are used for constructing a relationship between the structural fundamental period (T) and an average estimation of the LCC (LCCavg). Using the actual building properties related to damage probability, the T–LCCavg relationship is used to obtain the final LCC (LCCfin). The equivalent single degree of freedom (ESDOF) model and SAC-FEMA framework are utilized for damage probability calculation. The dispersion measure in demand is approximately calculated based on the mean plus one standard deviation of the seismic hazard response spectrum, and, then, verified through nonlinear time history (NLTH) analyses of the original structure. Five and three-story steel buildings are used as case studies for verification of the proposed method. The analysis results indicate that the proposed procedure provides reasonable LCC estimations for low-rise buildings dominated by the fundamental mode of vibration.

Potential bias of conventional structural seismic fragility for bridge structures under pulse-like ground motions: Bias evaluation and strategy improvement

Previous studies have highlighted the serious biases that may happen in probabilistic structural fragility analysis (PSFA) due to the ignorance of the effect of pulse period under pulse-like excitations. However, the distribution characteristics of the bias associated with structure-pulse damage parameters are less quantitatively investigated. This paper, therefore, focuses on the influence mechanism of the structure-pulse coupled period (defined by pulse period normalized by structural fundamental period) in PSFA and quantitatively describes the bias that occurred in different damage states. Meanwhile, the PSFA of ductile columns conditioned on two different groups of intensity measures are systematically presented and compared based on Artificial Neural Network prediction. Results reveal that the bias of PSFA, with the variation of the normalized period, can be divided into three different stages, including two ranges of normalized period overestimating structural damage probability and one interval indicating the underestimated condition. Additionally, significant biases (larger than 50%) have been frequently observed in the PSFA of structures with different fundamental periods under various damage states. Moreover, the formulas for quickly obtaining the interval that dangerously underestimates structural damage probability and bias modification factor are correspondingly proposed, which can provide a quite useful method and tool for fragility, risk, and resilience analysis of bridge structures in near-field regions.

An energy‐frequency parameter for earthquake ground motion intensity measure

AbstractA novel scalar ground motion intensity measure (IM), termed the energy‐frequency parameter, is proposed based on the Hilbert‐Huang transform. To validate the effectiveness of the proposed IM, the correlation analysis between the engineering demand parameter (EDP) and energy‐frequency parameter is performed using 1992 recorded ground motions, in which EDP is the maximum inter‐storey drift of structures obtained by nonlinear time‐history analysis. Results show that the energy‐frequency parameter has a strong linear correlation with EDP at natural logarithm, and this correlation is applicable for various structural fundamental periods. We also verified that the lognormal cumulative distribution function can characterize the energy‐frequency parameter‐based fragility function, which can further facilitate the application of the parameter in seismic risk analysis. Besides, the strong correlation between the energy‐frequency parameter and other IMs (such as PGA, PGV, PGD, CAV, , , and SI) potentially makes the proposed IM widely applicable in seismic risk analysis. Moreover, since the energy‐frequency parameter depends only on the frequency‐domain characteristics of the ground‐motion signal, it may closely link to seismological theory and provide new insights into seismology engineering.

Near-fault pulse seismic ductility spectra for bridge columns based on machine learning

The seismic ductility spectra (SDS) method is a crucial tool to quickly evaluate the ductility demand of bridge columns with varied constitutive models. However, conventional SDS methods usually do not consider the characteristics of pulse-like excitations, which tend to cause severe structural damage. To address this challenge, near-fault pulse seismic ductility spectra (NFPSDS) based on Machine learning (ML) are developed in this study, where two ML models, i.e., the Random Forest (RF) and the artificial neural network (ANN), are utilized to map the relationship between seismic demand and a pulse-structure coupled index α1-p (the structural fundamental period (T1) relative to pulse period (Tp)). Then, the influence of column parameters (such as fundamental period and longitudinal reinforcement ratio) and pulse parameters (such as pulse period and peak pulse velocity) on NFPSDS is quantitatively investigated. Thus, by employing the NFPSDS method, the reasonable design range of longitudinal reinforcement ratio can be obtained under different pulse periods and pulse velocities. Overall, the NFPSDS method significantly benefits the practice for seismic design of structures in near-fault regions.

Innovative Seismic Microzonation Maps of Urban Areas for the Management of Building Heritage: A Catania Case Study

Several urban areas in the Mediterranean have already been subjected to seismic microzonation studies aimed at determining the acceleration expected on the ground surface, therefore mitigating the associated seismic risks. These studies have been generally related to free-field conditions. The present paper shows innovative seismic microzonation maps based on a large-scale estimate of soil-structure interaction (SSI) effects on design accelerations for some areas characterized by a high seismic risk in Catania, Italy. The proposed procedure combined: (1) geotechnical characteristics; (2) building features; and (3) 1-D seismic response analyses in free-field conditions. The seismic hazard and site effects were evaluated using artificial inputs and inputs recorded recently in Catania. Structural fundamental periods and related spectral accelerations, considering both the fixed-base building configuration and flexible-base configuration, were mapped in the Google My Maps environment. These results showed that SSI often had a beneficial effect, but sometimes it had detrimental effects, especially for some masonry buildings. These maps provided important information for planning the seismic retrofitting of investigated buildings, which were based on more detailed analyses of SSI and the developed maps requiring them.

Shaking table test study on the functionality of rubber isolation bearing used in underground structure subjected to earthquakes

Steel-reinforced rubber isolation bearing has been widely adopted in ground structures to improve structural seismic resistance property. However its use in underground structures is not elaborately examined. Through a series of shaking table tests, the functionality of isolation bearings connected to structural intermediate columns' feet in underground structure during seismic actions is investigated, compared with the dynamic response characteristics of model structure with general reinforced concrete columns. Result analysis shows that dynamic reaction of underground structure is fundamentally determined by soil motions, the isolation bearing can not shift structural fundamental period away from the prominent frequency of seismic waves to enhance structural seismic resistance capacity like the way in the case of ground structures. However, as the soil-structure interaction changes a lot along structure height, isolation bearings can effectively obstruct lateral shear forces developed in top structural part from transferring into down structural part, which will avoid force concentration in low structural part, making structural deformation distributed uniformly along structure height in comparison with the deformation in structure without isolation device. Other changes of underground structural dynamic reactions to earthquakes brought out by isolation device will be also detailed.

Combination model for conventional pushover analysis considering higher mode vibration effects

SummaryThis paper aims to propose a combination model for conventional pushover analysis with invariant lateral load patterns to consider the effects of higher mode vibrations on the seismic responses of high‐rise buildings. Rectangular concrete‐filled steel tubular (RCFT) structures having two types of deformation, namely, shear type RCFT frame structures and shear‐flexural type RCFT frame‐shear wall structures, are selected and investigated. Finite element models are created using Perform‐3D. Both pushover analysis with three conventional lateral loading patterns, namely, uniformly distributed loading, first‐mode vibration loading, and concentrated loading at the vertex, and time‐history analysis with 15–21 earthquake records chosen for each RCFT structure are performed. Regression analysis is used to fit the interstory drift ratios obtained by the pushover analysis with those from the time‐history analysis. Further, the relations between the partial regression coefficients and the structural fundamental periods under certain lateral loading patterns are analyzed. On this basis, using these conventional lateral loading patterns, combination models for high‐rise buildings with two types of deformation are proposed and verified. The results demonstrate that the proposed method can estimate the seismic responses of high‐rise buildings with a high accuracy and has the advantages of ease of implementation and operation.

Sensitivity Analysis of Reinforced Concrete Frame Structures Under Near-Fault Pulse-Like Ground Motions Using a Broadband Simulation Method

ABSTRACT The effect of pulse characteristic of near-fault ground motions on multistory reinforced concrete frame structures is investigated by means of a synthetic broadband ground motion model (SBGM). A simplified analytical pulse model is used to describe the low-frequency components of ground motions, while a stochastic simulation method based on wavelet packet is adopted to simulate the high-frequency components of ground motions. First, the time histories, response spectrum, and structural response of synthetic ground motions are compared with those corresponding to recorded near-fault ground motions. The good agreement indicates that the SBGM model used in this article is a suitable and efficient tool for evaluating the structural response. Sensitivity analysis on structural response of 2-, 4-, 8-, and 12-story building models to the SBGM model input parameters is then performed to identify the key ground-motion parameters which control the main structural response indicators, that is, interstory drift ratio and maximum interstory drift ratio. Final results indicate that the amplitude of velocity pulse in the SBGM model has a significant influence on structural drift demands. Nevertheless, for low-rise buildings, the maximum drift demands would effectively decrease with increasing proportion of high-frequency components. Moreover, the ratio of pulse period to structural fundamental period and number of oscillations impose a large drift demands to the structure under near-fault pulse-like ground motions.

More adequate seismic design force pattern for yielding structures considering structural and ground motion uncertainties effects

SummaryIn the present paper, a new algorithm to achieve optimum lateral load pattern for inelastic steel shear‐building structures is proposed and the efficiency of the proposed algorithm in terms of convergence speed and stability is investigated. Then, by conducting this algorithm on 28,800 elastic and inelastic steel shear‐building structures having different dynamic characteristics subjected to 40 design compatible earthquakes, a new seismic force pattern incorporating higher modes effect is proposed, and the adequacy of the proposed load pattern is parametrically investigated on the basis of the concepts of structural weight and dissipated energy and cumulative damage index. Through conducting numerous nonlinear dynamic analyses, the effects of uncertainties in story shear strength, structural fundamental period, and damping ratio by using the Monte Carlo simulation are parametrically investigated. Result indicates that optimum structures are in general more sensitive to the random variation of fundamental period and story lateral strength, whereas up to 40% of damping ratio variation does not affect the seismic performance of the optimum design frames. Finally, compared with recently proposed optimum structures without consideration of higher modes and code‐complaint design structures, the proposed mean optimum designed buildings of this study exhibit up to 42% less cumulative damage under the design earthquakes.

Study on Comparison of Structural Fundamental Period within UBC -97 and ASCE 7-05

Study on Comparison of Structural Fundamental Period within UBC -97 and ASCE 7-05

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

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

A Spectral-Acceleration-Based Linear Combination-Type Earthquake Intensity Measure for High-Rise Buildings

ABSTRACTWith the consideration of higher modes, an attempt is made to develop a spectral-acceleration-based linear combination-type earthquake intensity measure (IM) for high-rise buildings. The modal mass participation factors are determined to take weighting coefficients. A parametric analysis on the correlation between IM and the maximum interstory drift that utilizes the bend-shear coupled continuum model yields a bilinear relationship between the optimal number of modes involved and structural fundamental period. The proposed IM and several other combination-type IMs are shown to be efficient and sufficient, while the scaling robustness of the proposed IM is more stable compared with that of fundamental-mode-based IMs.

Building contents sliding demands in elastically responding structures

This paper quantifies sliding of contents in simple elastic structures subject to ground motion excitation. Contents sliding spectra due to impulse records are developed as a function of normalised friction coefficient, equal to the friction coefficient divided by the structural spectral acceleration in terms of gravity, for structures with different periods. The spectra are not strongly dependent on the structural fundamental period, or the magnitude of the shaking. The total sliding displacement for impulse loading is generally close to that from the first sliding excursion when the normalised friction coefficient is greater than 0.35. However, for lower normalised friction coefficients subsequent sliding excursions also contribute to the total sliding displacement. Simple equations are developed to describe the impulse response. The median total sliding from earthquake motions was represented well by the sliding spectra based on impulse loading. The usefulness of the proposed sliding spectra is illustrated via a design example.

Parametric study on collapse margin ratio of structure

The determination of collapse margin ratio (CMR) of structure is influenced by many uncertain factors. Some factors that can affect the calculation of CMR, e.g., the elongation of the structural fundamental period prior to collapse, the determination of earthquake intensity measure, the seismic hazard probability, and the difference of the spectral shapes between the median spectrum of the ground motions and the design spectrum, were discussed. Considering the elongation of the structural fundamental period, the intensity measure S a(T 1) should be replaced with S a* in the calculation of CMR for short-period and medium-period structures. The reasonable intensity measure should be determined by the correlation analysis between the earthquake intensity measure and the damage index of the structure. Otherwise, CMR should be adjusted according to the seismic hazard probability and the difference in the spectral shapes. For important long-period structures, CMR should be determined by the special site spectrum. The results indicate that both S a(T 1) and spectrum intensity (SI) could be used as intensity measures in the calculation of CMR for medium-period structures, but SI would be a better choice for long-period structures. Moreover, an adjusted CMR that reflects the actual seismic collapse safety of structures is provided.

Fuzzy‐Valued Intensity Measures for Near‐Fault Pulse‐Like Ground Motions

Abstract Two fuzzy‐valued (FV) structure‐specific intensity measures (IMs), one based on squared spectral velocity and the other on inelastic spectral displacement, are presented to characterize near‐fault pulse‐like ground motions for performance‐based seismic design and assessment of concrete frame structures. The first IM is designed through fuzzying structural fundamental period to account for the period shift effect due to stiffness degradation, whereas the second IM is developed to take into account higher mode contribution in high‐rise buildings by employing a fuzzy combination of the first two or three modes for the lateral loading pattern in pushover analysis. A benchmark study of three example reinforced concrete frame structures shows that for moderate‐ to medium‐period structures, both of the proposed IMs improve prediction accuracy in comparison with the existing IMs. For short‐period structures, the FV inelastic spectral displacement is the best.

지진 구조 손상도 예측을 위한 지반 운동 수정법 평가

성능기반 내진설계 및 평가의 정밀도 향상에 있어서 적절한 지반운동 데이터 선정과 이를 합리적으로 수정하는 것에 대한 중요성이 부각되고 있다. 지반운동 데이터를 수정하는 방법으로 단일 진폭수정법 (Amplitude scaling)이 널리 사용되고 있으나, 단일 진폭수정법에서 는 단 하나의 주기, 특히 구조물의 고유주기에서만 그 응답스펙트럼 값이 설계스펙트럼의 값과 일치하도록 수정되므로 특정 지역의 지진 재해도에 대해 일관성 있는 구조 해석 결과를 기대하기 어렵다. 따라서 이에 대해 여러 가지 대안 수정법들이 제시되고 있으나 이들의 타당성을 평가할 수 있는 방안이 마련되어 있지 않다. 본 논문에서는 단일 진폭수정법의 문제점을 설명하고, 대안 수정법과 비교 평가하기 위한 구조 응답에 대한 회귀 모델을 제시하는데 목표를 두었다. 대안 수정법으로써 전체 주기 범위에서 지반운동의 응답스펙트럼이 설계스펙트럼의 값과 일치하도록 수정하는 다중 스펙트럼 수정법을 고려하였다. 설계스펙트럼은 ASCE7-05에 따라 구하였다. The selection of appropriate ground motions and reasonable modification are becoming increasingly critical in reliable prediction on seismic performance of structures. A widely used amplitude scaling approach is not sufficient for robust structural evaluation considering a site specific seismic hazard because only one spectral value is matched to the design spectrum typically at the structural fundamental period. Hence alternative approaches for ground motion selection and modifications have been suggested. However, there is no means to evaluate such methodologies yet. In this study, it is focused to describe the main questions resided in the amplitude scaling approach and to propose a regression model for structural damage as point of comparison. Spectrum compatible approach whose resulting spectrum matches the design spectrum at the entire range of the structural period is considered as alternative to be compared to the amplitude scaling approach. The design spectrum is generated according to ASCE7-05.

Comparison and Selection of Ground Motion Intensity Measures for Seismic Design of Super High-Rise Buildings

Ground motion intensity measures ( IMs) are an important basis of structural seismic design. Extensive research has been conducted on the selection of IMs for building structures with fundamental periods shorter than 6 s. However, minimal work has been performed for super high-rise buildings whose fundamental periods are much longer than 6 s. To fill the gap in this research area, this paper aims to develop a simplified analytical model for super high-rise buildings based on the flexural-shear coupled beam model. The variation in correlation and dispersion between different IMs is evaluated and the structural seismic response demand measures ( DMs) are analyzed for different structural fundamental periods. Subsequently, rational IMs for the seismic design of super high-rise buildings are suggested. In addition, the influence of different flexural and shear stiffness ratios, α0, on the selection of an IM for super high-rise buildings is also discussed. Finally, a series of incremental dynamic analyses (IDA) of the Shanghai Tower, with a total height of approximately 632 m, is performed to verify the rationality of using different IMs for super high-rise buildings. The numerical results indicate that with a minimum dispersion, the peak ground velocity (PGV) has a better correlation to the story drift ratio than any other IMs. While considering structural nonlinearity, PGV still yields the minimum coefficient of variation in the collapse analysis of the actual super high-rise building. It is therefore recommended that PGV be used as an IM for the seismic design of super high-rise buildings.