Earthquake Frequency Content Research Articles

Seismic vulnerability assessment of Venetian façades and artistic assets: Historical Digital Twin approach

The seismic vulnerability assessment of monumental façades and of their valuable artistic assets, along with considerations for protection and valorisation, requires the development of an integrated, multidisciplinary procedure able to enhance the accessibility, promotion and management of cultural heritage as well as to effectively model and simulate the structural performances of each artistic element. The multi-step methodology presented in this paper starting from an advanced survey and an appropriate tridimensional (3D) restitution, leads to the development of an Historical Digital Twin useful to create a detailed finite element model able to carry out structural simulations of both the historic façade and the artistic assets. To illustrate this methodology, the paper delves into a real case study involving a typical Venetian monumental façade, focusing on the seismic vulnerability assessment of two statues located at different levels. Emphasis is given to the importance of the 3D models to support vulnerability analysis, and to evaluate the seismic action at the points of the façade where the statues are placed. To this aim different methods are used and compared, showing on the one hand a strong dependence of the amplification of the seismic acceleration on earthquake frequency content and on the other hand the precautions to take using design-oriented predictive formulations.

Dynamic response of subsea tunnel in liquefiable layered seabed under combined earthquake and wave action

Liquefaction poses a potential threat to the safety of subsea tunnel during the earthquake. In the ocean environment, wave pressure is considered as a normal loading applied at the seabed surface. This study proposed a fully coupled dynamic effective stress finite element model for subsea tunnel in liquefiable layered seabed under combined earthquake and wave action. Biot u-p formulation integrated with a modified generalized plasticity model was adopted for liquefaction analyses of the seabed. The proposed model was validated through a wave flume model test in terms of excess pore water pressure (EPWP). The results showed that the tunnel – soil dynamic interaction significantly increased EPWP near the tunnel. Increasing the wave height significantly increased the liquefaction depth of the seabed; however, the wave loading can either suppress the displacement of the tunnel during the earthquake or increase the uplift of the tunnel during the subsequent wave loading. When investigating seismic response of subsea tunnels in liquefiable soils under combined earthquake and wave action, the ground motion was suggested to be input simultaneously with the wave pressure. This study also highlights the effect of the thickness of liquefiable layer and frequency content of earthquakes on dynamic responses of subsea tunnels.

The impact of the frequency content of far-field earthquakes on the optimum parameters and performance of tuned mass damper inerter

Tuned mass damper inerter is a passive control device that is proven to be effective in mitigating structural responses under earthquake excitations, however, its efficiency highly depends on its design parameters. This paper aims to investigate how the optimum parameters of TMDI change with the frequency content of far-field earthquakes to minimize the need for repeatedly optimizing these parameters for varying far-field earthquakes and structural characteristics. To achieve this objective, the ratio of the earthquake's frequency to the structure's frequency is defined as an index to simultaneously represent the structure and the earthquake. Case studies of 5, 10, 15, and 20-story building structures are analyzed under twenty-three far-field earthquakes which are categorized into three main groups based on their frequency (PGA/PGV) including “Low”, “Intermediate”, and “High”. Particle Swarm Optimization (PSO) is employed to obtain the optimum parameters of TMDI including the damping and the frequency ratio to minimize two distinct objective functions: (1) the peak displacement and (2) the peak acceleration of the top story in a time domain analysis. To validate the applicability of the proposed method in determining the optimal parameters of TMDI regardless of the earthquake and structure frequency, a 10-story benchmark building is employed. Moreover, this study demonstrates the effectiveness of TMDI in minimizing the objective functions concerning the frequency content of the earthquake. It also illustrates the trend of the PSO optimization process. The results show that the index provides a discernible pattern for the variation of the optimum parameters of TMDI. Furthermore, it is demonstrated that the difference in the structural response between tuning the TMDI with the PSO algorithm and the suggested method is less than 3 % when the index is greater than 1. As the ratio of earthquake frequency to the frequency of structure increases, the objective functions will correspondingly increase. The results also indicate that, an increment in the inertance ratio leads to an increase in the value of optimum parameters of TMDI. Furthermore, among all structures analyzed, those subjected to intermediate frequency earthquakes exhibit the most significant reduction in both objective functions.

Nonlinear dynamic assessment of sloshing in a seismically isolated rectangular liquid tank using laminated rubber bearing

The primary purpose of the research is to study the effect of free surface nonlinearity in the overall slosh dynamics of base-isolated liquid tank by developing a nonlinear finite element model under different frequency content of earthquakes. Six natural earthquakes are considered, which are categorized under low-, intermediate-, and high-frequency contents. The mixed Eulerian and Lagrangian technique is adopted based on the potential flow theory for developing the fluid domain. The efficacy of the developed computational model is verified with the existing results. The potential constraints of linear responses are demonstrated alongside the dominance of nonlinear counterparts. The slosh amplitudes are underestimated in the linear model, which emphasizes the importance of the present nonlinear approach in adequately determining the freeboard to prevent loss of liquid due to spillage and unexpected roof failure. The laminated rubber bearing isolator played a crucial role in reducing the total and impulsive components of hydrodynamic pressure as well as base shear for both linear and nonlinear approaches. However, the effect of nonlinearity is significant in the contribution of the convective component of pressure and base shear, irrespective of the frequency content of earthquakes. Also, the nonlinear convective base shear is greater than the linear counterpart for non-isolated and base-isolated tanks, and such phenomenon is marginal for higher frequency content motions. Furthermore, resonant studies of both the tank systems are performed using a harmonic ground acceleration. The seismic parameters of the base-isolated tank are amplified when the excitation frequency is very close to its fundamental sloshing frequency rather than the natural frequency of the isolator.

Analysis on the Behaviour of Hybrid Outrigger System in Relation to the Frequency Content of Earthquakes

Analysis on the Behaviour of Hybrid Outrigger System in Relation to the Frequency Content of Earthquakes

Seismic Fragility Assessment for a Newly Developed Buried Arch Bridge

This study aims to assess the seismic response of a newly developed buried arch bridge system. The proposed buried arch bridge system is comprised of precast concrete panels, external steel outriggers, and steel V-strips to solve the limitation encountered in the storage, transportation, and construction of traditional buried arch structures. The three-dimensional finite element analysis of this arch system is conducted under dynamic analysis emphasizing the frequency content of earthquakes. Then, the fragility curves are suggested for this arch system based on two damage states defined via incremental dynamic analysis. The results show that this proposed arch system is significantly affected under a high frequency content earthquake compared to the low and intermediate ones. Additionally, the arch system deflects the most at the mid-high position rather than at the arch crown. The deflection at the arch crown or at the mid-high position can be used for establishing the fragility curves as they both connect with the failure mechanism of the arch structure.

On the nonlinear dynamic analysis of annular baffled steel containers isolated by bearings

This paper focuses on numerically scrutinizing the simultaneous influences of the base-isolator devices and annular baffles on the dynamic behavior of a three-dimensional (3D) cylindrical water storage tank, considering anirrotationaland inviscidfluidundergoing smallvibrations. A coupled acoustic-structure finite element formulationis developed for the analysis of the nonlinear dynamic behavior of the thin-walleddeformable cylindrical tanksunder real ground excitations. The established FEM procedure is competent in assaying the precise three-dimensional behavior of the isolated ground-supported annular baffled containers, including the performance of laminated rubber-bearing isolation devices in frequency and time domains. Vibration characteristics of water sloshing inside the benchmark tank are investigated under five different earthquakes with long and short-period contents. Furthermore, the dynamic response components of the base shear force, base moment, hydrodynamic pressure, and bearing deformation of the isolation devices regarding some system parameters comprising lateral isolation and locations of baffle devices are quantified efficaciously. In conclusion, the numerical simulations in the time-domain revealed that satisfactory performance of the baffled liquid tanks might not be achieved by only relying on the first convective mode frequency of the tanks due to an unwanted increase of sloshing amplitudes in exceptional cases of liquid tank geometry and baffles; the baffles with smaller effects on the first convective modes were more effective on decreasing the sloshing wave amplitudes. Hence, in the case of slender tanks, it is recommended that a baffle geometry be selected for each earthquake frequency content and analyzed over time to obtain the best performance from the baffles, but for the broad tanks, a baffle selection independent of the earthquake frequency content might be acceptable. Also, the results indicate that in the board tanks, top-mounted baffles amplify the seismic response of the system; thus, remarkable attention would be required in using baffles in such tanks; therefore, it has been recommended to use mid-mounted baffles in these tanks.

The Duration Effect of Pulse-Type Near-Field Earthquakes on Nonlinear Dynamic Analysis and Damage Evaluation of Hydraulic Tunnels

Current research trends in significant hydraulic engineering projects focus on investigating the seismological properties of intensity and frequency content of pulse-type near-field earthquakes on the structural response. Conversely, the duration impact is not expressly addressed in the seismic design code for underground buildings. Currently, various duration indicators of as-recorded strong ground motions mainly consider the effective duration of the initial acceleration component record. In contrast, the duration indicators for the effective velocity duration (EVD) of the original velocity time-history component record have rarely been addressed. Specifically, there is a gap between the effective velocity duration and the structural response. To illustrate the impact on the structural response, an EVD of pulse-type NFGM duration was used. This EVD can be calculated for seismic excitations with set threshold values that enable a quantitative examination of the duration effects. A fluid-hydraulic tunnel-rock interaction system was built and used to estimate the seismic response characteristics induced by different duration NFGMs. The investigation’s findings highlight that the inelastic dynamic response and damage degree are strongly affected by the EVD. Additionally, the fixed threshold value of 5–95% showed an excellent correlation coefficient with the structural response. The significant duration was also found to be the most suitable alternative indicator to replace the EVD index. In addition, the reduced time-history methodology of near-fault earthquake records is presented and validated, with this method being used to improve the efficiency of the dynamic time-history analysis of hydraulic arched tunnels.

Seismic-induced vibration control of a multi-story building with double tuned mass dampers considering soil-structure interaction

This paper presents a methodology for the optimization of double tuned mass dampers (TMDs) positioned on the top floor of a multi-story building subjected to ground motions considering soil-structure interaction (SSI). In the optimization process, it is considered that double TMDs are connected both in series and in parallel. STMD and PTMD are used to denote the series TMDs and parallel TMDs, respectively. The equations of motion for an n-story shear building controlled by STMD and PTMD are derived by considering the SSI effect and the optimum parameters of both devices are obtained by minimizing the amplitude of the displacement transfer function for the top floor of the building in the frequency domain analysis. The effectiveness of the PTMD and STMD designed using the Jaya algorithm (JA) is verified by numerical examples of a ten-story shear building under twelve earthquake records with different frequency content and the comparison with the traditional TMD is also performed. In order to investigate the effect of earthquake frequency content on the control performance of the TMDs, earthquakes considered are divided into three different groups as low, intermediate, and high-frequency contents. In addition, the influence of the soil stiffness on the optimum parameters and effectiveness of the PTMD and STMD is discussed. Numerical results show that the optimally designed PTMD and STMD effectively suppressed the maximum floor displacements and accelerations of the building. It is also shown that SSI effects can be ignored when the building is built on stiff soil. In addition, it is concluded that the SSI and earthquake frequency content have a significant effect on the control performance of TMDs and the seismic response of the building.

Nonlinear finite element analysis for seismic site amplification assessment of urban slopes showing surface geology and topography irregularities

In urban areas, buildings close to the crest of a slope can undergo serious seismic disturbances due to seismic site amplifications, often induced by local site conditions. In this context, this paper aims to assess how combined surface geology and topography irregularities can amplify the site response to the ground surface of the Ciloc slope, subject to the reference earthquake that occurred in Constantine province on October 27, 1985. Therefore, a two-dimensional nonlinear dynamic finite element analysis was conducted on various geometric models, in which both slope angle and lithology were simultaneously varied. To describe properly the earthquake frequency content, an analytical solution based on the interpolation method of the general equation of the dynamic motion was programmed under MATLAB language. Fast Fourier Transform (FFT) was also programmed to compute the Fourier spectral amplitude of a selected accelerogramme. Likewise, the computer software SeismoSignal has been used to compare analytical outcomes. Four slope configurations were simulated namely, an actual slope, a layered slope, a homogeneous marl slope and a homogeneous alluvial slope with various slope angles. It was found that maximum site amplifications had occurred behind the crest and not at the exact crest of the slope as commonly expected. Due to the dilatancy phenomenon, alluvial homogenous formations as cohesionless soils, show high spectral parameter amplifications than the other cases. It was also concluded that a seismic response analysis of these sedimentary deposits is strongly recommended as a preliminary study for the seismic analysis of the neighbouring buildings, to avoid serious seismic destructions.

Effect of earthquake frequency content on seismic-induced vibration control of structures equipped with tuned mass damper

Effect of earthquake frequency content on seismic-induced vibration control of structures equipped with tuned mass damper

Seismic Damage Index Spectra Considering Site Acceleration Records: The Case Study of a Historical School in Kermanshah

The frequency content and time duration of earthquakes are as effective as the peak ground acceleration on structural damage. Therefore, using rapid seismic vulnerability assessment methods that consider the earthquake acceleration time history is noticeable. Kermanshah is a historical city that is generally affected by far-field earthquakes. Therefore, it is necessary to consider the effect of the low-frequency shocks in evaluating the vulnerability of buildings in this city. Herein, a historic school in Kermanshah is assumed as a case study and two well-known damage index formulas are used for determining the damage index spectra of this structure, considered as a single degree of freedom system. Then, the effective parameters of the damage index, including ductility, relative degradation of stiffness, and dissipated energy are determined from a nonlinear analysis of the structure under the effect of the most probable earthquake acceleration records. Finally, the damage index spectra can be used for rapid seismic vulnerability assessment of masonry buildings on similar sites with various fundamental periods for large-scale assessments. The result shows that the building tends to collapse at a peak ground acceleration of 0.15 g. Furthermore, results confirm the seismic resistance reduction effect of flexible floors.

Seismic Response of Rectangular Liquid Container with Dual Horizontal Baffles on Deformable Soil Foundation

ABSTRACT Seismic response of liquid sloshing in horizontally baffled rectangular container on deformable ground is evaluated. An equivalent mechanical model of baffled sloshing is developed. The strip partition method is presented to analytically derive the foundation impedances reproduced by nested lumped-parameter model. The system equations of motion are constructed via applying Hamilton’s principle. The detailed validations are performed against the available solutions. Effects of soil and baffle parameters on surface wave elevation and base loads under three earthquake records with different frequency contents are examined. Results highlight that seismic behaviors of baffled container have a high sensitivity to earthquake frequency content.

Influence of ground motion frequency content on the nonlinear response and seismic performance of RC moment frame structures

Several parameters may affect the response of structures to seismic excitation. These include features of the structures, properties of imposed ground motion and geological specifications of building location. This research has been conducted to investigate the effects of the frequency content of earthquakes as an important property of ground motion on the seismic performance and nonlinear response of reinforced concrete moment frame (RCMF) structures. To this end, forty-two earthquake records have been selected from the stations on site classes A and B based on ASCE7-10. These input excitations have been classified into three groups based on PGA to PGV ratios namely: Low, Intermediate, and High frequency motions. Three RCMFs with 2, 6, and 10 stories have been designed according to ACI318-14 and ASCE7-10. Finally, utilizing OpenSEES platform, based on the FE method a numerical model has been built to perform incremental dynamic analysis (IDA). After interpreting the results of the IDA, fragility curves have been obtained as a function of PGA for pre-defined damage states. The results showed that the associated PGA with the median of the fragility curve is in ascending order Low, Intermediate and High frequency motions. Accordingly, it is concluded that in the same PGA level, Low frequency motions are more probable to reach a damage threshold than Intermediate and High frequency motions. Similarly, Intermediate frequency motions is more capable reaching the damage threshold in comparison to High frequency motions.

On the seismic performance evaluation of dam-foundation-reservoir system for the effect of frequency content and foundation flexibility

The present paper investigates the effect of earthquake frequency content and foundation flexibility on the performance of the Koyna dam-foundation-reservoir system. Ground motions that match the conditional mean spectrum (CMS) are adopted for the seismic analysis. The concrete damaged plasticity model is used to represent the dam's nonlinear behavior; however, the foundation is assumed to be linear elastic. To study the foundation flexibility effect on the seismic performance of the dam, three different cases which comprise different elastic modulus of the foundation are considered. The damage indices, based on the crack length and dissipation energy, are evaluated for the performance assessment of the dam-foundation-reservoir system. The ground motion parameters such as predominant period, mean period, and effective ground period are chosen in order to explore the earthquake frequency content effect on the performance of dam-foundation-reservoir system. Results indicate that foundation flexibility has a significant effect on the dam. Further, the frequency content has a substantial impact on the dam's seismic response compared to the intensity and duration of ground motion. It can be concluded that the mean period is a good indicator of the earthquake frequency content and has a strong correlation with the damage parameters.

Estimation of earthquake frequency content and its effect on dynamic analysis using continuous and discrete wavelet transform

Estimation of earthquake frequency content and its effect on dynamic analysis using continuous and discrete wavelet transform

Seismic Analysis of Double Deck Floating Roofs of Siraf Storage Tanks with Condensate, Light and Heavy Crude Oils

Seismic vibration of double deck floating roof of Siraf storage tanks located in southern Iran has been studied. Condensate of Nar and Kagan gas field in south of Iran as a very light hydrocarbon, Lavan as light and Soroosh as heavy crude oil content have been chosen. In addition to fluid-structure interaction, intermediate stiffeners, foam seal with nonlinear radial compression behavior and contact friction between the seal and the inner side of the wall are also considered. Under the above conditions, modal and time history analysis has been performed. For time history analysis, Sarpol-e Zahab and Shonbeh earthquakes in Zagros seismotectonic province of Iran and Sakaria as an earthquake near Iran were selected. Dominant natural frequencies, mode shapes of the roof parts and damping ratios of the first and second natural frequencies in addition to overall and spectral behavior of the roof in each liquid cases were obtained and discussed. Changing condensate to Soroosh oil made about 17% hydroelastic natural frequency decrement and about 10% damping ratio decrease for the first natural frequency. The results showed that dominant natural frequencies and the relevant damping ratios decrease with moving from light to heavy liquid. Vibration of the roof fundamentally depends on the frequency content of earthquake in relation to such natural frequencies. Also, floating roof in heavier liquid is more vulnerable to vibration according to the scaling method and steady state amplitude.

DYNAMIC SOIL-STRUCTURE INTERACTION ANALYSIS: DETECTING THE RELIABILITY OF MODELLING THE PILES AS A PLATE ELEMENT FOR A MULTISTORY BUILDING RESTING ON DEEP FOUNDATION

The assessment of seismic responses of buildings in dynamic-soil-pile-structure interaction problems has been one of the main interests among researchers in recent decades. Simulating such problems is usually done by two-dimensional models to overcome the difficulties encountered in 3D models. Commonly, piles were represented by plate elements of infinite length, disregarding the soil flowing between piles. Recently, Plaxis – a finite element software- implemented a new feature known as “the embedded pile row” that allows the definition of piles' out of plane spacing in a 2D model. Many researchers proved its validity in accurately simulating the real 3D pile’s behavior. The objective of this paper is to detect the reliability of modeling the piles as plate elements, by comparing the performance of the structural-pile system with the plate feature to that with the embedded pile row feature. A series of 2D finite element models are generated while varying the soil type, the earthquake frequency content, and the out-of-plane piles' spacing. This paper demonstrated that the building response with piles modeled as plate elements is just adequate when the surrounding soil is dense. Yet, regarding the pile response, the plate feature is unable to capture the real behavior for all soil types.

Generalized modified modal superposition procedure for seismic design of rocking and pivoting steel spine systems

To mitigate structural damage and associated losses due to strong earthquakes, rocking and pivoting steel spine systems have been proposed to control story drifts and localize inelastic deformations in ductile energy dissipating components. One of the challenges of designing these systems is proportioning the spine members to remain essentially elastic under earthquakes. Previous studies have shown that modified modal analysis can efficiently and accurately capture the forces developed in rocking braced frames. One of these approaches, the modified modal superposition (MMS) method, consists of superimposing the first inelastic modal force(s) with the elastic higher modal forces. The methodology, previously developed for single rocking braced frame, is extended for coupled and stacked rocking braced frames as well as strongback systems, equipped with various hysteretic and viscous nonlinear dampers. Nonlinear dynamic analyses run with a suite of 50 hazard-consistent ground motions for seven archetype rocking and pivoting systems demonstrate the accuracy of the capacity design procedure for predicting member forces in braced frame steel spines as well as global forces: story shear and overturning moments. Using the MMS methodology, peak story drifts and floor accelerations are reliably estimated. Comparison of the alternative spine configurations demonstrate the effects of various energy dissipation properties, global hysteresis behavior and earthquake frequency content on the nonlinear dynamic response of these systems.

Seismic analysis of a system of dam-massed foundation-reservoir under inclined excitation

One of the acceptable assumptions in engineering practice is vertical propagation of earthquake waves. When the source of earthquake is located very deep in the ground, this assumption is valid, but for sources located in shallow ground, it loses its viability. In this study, linear seismic analysis of a system of concrete dam-massed foundation-reservoir is performed under inclined earthquake excitation. Both P- and SV-type earthquakes are considered for the purpose of the seismic analysis. To consider the effects of inhomogeneous waves for the case of SV wave propagation, post-critical angles are also considered in the analysis. To investigate the effects of earthquake frequency content on the results, three different records with contents of low, intermediate, and high frequencies are selected. Results indicate that considering vertical propagation underestimates the obtained responses. For the case of SV-type earthquakes, post-critical angles must be looked at. Frequency content of the earthquake also has considerable effects on trend and absolute values of responses.