Microtremor-based analysis of the dynamic response characteristics of a site containing grouped earth fissures

In this study,the Beibu earth fissure site in the northeastern part of Weihe Basin,which contains four nearly parallel earth fissures,was studied.A long straight microtremor measuring line,containing 49 measuring points across four earth fissures,was established to investigate the dynamic response of this site using Fourier spectrum,response acceleration spectrum,Arias intensity,and HVSR analyses.The main results are as follows:(1)The fundamental frequencies of 44 measuring points obtained from HVSR analysis are concentrated within 1.67 Hz-2.25 Hz,and the existence of the earth fissures has little effect on the fundamental frequency changes.(2)There is an amplification effect near a single earth fissure.The dynamic responses are large at the measuring points near the earth fissure,and the values decrease with increasing distance from the earth fissure.In areas between two adjacent earth fissures,these values decrease and are even lower than those in sites without amplification effects.(3)In this earth fissure site,the general area(or less affected area)and affected areas were delineated based on the amplification effect.In engineering applications,construction design should avoid these affected areas and existing structures should be reinforced to satisfy the seismic fortification requirements.

An extended multiple-support response spectrum method incorporating fluid-structure interaction for seismic analysis of deep-water bridges

The effects of ground motion spatial variability(GMSV)or fluid-structure interaction(FSI)on the seismic responses of deep-water bridges have been extensively examined.However,there are few studies on the seismic performance of bridges considering GMSV and FSI effects simultaneously.In this study,the original multiple-support response spectrum(MSRS)method is extended to consider FSI effect for seismic analysis of deep-water bridges.The solution of hydrodynamic pressure on a pier is obtained using the radiation wave theory,and the FSI-MSRS formulation is derived according to the random vibration theory.The influence of FSI effect on the related coefficients is analyzed.A five-span steel-concrete continuous beam bridge is adopted to conduct the numerical simulations.Different load conditions are designed to investigate the variation of the bridge responses when considering the GMSV and FSI effects.The results indicate that the incoherence effect and wave passage effect decrease the bridge responses with a maximum percentage of 86%,while the FSI effect increases the responses with a maximum percentage of 26%.The GMSV and FSI effects should be included in the seismic design of deep-water bridges.

Response Spectrum Analysis of 7-story Assembled Frame Structure with Energy Dissipation System

Viscoelastic damper is an effective passive damping device,which can reduce the seismic response of the structure by increasing the damping and dissipating the vibration energy of structures.It has a wide application prospect in actual structural vibration control because of simple device and economical material.In view of the poor seismic behaviors of assembled frame structure connections,various energy dissipation devices are proposed to improve the seismic performance.The finite element numerical analysis method is adopted to analyze relevant energy dissipation structural parameters.The response spectrum of a 7-story assembled frame structure combined the ordinary steel support,ordinary viscoelastic damper,and viscoelastic damper with displacement amplification device is analyzed.The analysis results show that the mechanical behavior of assembled frame structure with ordinary steel supports are not significantly different from those without energy dissipation devices.The assembled frame structure with viscoelastic damper has better seismic performance and energy dissipation,especially for the viscoelastic damper with displacement amplification devices.The maximum value of inter-story displacement angle decreases by 32.24%;the maximum floor displacement decreases by 31.91%,and the base shear decreases by 13.62%compared with the assembled frame structures without energy dissipation devices.The results show that the seismic fortification ability of the structure is significantly improved,and the overall structure is more uniformly stressed.The damping structure with viscoelastic damper mainly reduces the dynamic response of the structure by increasing the damping coefficient,rather than by changing the natural vibration period of the structure.This paper provides an effective theoretical basis and reference for improving the energy dissipation system and the seismic performance of assembled frame structures.

Time-frequency response spectrum of rotational ground motion and its application

The rotational seismic motions are estimated from one station records of the 1999 Jiji （Chi-Chi）, Taiwan, earthquake based on the theory of elastic plane wave propagation. The time-frequency response spectrum （TFRS） of the rotational motions is calculated and its characteristics are analyzed, then the TFRS is applied to analyze the damage mechanism of one twelve-storey frame concrete structure. The results show that one of the ground motion components can not reflect the characteristics of the seismic motions completely; the characteristics of each component, especially rotational motions, need to be studied. The damage line of the structure and TFRS of ground motion are important for seismic design, only the TFRS of input seismic wave is suitable, the structure design is reliable.

Response spectra for nuclear structures on rock sites considering the near-fault directivity effect

Near-fault ground motions, potentially with large amplitude and typical velocity pulses, may significantly impact the performance of a wide range of structures. The current study is aimed at evaluating the safety implications of the near-fault effect on nuclear power plant facilities designed according to the Chinese code. To this end, a set of near- fault ground motions at rock sites with typical forward-directivity effect is examined with special emphasis on several key parameters and response spectra. Spectral comparison of the selected records with the Chinese and other code design spectra was conducted. The bi-normalized response spectra in terms of different comer periods are utilized to derive nuclear design spectra. It is concluded that nuclear design spectra on rock sites derived from typical rupture directivity records are significantly influenced both by the earthquake magnitude and the rupture distance. The nuclear design spectra specified in the code needs to be adjusted to reflect the near-fault directivity effect of large earthquakes.

Bi-normalized response spectral characteristics of the 1999 Chi-Chi earthquake

To develop uniform and seismic environment-dependent design spectrum,common acceleration response spectral characteristics need to be identified.In this paper,a bi-normalized response spectrum (BNRS) is proposed,which is defined as a spectrum of peak response acceleration normalized with respect to peak acceleration of the excitation plotted vs.the natural period of the system normalized with respect to the spectrum predominant period,Tp.Based on a statistical analysis of records from the 1999 Chi-Chi earthquake,the conventionally normalized response spectrum(NRS) and the BNRS are examined to account for the effects of soil conditions,epicentral distance,hanging wall and damping.It is found that compared to the NRS the BNRS is much less dependent on these factors.Finally,some simple relationships between the BNRS for a specified damping ratio and that for a damping ratio of 5%,and between the spectra predominant period and epicentral distance for different soil types are provided.

Artificial ground motion compatible with specified ground shaking peaks and target response spectrum

This article describes a hybrid simulation method to generate artificial ground motion time histories that are compatible with specified peak seismic acceleration, velocity and displacement as well as the target response spectrum of absolute acceleration. First, based on traditional methods that match the target spectrum in the frequency domain, an initial acceleration time history was synthesized to satisfy the specified peak acceleration, target spectral acceleration and intensity envelope. Second, by using the inversion formula of the seismic input to a linear single-degree-of-freedom system and by superimposing a series of narrow-band time histories in the time domain, the initial time history is further modified to allow its peak velocity and displacement to approach the targets and improve its matching precision with the target spectrum. Numerical examples are provided to demonstrate that the proposed method achieves good agreement with the target values.

Characteristics of response spectra for long-periods of main-shock recordings of the Chi-Chi earthquake

Current practice uses predictive models to extrapolate long-period response spectra based on far-field recordings in moderate and weak earthquakes. However, the spectra are not long enough and the data are often not reliable, which means that the seismic design code cannot accurately define seismic design requirements for long-period structures. The near-field recordings in the main-shock of the Chi-Chi earthquake have a large signal-to-noise ratio （SNR）, which makes them suitable for studying the long-period acceleration response spectrum up to 20 sec. The acceleration response spectra from 246 stations within 120 km of the causative fault are statistically analyzed in this paper. The influence of distance and site conditions on long-period response spectrum is discussed, and the shapes of the amplification spectra are compared with the standard spectra specified in the seismic design code of China. Finally, suggestions for future revisions to the code are proposed.

Attenuation relations for horizontal peak ground acceleration and response spectrum in northeastern Tibetan Plateau region

The seismic intensity attenuation relations in northeastern Tibetan Plateau region are established by a regression analysis on isoseismal data. Then the attenuation relations for horizontal peak ground acceleration and short-period response spectrum for western North America are derived based on the database of HUO Jun-rong and strong mo-tion data from recent earthquakes. The attenuation relations of long-period response spectrum for western North America are developed by analyzing the broadband digital seismic recordings of southern California. By integrat-ing the short-period and long-period attenuation relationships, the attenuation relations for horizontal acceleration response spectrum in the period range of 0.04~6 s for western North America are established. The attenuation equation that accounts for the magnitude saturation and near-field saturation of high frequency ground motion is used. Finally the attenuation relations for horizontal peak ground acceleration and response spectrum for the region of northeastern Tibetan Plateau are developed by using the transforming method.

Generating ground motion by two new techniques of adding harmonic wave in the time domain and approximating to response spectrum as a whole

In this paper,two new methods are introduced to fit response spectrum in generating earthquake acceleration time history.The first method is Adding Harmonic Wave in Time Domain(AHWTD).In this method, a control point of response spectrum is adjusted by adding a harmonic time history to the adjusted one.Three features of the method are that it has small cross interference,small amount of computation and it can give consideration to the amplitude envelope.The second one is Approximating Response Spectrum as a Whole(ARSW).This method has following feature. When adjust a time history that is decided by amplitude spectrum A k and phase spectrum φ k(k =0, 1, 2, …, n ), the mean square root of every relative error E j(j= 1, 2, …, M ) between response spectrum and object spectrum V r=∑Mj=1E 2 j/M is used to decide adjusting direction of any amplitude spectrum A k . Because E j and V r are functions of A k and φ k , the problem of fitting response spectrum in generating earthquake acceleration time history can be changed to a problem of finding minimum point of V r . Restricted by Nyquist frequency, AHWTD is not suitable for high frequencies of response spectrum. Restricted by frequency distribution of FFT, the density of control points in the low frequency part can′t be too dense for ARSW. But two methods can replenish each other and get such a good fitting effect that we can fit the given peak ground acceleration and peak ground velocity well at the same time.

A comparison of IBC with 1997 UBC for modal response spectrum analysis in standard-occupancy buildings

This paper presents a comparison of the seismic forces generated from a Modal Response Spectrum Analysis （MRSA） by applying the provisions of two building codes, the 1997 Uniform Building Code （UBC） and the 2000-2009 International Building Code （IBC）, to the most common ordinary residential buildings of standard occupancy. Considering IBC as the state of the art benchmark code, the primary concern is the safety of buildings designed using the UBC as compared to those designed using the IBC. A sample of four buildings with different layouts and heights was used for this comparison. Each of these buildings was assumed to be located at four different geographical sample locations arbitrarily selected to represent various earthquake zones on a seismic map of the USA, and was subjected to code-compliant response spectrum analyses for all sample locations and for five different soil types at each location. Response spectrum analysis was performed using the ETABS software package. For all the cases investigated, the UBC was found to be significantly more conservative than the IBC. The UBC design response spectra have higher spectral accelerations, and as a result, the response spectrum analysis provided a much higher base shear and moment in the structural members as compared to the IBC. The conclusion is that ordinary office and residential buildings designed using UBC 1997 are considered to be overdesigned, and therefore they are quite safe even according to the IBC provisions.

A simplified multisupport response spectrum method

A simplified multisupport response spectrum method is presented.The structural response is a sum of two components of a structure with a first natural period less than 2 s.The first component is the pseudostatic response caused by the inconsistent motions of the structural supports,and the second is the structural dynamic response to ground motion accelerations.This method is formally consistent with the classical response spectrum method,and the effects of multisupport excitation are considered for any modal response spectrum or modal superposition.If the seismic inputs at each support are the same,the support displacements caused by the pseudostatic response become rigid body displacements.The response spectrum in the case of multisupport excitations then reduces to that for uniform excitations.In other words,this multisupport response spectrum method is a modification and extension of the existing response spectrum method under uniform excitation.Moreover,most of the coherency coefficients in this formulation are simplified by approximating the ground motion excitation as white noise.The results indicate that this simplification can reduce the calculation time while maintaining accuracy.Furthermore,the internal forces obtained by the multisupport response spectrum method are compared with those produced by the traditional response spectrum method in two case studies of existing long-span structures.Because the effects of inconsistent support displacements are not considered in the traditional response spectrum method,the values of internal forces near the supports are underestimated.These regions are important potential failure points and deserve special attention in the seismic design of reticulated structures.

Study on the effect of ground motion direction on the response of engineering structure

Due to the randomness of earthquake wave magnitude and direction, and the uncertain direction of strong axis and weak axis in the construction of engineering structures, the effect of the direction of ground motion on a structure are studied herein. Ground motion records usually contain three vertical ground motion data, which are obtained by sensors arranged in accordance with the EW （East -West） direction, NS （South- North） direction and perpendicular to the surface （z） direction, referring to the construction standard of seismic stations. The seismic records in the EW and NS directions are converted to Cartesian coordinates in accordance with the rotation of θ = 0°-180°, and consequently, a countless group of new ground motion time histories are obtained. Then, the characteristics of the ground motion time history and response spectrum of each group were studied, resulting in the following observations： （1） the peak and phase of ground motion are changed with the rotation of direction θ, so that the direction θ of the maximum peak ground motion can be determined; （2） response spectrum values of each group of ground motions change along with the direction θ, and their peak, predominant period and declining curve are also different as the changes occur; then, the angle θ in the direction of the maximum peak value or the widest predominant period can be determined; and （3） the seismic response of structures with different directions of ground motion inputs has been analyzed under the same earthquake record, and the results show the difference. For some ground motion records, such as the Taft seismic wave, these differences are significant. Next, the Lushan middle school gymnasium structure was analyzed and the calculation was checked using the proposed method, where the internal force of the upper space truss varied from 25% to 28%. The research results presented herein can be used for reference in choosing the ground motion when checking the actual damage to structures following earthquakes and explaining the seismic damage. Meanwhile, it also provides a reference value for research into the most severe ground motion.

Study of characteristics of long-period ground motion response spectra by using broad-band records of the Chinese Digital Seismograph Network

Broad band and very broad band (BB and VBB) records of Chinese Digital Seismograph Network (CDSN) from 65 earthquakes are used to calculate the horizontal relative displacement, relative velocity and absolute acceleration response spectra with critical damping ratio ζ =0.005, 0.01, 0.02, 0.05 and 0.10, respectively. The results show that it is insufficient to obtain the credible characteristics of long-period ground motion response spectra only with the common ground acceleration records in engineering, while the broad band records of CDSN, as an important supplementary to ground acceleration records, can be used to study the characteristics of long-period ground motion response spectra.

The relation between the response spectrum and the phase diference spectrum

The relation between the phase difference spectrum and the response spectrum is studied in this paper. It is found that the phase difference spectrum influences the response spectrum through affecting the response motion′s envelope function shape of a single degree of freedom system. Decreasing the variance of phase difference spectrum causes the increasing of response spectrum when its mean value curve keeps the same, otherwise the situation is opposite. As the increase of the tangent of the mean value curve, the response spectrum decreases, otherwise it increases. The damping plays an important role while the phase difference spectrum influences the response spectrum. The effect of the phase difference spectrum on the absolute acceleration response spectrum becomes more and more obvious with the increase of the damping. On the other hand, the increase of damping weakens the effect of the phase difference spectrum on the amplification factor spectrum.

Parametric characteristic of the random vibration response of nonlinear systems

Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.

Consecutive combined response spectrum

Appropriate estimates of earthquake response spectrum are essential for design of new structures, or seismic safety evaluation of existing structures. This paper presents an alternative procedure to construct design spectrum from a combined normalized response spectrum （NRSc） which is obtained from pseudo-velocity spectrum with the ordinate scaled by different peak ground amplitudes （PGA, PGV, PGD） in different period regions. And a consecutive function./（/） used to normalize the ordinates is defined. Based on a comprehensive study of 220 strong ground motions recorded during recent eleven large worldwide earthquakes, the features of the NRSc are discussed and compared with the traditional normalized acceleration, velocity and displacement response spectra （NRSA, NRSv, NRSD）. And the relationships between ground amplitudes are evaluated by using a weighted mean method instead of the arithmetic mean. Then the NRSc is used to define the design spectrum with given peak ground amplitudes. At last, the smooth spectrum is compared with those derived by the former approaches, and the accuracy of the proposed spectrum is tested through an analysis of the dispersion of ground motion response spectra.

An alternative approach for computing seismic response with accidental eccentricity

Accidental eccentricity is a non-standard assumption for seismic design of tall buildings. Taking it into consideration requires reanalysis of seismic resistance, which requires either time consuming computation of natural vibration of eccentric structures or finding a static displacement solution by applying an approximated equivalent torsional moment for each eccentric case. This study proposes an alternative modal response spectrum analysis （MRSA） approach to calculate seismic responses with accidental eccentricity. The proposed approach, called the Rayleigh Ritz Projection-MRSA （RRP-MRSA）, is developed based on MRSA and two strategies： （a） a RRf＂ method to obtain a fast calculation of approximate modes of eccentric structures; and （b） an approach to assemble mass matrices of eccentric structures. The efficiency of RRP-MRSA is tested via engineering examples and compared with the standard MRSA （ST-MRSA） and one approximate method, i.e., the equivalent torsional moment hybrid MRSA （ETM-MRSA）. Numerical results show that RRP-MRSA not only achieves almost the same precision as ST-MRSA, and is much better than ETM-MRSA, but is also more economical. Thus, RRP-MRSA can be in place of current accidental eccentricity computations in seismic design.

Stochastic Response Analysis of Piled Offshore Platform Excited by Stationary Filtered White Noise

In this paper, the analysis method of stochastic response of piled offshore platform excited by stationary filtered white noise is presented. With this method, the strong ground motion is considered as three direction stationary filtered white noise process, the theoretic solutions of three special integration equations are derived with the residue theorem, and the expression of response nodal displacements and member forces of offshore platform excited by the stationary filtered white noise is put forward. The stochastic response of a piled offshore platform excited by the stationary filtered white noise, which is located 114.3 m in water depth, is computed. The results are compared with those obtained with the response spectrum analysis method and the stationary white noise model analysis method, and the corresponding conclusion is drawn.

CONVEX-MODEL ANALYSIS OF THE SEISMIC RESPONSE

An ellipsoidal Fourier-bound convex model (EFB model) is proposed in the present paper to express the uncertainty of seismic excitation, and several methods of selecting parameters of the model are explained. An analytical expression is obtained for the worst response of the single-degree-of-freedom (SDOF) system with the EFB model. A numerical simulation shows that the traditional prediction of maximum response can yield the value substantially lover than that predicted by the EFB model. This means that the traditional designing method based on standard seismic inputs may lead to unsafe design decisions.